Shining a light on silicon etching - Technische Universiteit Eindhoven

Shining a light on silicon etching

proefschrift

ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van de

Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor eencommissie aangewezen door het College voor

Promoties in het openbaar te verdedigenop maandag 29 mei 2006 om 16.00 uur

door

Alquin Alphons Elisabeth Stevens

geboren te Roermond

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr. H.C.W. Beijerinckenprof.dr.ir. M.C.M. van de Sanden

Copromotor:dr.ir. W.M.M. Kessels

The work presented in this thesis is part of the research project Dynamics of plasma-activated surface processes (FOM: 99TF24) supported by The Netherlands Foundationfor Fundamental Research on Matter FOM.

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Stevens, Alquin Alphons Elisabeth

Shining a light on silicon etching / by Alquin Alphons Elisabeth Stevens. -Eindhoven : Technische Universiteit Eindhoven, 2006. -Proefschrift.ISBN-10 90-386-2491-3ISBN-13 978-90-386-2491-4NUR 926Trefw.: silicium / plasma etsen / amorf silicium / ellipsometrie / nietlineaire optica /oppervlakteruwheid.Subject headings: silicon / plasma etching / amorphous silicon / ellipsometry / nonlinearoptics / surface roughness.

Printed and bound by Universiteitsdrukkerij Technische Universiteit Eindhoven.Cover: the image in the square is an artists impression of the beam etching experiment.A crystalline silicon (blue balls: Si) substrate is exposed to ions (purple balls: Ar+) andXeF2 (green balls: Xe, red balls: F), which leads to an amorphous silicon layer terminatedwith chemisorbed F-atoms. The optical diagnostics that have been used to shine alight on silicon etching are spectroscopic ellipsometry (yellow lights) and second-harmonicgeneration (red light in, green light out).Image design by Alquin Stevens. Cover realization by Paul Verspaget.

Contents

1 Introduction 1

1.1 Silicon etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Plasma etching of silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Beam etching of silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Ar+/XeF2/Si reaction mechanism . . . . . . . . . . . . . . . . . . . . . . 5

1.3.3 Selected opportunities in beam etching studies . . . . . . . . . . . . . . . 8

1.4 Shining a light on silicon etching . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Contents of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Beam etching experiment SCEPTER 13

2.1 High vacuum setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 XeF2-beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Ar+-beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Etch product analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Ellipsometry 19

3.1 Introduction to ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Ellipsometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.1 Single-wavelength ellipsometer . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.2 Spectroscopic ellipsometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Second-harmonic generation 25

4.1 Introduction to second-harmonic generation . . . . . . . . . . . . . . . . . . . . . 25

4.2 Laser and optical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 System response calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Multipolar, higher-order contributions to SHG . . . . . . . . . . . . . . . . . . . 29

4.5 Spectroscopic SHG from H:Si(100) and native oxide on Si(100) . . . . . . . . . . 31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

i

ii CONTENTS

5 Amorphous silicon layer characteristics during 70-2000 eV Ar+-ion bombard-

ment of Si(100) 37

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2.2 Si(100)-samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2.3 Measured pseudo-dielectric functions . . . . . . . . . . . . . . . . . . . . . 40

5.3 Multi-layer dielectric modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.4 a-Si layer thickness and roughness . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.5 Dynamics of Ar+ bombardment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.5.1 Time-resolved amorphization . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.5.2 Relaxation dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Appendix: Tauc-Lorentz model of a-Si . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Surface roughness in XeF2 etching of a-Si/c-Si(100) 55

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55


6.2.1 Vacuum apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.2.2 Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2.3 Rotating-compensator ellipsometer . . . . . . . . . . . . . . . . . . . . . . 58

6.2.4 Product flux calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.3 Amorphization of c-Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3.2 a-Si layer thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.3.3 Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.4 Chemical XeF2 etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.4.2 Results ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.4.3 Evolution of roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.4.4 AFM data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.4.5 Anomalous roughening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.5 Roughness in reaction layer models . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.6 Surface morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

CONTENTS iii

7 Roughening during XeF2 etching of Si(100) through interface layers: H:Si(100)

and a-Si/Si(100) 79

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

7.2 XeF2/Si etch mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.1 Initial reaction steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.2 Influence of initial surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 82


7.4 Multi-layer dielectric model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.4.1 H-terminated Si(100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.4.2 a-Si/Si(100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.5 H:Si(100) etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.6 a-Si/Si(100) etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.7 Roughening, initial conditions and reaction layer . . . . . . . . . . . . . . . . . . 91

7.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

8 Spectroscopic second-harmonic generation during XeF2 etching of H-terminated

Si(100) 97

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

8.2 SHG in beam etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

8.2.1 high-vacuum setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

8.2.2 Si(100) samples and preparation . . . . . . . . . . . . . . . . . . . . . . . 100

8.2.3 SHG optical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.3 Spectroscopic SHG from fluorinated Si(100) . . . . . . . . . . . . . . . . . . . . . 103

8.4 SHG during XeF2 etching of H:Si(100) . . . . . . . . . . . . . . . . . . . . . . . . 106

8.5 Discussion on microscopic origin of SHG . . . . . . . . . . . . . . . . . . . . . . . 109

8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

9 Surface roughness and subsurface ion-damage layer in Ar+-ion assisted XeF2

etching of Si(100): preliminary results 113

Summary 117

Samenvatting 119

Dankwoord / Acknowledgements 121

Curriculum Vitae 124

Chapter 1

Introduction

1.1 Silicon etching

Silicon technology is a cornerstone of present day society. Integrated circuits (ICs) pat-

terned onto silicon substrates are at the heart of every computer, mobile phone and nu-

merous other consumer-electronic appliances. Performing complex computations, storing

large quantities of information and fast handling of this information has been made pos-

sible by semiconductor devices such as micro-processors and memory chips with complex

architecture consisting of nanometer scale transistors, capacitors and multiple levels of

interconnects. Mobile phones and computers by means of the Internet have enabled users

to communicate and exchange information fast, from just about any place and around

the clock with clients, colleagues, family and friends. Also small, micrometer scale micro-

electro-mechanical-system (MEMS) devices have been produced from silicon which have

been incorporated into cars as fuel, pressure and acceleration sensors. MEMS devices have

been designed to perform specific tasks in optical, acoustical and microwave applications.

Their size enables the use for future medical applications such as biosensors, micropumps,

and microlabs on chips or even in the human body to take over tasks such as, e.g., failing

basilar membranes, heart-function monitoring and automatic drug delivery at predefined

times. One last example using structured silicon are photonic crystals, which are the op-

tical equivalent of electronic semiconductors. A small collection of examples where silicon

has been used is shown in Fig. 1.1.

One of the crucial steps in the production of these devices is the etching of silicon or

silicon-based materials. Components are ”machined” from the silicon substrate through

lithography and etching. The substrate is coated with a photosensitive resist and ex-

posed to light through a patterned mask. The exposed resist is washed off and, where

the photoresist has been removed, deep trenches or holes can be etched in the substrate

material using either a wet chemical etch or a plasma dry etch. In wet etching a chemi-

cally reactive solution is introduced on the substrate that selectively etches the substrate

material over the photoresist material. Wet etching is an isotropic etch process, which

means that the etch rate is equal in all directions, as depicted in Fig. 1.2. Hence, the

1

2 Chapter 1. Introduction

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 1.1: Examples of small structures etched in silicon. (a) MEMS motion control mechanismwith the legs of a mite (Courtesy of Sandia National Laboratories). (b) MEMS-mirror, 100 µmin diameter. (c) Photonic crystal: 2.3 µm diameter holes etched in silicon up to 75 µm deep. (d)BioMEMS needle structures for drug delivery. (e) Multiple, 30 nm diameter silicon wires createdin a specific etch process (Philips research laboratories, press release 11/18/2005). (f) Introductionof a 70 nm transistor (Intel). (if not specified, multiple websources are available)

spacing between neighboring structures is restricted, which imposes limits on the number

density of functional components per unit area. Nonetheless, wet etching is very useful

in the pre-treatment of silicon wafers, i.e. removal of native oxide by hydro-fluoric acid

etch, and the release/lift-off of component parts in MEMS devices.

An increased number density of electronic components per unit area leads not only to

an increase in processing speed of microprocessors and the data storage density on memory

modules, but also to a cost reduction of the production process, thus the sales price of the

consumer product. Size reduction of the components to increase the component density

per unit area requires an anisotropic etch process with little or no lateral etch. The

required directionality for anisotropic etching of high aspect-ratio (=height over width)

structures, as shown in Fig. 1.2(b), can be achieved by means of plasmas.

The production process of, e.g., a microprocessor involves hundreds of process steps, in-

cluding multiple steps of etching, depositing new thin films and doping by foreign species,

where each step requires lithography.

1.2. Plasma etching of silicon 3

(b)(a)

Fig. 1.2: (a) Isotropic versus (b) anisotropic etching. (a) The silicon has been etched with an etchrate equal in all direction, resulting in a curved surface underneath the circular disc of the SiO2

hard mask. (b) The faster etching of the bottom of the holes with respect to lateral etching resultsin high aspect-ratio holes with straight sidewalls as can be obtained in plasma etching.

1.2 Plasma etching of silicon

Etching of silicon by means of plasmas takes place in a low-pressure, vacuum environment

(typically p ≡ 10−1 Torr). For silicon etching, a gas of halogen based gases, such as

CF4, C4F8, SF6 or Cl2 with possible additives such as H2, O2 or Ar, is commonly used

as atomic F, Cl, Br and I are known to etch silicon. The gas is excited by a radio-

frequency excitation either capacitively coupled (= by an electric field between a powered

and grounded electrode) or inductively coupled (=field-coupling to the electrons by an

induction coil). The gas molecules then dissociate into electrons, ions and reactive neutrals

(radicals). Within the plasma the ion and electron density is fairly equal, hence no

significant electric fields exist within the plasma on length scales large than the Debye

screening length, i.e., the length over which ions are screened from other ions by the

electrons. Electrons and ions move diffusively outward from the plasma region towards

the walls of the vacuum environment. Since the electrons are much more mobile than the

ions, a positive space charge region builds up close to the wall. Hence, at the boundary

of the plasma, close to the walls of the vacuum environment, a region exist where the

potential drops from a positive plasma potential on the order of a few eV to 0 V at the

grounded walls, the so-called plasma sheath. Consequently, ions moving in the plasma may

enter the sheath region where they experience the potential drop and are, subsequently,

accelerated towards the wall.

The sheath is the main feature that makes plasmas suitable for anisotropic etching.

The electric field across the sheath ensures that the ions impinge perpendicular to the

surface of the wall and, thus, imposes a directionality on the ions. A (patterned) silicon

substrate, is placed in vicinity of the plasma. Reactive neutral species created in the

plasma are not influenced by the sheath and move freely towards the substrate where the

can chemisorb and create volatile etch products. The energetic ions activate the surface to

enhance the reaction probability of the plasma activated neutrals/radicals to form volatile

etch products, and the energy delivered to the surface by the ions enhances the release

of these etch products. The synergy between ions and reactive neutrals causes the etch


CF3

Ar CF4 , Ar pumpAr

e-

e-e-

e-e-

CF2

F

CF

F

CF F

e-

e-

600 nm

photoresist

Si

(b)

(c)

(a)

sheath

F

Fig. 1.3: (a) Schematic representation of an inductively coupled plasma frequently used to etchsmall structures. The plasma consists of electrons (e−), ions (⊕) and reactive neutrals (F, CF,CF2 CF3). (b) Photograph of an actual etch reactor. The glow is caused by light generated in theplasma. (c) Result of anisotropic, selective etching of silicon-over-photoresist by means of plasmasresults in high-aspect ratio trenches in silicon.

rate to be disproportionately higher than the sum of pure gas phase chemical etching by

reactive neutrals and pure physical sputtering by ions. The directionality of the ions then

ensures that they impinge primarily on the bottom of the holes and trenches. The etch

rate straight down is therefore much higher than the lateral etch rate. The end result

is the anisotropic etching of high aspect-ratio holes and trenches with straight sidewalls.

Often the substrate can be biased with a negative voltage typically between 0 and a few

hundred volts, to influence the ion energy and, thus, to tailor the etch process.

The parameter space of a plasma is enormous, e.g. plasma source power and frequency,

bias voltage (=ion energy), partial pressures of the halogen-based gases and additives, to-

tal gas pressure and type of gases. This basically means that a large number of ”knobs”

are available to optimize the etch process and to improve the quality of the etched struc-

tures. Size reduction of etched structures, especially in the IC industry, is pushing the

fundamental limits. Critical dimensions of MOSFET structures for microprocessors are

going to be 90 nm in 2006 and have to decrease to 45 nm in 2010.1 Present day problems

in trench etching are aspect-ratio dependent etching (ARDE or RIE-lag), micro-trenching,

notching and undercutting.2 Furthermore, the smaller the structures, the more important

surfaces and interfaces become in the performance of the devices. Interface roughness

and line-edge roughness (LER) as well as plasma damage to subsurface regions caused by

radiation and/or energetic ions are going to be issues that need to be addressed in order to

1.3. Beam etching of silicon 5

meet the standards imposed by the industry.1 All these aspects will have an influence on

the performance of the IC devices and will even reduce the yield (=successfully produced

chips per unit processed area), which has a negative impact on the price of the consumer

product.

Fundamental understanding of the role of ions and reactive neutrals in the etch mech-

anism can provide insight into the mechanisms causing these problems. Fundamental

studies of etch mechanisms in plasma environments are, however, rather complex. Plasma

”knobs” are interconnected, hence by adjusting one parameter, many other parameters

will be simultaneously influenced. To be able to circumvent the complexity of the plasma

itself and, moreover, the interaction of the plasma with a surface, the concept of beam

etching studies was introduced in the late 70’s by Coburn and Winters,3 and other beam

etching studies followed.4–6

1.3 Beam etching of silicon

1.3.1 Motivation

Beam etching mimics plasma etching by replacing the complex plasma environment by

beams of the most relevant plasma species involved in the etch reactions, which are the

ions and reactive neutrals. In the present case, the ions and neutrals are simulated by

beams of Ar+-ions and XeF2, where XeF2 is a weakly-bound carrier molecule for F-atoms.

The beams of ions and reactive neutrals are characterized such that the absolute fluxes are

well-known. Furthermore, the Ar+-ion and XeF2 fluxes can be controlled independently,

as well as the Ar+-ion energy. These aspects allow quantitative studies of the dynamics of

the silicon etch mechanism by Ar+-ions and XeF2 as a function of ion-to-neutral flux ratio

and ion energy, which are both the most important parameters of the etch mechanism.

Knowledge of etch mechanisms on a fundamental level as obtained by beam etching studies

can provide a recipe for ”turning the right knobs” of an etch plasma, ultimately, to realize

well-defined nano-/micrometer scale structures in silicon by plasma etching.

1.3.2 Ar+/XeF2/Si reaction mechanism

In general, three steps must take place in etching: (1) reactant adsorption, (2) chemical

reaction to produce reaction products, and (3) desorption of reaction products. In the

absence of ions, XeF2 reacts spontaneously with Si with a reaction probability of ε ≈0.1 at room temperature. Before the XeF2 reacts with the Si it first physisorbs in a

precursor state. Then a reaction layer is formed. Consecutive steps of F-atoms being

bonded to surface silicon atoms leads to the formation of etch products. In the case

of spontaneous etching at room temperature SiF4 is the only etch product. At higher

substrate temperatures also SiFx products can desorb from the surface. Summarized,


etch products

to QMSXeF

2

silicon

Ar+

Fig. 1.4: Schematic representation of Ar+/XeF2 beam etching of silicon, where amass spectrometer, positioned perpendicular to the Si sample surface, is used to monitor etchproducts. The Central Detection Area of 3 mm in diameter is processed by the overlapping beamsand is viewed by the mass spectrometer.

spontaneous etching can be described by the following global reaction scheme:

XeF2(g)τ−→←− XeF2(p), (1.1)

XeF2(p) + Si(s) −→ Xe(g) + SiF2(s), (1.2)

XeF2(p) + SiF2(s) −→ Xe(g) + SiF4(g), (1.3)

SiF2(s)T↑−→ SiF2(g). (1.4)

The first step describes the physisorption of XeF2 in a precursor state. Because of thermal

desorption, physisorbed XeF2 can also leave the precursor state again and go back into

the gas phase after a characteristic time τ . Step 2 describes the formation of a fluorinated

surface, modeled with SiF2 surface species. Step 3 describes the etching reaction of the

formation of volatile SiF4 which leaves the surface spontaneously. Finally, step 4 describes

the desorption of, on average, SiF2 surface species, which only becomes important above

600 K.5 The SiFx reaction layer thickness is on the order of 1 to 2 mono-layers, depending

on the duration of the exposure to XeF2, and is composed of primarily SiF3 and SiF

species.

In the presence of ions the reaction probability of XeF2 is enhanced from 0.1 at an ion-

to-neutral flux ratio R = ΦAr+/ΦXeF2 <0.01 to 0.8 at R >0.1.6 In addition to an increased

SiF4 production, SiF2 is also released from the surface by the ion bombardment. The etch

rate during ion-assisted etching is disproportionately higher that the sum of spontaneous

etch rate and ion sputter rate. This synergistic effect was first demonstrated by Coburn

and Winters.3 The synergistic effect has been explained in terms of reaction steps as

follows.5,6 The first four steps are the same as in the case of spontaneous etching. Due

to a thinner reaction layer during ion bombardment, the spontaneous SiF4 formation

[Eq. (1.2)] decreases. However, an enhanced release of SiF4 is observed during ion-assisted

etching and is generally explained by chemical sputtering, defined as the production of

1.3. Beam etching of silicon 7

(a) before ion impact

(b) chemical sputtering (c) physical sputtering

F

Si

free site

Fig. 1.5: Simplified representation of (a) the silicon-fluoride reaction layer on Si(100) before ionimpact, (b) chemical sputtering, where SiF4 is produced from surface F-atoms and SiF2-species,and (c) physical sputtering, where two SiF2 molecules are released from the surface. Free reactivesites (=dangling bonds) are left behind, where XeF2 can more easily react.

weakly bound species by ion bombardment, followed by desorption:

2F(s) + SiF2(s)Ar+−→ SiF4(g). (1.5)

The release of SiF2 is explained by physical sputtering, defined as the direct release of

surface species upon ion impact:

SiF2(s)Ar+−→ SiF2(g). (1.6)

In both the chemical and physical sputtering process, reactive sites, so-called dangling

bonds, are created. These dangling bonds enhance, in their turn, the chemisorption of

F-atoms to the surface. In total, these steps leads to an increase of the XeF2 reaction

probability, the etch product formation probability and, thus, the etch rate. The im-

portance of the various etch steps strongly dependent on the ion-to-neutral flux ratio.6


1.3.3 Selected opportunities in beam etching studies

The interaction of ions and reactive neutrals with silicon, ion-assisted etching, and the

interaction of reactive neutrals only with silicon, spontaneous etching, has been studied

in the past using mass spectrometry (QMS) to analyze the etch products, quartz-crystal-

microbalance (QCM) to measure etch rates, thermal desorption spectroscopy (TDS) and

X-ray photoemission spectroscopy (XPS) to analyze the silicon-fluoride reaction layer.

Despite all the efforts, the details of the silicon-fluoride reaction layer, such as layer

thickness and composition in terms of SiFx-species distribution, is still the big unknown

and very much under debate. For XPS and TDS measurements the actual etch process has

to be terminated before the surface layer can be analyzed. After termination of the etch

process, reactions of XeF2 (reactive neutrals in general, thus also in plasma environments)

remaining in the background of the vacuum chamber may alter the reaction layer. Another

way to derive reaction layer information is etch product monitoring (QMS) employed in a

relative manner, i.e. “XeF2/ions on” versus “XeF2/ions off”, however it always requires an

assumption-based model to deduce information regarding the reaction layer composition

and thickness. A direct measurement of the reaction layer thickness and composition

during the etch process is demanded to answer this question.

In addition, energetic ions penetrate into the subsurface region, where they distort

the crystalline Si matrix resulting in a so-called ion-damage layer. The penetration depth

depends on the ion energy and characterization of this ion-damage layer has not been

attempted in beam etching experiments before. Ion-induced alteration of the surface has

an important, positive effect on etch reactions as it accommodates chemical and physical

sputtering (etch steps in Eqs. 1.5 and 1.6). Through the creation of Si surface sites, such as

modified Si-Si bonds and dangling bonds, the reaction of reactive neutrals with surface Si

atoms are enhanced and the ion energy deposited at surface enables an enhanced release

of etch products. These Si surface sites are an integral part of the reaction layer and

assessing the importance of these surface sites could contribute to a better understanding

of the synergistic effect between ions and reactive neutrals on an atomic scale. Their

contribution to the reaction mechanism can only be assessed from a direct measurement

of modified Si-Si bonds and dangling bonds during the etch process.

One last aspect, which has had little attention in beam etching experiments, is that

the surface morphology is changing during beam etching. Often, surface morphology has

been used as an argument in literature to explain some not well understood experimental

observations.4,7–9 Insight into the fundamentals of surface morphology evolution in etch

processing could provide a better understanding of the microscopic etch mechanisms.

Characterization of surface morphology and ion-damage to the subsurface region is not

only of fundamental interest for etch dynamics, but also for the applied plasma etch pro-

cessing of, e.g., nanometer-scale electric components. Inherent to size reduction of these

components, surfaces and interfaces become critically important for the performance of

1.4. Shining a light on silicon etching 9

etch products

(QMS)

- SiF, SiF2 , SiF3

(XPS, TDS)

surface morphology

(ellipsometry)

ion damage layer

(ellipsometry)

Reaction layer:

- surface Si-Si bonds

- dangling bonds

(SHG)

XeF2

Ar+

Xe

F

Si

Fig. 1.6: Schematic representation of the reaction layer in Ar+/XeF2 etching of Si. Past ex-periments have been devoted to etch rate determination and reaction layer dynamics by meansof etch product analysis (QMS) and reaction layer thickness and composition in terms of SiFx-species (XPS, TDS). The reaction mechanism described in Sec. 1.3.2 has been derived from thesestudies. Complementary studies, such as surface morphology and ion-damage layer characteristicsby means of ellipsometry and dangling bonds and surface Si-Si bond characteristics by means ofsecond-harmonic generation (SHG), could provide more detailed information regarding the reactionmechanism and the etch dynamics in Ar+/XeF2 etching of Si.

devices composed from these components. For the devices to perform optimally requires,

therefore, well-defined, low-damage surfaces/interfaces. The current status of beam etch-

ing studies and the areas of interest, that could improve the current knowledge of the etch

dynamics, have been schematically summarized in Fig. 1.6.

1.4 Shining a light on silicon etching

Some of the areas of interest and opportunities in beam etching studies have been ad-

dressed in Sec. 1.3.3, which have motivated the research presented in this thesis. To be

able to address these areas of interest requires non-intrusive, direct, in situ and real-time

probing of the surface during Ar+/XeF2-etching of silicon. To meet these demands, an

all optical diagnostics approach has been chosen and introduced in the beam etching

experiment SCEPTER (=Surface Chemistry Experiment for a Physical Theory of Etch

Reactions): shining a light on silicon etching.

From a number of alternatives of optical diagnostic tools the choice has been made to

introduce and employ (spectroscopic) ellipsometry and second-harmonic generation in the


beam etching experiment. The objective of this thesis is therefore to introduce and explore

the use of (spectroscopic) ellipsometry and second-harmonic generation as diagnostic tools

in the Ar+/XeF2 beam etching of Si, thereby aiming at fields of interests, as presented

in the previous section, which were difficult to explore in the past. In addition, the use

of optical diagnostics is not limited by the pressure in the processing environment, which

is typically 10−5 Torr during beam etching, unlike, e.g., XPS and electron-energy-loss-

spectroscopy (EELS).

Spectroscopic ellipsometry is a well-established optical technique to study layered sys-

tems, including surface morphology aspects. Ellipsometry uses the principle of polar-

ization change of an electromagnetic wave upon reflection on a sample. From optical

modeling information regarding the thickness of separate layers on the sample and the

dielectric properties of the materials within the layers can be derived from ellipsometric

measurements, which in the present case should lead to improved insight in the subsurface

damage layer as a result of impinging ions and the surface morphology as a result of ion

bombardment, spontaneous etching or ion-assisted etching.

Second-harmonic generation (SHG) is described by a second-order nonlinear polariza-

tion in a medium induced by an incident electric field. Inversion symmetry considerations

imply that SHG is forbidden in the bulk of centro-symmetric materials, such as c-Si.

Ideally, SHG occurs only if the inversion symmetry is broken, which is true for surfaces

and interfaces and, thus, SHG is potentially surface and interface specific. Microscopi-

cally, SHG is the conversion of two photons with energy ~ω into a single photon with

energy 2~ω. Furthermore, if either ω or 2ω is resonant with an electronic transition of

the medium, the second-harmonic signal is resonantly enhanced. Resonantly enhanced

SHG can be employed to directly measure electronic states related to surface Si-Si bonds

and dangling bonds,10 and allows the study of these surface states both spectroscopically

and in real-time during modification of the surface. In this case, SHG should be able to

provide new information regarding the silicon-fluoride reaction layer dynamics and, more

specifically, insight in the change of surface Si-Si bonds as a result of Ar+-ion impacts and

bonding to F-atoms, and the creation of dangling bonds through ion impacts.

1.5 Contents of the thesis

The beam etching experiment SCEPTER has been designed to produce quantitative in-

sight in the etch mechanism of silicon by Ar+-ions and XeF2. Details on the vacuum

apparatus, Ar+-ion beams and XeF2 beam, and etch product monitoring are presented

in Chapter 2. Chapters 3 and 4 are devoted to elaborate on the theoretical background

when employing ellipsometry and second-harmonic generation, respectively. The next

five chapters describe the experimental studies performed using ellipsometry and second-

harmonic generation. Separate studies of Ar+-ion bombardment and spontaneous XeF2

1.5. Contents of the thesis 11

etching of silicon have been undertaken to create a solid basis of the important aspects

that can be observed with ellipsometry and SHG during ion bombardment and sponta-

neous etching (Chapters 5-8). These separate studies provide an excellent starting point

for the employment of both optical diagnostics in ion-assisted etching, when both Ar+

and XeF2 are used simultaneously (Chapter 9).

• Chapter 5 describes the spectroscopic ellipsometry study performed on Ar+-ion

bombardment of Si(100). The optical properties of the ion-damaged, amorphous

Si layer as well as the ion-damage layer thickness and surface roughness have been

determined during ion bombardment. Beam etching studies in the past have used

ion energies in the range of 500-2500 eV ions, which is somewhat higher than typical

for ’real’ plasma etch conditions (<500 eV) and what can be used in MD simulation

studies (<200 eV). For this purpose, a low-energy ion source was installed to explore

the ion energy range below 500 eV. Chapter 5 is submitted for publication in J. Vac.

Sci. Technol. A.

• Chapter 6 describes the real-time single-wavelength ellipsometry results on XeF2

etching of an amorphous Si layer on Si(100). Using ellipsometry it has been shown

that the surface severely roughens during spontaneous etching. Chapter 6 has been

published: J. Vac. Sci. Technol. A 23, 126 (2005).

• Chapter 7 describes the real-time spectroscopic ellipsometry study on XeF2 etching

of amorphous Si layers on Si(100) and hydrogen-terminated Si(100). This study

is a follow-up on some questions that have risen in the single-wavelength study as

described in Chapter 6. The state of the initial surface is shown to have an important

influence on the roughness evolution during XeF2 etching of amorphous Si layers on

Si(100) and hydrogen-terminated Si(100). Chapter 7 is submitted for publication

in J. Vac. Sci. Technol. A.

• Chapter 8 describes spectroscopic and real-time second-harmonic generation on

XeF2-etching of hydrogen-terminated Si(100). In this study it shown that the sur-

face Si-Si bond states change when etching hydrogen-terminated Si(100). Chapter

8 is submitted for publication in Phys. Rev. B. Parallel to this study the second-

harmonic response to Ar+-ion bombardment of Si(100) has been investigated, which

will not be presented in this thesis, and has been submitted for publication in Phys.

Rev. B.11

• Chapter 9 gives an outlook to future research involving the characterization of the

ion-damage layer and surface roughness during ion-assisted etching by means of

spectroscopic ellipsometry.

Finally, in chapter 10, the general conclusions of the presented studies will be summarized.


References

1 International roadmap for semiconductors edition 2005, http://public.itrs.net/.

2 I. W. Rangelow, J. Vac. Sci. Technol. A 21, 1550 (2003).

3 J. W. Coburn and H. F. Winters, J. Appl. Phys. 50, 3189 (1979).

4 J. W. Coburn and H. F. Winters, Surf. Sci. Rep. 14, 161 (1992).

5 M. J. M. Vugts, Reaction layer dynamics in silicon etching (PhD thesis, 1995).

6 P. M. Sebel, Dynamics of ion-assisted etching (PhD thesis, 1999).

7 M. J. M. Vugts, M. F. A. Eurlings, L. J. F. Hermans, and H. C. W. Beijerinck, J. Vac. Sci. Technol.A 14, 2780 (1996).

8 Y. Morikawa, K. Kubota, H. Ogawa, T. Ichiki, A. Tachibana. S. Fugimura, Y. Horiike, J. Vac. Sci.Technol. A 16, 345 (1998).

9 C. W. Lo, D. K. Shuh, V. Chakarian, T. D. Durbin, P. R. Varekamp, and J. A. Yarmoff, Phys. Rev.B 47, 648 (1993).

10 U.Hofer, Appl. Phys. A 63, 533 (1996).

11 J. J. H. Gielis, P. M. Gevers, A. A. E. Stevens, H. C. W. Beijerinck, M. C. M. van de Sanden,W. M. M. Kessels, submitted to Phys. Rev. B.

Chapter 2

Beam etching experiment SCEPTER

Abstract

The multiple-beam setup SCEPTER (Surface Chemistry Experiment for a Physical The-ory of Etch Reactions) has been designed to produce quantitative insight in the etchmechanism of silicon by Ar+-ions and XeF2. The main changes to the setup with respectto the setup described in Refs.1–3 will be presented here. Furthermore, the absolute fluxesof the ion beams and XeF2 beam, and the calibration of the mass spectrometer to de-termine the XeF2 reaction probability and the etch product formation probability will bediscussed.

2.1 High vacuum setup

The high vacuum setup consists of three separately pumped chambers: the main chamber,

the load-lock and the detection chamber as shown in Fig. 2.1. The main chamber is

pumped by two turbomolecular pumps of 500 `s−1 and 50 `s−1 in series, which results

in a base pressure of 1·10−8 Torr. The Si sample is positioned in the center of a semi-

spherical flange with ten ports. Beams of ions and XeF2 and the incident/reflected light

of the optical diagnostics laser beams intersect at the sample center. The stress free

view ports of the optical diagnostics ensure conservation of the polarization state of the

incident/reflected light. The orientation of various beams with respect to the sample is

schematically drawn in Fig. 2.2.

The load-lock accommodates a sample storage for six samples. The load-lock is

pumped by a turbomolecular pump of 56 `s−1, which results in a base pressure of 1·10−8

Torr. Using a magnetic linear drive the samples can be transported from the sample

storage to the rotatable sample mechanism in the main chamber. This sample exchange

mechanism facilitates frequent use of new samples without having to bring the main cham-

ber up to atmospheric pressure. The sample rotation mechanism has two sample holders:

one for the Si sample and one for the Ni reference sample, to calibrate the XeF2 sample

flux. The samples can be rotated 180 in to and out of line of sight of the beams.

13

14 Chapter 2. Beam etching experiment SCEPTER

optical access

Magnetic

linear drive

Loadlock

main chamber

detector

chamber

3

42

1

500 mm0

6

7

5b

5a

Fig. 2.1: Revised setup in horizontal cross-section. The sample is mounted in a rotatable sampleholder (1) that can be operated manually via an external drive(2). Samples can be exchangedbetween the sample holder and the sample storage (3) in the load lock with a linear magneticdrive. The XeF2 source (4), the high-energy ion source (5a) and the low-energy ion gun (5b) areat 52, 45 and 45 from surface normal, respectively. The optical acces is at 74 from the samplesurface normal. Flow resistances with a differentially pumped stage (6) separate the main chamberfrom the detector chamber, which is located perpendicular to the sample surface. Etch productsare detected with a mass spectrometer (7) in the detector chamber.

single -wavelength

ellipsometer

spectroscopic ellipsometer or

second harmonic generation

sample

CDA

low-energy Ar+ ion beamproduct analysis

to QMS

XeF2 beam

reflected light

to detectors

(74o,0o)

(74o,30o)

(45o,0o)

(-52o,135o)

(θ,φ) = (0o,0o)

φ = 0o

high-energy Ar+ ion beam

(-45o,180o)θ

Fig. 2.2: Orientation in spherical coordinates (θ,φ) of the XeF2-beam, Ar+-beam, etch productdetection (QMS), and the light beams with respect to the sample surface normal. The CentralDetection Area (CDA) is 3 mm in diameter, which is the area seen by the mass spectrometer.

2.2. XeF2-beam 15

2.2 XeF2-beam

The XeF2 source is positioned at a 52 angle with respect to the surface normal. The

temperature of the storage vessel containing XeF2 crystals is controlled between 0C and

25C with a Peltier element. This way the vapor pressure of the XeF2 and, ultimately, the

XeF2 sample flux can be controlled. From the vessel, the XeF2-vapor flows through a flow

resistance (0.17 mm diameter, 10 mm length) to a multichannel array (16 µm diameter,

450 µm long channels in a stainless steel disk) to ensure an highly collimated, 3 mm

FWHM, beam of XeF2 molecules with a wide dynamic range of well-calibrated fluxes.

The XeF2 flux can be varied this way between 0.06 and 3.6 mono-layers per second (ML

s−1), where 1 ML≡6.86·1014 cm−2 on Si(100).

2.3 Ar+-beams

Two ion guns are available to generate Ar+-ion beams. The high-energy ion beam source

is a Kratos WG 537 Macrobeam ion gun. The ion gun is differentially pumped by a

turbomolecular pump (150 `s−1). Argon gas is introduced in the ion gun through a

needle valve at a fixed flow rate, creating a 5·10−5 Torr Ar gas pressure in the ion gun.

The gas is ionized by electrons generated by a hot filament. The ions are extracted,

accelerated and focussed onto the CDA. The ion energy can be varied between 500 and

2500 eV and the ion current can be adjusted continuously up to 10 µA by changing the

filament current. A sample flux of 1 µA corresponds to 0.01 ML s−1 (= 0.7·1013 cm−2).

The FWHM of the ion beam is typically 5 mm.

The low-energy ion beam source (Nonsequitur Technologies, customized version of

Model LEIG-2) can be used to generated Ar+ ions with ion energies in the range of 10 to

2000 eV. This source is also differentially pumped by a turbomolecular pump (150 `s−1).

The Ar gas is introduced in the ion gun through a needle valve and the gun is operated at

a pressure of 9·10−5 Torr. The operating principle is the same as for the high-energy ion

source. The ion beam diameter is set for all ion energies to ∼3 mm FWHM by adjusting

the focus voltage. The ion beam profile has been characterized in a separate setup using

a wire scanner. Typical beam profiles, that were measured for ion energies ≤500 eV, are

shown in Fig. 2.3.

The orifice of the ion source is located at 20 mm from the center of the sample, which

is necessary for low-energy operation. The ions impinge onto the silicon surface at a

45 angle with the surface normal. The ion flux is determined from the measured, total

current on the sample and the ion beam profile. The ion flux can be varied by adjusting

the filament current in steps (3 µA, 30 µA, 0.3 mA and 3 mA). The maximum flux, that

can be achieved with this source, is 0.07 ML s−1 ≡ 5·1013 cm−2s−1 at 70 eV ion energy

up to 1 ML s−1 above 1000 eV ion energy.


-6 -4 -2 0 2 4 60.0

0.2

0.4

0.6

0.8

1.0 30eV

50eV

100eV

500eV

no

rm.

be

am

cu

rre

nt

Ι /Ι p

ea

k

position (mm)

3 mm

Fig. 2.3: Ion beam profiles for 30, 50, 100 and 500 eV ion energy of the new low energy ion beamsource.

2.4 Etch product analysis

Inside the detector chamber a mass spectrometer is placed to be able to analyze etch

products (Fig. 2.1). The entrance of the detector chamber is positioned perpendicular to

the sample surface (Fig. 2.2). The detector chamber is pumped by an ion-getter pump (50

`s−1). A differential pumping stage (25 `s−1 ion-getter pump) with two flow resistances

separates the main chamber from the detector chamber and acts as angular selector to

ensure that 85% of the detected species originate from a 3 mm diameter area of the sample,

the central detection area (CDA). The molecules that are created or reflected from the

CDA reach the ionizer without wall collisions, are then ionized by a 70 eV electron beam,

extracted and injected in a Balzers quadrupole mass spectrometer. The mass-selected

ions are finally detected by an electron multiplier.

With the mass spectrometer, the non-reacted XeF2 (XeF+ signal) and the SiF4 re-

action products (SiF+3 signal) are measured. From comparison of the incident XeF2 flux

Φs(XeF2) measured on a Ni reference sample, which is inert to XeF2, and the non-reacted

flux Φ(XeF2) leaving the Si, the reaction probability ε is calculated

ε =Φs(XeF2)− Φ(XeF2)

Φs(XeF2). (2.1)

In a steady-state etch situation a fluorine balance must apply for the system, such that

the total reacted F-atoms is equal to the F-atoms detected in the SiFx etch products:

ε =∑

x

δx , (2.2)

where δx is the production coefficient of SiFx etch products (x=1,2,3). The production

References 17

coefficient δx is determined from the SiFx reaction product signals

δx =x Φ(SiFx)

2 Φs(XeF2). (2.3)

In the case of spontaneous etching at 300 K, for which SiF4 is the only etch product, the

reaction probability ε serves as a calibration of the detection efficiency of SiF4. For ion-

assisted etching and spontaneous etching at elevated temperatures (above 500 K), SiF2

etch products (SiF+ signal) can be measured and have to be taken into account. The

silicon etch rate ER (ML s−1) is then proportional to the total etch product flux:

ER =∑

x

Φ(SiFx) =∑

x

2δx

xΦs(XeF2). (2.4)

The main disadvantage is that mass spectrometry does not probe the surface itself

and details of the reaction layer, such as SiFx-species composition and layer thickness, can

only be indirectly derived through assumption-based modeling. Mass spectrometry can

however be used to obtain absolute reaction and etch rates, which is hard to obtain from

other diagnostics. Etch product analysis has proven in the past to be a powerful diagnostic

to study spontaneous and ion-assisted etching1,2,4 and, also, the dynamic aspects of the

etch mechanism.2

References



3 M. J. M. Vugts, G. J. P. Joosten, A. van Oosterum, H. A. J. Senhorst, and H. C. W. Beijerinck, J.Vac. Sci. Technol. A 12, 2999 (1994).


Chapter 3

Ellipsometry

Abstract

Ellipsometry is a well-known optical diagnostic to determine thicknesses and optical prop-erties of thin films. An introduction to the basic principles of ellipsometry1,2 and theexperimental details of the single-wavelength and spectroscopic ellipsometers are givenhere.

3.1 Introduction to ellipsometry

Ellipsometry uses the principle of polarization change of an incident electric field upon re-

flection from a substrate. The different phase and amplitude (Fresnel coefficient) changes

for the parallel p and perpendicular s “senkrecht”) electric field components of the electric

field upon reflection from interfaces of a (stacked) sample lead to a change in polarization.

The polarization change contains information regarding optical properties, expressed in

the complex refractive index n = n−ik with n the index of refraction and k the extinc-

tion coefficient of the bulk sample or the thickness and optical properties of one or more

layers on the sample. This polarization change is then measured and expressed in the

ellipsometric angles Ψ and ∆, which are defined as tan Ψ exp(i∆)=rp/rs, where rp and rs

are the complex amplitude reflection coefficients of the electric field components p and s

to the plane of incidence, respectively. According to Fresnel laws,3 upon reflection both

electric field components will have different amplitudes of reflection:

rp =Er

p

Eip

= n1 cos θ0 − n0 cos θ1n0 cos θ0 + n1 cos θ1

rs =Er

s

Eis

= n0 cos θ0 − n1 cos θ1n0 cos θ0 + n1 cos θ1

(3.1)

In these equations, the superscripts i and r stand for incident and reflected, respectively.

The angle of incidence is called θ0, the angle of transmission θ1.

In the case of a single film on top of an semi-infinite substrate one needs to include the

propagation of the light through the film, including multiple reflections and absorption

19

20 Chapter 3. Ellipsometry

tt01,xr1

2,x

θ0

Ε

Εs

Εp

i

i

Εpr

Εsr

θ1

d1

n2~

n1~

n0~

plane of incidence

1

145

o

rs

Ψrp

t01,x r12,x t10,x

r01,x

t01,x

t12,x

Fig. 3.1: Interaction of the electric field components with a single film, with thickness d1 andrefractive index n1, on a semi-infinite substrate, with refractive index n2. Multiply reflectionsri/i+1,x and transmissions ti/i+1,x for both s and p polarized light add up and converge to the totalreflection coefficient rt,x=p,s as defined in Eq. 3.4.

as illustrated in Fig. 3.1. The total reflection coefficient rt,x then becomes:

rt,x = r01,x + t01,xe−jβ1r12,xe

−jβ1t10,x + t01,xe−jβ1r12,xe

−jβ1r10,xe−jβ1r12,xe

−jβ1t10,x + . . .= r01,x + t01,xt10,xr12,xe

−2jβ1 [1 + r10,xr12,xe−2jβ1 + (r10,xr12,xe

−2jβ1)2 . . . ],

(3.2)

where the subscript x denotes the polarization of the light (p or s), and β is the phase

thickness, i.e. the phase shift of the propagating wave:

β1 =2π

λd1 n1 cos θ1 (3.3)

in which d1 is the thickness of the film. Using r01 = −r10 from equation 3.1 and conser-

vation of energy in the form t01t10 = 1− r201, the total reflection coefficient rt,x (Eq. 3.2)

becomes

rt,x =r01,x + r12,xe

−2jβ1

1 + r01,xr12,xe−2jβ1. (3.4)

In case of multiple films covering the substrate, the calculation becomes even more in-

tricate considering all possible internal reflections that have to be taken into account.

3.2. Ellipsometers 21

Therefore, a modeling program is used to simulate (Ψ, ∆) based on the assumed (multi-

)layer configuration of the measured substrate and Eqs. 3.1, 3.3 and 3.4. By curve-fitting

the simulated (Ψ, ∆) to the measured (Ψ, ∆), information regarding the complex optical

properties ni, more often expressed in the complex dielectric properties εi = n2i , and the

film thicknesses di can be obtained.

If the surface is not flat but exhibits roughness, a roughness layer needs to be incor-

porated in the multi-layer model. A surface roughness layer is modeled as a separate

layer with an effective dielectric constant εe. An effective-medium-approximation (EMA)

is then used to obtain an effective dielectric constant for the surface roughness layer. In

our case we have chosen to use the Bruggemann EMA,4 which is most commonly used

in the analysis of ellipsometric measurements where surface roughness is present. The

Bruggemann EMA is derived from the Claussius-Mossotti relation,1,4 which describes the

dipole polarization α of a single dipole in an external electric field, and from the assump-

tion that the effective dipole polarization of the mixed medium is a weighted sum of the

different dipole polarizations of the various media in the mix. In the case of a mix of two

media, the Bruggemann equation is expressed as:

fmεm − εe

εm + 2εe

+ fvεv − εe

εv + 2εe

= 0 (3.5)

fm + fv = 1, (3.6)

where fi and εi are the fractions and complex dielectric constant of each component i,

respectively, and εe the complex dielectric constant of the mixture. In the case of a rough

top layer, two media are used, where one of the media is vacuum with εv = 1 and the

media are assumed to have equal fractions fm = fv = 0.5.

The main disadvantage of ellipsometry is that the measured quantities Ψ and ∆ do

not have a direct physical meaning, but may require some knowledge of the surface un-

der investigation in advance, depending on the complexity of the layered system, before

the desired physical information can be derived. In general, ellipsometry is a fast and

extremely sensitive diagnostic to relative changes of the sample under investigation. For

example, in the case of layer thicknesses, ellipsometry is sensitive to changes on the order

of a few Angstrøm.

3.2 Ellipsometers

3.2.1 Single-wavelength ellipsometer

The ellipsometer is a rotating-compensator ellipsometer in the polarizer-compensator-

sample-analyzer (PCSA) configuration (see Fig. 3.2). The linearly polarized laser light

with a wavelength of 632.8 nm (He-Ne laser, Melles Griot 05-LHP-111) is first circularly

polarized with a λ/4 retarder, such that the intensity of the light is equal for all polariza-

tion angles for calibration purposes. The laser light then passes through a dichroic sheet


polarizer

encoder with

rotating compensator

HeNe-laser

λ/4

analyzer

sample

photodiode

Fig. 3.2: Optical setup for ellipsometry measurements in a PCSA-configuration.

polarizer (Melles Griot 05-FPG-001), mounted on a manual rotary stage (sensitivity of

1/60), sets the polarization of the light to 45 with respect to the plane of incidence. The

light then passes through the rotating compensator, which is a zero-order quartz λ/4 re-

tardation plate, anti-reflection coated on both sites (Dohrer Elektrooptik WZQ 150-633).

The compensator is driven by a synchronous motor with a 2:3 transmission, resulting

in a rotation frequency of 33 Hz. The laser beam is directed in and out of the vacuum

through stress-free quartz windows. The laser light reflects from the sample at an angle

of incidence of 74 with respect to the sample surface normal. It was assured that these

windows do not have any influence on the polarization of the incoming and reflected laser

light. The reflected beam then passes an analyzer (identical to the polarizer), which is set

to 0 with the plane of incidence to translate the polarization variation into an intensity

variation. The periodic intensity variations are measured by a photodiode detector. Con-

nected to the compensator is an encoder which generates 256 pulses and one start pulse

per cycle of the compensator. These pulses are used to trigger a 12-bit parallel sampling

ADC (TUeDACS) to measure the output voltage of a photodiode on which the reflected

laser light is incident. The measured intensity modulation per cycle of the compensator

is Fourier-analyzed and from the Fourier-coefficients the ellipsometric parameters Ψ and

∆ are determined.

The time resolution of this ellipsometer is limited by the 33 Hz rotation frequency of

the rotating compensator, data-acquisition and analysis. This results in a time resolution

on the order of 100 ms, hence the dynamics of surface processes occurring on time scales

larger than 100 ms can be resolved in ’real-time’.

3.2.2 Spectroscopic ellipsometer

For this purpose a commercially available spectroscopic ellipsometer has been used (Wool-

lam M2000U, with infrared extension). A broadband Xenon-arc light source generates

light in the spectral range from 250 to 1700 nm (5-0.70 eV photon energy). The ellip-

someter is used in a polarizer-sample-compensator-analyzer (PSCA) configuration. From

the analyzer the light is coupled into optical fibers after which the light is dispersed

onto CCD chips to measure the intensity of the whole spectral range (662 wavelengths).

WVASE32r software has been used to perform the ellipsometry measurements. The

References 23

resulting (Ψ(ω), ∆(ω))-spectra are then analyzed with either WVASE32r or EASETM

software, which make use of Eqs. 3.1, 3.3, 3.4 and 3.5 to obtain the optical properties

and/or layer thickness information from the measurements. In the experiments presented

here, one data point is typically the result of an average over 100 recorded SE spectra

(with 662 wavelengths) resulting in a time resolution of ∼5 s. Hence, a single SE spectrum

is measured with a time resolution of 50 ms.

References

1 G. M. W. Kroesen, Ellipsometrie (Lecture notes, 3P200, 1996).

2 R. M. A. Azzam and N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam,1992).

3 F. L. Pedrotti and L. S. Pedrotti, Introduction to optics, second edition (Prentice-Hall International,Inc., New York, 1993).

4 D. A. G. Bruggeman, Ann. Phys. 24, 636 (1935).

Chapter 4

Second-harmonic generation

Abstract

Second-harmonic generation (SHG) is the conversion of two photons with energy ω intoone photon with energy 2ω. SHG is a nonlinear optical diagnostic suitable to character-ize surfaces and interfaces. An unique feature of SHG is its potential surface/interfacespecificity and, furthermore, SHG is sensitive to crystallographic symmetry and electronicsurface states.1–4 Here, an introduction to basic principles of SHG will be given with theemphasis on aspects relevant in this thesis. Next, the optical setup for SHG experimentswill be described. To be able to correct for wavelength-dependent transmission of ω and2ω radiation and wavelength-dependent detection efficiency of SH photons, the systemresponse of the optical setup has been calibrated. Finally, oxidized and hydrogenatedSi(100) samples have been studied to verify the measurement procedure and to introducethe art of interpretation of SH spectra.

4.1 Introduction to second-harmonic generation

An electromagnetic field ~E(ω) induces a polarization ~P within a medium upon reflection,

given by

~P (2)(2ω) = ε0

[χ(1)(ω) ~E(ω) + χ(2)(2ω) : ~E(ω) ~E(ω) + ...

], (4.1)

where ε0 is the permittivity of the vacuum and χ(i) is the i-th order electric susceptibility

tensor. In everyday, linear optics the electric fields are considered small, such that higher-

order polarizations can be ignored. However, in the case of sufficiently strong electric

fields, higher-order polarization can become significant and can lead to generation of light

at the second-harmonic, third-harmonic, etc., of the fundamental frequency ω. This basic

principle is used in nonlinear optical diagnostics, such as second-harmonic generation

(SHG). SHG probes a medium at frequency ω and detects the response of the medium at

frequency 2ω.

Within the electric-dipole approximation, SHG is described by a second-order nonlin-

ear polarization ~P (2)(2ω) in a medium induced by an incident electric field ~E(ω):

~P = ε0χ(2)(2ω) : ~E(ω) ~E(ω), (4.2)

25

26 Chapter 4. Second-harmonic generation

where χ(2) is the nonlinear susceptibility tensor. Writing Eq. 4.2 in components yields:

P(2)x (2ω)

P(2)y (2ω)

P(2)z (2ω)

= ε0

χ(2)xxx χ

(2)xyy χ

(2)xzz χ

(2)xyz χ

(2)xxz χ

(2)xxy

χ(2)yxx χ

(2)yyy χ

(2)yzz χ

(2)yyz χ

(2)yxz χ

(2)yxy

χ(2)zxx χ

(2)zyy χ

(2)zzz χ

(2)zyz χ

(2)zxz χ

(2)zxy

E2x(ω)

E2y(ω)

E2z (ω)

2Ey(ω)Ez(ω)2Ex(ω)Ez(ω)2Ex(ω)Ey(ω)

,

(4.3)

where the subscript xyz corresponds to the orientation of the electric field components

with respect to the plane of incidence. SHG is forbidden in the bulk of centro-symmetric

materials, such as c-Si and a-Si, as in these media symmetry considerations imply χ(2)(2ω)=0.

However, at a surface or interface the symmetry is broken and χ(2)(2ω) is non-zero, thereby

making the technique of SHG particularly surface and interface sensitive.

By assessing the allowed symmetry operations with respect to the crystallographic

structure of the surface/interface, the nonlinear susceptibility tensor χ(2)(2ω) can be sim-

plified. For the Si(100)-surface (4mm-symmetry) and amorphous Si (∞m-symmetry),3

which are the two media relevant in this thesis, the tensor simplifies to

χ(2)(2ω) =

0 0 0 0 χ(2)xxz 0

0 0 0 χ(2)yyz 0 0

χ(2)zxx χ

(2)zyy χ

(2)zzz 0 0 0

, (4.4)

with χ(2)zxx = χ

(2)zyy and χ

(2)xxz = χ

(2)yyz. Depending on geometry of the SHG setup and

sample crystal structure, the elements of the tensor may contribute to the detected, total

SH signal with different weights. By choosing smart combinations of probe- and signal-

polarization specific elements in the second-order susceptibility tensor can be selected in

order to determine their contributions, as will be demonstrated in Sec. 4.4.

Microscopically, SHG is the conversion of two photons with energy ~ω into a single

photon with energy 2~ω. The process of SHG is resonantly enhanced when the photon

energy of either the fundamental or the SH radiation coincides with the energy of an

electronic transition in the material. Consequently, SHG is a technique that is potentially

sensitive to both the symmetry and the electronic states of surfaces and interfaces. The

resonant behavior and the corresponding surface states will be addressed in Sec. 4.5.

4.2 Laser and optical setup

A Ti:Sapphire oscillator (Spectra Physics (SP) Tsunami) with broadband optics, which is

pumped by an intra-cavity doubled continuous-wave Nd:YVO4 laser (SP Millennia Vsj),

is used to generate the fundamental laser radiation. The laser pulses have a pulse duration

of ∼90 fs, a repetition rate of 80 MHz and the photon energy is tunable between 1.35

- 1.75 eV (920-710 nm). The laser beam is guided to the sample in the high-vacuum

setup with broadband silver coated mirrors (New Focus (NF) 5103). A variable wave

4.2. Laser and optical setup 27

sample

lens

polarizerfilter Ti:Sapphire

~90 fs, 80 MHz

920 - 710 nm, 1.35 - 1.75 eV

5 W CW

532 nm

lens

prism

PellinBroca

slit

PMT

filterpolarizerpinhole

compensator

ω

ω

2ω2ω

74o

Fig. 4.1: Optical setup for the SHG experiments.

plate (NF 5540) and a Glan-Thompson polarizer (NF 5525) have been used to select the

desired polarization of the fundamental radiation and to set the power of the laser beam

at the sample to typically 50 mW. Any radiation at the second-harmonic (SH) wavelength

generated in the laser or in optical components in the beam path is suppressed using a color

filter (Schott OG 570). The fundamental beam enters and leaves the vacuum chamber

through stress free fused silica view ports at 74 angle with respect to the sample surface

normal. The fundamental radiation is focused onto the sample using a BK7 lens (CVI

PLCX 25.4-103.0-C) to a spot with an estimated radius of 100 µm, which leads to a typical

fluence of 2 µJ/cm2 per pulse. The reflected beam passes a second polarizer (Thorlabs

GL10A) to select the desired polarization of the second-harmonic radiation. Two color

filters (Schott BG40) are used to suppress most of the fundamental radiation. Next,

the beam is focused with a lens (CVI PLCX 25.4-64.4-C) onto a slit placed in front of a

photomultiplier tube (Hamamatsu R585). Before passing the slit, a 90 prism and a Pellin

Broca dispersion prism spatially separate the remaining fundamental radiation from the

SH radiation and the slit is positioned such that only the SH radiation is allowed to pass

and to be detected by the photomultiplier tube. The photomultiplier tube is connected to

photon counting electronics to record the SH signal. The dark count rate of this detection

scheme was below 4 Hz.

Spectroscopic SHG measurements are performed by tuning the fundamental radiation

wavelength of the Ti:Sapphire laser. The laser pulse width is set to a FWHM of ∼12 nm

(0.02-0.03 eV) for each laser wavelength using a spectrometer (Ocean Optics USB2000).

Next, the power is set and the SH intensity is recorded. The measurement of a SH

spectrum takes typically 1-1.5 hour by this procedure. The SH intensity I(2ω) has been

calculated from the measured SH signal after correction for the laser intensity and the

response of the optical system.


2.6 2.8 3.0 3.2 3.4 3.60.0

0.1

0.2

0.3

2.6 2.8 3.0 3.2 3.4 3.60.0

0.2

0.4

0.6

0.8

1.0

Qua

rtz S

H s

igna

l (ar

b. u

nits

)

SH photon energy (eV)

Nor

m. s

yste

m re

spon

se (-

)


Fig. 4.2: SH spectrum for p-polarized fundamental and SH radiation as measured on single-sidepolished z -cut α-quartz sample (dots) and the system response (line) as determined from trans-mission measurements of polarizers and filters and the detection efficiency of the photomultiplier.Correction of the quartz SH spectrum for system response would result in, as expected, a wave-length independent quartz SH signal.

4.3 System response calibration

Optical elements such as polarizers and filters have a wavelength dependent transmission

characteristic and photomultiplier tubes have a wavelength dependent sensitivity. To be

able to correct for the transmission of the fundamental and SH radiation to the system

response, the transmission characteristics of polarizers and filters have been measured.

Furthermore, the wavelength dependent sensitivity of the photomultiplier tube has to be

included, which is given by the manufacturer. The resulting sum response of the optical

system was then verified by measuring the SH spectrum on a z -cut α-quartz sample.

Quartz is often used as a reference in SHG experiments, as its SH signal is indepen-

dent of wavelength in the visible range.5,6 A single-side polished quartz sample has been

positioned at the same position in the setup as the Si(100) samples that are going to be

studied. Only the frontside of the quartz sample has been polished to prevent SH signal

to be generated and detected originating from the backside of the quartz sample. This

way a reference for the SH signal in reflection is measured for the surface region only,

as this interface region is only of interest in the presented experiments. The SH signal

is then measured in reflection for p-polarized fundamental and SH radiation∗ by tuning

the Ti:Sapphire laser as described above. In Fig.4.2, both system response (line) and

the SH spectrum measured on quartz (dots) are shown. The independently determined

system response is in good agreement with the measured SH spectrum on quartz. Hence,

when correcting the SH spectrum for system response, the quartz spectrum would be, as

∗definition of polarization directions is given in the Sec. 4.4

4.4. Multipolar, higher-order contributions to SHG 29

expected, almost fully independent of photon energy. Since the independently determined

system response involves only transmission through optical elements and detection effi-

ciency of the photon multiplier and still shows such good agreement with the measured

quartz SH spectrum, implies that dispersion of the 90 fs pulse cannot be significant and

diffraction-limitations as a result of focussing is not an issue here. By keeping the mea-

surement procedure for all the spectra presented here identical, this calibration method

allows us to correct the spectra for the transmission characteristics of the optical elements

and the detection efficiency of the photomultiplier tube.

4.4 Multipolar, higher-order contributions to SHG

The interpretation of the microscopic origin of the measured SH signal is a major challenge.

One should consider that the SH source could also be from multipolar and/or higher-order

polarization contributions, such as a bulk-quadrupole contribution7–9

~P(2)Q (2ω) = ε0Γ

(2)(2ω) : ~E(ω)~O ~E(ω), (4.5)

where O ~E(ω) is the gradient of the incident electric field and Γ(2)(2ω) is the bulk-

quadrupole susceptibility tensor. The symmetry difference between bulk-quadrupole and

surface-dipole contributions can, in some cases, be used to determine the presence of bulk-

quadrupole contributions. The surface electric-dipole polarization on Si(100)-surfaces re-

sults in an isotropic SH signal when the sample is rotated about the surface normal, i.e.,

azimuthal angular dependence. The bulk-quadrupole polarization contribution is known

to have not only an isotropic but also an anisotropic response in the azimuthal angular

dependence.2,7

As a demonstration, the azimuthal angular dependence is measured in an ex situ op-

tical setup, identical to the setup described in Sec. 4.2. A Si(100) sample with a native

oxide on top (NO-Si(100)) is used and the azimuthal angular dependence is measured for

polarization combinations (p,P ) and (mix,S)†, as shown in Fig. 4.3. On the left is the ori-

entation shown of the incoming and reflected electric field polarizations with respect to the

xyz-coordinate system and the crystal orientation of Si(100). On the right the azimuthal

angle dependence, measured at 3.31 eV SH photon energy, is shown. Clearly, a fourfold-

symmetry is observed in the azimuthal angle dependence, which is not expected from the

isotropic (=independent of azimuth) contributions related to the second-order nonlinear

surface susceptibility tensor elements. This anisotropic contribution has been attributed

to a higher-order, bulk-quadrupole term.7 The total observed SH intensity signal as a

function of azimuthal angle is the result of destructive and constructive interference be-

tween the bulk-quadrupole and isotropic contributions from the surface electric-dipole

†(a,B): a=polarization direction of the input (fundamental) light, B=polarization direction of theoutput (second-harmonic) light. By mix we denoted a mixed polarization state of s and p, defined asmix = 1

2

√2(p + s)


y

x

z

s pP

S α

[001]

74o

0 45 90 135 180 225 270 315 3600.0

0.5

1.0

1.5

2.0

2.5

(mix,S) (x 30)

SH

inte

nsity

(arb

. uni

ts)

sample azimuth ( O )

(p,P)

[001] [011]

Fig. 4.3: Sample orientation with respect to the incoming (p, s) and reflected (P, S) electric fieldpolarization (left). Azimuthal angle α dependence is the SH intensity as a function of rotationof the sample about its surface normal. The azimuthal angle dependence for (p, P ) and (mix, S)polarization combination as measured on NO-Si(100) are shown on the right. All in situ measure-ments are performed with the [011]-axis parallel to the plane of incidence.

and the bulk-quadrupole. For this case, the anisotropic bulk-quadrupole contribution is

only ∼15% of the total signal.

Figure 4.3 also shows that the SH intensity for (mix, S) is much smaller than (p,P ). For

p-polarized fundamental radiation the elements in columns 1, 3 and 5 of the second-order

susceptibility tensor (Eq. 4.4) are activated and for s-polarized fundamental radiation

only the elements in column 2 are activated. Then, by selecting the P -polarized SH

photons the SH signal resulting from elements in rows 1 and 3 are detected. By selecting

the S-polarized SH photons the SH signal resulting from elements in row 2 are detected.

By choosing the polarization combination (mix, S), the tensor elements χ(2)xxz = χ

(2)yyz in

Eq. 4.4 are being probed. This means that contributions to the detected SH signal from

χ(2)xxz = χ

(2)yyz are much smaller than the other tensor elements. Additional, polarization

dependence ‡ measurements revealed also that contributions to the detected SH signal

from χ(2)zxx = χ

(2)zyy are much smaller than from the tensor element χ

(2)zzz. The reason that

most of the detected SH signal arises from χ(2)zzz is the large fresnel coefficients for the

zzz-symmetry in our experimental configuration with a 74 angle of incidence.

One other higher-order polarization contribution that could result in SH signal is

bulk-dipole polarization in the presence of a significant electric field Edc, which is called

electric-field-induced-second-harmonic (EFISH):8–12

~P(2)E (2ω) = ε0χ

(3)(2ω) : ~E(ω) ~E(ω) ~Edc. (4.6)

‡Polarization dependence= rotation of the incoming polarization and detection with a fixed polariza-tion

4.5. Spectroscopic SHG from H:Si(100) and native oxide on Si(100) 31

This contribution is isotropic for Si(100) and can be investigated by applying a bias field

to the surface region. EFISH has been observed for, e.g., Cr-SiO2-Si(100) MOS structures

with electric fields on the order of Edc ≡ 106 kV/cm.10

SH signal from multipolar, higher-order polarization can at present not be fully ex-

cluded or corroborated in our setup. To be able to asses the presence and importance

of these contributions would require in situ rotation of the sample, surface manipulation

or applying additional dc bias fields to the sample,2 although a full identification of all

separate contributions, and their importance, is in general not possible.

4.5 Spectroscopic SHG from H:Si(100) and native oxide on Si(100)

SHG from Si(100) and Si(111) has been studied intensively in the same wavelength region

as presented here, either with a native oxide on top of the silicon (NO-Si) or a hydrogen-

terminated silicon (H:Si).7,12–15 As a ‘proof of principle’, SH spectra have been measured

in our setup on NO-Si(100) and H:Si(100) as shown in Fig. 4.4. The SH spectrum of

H:Si(100) shows a symmetric resonance peak with the peak intensity at 3.33 eV SH photon

energy. The spectrum of NO-Si(100) appears non-symmetric with the peak intensity at

3.30 eV and a minimum SH intensity at 3.44 eV. A non-symmetric spectrum is commonly

related to multiple contributions to the SH signal. The measured SH spectra are in good

agreement with the SH spectra of NO-Si(100) and H:Si(100) reported in literature. The

lines through the data points in Fig. 4.4 are the result of a fit using a model to reproduce

SH spectra as described next.

To be able to distinguish the various contributions to the SH signal and, thus, identify

the microscopic origin of the various resonance contributions, the SH intensity spectra

I(2ω) can be reproduced with a coherent superposition of critical-point-like (CP) reso-

nances: 12,13,15–17

I(2ω) =

∣∣∣∣∣∑

L

∑

αβγ

AL,αβγ(ω, θ) χ(2)L,αβγ(2ω)

∣∣∣∣∣

2

I2(ω), (4.7)

where the nonlinear nonlinear susceptibility tensor element χ(2)L,αβγ can be approximated

by a sum of CP-resonances with excitonic line shapes, defined as:

χ(2)L,αβγ(2ω) =

∑q

χ(2)L,αβγ,q(2ω; ωq, hq, Γq, φq) =

∑q

hq eiφq

2ω − ωq + iΓq

, (4.8)

with resonance amplitude hq, excitonic phase φq, frequency ωq and line width Γq. The

subscript L denotes the spatial, macroscopic origin (e.g. L = S for surface and L = I for

interface), αβγ denotes the specific element of the nonlinear susceptibility tensor χ(2)(2ω)

(Eq. 4.2) and q denotes the specific CP resonance contribution χ(2)L,αβγ,q(2ω; ωq, hq, Γq, φq).

The complex functions AL,αβγ(ω, θ) represent the linear propagation of the fundamental


2.6 2.8 3.0 3.2 3.4 3.60.0

0.5

1.0

H:Si(100) NO-Si(100)

SH

inte

nsity

(arb

. uni

ts)


Fig. 4.4: SH spectra measured on H:Si(100) (squares) and NO-Si(100) (circles). The lines are fitsto the SH spectra using a coherent sum of critical-point-like resonances.

2.6 2.8 3.0 3.2 3.4 3.60.0

0.1

0.2

0.3

0.4

0.5

2.6 2.8 3.0 3.2 3.4 3.60

1

2

3

(2)

I,NO2

(2)

I,NO1

(2)

S,H

(2)

L,q

2


(1

)2 (

x 10

3 )


c-Si

Fig. 4.5: Resonances |χ(2)L,q|2 derived from the fits to the H:Si(100) and NO-Si(100) spectra pre-

sented in Fig. 4.4. For the measured H:Si(100) spectrum a single resonance χ(2)S,H at 3.33 eV

(dashed line) has been identified and for the measured NO-Si(100) spectrum two resonances havebeen identified: χ

(2)I,NO1 at 3.34 eV (thin solid line) and χ

(2)I,NO2 at 3.53 eV (thick solid line). For

reference the squared magnitude of the linear susceptibility |χ(1)|2 of silicon is shown.

and SH radiation through the system including absorption, refraction and interference

from multiple reflections for the fundamental and SH photon energy in the system. The

propagation depends on the angle of incidence θ, the radiation frequency ω and the specific

element of the nonlinear susceptibility tensor χ(2), and is obtained by assessing the fresnel

coefficients in an interface region between two media, which is treated as a polarized sheet

placed in an infinitesimal vacuum gap between the two media, where the SH radiation is

generated.16,18,19

For the studies presented in this thesis, the SH intensity spectra have been measured

4.5. Spectroscopic SHG from H:Si(100) and native oxide on Si(100) 33

Tab. 4.1: Overview of the χ(2)L , q(2ω; ωq, hq, Γq, φq)-resonance contributions to the SH signal de-

rived from modeling of SH spectra measured on H:Si(100) and NO-Si(100) for polarization combi-nation (p, P ). The analysis of SH spectra has been performed in both cases with the assumptionthat the SH signal arises from χ

(2)L,zzz(2ω). The subscript q denotes the specific CP resonance

contribution. The macroscopic origin is described in the last column. The phase factor φq denotesa phase difference between resonances when more than one resonance is present, otherwise φq=0.The error margins in the resonance parameters are typically ∆ωq= 0.001 eV/~, ∆hq=0.01 (arb.units), ∆Γq=0.002 eV/~ and ∆φq=0.03 rad.

system χ(2)L,q(2ω; ωq, hq,Γq, φq)-resonances macroscopic origin

NO-Si(100) χ(2)I,NO1(2ω; 3.34, 0.052, 0.094, 0) + Si(100)/SiO2-interface

χ(2)I,NO2(2ω; 3.53, 0.040, 0.091, 4.96) Si(100)/SiO2-interface

H:Si(100) χ(2)S,H(2ω; 3.33, 0.052, 0.13, 0) H:Si(100)-surface

for p-polarized fundamental and SH radiation. For this polarization combination the SH

response of Si(100) is expected to arise predominantly from the χ(2)L,zzz element. The use

of an angle of incidence of 74 is one of the reason that χ(2)L,zzz is mostly responsible for

the detected SH signal, since the fresnel coefficients for this element are much larger than

for other tensor elements as follows from the assessment of the propagation functions

AL,αβγ(ω, θ).

Hence, the SH spectra measured for p-polarized fundamental and SH radiation have

been analyzed with the assumption that the SH signal arises from χ(2)L,zzz(2ω) and, thus,

the propagation functions AL,zzz(ω, θ) have been used and have been evaluated with the

available information including angle of incidence, layer thickness and optical properties.

Here, the subscript αβγ = zzz is further ignored and, hence, the SH spectra have been

reproduced by combined version of Eqs. 4.7 and 4.8:

I(2ω) =

∣∣∣∣∣∑

L

AL(ω, θ)∑

q

χ(2)L,q(2ω; ωq, hq, Γq, φq)

∣∣∣∣∣

2

I2(ω). (4.9)

For the fit to the SH spectrum of H:Si(100) in Fig. 4.4, only one resonance positioned

at the surface (L = S) has been used. Since the absolute phase φq of the resonance can

not be determined from these experiments, φq is kept equal to 0, which leaves a total of

three fit parameters: hq, ωq and Γq. For the NO-Si(100) two resonances at the interface

(L = I) are included. Only the phase difference between the two resonances is included

in the fit, resulting in a total of seven fit parameters. The fit parameter values that have

been found are listed in Table 4.1, together with the results of other systems that have

been studied in our experimental configuration.

The separate resonances from the fits are shown in Fig. 4.5. For H:Si(100) the res-


onance is located at 3.33 eV SH photon energy and for NO-Si(100) the two resonances

are located at 3.34 eV and 3.53 eV, respectively. For reference the squared magnitude of

the linear susceptibility |χ(1)|2 is also shown. The squared linear susceptibility has a res-

onance feature at approximately 3.36 eV photon energy, which is the result of two direct

inter-band transitions in bulk silicon, which are known as E ′0 and E1 direct inter-band

transitions.20 Throughout this chapter and in Chapter 8, this resonance will be denoted

by E ′0/E1.

The microscopic (electronic transitions) and macroscopic (surface and/or interfaces)

origin of the SH signal for these systems is fairly well understood. Both the SH spec-

trum of H:Si(100) and NO-Si(100) show a resonance feature close to 3.36 eV, although

slightly red-shifted. This SH resonance is in both cases related to bulk-like E ′0/E1 direct

inter-band transitions.13,15,20 The difference in resonance frequency with respect to the

bulk transitions is in the H:Si(100) case caused by the presence of the vacuum-Si(100)

interface and the presence of H-atoms at surface Si atoms. For the NO-Si(100) case the

resonance at 3.34 eV has a similar microscopic origin, but the signal arises from the Si-

SiO2 interface. The second resonance in the SH spectrum of NO-Si(100) at 3.53 eV is

Si-SiO2-interface specific. A similar resonance has also been observed on NO-Si(111) at

3.52 eV13 and on NO-Si(100) at around 3.60 eV.15 This CP resonance is only observed

in nonlinear spectroscopy in the presence of the Si-SiO2 interface but is not observed in

bulk Si as is known from linear spectroscopy.20 The microscopic origin of this additional,

interface specific resonance is believed to arise from Si-Si transitions for a specific Si-O

bonding complex at the interface.13 The phase difference between the two contributions

is responsible for the fact that the peaks in the measured SH spectrum of NO-Si(100)

appear non-symmetric and causes a minimum in the SH intensity at 3.44 eV.

The disadvantage of SHG lies in the interpretation of the microscopic origin of the SH

signal is in some cases, which is still a major concern in literature, even for, e.g., intensively

studied oxidized silicon. The advantages of SHG are the proven interface specificity and

sensitivity to symmetry and electronic states. In that respect the use of SHG in such

a potentially dynamic experiment as beam-etching is fairly unique and could give more

detailed information regarding the silicon-fluoride reaction layer.

References

1 Y. R. Shen, The principles of nonlinear optics (Wiley, New York, 1984).

2 G.Lupke, Surf. Sci. Rep. 35, 75 (1999).

3 R. W. Boyd, Nonlinear optics (Academic Press, Amsterdam, 2003).

4 P. Haleri, ed., Photonic probes of surfaces (Elsevier, Amsterdam, 1995), chap. 9, by G. A. Reider andT. F. Heinz.

5 C. Flueraru, C. P. Grover, Appl. Opt. 42, 6666 (2003).

References 35

6 Lu R., Wang H. F., Chin. Phys. Lett. 20, 1269 (2003).

7 Y. Q. An and S. T. Cundiff, Phys. Rev. B 67, 193302 (2003).

8 J. G. Mikaychuk, N. Shamin, H. M. van Driel, Phys. Rev. B 59, 2164 (1999).

9 H.-E. Ponath and G. I. Stegeman, ed., Nonlinear surface electromagnetic phenomena (Elsevier, Am-sterdam, 1991), chap. 5, by T. F. Heinz.

10 O. A. Aktsipetrov, A. A. Fedyanin, A. V. Melnikov, E. D. Mishina, A. N. Rubtsov ,M. H. Anderson,P. T. Wilson, M. ter Beek, X. F. Hu, J. I. Dadap, and M. C. Downer, Phys. Rev. B 60, 8924 (1999).

11 Y. G. An and S. T. Cundiff, J. Appl. Phys. 96, 2638 (2004).

12 J. I. Dadap, Z. Xu, X. F. Hu, M. C. Downer, N. M. Russel, J. G. Ekerdt, O. A. Aktsipetrov, Phys.Rev. B 56, 13367 (1997).

13 S. Bergfeld, B. Braunschweig, and W. Daum, Phys. Rev. Lett. 93, 097402 (2004).

14 Z. Xu, X. F. Hu, D. Lim, J. G. Ekerdt, M. C. Downer, J. Vac. Sci. Technol. B 15, 1059 (1997).

15 G. Erley, W. Daum, Phys. Rev. B 58, R1734 (1998).


17 G. Erley, R. Butz, W. Daum, Phys. Rev. B 59, 2915 (1999).

18 B. Koopmans, A. Anema, H. T. Jonkman, G. A. Sawatzky, and F. van der Woude, Phys. Rev. B 48,2759 (1993).

19 V. Mizrahi and J. E. Sipe, J. Opt. Soc. Am. B 5, 660 (1988).

20 P. Lautenschlager, M. Garriga, L. Vina, M. Cardona, Phys. Rev. B 36, 4821 (1987).

Chapter 5

Amorphous silicon layer characteristics during

70-2000 eV Ar+-ion bombardment of Si(100)

Abstract

Spectroscopic ellipsometry (SE) has been applied to characterize the damaged, amorphoussilicon (a-Si) layer created by Ar+-ion bombardment in the ion energy range of 70 to2000 eV impinging at 45 angle of incidence on Si(100). The dielectric functions of a-Siduring ion bombardment have been determined using the Tauc-Lorentz model for thedielectric functions ε1 and ε2. The dielectric functions resemble literature reports on a-Si-like dielectric functions. The a-Si layer thickness under ion bombardment conditions,reaches values from ≈ 17 A at 70 eV up to ≈95 A at 2000 eV. These values comparereasonably well with SRIM∗ and molecular dynamics simulations. The surface roughness,as determined with SE, is typically 5-15 A during ion bombardment, with a minimumroughness at Eion= 250 eV. The creation of the amorphous silicon top-layer upon 70eV Ar+ ion bombardment with an ion flux of 0.07 mono-layers s−1 has been resolvedusing real-time spectroscopic ellipsometry. The creation of the amorphous layer shows adouble exponential ion-dose dependence: a fast, initial period of a-Si creation, with 1/e

constant ∆τ1 = 2 mono-layer (ML), and a slower period, ∆τ2= 9 ML, until the matrix isfully amorphous after ∼30 ML of Ar+-dosing. Relaxation of the a-Si top-layer has beenobserved after the ions are switched off and has been analyzed with a stretched-exponentialdecay as a function of time, which is characteristic for a defect-controlled relaxation inthe bulk a-Si layer. The corresponding time constant τ is found to be ∼360 s, which istypically observed for self-annealing in amorphous silicon materials.

∗SRIM= stopping and range of ions in matter. SRIM is a program which calculates the stopping andrange of ions into matter using a quantum mechanical treatment of ion-atom collisions. It can calculateboth the final 3D distribution of the ions and also all kinetic phenomena associated with the ion’s energyloss: target damage, sputtering, ionization, and phonon production. A full description of the calculationsis found in the book The Stopping and Range of Ions in Solids, by J. F. Ziegler, J. P. Biersack and U.Littmark, Pergamon Press, New York, 1985 (new edition in 2003). The SRIM software package is free ofcharge and can be downloaded from http:www.srim.org.

37

38 Chapter 5. Amorphous silicon layer characteristics during 70-2000 eV Ar+-ion bombardment of Si(100)

5.1 Introduction

Ion bombardment plays a key role in fabrication processes of semiconductor and optical

devices. Ion bombardment is, e.g., used to manufacture extremely low roughness X-ray

mirrors1,2 and to implant dopants.3,4 In plasma etching ions are known to enhance etch

rates5 and for their ability to etch highly anisotropic nanometer scale structures. The

ion energy ranges of interest for these type of applications are Eion=10-500 eV for radio-

frequency or inductively-coupled etch plasmas, 100-1000 eV for ion-polishing applications

and ∼1000-2500 eV for shallow implantation of dopants. Ions penetrate to a certain depth

into a substrate depending on their energy, thereby creating a damaged amorphous layer.

This ion-damage layer will especially have an increasing influence on semiconductor device

performance as device dimensions are steadily reducing. On the other hand the change

from a crystalline to an amorphous surface layer is beneficial in plasma etching. The

modified atomic bonding configuration allows chemically reactive species to adsorb more

easily, and ion bombardment promotes the release of etch products.5–7 The amorphous ion

damage layer has not had much attention in fundamental beam etching studies, although

a few theoretical studies8,9 and a number of experimental studies report on the Ar+-ion

damage aspects in the ion energy range <2500 eV on silicon, such as the damage layer

thickness10–12 or surface morphology.13,14 Characterization of the ion-damage layer could

aid in a better understanding of etch mechanisms.

A diagnostic tool that can be employed insitu to characterize optical properties and

thicknesses of thin films is spectroscopic ellipsometry (SE). Here, we report on the use of

SE to characterize amorphous silicon (a-Si) layers created by Ar+ ion bombardment of

Si(100) in the 70-2000 eV ion energy range. SE has been used previously to study Ar+-

ion bombarded silicon substrates with ion energies up to tens of keV.3,15 The experiments

presented here have been performed in an Ar+/XeF2 beam etching apparatus designed to

study fundamental aspects of ion-assisted etch mechanisms.

Not only the saturated amorphous layer thickness under ion bombardment conditions,

but also the surface roughness and the dynamics of creation and relaxation of the damaged,

amorphous layer as a function of ion energy have been investigated using SE. In addition,

the ion energy range down to 70 eV will be explored, ultimately to close the existing

experimental gap between beam-etching and plasma-etching studies.

After addressing the experimental details (Sec. 5.2), the multi-layer dielectric modeling

and dielectric properties of the damaged, amorphous silicon will be described in Sec. 5.3

and will be compared to other a-Si-like dielectric functions reported in the literature.

The a-Si layer thickness and surface roughness during ion bombardment are presented

in Sec. 5.4. Also, a comparison is made between the measured a-Si layer thickness as a

function of ion energy and SRIM and molecular dynamics simulations. In Sec. 5.5, it will

be shown that real-time SE can be used to monitor the creation and the relaxation of the

5.2. Experimental details 39

Magnetic

linear drive

loadlock

UHV chamber

detector

chamber

2

11. Sample rotator

2. XeF2 source

3. Ar+ -ion source3

P light source

A R

C

D

Fig. 5.1: Experimental setup in horizontal cross-section. Samples can be exchanged between arotatable sample holder and the sample storage in the load lock with a linear magnetic drive.The sample is mounted in a rotatable sample holder (1) that can be operated manually via anexternal drive. The XeF2 source (2) and Ar+-ion source (3) are at 52 and 45 from surfacenormal, respectively. Etch products are detected in a separate detector chamber perpendicular tothe sample surface. The spectroscopic ellipsometer is incident at 74.3 from the sample surfacenormal. The SE consists of a broadband light source, polarizer(P), rotating compensator(RC),analyzer(A) and a fiber-coupled CCD-array detector(D).

a-Si top-layer produced by ion bombardment.

5.2 Experimental details

5.2.1 Experimental setup

The experimental setup has been described extensively in previous publications.16–18 In

Fig. 5.1 a top-view cross-section of the setup is shown. The setup is equipped with a

load-lock system for storage and easy sample exchange, a single-wavelength ellipsometer

and a mass spectrometer for etch product monitoring. The spectroscopic ellipsometer

is a Woollam M2000U with an infrared extension covering the photon energy range of

0.7-5 eV (250 - 1700 nm). The angle of incidence of the light is typically 74.3 off the

surface normal and the light is focused onto a 1 mm2 area of the sample. Each measured

spectrum is an average over typically 100 spectra recorded by the ellipsometer resulting

in a time resolution of typically 5 s. The spectroscopic ellipsometry data are analyzed

with EASETM software version 1.98.

A low energy (10-2000 eV) ion beam source (Nonsequitur Technologies, customized

version of Model LEIG-2) has been installed recently to access the lower (< 500 eV)

energy range. The ion beam diameter is set to 3 mm FWHM for all ion energies. The

ions impinge onto the silicon surface at a 45 angle with respect to the surface normal. The


ion flux is determined from the measured, total current on the sample. From calibration

a sample current of 1 µA relates to an ion flux of 0.09 mono-layer s−1 (ML s−1), which

is equal to 0.6·1014 cm−2s−1 (1 ML≡6.86·1014 cm−2). The maximum fluxes that can be

achieved with this source are typically 0.1 ML s−1 for ion energies below 100 eV and 1

ML s−1 for ion energies above 1000 eV ion energy.

5.2.2 Si(100)-samples

The silicon samples used in this study are n-type Si(100) with a resistivity of 10-30

Ωcm. The 10×10 mm2 Si substrates are pre-treated to remove the native oxide in a 2

% hydrofluoric acid (HF) solution for 2 minutes after ultrasonic cleaning with ethanol

at 40C. This leads to a mono-, di- and trihydride-terminated Si substrates with mostly

dihydrides19 with an initial roughness of typically 0.6-1.0 nm measured with SE and

∼0.15 nm root-mean-square roughness measured with AFM (NT-MDT Solver P47) in

non-contact mode (scan size: 1.5×1.5 µm).

5.2.3 Measured pseudo-dielectric functions

On three Si(100) samples SE spectra have been collected in situ and in real-time for ion

energies from 70 eV up to 2000 eV by increasing the ion energy stepwise and waiting

until the measurement reached a steady state. The ion flux was 0.07 ML s−1 for each ion

energy.

Figure 5.2 shows examples of steady-state pseudo-dielectric functions 〈ε1〉 and 〈ε2〉measured with SE on substrates during 70, 300 and 1000 eV Ar+ ion bombardment. For

reference the dielectric functions ε1 and ε2 for c-Si have been shown.20 Pseudo-dielectric

function spectra 〈ε1〉 and 〈ε2〉 are derived from the measured ellipsometric angles Ψ and

∆ assuming a two-phase (ambient/substrate) layer model, where the ellipsometric angles

Ψ and ∆ are defined as tanΨ exp(i∆)=rp/rs with rp and rs the complex amplitude reflec-

tion coefficients of the electric field components parallel and perpendicular to the plane of

incidence, respectively. The c-Si dielectric functions show the typical critical-point (CP)

resonances related to E′0/E1 ( 3.36 eV) and E2 ( 4.30 eV) electronic interband transi-

tions.21 Ion bombardment results in the loss of crystallinity and, thus, the distortion or

disappearance of the CP resonances of c-Si in a layer penetrated by the ions. Conse-

quently, a shift to lower energies and a broadening of the pseudo-dielectric functions can

be observed due to a top-layer of amorphized silicon (a-Si) with a characteristic broad

spectrum of Si-Si bond energies and disordered bond lengths and angles.15

To obtain information regarding dielectric properties or the thickness of the a-Si layer,

a multi-layer model is chosen. The unknown parameters within the multi-layer model are

the curve-fit variables to match the calculated pseudo-dielectric functions to the measured

spectra in order to obtain either unknown dielectric properties or layer thickness defined


0 1 2 3 4 5-20

-10

0

10

20

30

40

0 1 2 3 4 5

0

10

20

30

40

50

c-Si

70 eV

300 eV

1000 eV

⟨ε1⟩

photon energy (eV)

⟨ε2⟩

Fig. 5.2: Pseudo-dielectric functions of the measured steady-state spectra during Ar+-ion bom-bardment with 70, 300 and 1000 eV ion energy and an ion flux of 0.07 ML s−1. For reference, thedielectric functions of silicon are also shown (solid lines).

in the layer model. With a linear regression analysis method the fit variable values are

optimized by reducing the absolute value of χ2 of the fit:

χ2 =1

2N − P

N∑j=1

[(〈ε1〉calc

j − 〈ε1〉expj )2

σexp〈ε1〉

+(〈ε2〉calc

j − 〈ε2〉expj )2

σexp〈ε2〉

], (5.1)

where N is the number of measurement points (N=662), P is the number of fit variables

(typically P ∼2-6<< N) and σexp〈ε1〉 and σexp

〈ε2〉 are the experimental standard deviations

for 〈ε1〉 and 〈ε2〉, respectively. The experimental standard deviation is typically σexp〈ε1〉 =

σexp〈ε2〉=0.1. The next section discusses the multi-layer model choice and dielectric functions

ε1 and ε2 (ε = ε1−iε2) of the layers.


50 % void / 50 % a-Si

a-Si

c-Si

da-Si

dr

Fig. 5.3: Multi-layer dielectric model that has been used to analyze the measurements.

5.3 Multi-layer dielectric modeling

To obtain the thickness and/or optical properties of one or more layers on a sample,

a multi-layer model is defined and for each separate layer either known dielectric func-

tions or model dielectric functions are assigned. The multi-layer model that will be used

throughout this report consists of a semi-infinite c-Si substrate with an a-Si over-layer

and a surface roughness layer as shown in Fig. 5.3.

The dielectric functions for c-Si have been taken from literature.20 The dielectric

functions of the surface roughness layer are approximated using a Bruggemann effective-

medium-approximation under the assumption that the effective dielectric function of the

roughness layer can be described by a random mixture of 50% void and 50% a-Si. The

dielectric functions of amorphous silicon are, however, not unique and are subject to

specific processing/production methods, whether after ion bombardment (static equilib-

rium), during ion bombardment (dynamic equilibrium) or chemical-vapor-deposition has

been used.3,15,22 Since dielectric functions for a-Si during ion bombardment are to the

best of our knowledge not reported in literature, a full scale analysis of SE spectra mea-

sured in dynamic equilibrium has been undertaken to obtain dielectric functions of a-Si

and to investigate a potential dependence on ion energy and ion flux, as described in the

Appendix. To obtain dielectric functions of a-Si the Tauc-Lorentz (TL) model has been

used (see Appendix), which has been proposed by Jellison and Modine23 and has been

used successfully to model dielectric functions of amorphous materials.15,22–25

The dielectric functions ε1 and ε2 of a-Si during ion bombardment are shown in Fig. 5.4.

As can be seen the dielectric functions reveal a single broad spectral feature unlike the

specific resonance features observed for crystalline silicon. This single, broad resonance

spectrum is characteristic for a broad spectrum of Si-Si bond energies and disordered

bond lengths. By comparing these dielectric functions with dielectric functions for dif-

ferent types of amorphous silicon reported in the literature, it can be concluded that

the dielectric functions obtained in this study show good agreement with the literature

dielectric functions for amorphous silicon. The observed differences can be ascribed to

differences in the way the amorphous silicon has been generated. The dielectric functions

of a-Si, presented in Fig. 5.4, have been used to analyze all SE measurements presented in

5.3. Multi-layer dielectric modeling 43

0 1 2 3 4 5 6-10

0

10

20

0

10

20

30

1

photon energy (eV)

(b)

(c)

(a)

(b)(c)

a-Si (this work) (a) (b) (c)

2 (a)

Fig. 5.4: Dielectric function of a-Si obtained in this work and other amorphous-like silicon ma-terials reported in literature: (a) 150 keV implanted a-Si,15 (b) 50-250 keV implanted a-Si,3 and(c) chemical vapor deposited a-Si.23

this paper. A possible ion energy dependence of the TL-parameters has been investigated

with two multi-layer models that include TL-parameters as fit variables, in addition to

(a) da-Si, and (b) dr and da-Si as described in the Appendix. A short summary of the

Appendix is given here to give support to our choice of modeling of the ellipsometry

measurements.

An ion energy dependence of TL-parameters has been observed, but it can not be

excluded that correlations between TL-model parameters are responsible for the observed

trends. The amorphous layer thicknesses resulting from the various multi-layer models,

with and without including TL-parameters in the curve-fit, show identical trends as a

function of ion energy. At ion energies Eion ≥300 eV no difference in absolute values of

da−Si(Eion) and dr(Eion) are observed for the various multi-layer models. Below 300 eV

the variations in da−Si(Eion) are within a factor of two, that is because the amorphous

material in rough layer is not accounted for. This can be taken care of by introducing the

effective amorphous layer thickness deff = da−Si + 0.5 · dr, which varies only by a factor

of 1.3 between the various multi-layer models at a specific ion energy. Sample-to-sample

variations and variations in fit results for different ion fluxes at a fixed ion energy are


100 10000

5

10

15

0

20

40

60

80

100

120

d r (

Å)

Eion (eV)

(b)

d a-Si (Å)

(a)

Fig. 5.5: (a) Amorphous layer thickness da-Si and (b) roughness layer thickness dr as a functionof ion energy. The variance in layer thickness at a specific ion energy are caused by differences inion flux and sample-to-sample fluctuations.

found to be small (< 10%) and are therefore ignored. Furthermore, multi-layer models

including TL-parameters as fit variables resulted in curve-fits with χ2 ≈2.5 whereas using

the simplified multi-layer model with only two fit variables, being the amorphous layer

thickness da-Si and the roughness layer thickness dr, resulted in values of χ2=3-4. This

difference in χ2 is negligibly small. For these reasons, the TL-model parameters are not

included in the curve-fit analysis of the SE measurements presented in this paper, which

simplifies the curve-fit analysis to a multi-layer model with only two fit variables.

5.4 a-Si layer thickness and roughness

The surface roughness dr and a-Si layer thickness da-Si as a function of ion energy have

been derived from SE measurements using the multi-layer dielectric model described in

Sec. 5.3. The results are shown in Fig. 5.5. The amorphous layer thickness increases

with ion energy. Ions with a higher ion energy penetrate deeper into the sample and

create, therefore, a thicker amorphous silicon layer. The surface roughness is found to be

extremely small, typically between 5-15 A, with a minimum roughness at approximately

250 eV. AFM measurements of 70, 200, 1000 and 2000 eV ion bombarded samples resulted

in a root-mean-square roughness σ=0.9±0.2 Aon . The AFM roughness is lower than the

5.4. a-Si layer thickness and roughness 45

10 100 10000

20

40

60

80

100

120

140

160

18010-4

10-3

10-2

10-1

SE measurements MD simulations

d eff =

da-

Si +

0.5

·dr (

Å)

Eion (eV)

Fig. 5.6: Effective amorphous layer thickness (= da-Si+0.5 ·dr) as a function of ion energy. Molec-ular dynamics simulations8 (diamonds) and SRIM simulation (lines) are shown for comparison.The lines are labeled by numbers that correspond to the vacancy level for which the amorphouslayer thickness is determined from the SRIM simulations in units of vacancies per A.

SE roughness, because AFM measures the root-mean-square deviation σ of the heights-

distribution on a area defined by the scan-size, whereas SE measures the rough layer

thickness which corresponds to a larger fraction of the heights-distribution, typically 2-6×larger than σ.16 Furthermore, SE samples a larger (1 mm2) area than the AFM (1.5×1.5

µm) and thus height fluctuations on length-scales larger than 1.5 µm are measured by SE

but not by AFM. The trend is difficult to corroborate with AFM measurements due to the

extremely low roughness values. These absolute roughness values are typically observed

on Si samples after ion bombardment.2,13,26 Figure 5.6 shows the comparison between

the effective a-Si layer thickness deff , defined as deff = da−Si + 0.5 · dr, and predictions

from SRIM simulations27 performed by the authors and molecular dynamics simulations

performed by Humbird et al.8 The SRIM simulations were performed using Ar+ ions

impinging onto a Si substrate at a 45 angle from the surface normal. The creation of

vacancies is chosen to be the measure for permanent damage of the c-Si. The thickness of

the a-Si layer has been derived from the depth distribution of vacancies created by an ion

impact. SRIM calculates the average number of vacancies generated at a certain depth

by an ion given a specific ion energy. The number density of vacancies decreases with the

depth in the target, since the probability of ions with sufficient energy left to cause the

creation of a vacancy decreases with target depth. Now, by defining a minimum level of

vacancies as being sufficient such that the material can no longer be considered crystalline,

a corresponding depth can be derived being the a-Si layer thickness. Figure 5.6 shows


the a-Si layer thickness (lines) as a function of ion energy for the vacancy levels 10−1,

10−2, 10−3 and 10−4 vacancies per A averaged over 106 single ion-impact calculations.

As can be seen, the agreement between the measurements and the SRIM simulations is

remarkably good. Almost all measured layer thicknesses fall within the SRIM simulations

for 10−1 and 10−2 vacancies per A. Below 100 eV ion energy the measurements coincide

with SRIM simulation at lower vacancy levels.

The measured a-Si layer thickness also shows good qualitative agreement with MD

simulations for Eion < 200 eV by Humbird et al.8 Although the absolute values differ

at lower energies, the trend is similar and coincides nicely with the measured a-Si layer

thicknesses at higher ion energies.

5.5 Dynamics of Ar+ bombardment

5.5.1 Time-resolved amorphization

The creation of the amorphous layer is a fast process as has been observed in MD sim-

ulations.8 Here, we have investigated the creation of the amorphous silicon layer on a

H:Si(100) sample as a result of ion bombarment.

Figure 5.7 shows how the amorphous layer develops for 70 eV Ar+-ion bombardment

with an ion flux Φion=0.07 ML s−1 as a function of time t and ion-dose D = Φion · t. The

amorphous fraction fa = deff (t)/deff (tsat) shows an initially very rapid increase, followed

by a slower increase towards saturation after t = tsat=400 s, which corresponds to a

total of ∼30 mono-layers Ar+-dose. Despite the fact that the MD simulation for 100 eV

Ar+ ions shows a much more rapid creation of the amorphous layer,8 the SE measurement

shows the same initially fast followed by a slower amorphization process. Curve-fitting the

measurement with single exponential growth function failed, which suggests that at least

two processes occur during the creation of the amorphous layer. Hence, the measurements

have been curve-fitted with a double exponential growth function of time:

fa(t) = f1 [1− exp(−t/τ1)] + f2 [1− exp(−t/τ2)] , (5.2)

which has been used to derive characteristic 1/e constants for the creation processes. The

curve-fit results in 1/e time constants for amorphization τ1= 28±2 s corresponding to a

1/e ion dose constant ∆τ1=2 ML Ar+-dose (f2=0.43) and τ2= 124±5 s corresponding to

∆τ1=9 ML Ar+-dose (f2=0.57). We believe that the observation of two 1/e constants

for amorphization is related to a fast initial damage creation throughout the whole layer,

followed by a slower process during which subsequent ion impacts fully modify the crys-

talline matrix into an amorphous matrix. A full SE study of the ion energy and ion flux

dependence has not yet been undertaken, but could give more insight into the two ob-

served processes. Here, it has been demonstrated that real-time SE can resolve the details

of the amorphous layer creation process.

5.5. Dynamics of Ar+ bombardment 47

-100 0 100 200 300 400 5000.0

0.5

1.0

-7 0 7 14 21 28 35

a

Ar+-ion dose D (ML)

=deff (t)

/ deff(t

sat)

t (s)

Fig. 5.7: Time-resolved creation of a-Si, modeled as the change in amorphous fraction, as afunction of time (bottom ordinate) and Ar+-dose (top ordinate) for 70 eV Ar+-ion bombardmentwith an ion-flux of 0.07 ML s−1.

5.5.2 Relaxation dynamics

When the ion bombardment is terminated, a relaxation of the amorphous matrix has been

observed. The change in the effective a-Si layer thickness ∆deff (t) = deff (t)− deff (tsat)

from the saturation thickness deff (tsat) measured during ion bombardment, has been

studied as a function of ion energy. It should be noted that the true physical process

governing the relaxation is probably not a physical change in the effective layer thickness,

but more likely a change in optical properties of the thin film as a result of changes in the

amorphous matrix due to bulk reconstruction and relaxation of defects such as dangling

bonds and highly strained (stretched and compressed) Si-Si bonds. A full modeling of the

measured relaxation should include the analysis of the changes in the dielectric properties,

i.e. the Tauc-Lorentz model of the a-Si. This extended analysis is more complex, since

more parameters are involved in the description of the relaxation process. However,

preliminary tests of such an extended analysis yielded no difference in the observed time

dependence of the relaxation. Hence, here we show that a first order analysis based on

the change of the a-Si layer thickness can be used to elucidate the relaxation process.

Figure 5.8 shows the change in the effective layer thickness ∆deff (t) as a function

of time for the relaxation measured after various ion energy and ion flux bombard-

ment conditions. The lines in Fig. 5.8 are curve-fits to the measurements using the

stretched-exponential time dependence as commonly used and observed in defect relax-

ation/annealing in amorphous materials:28,29

∆deff (t) = d∞ exp[−(t/τ)α]− 1 , (5.3)


0 1000 2000 3000-10

-8

-6

-4

-2

0 ion Eion 0.070.120.130.070.170.35

0.95

0.47

100 100 200 300 300 300

1000

2000

d eff

(Å)

t (s)

Fig. 5.8: Relaxation of a-Si, modeled as the total change in effective a-Si layer thickness ∆deff , asfunction of time after termination of the ion bombardment at t = 0 with various ion energies Eion

(eV) and ion fluxes Φion (ML s−1). The lines are fits to the data using a stretched-exponentialdecay typically used to describe defect-controlled relaxation. Note that the true physical processgoverning the relaxation is probably not a physical change in the effective layer thickness, but morelikely a change in optical properties of the thin film.

where d∞ is the fully relaxed (in static equilibrium) amorphous layer thickness, τ is the 1/e

time constant for the relaxation process and α a dispersion parameter related to the fact

that with increasing time the relaxation becomes more difficult due to an increase in the

activation energy for defect relaxation. This model is called defect-controlled-relaxation

(DCR) in which an ensemble of local defects relax without the aid of diffusing atoms.28

The first observation that can be made is that ∆deff (t) becomes larger with ion energy.

This can be understood from the fact that with increasing ion energy the thickness of the

amorphous layer increases and, thus, the number density of defects. The total change in

effective layer thickness d∞ from the fit also showed a linear dependence on the starting

thickness of the amorphous layer deff (tsat). This observation is indicative for the fact

that a bulk process is being observed and not a modification of the surface by molecular

background gases (background pressure HV chamber pHV = 10−8 Torr). All measurements

have been fitted simultaneously with the same time constant τ= 360 s and α=0.32.

The parameter α is close to the value of 13, as observed for relaxation in hydrogenated

amorphous silicon.28–30 The time constant τ=360 s is on the order of previously observed

time constants for relaxation in ion implanted a-Si.10 Holtslag et al. also observed a

substrate temperature dependence in the relaxation process, which was used to determine

the activation energy for relaxation.

5.6. Conclusions 49

5.6 Conclusions

Spectroscopic ellipsometry has been applied to study the ion-induced damage of crystalline

silicon. Dielectric functions for the amorphous, ion-induced damaged silicon have been

established using a Tauc-Lorentz parameterization. The dielectric functions resemble

dielectric functions found for other a-Si-like materials in literature. Using these dielectric

functions of a-Si, the layer thickness has been derived as a function of ion energy. The a-Si

layer thickness shows an increase with ion energy. Good agreement with predictions for

the amorphous layer thickness as a function of ion energy from SRIM and MD calculations

has been found. The steady-state surface roughness during ion bombardment is shown

to be extremely low. The rough layer thickness measured by spectroscopic ellipsometry

yields typically ≈ 5-15 A. The surface roughness shows a minimum roughness at approx.

250 eV, and increases for both higher and lower ion energies.

Spectroscopic ellipsometry has proven to be able to resolve the dynamics of amor-

phization of the crystalline silicon and self-annealing/relaxation of damaged, amorphous

silicon layers. The creation of the a-Si layer is shown to be a very rapid process. The

creation dynamics for 70 eV Ar+-ions with an ion-flux of 0.07 ML s−1 can be described

by two 1/e ion-dose constants: a initially fast process with ∆τ1= 2 ML Ar+-dose, the

initial damage creation, followed by a slower process with ∆τ1= 9 ML, in which the dam-

aged layer is fully amorphized. Well within about 30 ML of ion-dose the damaged layer

is fully amorphous. An ion energy and dose dependence study has not yet been under-

taken, which could shed a light on the origin of the two processes. A relaxation process

of the amorphous layer has been observed and has been ascribed to self-annealing of bulk

defects. The relaxation process shows a stretched-exponential time dependence, fully in

accordance with a literature model for defect-controlled relaxation. The time scale of

τ=360 s correspond with literature reports for relaxation dynamics in amorphous silicon.

Hence, it has been established that the dielectric functions and the thickness of the

a-Si layer are in good agreement with literature and model predictions and, furthermore,

surface roughness and dynamic aspects of ion bombardment can be resolved with spectro-

scopic ellipsometry, which is important for future studies of Ar+/XeF2 etching of Si(100).

5.7 Acknowledgements

Authors wish to acknowledge J.A.C.M. van de Ven, L.H.A.M. van Moll, A.B.M. Husken,

M.J.F. van de Sande and J.F.C. Jansen for the technical support. This research is sup-

ported by The Netherlands Foundation for Fundamental Research on Matter (FOM:

99TF24). The work of W.K. has been made possible by the fellowship of the Royal

Netherlands Academy of Arts and Sciences.


Appendix: Tauc-Lorentz model of a-Si

To obtain dielectric functions of a-Si the Tauc-Lorentz (TL) model has been used. The

model is a combination of a classical Lorentz oscillator and an expression for the imaginary

part of the dielectric function above the band edge given by:31

ε2(E) =

AT (E − Eg)

2/E2 for E ≥ Eg

0 for E < Eg,(5.4)

where AT is a strength parameter (dimensionless). The expression given by Tauc etal.

in Eq. 5.4 is based on the assumption that, due to a broad distribution of bonding con-

figurations in amorphous media in contrast to crystalline media, the density of states

above the band edge Eg can be decreases with the energy E. As a consequence the in-

terband absorption can be described by a quadratic decrease, which is captured by ε2(E)

in Eq. 5.4. The Tauc expression combined with a classical Lorentz oscillator leads to the

Tauc-Lorentz oscillator model, for which ε2(E) given by

ε2(E) =A E0 C (E − Eg)

2

(E2 − E20)

2 + C2E2

1

E, (5.5)

where A is the oscillator amplitude, E0 is the central oscillator energy, C is the broadening

of the oscillator and Eg is the optical band gap, all in units of energy (eV). The real part

of the dielectric function ε1(E) is obtained by Kramers-Kronig integration of ε2(E), which

leads to an additional parameter ε1(∞). The additional fit variable ε1(∞) is often used

to improve fits but has been kept equal to 1 in this case.

Three multi-layer models have been evaluated on the SE measurements. There are

basically three reasons for testing various multi-layer models. (1) The optical properties

of amorphous silicon are not unique and are subject to specific processing/production

methods, whether ion bombardment (relaxed/unrelaxed) or chemical-vapor-deposition

has been used.3,15 The optical properties may depend on the ion energy used. (2) Ions

are known for their polishing behavior, which means the roughness can be expected to

be extremely low. The question is therefore whether or not roughness can be derived

from the measurements presented here. (3) Fitting both layer thicknesses and dielectric

function models results in a large number (up to 7) fit variables P . A large number of

fit variables will almost certainly result in extremely good fits. However, correlations

may exist between fit variables and, consequently, fit results may not be very reliable for

interpretation in terms of physical problems.

The three multi-layer models that have been used are defined as follows. Model (a)

consists of an a-Si layer with thickness da-Si on top of a semi-infinite c-Si substrate. The

fit variables in this model are the TL-model parameters for the dielectric functions of a-Si

and the a-Si layer thickness da-Si, which is a total number of five fit variables. Model (b)

includes, with respect to model (a), a surface roughness layer with thickness dr, which

5.7. Acknowledgements 51

100 1000123456

3.33.43.53.63.7

0.60.81.01.21.42.0

2.2

2.4

2.6

100

150

200

Model (c)

2

Eion (eV)

E0 (

eV)

3.58

0.86

Eg (

eV)

2.30

C (e

V)

Model (a) Model (b) Model (c)

120

A (e

V)

Fig. 5.9: Tauc-Lorentz parameters and the χ2 of fits as a function of ion energy as determinedusing multi-layer models 1 and 2. The Tauc-Lorentz parameters have been fixed for multi-layermodel 3 at the shown values (lines). The variance in the TL-parameters at a specific ion energyare caused by differences in ion flux and sample-to-sample fluctuations.

is modeled by a Bruggemann effective-medium-approximation (BEMA).32 Here, we have

used a mixture for the surface roughness layer of 50% a-Si and 50% voids. Thus, model (b)

has a total of six fit variables. Model (c) uses fixed dielectric functions for a-Si, which are

derived from the modeling with models (a) and (b). The latter one allows us to reduce

the number of fit variables to two, only if the dielectric function model for a-Si is not

extremely sensitive to the Ar+ ion energy or flux. Figure 5.9 shows the Tauc-Lorentz (TL)

parameters for models (a) and (b) as a function of ion energy, including the absolute values

of χ2. As can been seen, both A and Eg decrease with increasing ion energy up to 500 eV,

whereas E0 and C increase. The absolute values of χ2 for these models are typically 2.5

and independent of ion energy. The multiple data points at a specific ion energy are the

result of different ion fluxes and sample-to-sample reproducibility. These two variables

are of minor importance and are therefore ignored. The TL-model parameters seem to


100 10000

5

10

15

0

20

40

60

80

100

120

d r (

Å)

Eion (eV)

(a)

(b)

d a-Si (Å)

Fig. 5.10: (a) Amorphous layer thickness da−Si and (b) roughness layer thickness dr as a functionof ion energy, resulting from the Tauc-Lorentz parameters for multi-layer model (a)(open squares),(b)(open circles) and (c)(closed circles). The variance in layer thickness at a specific ion energyare caused by differences in ion flux and sample-to-sample fluctuations.

depend on ion energy. The reason for the observed trends in the TL-parameters is believed

to result from correlations between the TL-parameters, but a minor dependence on the

ion energy cannot be fully excluded.

Therefore, model (c) has been tested on the measured spectra, i.e. fixed TL-model

parameters. The lines and numbers mentioned in Fig. 5.9 correspond to the values at

which the TL parameters have been fixed, thus A=120 eV, E0=3.58 eV, C=2.30 eV

and Eg=0.86 eV. The reasons for fixing the TL-parameters at these values are: (1) it is

more reliable to determine TL-parameters from thick films, thus for a-Si layers generated

by higher ion energy bombardment, and (2) the absolute values of χ2 for model (c) show

again almost no dependence on the ion energy, whereas fixing the TL-parameters at values

obtained for 70 eV ion bombardment resulted in significantly increasing absolute values

of χ2 when going to higher ion energies.

In Fig. 5.10 the layer thickness obtained for all three models is shown. Above an

ion energy of 300 eV the amorphous layer thickness da-Si is independent of model choice,

whereas below 300 eV the models show small variations. The surface roughness dr is equal

to zero for model (a), since no roughness layers is included in the model. For model (b)

the roughness shows a minimum at 500 eV and an increasing trend towards both lower

References 53

and higher ion energies. Model (c) shows a similar trend but with the minimum at 250

eV ion bombardment and a less pronounced increase towards lower ion energies. Since

the TL-parameters were found to be constant above 300 eV the trend at higher energies

is believed to be genuine. At ion energies Eion ≥300 eV no difference in absolute values

of da−Si(Eion) and dr(Eion) are observed for the three multi-layer models. Below 300 eV

the variations in da−Si(Eion) are within a factor of two, that is because the amorphous

material in rough layer is not accounted for. This can be taken care of by introducing the

effective amorphous layer thickness deff = da−Si + 0.5 · dr, which varies only by a factor

of 1.3 between the various multi-layer models at a specific ion energy. It seems that at

lower ion energies the modeling results become slightly less accurate. The main reason

is of course that the penetration depth of the Ar+-ions is low, thus, the thickness of the

amorphous layer will be rather small.

All these aspects and the fact that the absolute values of χ2 are only slightly higher

for model (c) (χ2=3-4) than for models (a) and (b) (χ2=2.5), have resulted in a choice for

the use of model (c) in the analysis of all SE measurements discussed in this report, which

means fixed dielectric functions for the a-Si and only two fit variables: the amorphous

layer thickness da-Si and the surface roughness layer thickness dr.

References

1 E. Spiller, S. L. Baker, P. B. Mirkarimi, V. Sperry, E. M. Gullikson, and D. G. Stearns, Appl. Optics42, 4049 (2003).

2 R. Stuik, E. Louis, A. E. Yakshin, P. C. Gorts, E. L. G. Maas, F. Bijkerk, D. Schmitz, F. Scholze,G. Ulm, M. Haidl, J. Vac. Sci. Technol. B 17, 2998 (1999).

3 M. Fried, T. Lohner, W. A. M. Aarnink, L. J. Hanekamp, and A. van Silfhout, J. Appl. Phys. 71,5260 (1992).

4 T. Shinada, S. Okamoto, T. Kobayashi, and I. Ohdomari, Nature 437, 1128 (2005).


6 David Humbird and David B. Graves, J. App. Phys. 96, 791 (2004).

7 P. G. M. Sebel, L. J. F. Hermans, and H. C. W. Beijerinck, J. Vac. Sci. Technol. A 17, 3368 (1999).

8 D. Humbird and D. B. Graves, Pure and Applied Chemistry 74, 419 (2002).

9 M. Koster and H. M. Urbassek, J. Appl. Phys. 90, 689 (2001).

10 A. H. M. Holtslag and A. van Silfhout, Phys. Rev. B 38, 10556 (1988).

11 M. Ishii, Y. Hirose, T. Sato, T. Ohwaki, and Y. Taga, J. Vac. Sci. Technol. A 15, 820 (1997).

12 J. L. Buckner, D. J. Vitkavage, E. A. Irene and T. M. Mayer, J. Electrochem. Soc. 133, 1729 (1986).

13 F. Ludwig Jr., C. R. Eddy Jr., O. Malis, and R. L. Headrick, Appl. Phys. Lett. 81, 2770 (2002).

14 A. C.-T. Chan, G.-C. Wang, Surf. Sci. 414, 17 (1998).

15 S. Adachi and H. Mori, Phys. Rev. B 62, 10158 (2000).


16 A. A. E. Stevens and H. C. W. Beijerinck, J. Vac. Sci. Technol. A 23, 126 (2005).

17 G. J. P. Joosten, M. J. M. Vugts, H. J. Spruijt, H. A. J. Senhorst, and H. C. W. Beijerinck, J. Vac.Sci. Technol. A 12, 636 (1994).


19 Y. J. Chabal, G. S. Higashi, K. Raghavachari, and V. A. Burrows, J. Vac. Sci. Technol. A 7, 2104(1989).

20 G. E. Jellison, Jr. and F. A. Modine, J. Appl. Phys. 76, 3758 (1994).


22 D. Daineka, V. Suendo, P. Roca i Cabarrocas, Thin Solid Films 468, 298 (2004).

23 G. E. Jellison, Jr. and F. A. Modine, Appl. Phys. Lett. 96, 371 (1996).

24 S. Adachi, H. Mori, and S. Ozaki, Phys. Rev. B 66, 153201 (2002).

25 S. Gupta, B. R. Weiner, G. Morell, J. Vac. Sci. Technol. A 23, 1668 (2005).

26 X. L. Peng, Z. H. Barber, T. W. Clyne, Surf. Coat. Technol 138, 23 (2001).

27 J. F. Ziegler, J. P. Biersack, and U. Littmark, The stopping range of ions in solids (Pergamon, Oxford,1985).

28 R. S. Crandall, Phys. Rev. B 43, 4057 (1991).

29 J. Kakalios, R. A. Street, and W. B. Jackson, Phys. Rev. Lett. 59, 1037 (1987).

30 D. Redfield and R. H. Bube, Appl. Phys. Lett. 54, 1037 (1989).

31 J. Tauc, R. Grigorovici, and A. Vancu, Phys. Status Solidi 15, 627 (1966).


Chapter 6

Surface roughness in XeF2 etching of a-Si/c-Si(100)

Abstract

Single wavelength ellipsometry and atomic force microscopy (AFM) have been applied ina well-calibrated beam-etching experiment to characterize the dynamics of surface rough-ening induced by chemical etching of a ∼12 nm amorphous silicon (a-Si) top layer and theunderlying crystalline silicon (c-Si) bulk. In both the initial and final phase of etching,where either only a-Si or only c-Si is exposed to the XeF2 flux, we observe a similar evo-lution of the surface roughness as a function of the XeF2 dose proportional to D(XeF2)β

with β ≈ 0.2. In the transition region from the pure amorphous to the pure crystallinesilicon layer, we observe a strong anomalous increase of the surface roughness proportionalto D(XeF2)β with β ≈ 1.5. Not only the growth rate of the roughness increases sharply inthis phase, also the surface morphology temporarily changes to a structure that suggests acusp-like shape. Both features suggest that the remaining a-Si patches on the surface acteffectively as a capping layer which causes the growth of deep trenches in the c-Si. Theellipsometry data on the roughness are corroborated by the AFM results, by equating thethickness of the rough layer to 6 σ, with σ the root-mean-square variation of the AFM’sdistribution function of height differences. In the AFM data, the anomalous behavior isreflected in a too small value of σ which again suggests narrow and deep surface featuresthat cannot be tracked by the AFM-tip. The final phase morphology is characterized byan effective increase in surface area by a factor two, as derived from a simple bilayer modelof the reaction layer, using the experimental etch rate as input. We obtain a local reactionlayer thickness of 1.5 monolayer consistent with the 1.7 ML value of Lo et al. [Lo et al.,Phys.Rev.B 47, 648 (1993)] that is also independent of surface roughness.

6.1 Introduction

Plasma etching is the standard etching technique in the production of integrated circuits,

MEMS devices and photonic devices. The main advantage of plasma etching is the direc-

tionality that is imposed by the ions that bombard the surface of the device.1 However,

the etch process gives rise to surface roughness depending on the various plasma param-

eters, such as ion energy and ion-to-etchant flux ratio. As device dimensions continue

to shrink, any roughness, caused by the device production process, plays a key role in

eventual device performance.

55

56 Chapter 6. Surface roughness in XeF2 etching of a-Si/c-Si(100)

In optimizing plasma etch processes, the main problem one comes across is the tremen-

dous complexity of the plasma environment. This makes it exceedingly difficult to get an

understanding of the reaction mechanisms involved. To circumvent the difficulties asso-

ciated with plasma etching, many experiments have been performed2 that give a picture

of the processes involved. In several beam etching systems, fairly complete and accurate

models have been developed. The present system has also been studied intensively by

etch product analysis.3–12 However, surface roughness caused by the etching has never

been characterized in detail, although various authors2,11,13 mention the importance in

fully understanding the obtained models inspired by etch product analysis.

Ellipsometry is by far the most commonly used in situ surface diagnostic to look at

the surface roughness. Therefore, ellipsometry is applied for the first time to a beam

etching experiment to characterize the surface roughness. The fact that ions and etchant

can be manipulated independently helps in revealing the role of ions and etchant in the

roughening process on a more fundamental level. Aliev et al.14 looked into the initial

stage of c-Si surface roughening caused by XeF2 etching with ellipsometry. This work

will report on the roughness caused by XeF2 etching of an amorphous silicon (a-Si) layer

and subsequently the underlying crystalline silicon (c-Si(100)) sample. The a-Si layer is

produced by 2.5 keV Ar+ ion bombardment. The amorphization of c-Si has been studied

quite intensively in terms of roughness, damage profiling and simulations by Refs.15–21

and many others, although most studies are done by surface probe measurements, such

as atomic force microscopy (AFM) and scanning tunnelling microscopy (STM), and for

ion energy ranges other than 0.5-2.5 keV as presented here. In Sec. 6.3 the ellipsometric

characterization of the a-Si layer will be addressed and also the surface roughness caused

by the impinging ions. This information is required in Sec. 6.4, addressing the subsequent

chemical XeF2 etching of the a-Si layer and the underlying c-Si sample. A comparison will

be made between the roughness determined with in situ ellipsometry and the roughness

of samples which have been analyzed ex situ with atomic force microscopy (AFM). The

surface roughness caused by the XeF2 etching affects the interpretation of the existing

reaction layer models for XeF2 etching of silicon deduced from product analysis. A dis-

cussion based on the bilayer model11,13 will address the issue of silicon-fluoride reaction

layer thickness in Sec. 6.5. The gathered information from ellipsometry and AFM can be

used to obtain a geometrical picture of the rough surface. Some characteristic measures

of the rough surface are described in Sec. 6.6. And, finally, some conclusions are made in

Sec. 6.7.


The setup used has been described extensively in earlier publications.9,10 In this section

only the two modifications that have been made recently will be discussed. These are the


ellipsometer

Magnetic

linear drive

Loadlock

sample chamber

detector

chamber

3

42

1

500 mm0

Fig. 6.1: Revised setup in horizontal cross-section. The sample is mounted in a rotatable sampleholder (1) that can be operated manually via an external drive(2). Samples can be exchangedbetween the sample holder and the sample storage (3) in the load lock with a linear magneticdrive. The ion gun and the XeF2 source (4) are at 45 and 52 from surface normal, respectively.The ellipsometer is at 74 from the sample surface normal. Etch products are detected in a separatedetector chamber perpendicular to the sample surface.

addition of a sample exchange mechanism and the addition of an ellipsometer. A brief

description of ellipsometry and measurement interpretation will also be given.

6.2.1 Vacuum apparatus

A schematic view of the setup and relative orientation of the beams onto the sample is

shown in Fig. 6.1. The sample holder has been replaced by a rotatable two-slot sample

holder. This sample holder has two slots in order to enable the calibration of the mass

spectrometer. In the standard position of the sample holder, the sample surface is oriented

towards the multiple-beam setup. The sample can be rotated to be in the path of a

magnetic linear drive in the vacuum. With this linear drive, the sample can be transported

to the load lock. The load lock has a capacity of six samples and a base pressure of 1×10−8 mbar, achieved by a turbomolecular pump of 56 l/s . A valve separates the loadlock

from the main chamber. The sample chamber has a base pressure of 1×10−8 mbar and is

pumped by turbomolecular pumps. All fluxes impinging on the sample are measured in

monolayers per second (ML/s); one monolayer corresponds to 6.86×1018m−2, the surface

density of Si(100). The Ar+ ion flux can be varied from 0 to 0.11 ML/s and the ion energy

ranges from 0.5 to 2.5 keV. The ion beam impinges at a 45 angle of incidence. The XeF2

flux can be varied from 0 to 3.6 ML/s and impinges at a 52 angle of incidence.


6.2.2 Ellipsometry

This section gives a brief outline of ellipsometry. A full theory can be found in the book

by Azzam and Bashara.22 Ellipsometry is a surface diagnostic that uses the change in

ellipticity that a light beam undergoes during reflection at a surface. The Fresnel equations

require that reflection coefficients for polarization parallel (Rp) and perpendicular (Rs) to

the plane of incidence differ. This is usually expressed as a reflectance ratio ρ:

ρ =Rp

Rs

= tan(Ψ) · ei∆. (6.1)

Equation 6.1 defines the ellipsometric angles Ψ and ∆. The factor tan Ψ is the ratio of

the reflected amplitudes of the p and s waves. The phase difference between the reflected

p and s waves is called ∆. Both angles are traditionally expressed in degrees.

The reflectance ratio ρ that is measured depends on the refractive index and the

morphology of the surface under investigation, as well as on the wavelength used, the

angle of incidence and the presence of thin films on the surface. A medium consisting of a

mixture of two different substances (labelled 1 and 2) is modelled as an effective medium.

The dielectric constant εr of the effective medium is found by solving the Bruggemann

equation:23

0 = ν1εr,1 − εr

εr,1 + 2εr

+ ν2εr,2 − εr

εr,2 + 2εr

. (6.2)

Here the (complex) dielectric constants of media 1 and 2 are called εr,1 and εr,2, respec-

tively. Medium i (i = 1, 2) occupies a volume fraction νi, with∑

i νi = 1. The complex

refractive index of a medium is given by ε = n2. In the case of a rough top layer, one of

the media is vacuum with εr = 1.

The interpretation of the measured Ψ and ∆ is quite cumbersome. The Fresnel equa-

tions have no easy proportionalities in them. In the case of a substrate with a film on

top, all internal reflections in the film have to be taken into account, further complicat-

ing matters. This is why the interpretation of the data measured is done by comparison

with computer simulations. For this work, a computer program based on the impedance

algorithm24 was used. This allows the interpretation of measurements on substrates that

have several thin layers stacked on top of one another. The refractive indices used in the

analysis of these measurements are given in Table 6.1.

6.2.3 Rotating-compensator ellipsometer

The setup for the ellipsometry is a rotating-compensator ellipsometer (RCE) in the

polarizer-compensator-sample-analyzer (PCSA) configuration. The laser light used is lin-

early polarized 632.8 nm light from a He-Ne laser. The angle of incidence onto the sample

was chosen to be around 74 for maximum sensitivity on silicon. The light is made circular


with a λ/4 retarder. The polarizer and analyzer used are dichroic sheet polarizers with

an extinction coefficient of 104. They can both be manually adjusted to within 0.05 of

the desired settings. The rotating compensator is driven by a synchronous motor at line

frequency, with a 2:3 transmission in between for noise suppression, rotating at 33 Hz. An

encoding system gives off trigger pulses at every 2π/256 radians. The compensator itself

is a zero-order λ/4 retarder, with a double anti-reflective coating (R < 0.05%). The polar-

izing properties of the compensator are also expressed in terms of ellipsometric angles Ψ

and ∆. The light beam enters and leaves the vacuum through stress-free, non-polarizing

quartz windows. The reflected light is detected by a photodiode, and amplified. Then the

detected signal is fed into a 12-bit parallel sampling ADC (resolution 2.44 mV). The ADC

is read at every trigger pulse. The resulting signal is Fourier-analyzed in real time by a

computer. The resulting values of Ψ and ∆ are extracted from the Fourier coefficients.

Furthermore, the computer program used for the measurements allowed synchronously

monitoring various chemical species coming from the sample by the mass spectrometer.

In Sec. 6.2.4 a brief description of the product flux calibration is given.

Before each insertion into the vacuum system the n-type Si(100) samples (ρ = 10-30

Ωcm) are cleaned with alcohol, leaving the native oxide layer in place. All measurements

presented here are performed at room temperature. Prior to a series of measurements,

the plane of incidence onto the sample was calibrated using the native oxide layer, as first

done by Smets et al.25 Subsequently, the compensator is calibrated. Again, the native

oxide layer serves its purpose by allowing the determination of the angle of incidence

of the laser beam on the sample. The native oxide layer is found to be 2.2 ± 0.3 nm

thick from sample to sample. The angle of incidence is found to vary between 73.95 and

74.15, since each sample is inserted into the sample holder in a slightly different position.

Rotating the sample back and forth for product flux calibration resulted in variations of

less than 0.05 in the angle of incidence.

6.2.4 Product flux calibration

To calibrate the pulse counting system of the mass spectrometer to absolute values of the

flux leaving the sample an inert Ni sample is used, which does not interact with XeF2.

For this purpose the sample holder is rotated such that a Ni sample is in the focus of

the beams and the detector acceptance. The XeF+ count rate is calibrated with the

absolute value of the impinging XeF2 flux of 0.9 ML s−1 (= 6.2×1014 cm−2 s−1). Rotating

the Si sample back into position, the loss of XeF2 flux due to etching (as visible in the

loss of XeF+ count rate) is equal to the SiF4 flux leaving the sample, because SiF4 is

known to be the only etch product at room temperature [3]. This absolute flux is used

to calibrate the SiF+3 count rate which is used as a fingerprint of SiF4. Now, the mass

spectrometer count rates directly represent an absolute flux of reagents and products, an

essential condition for understanding etch dynamics. The etch rate is now expressed in


the production coefficient δ defined as

δ =2 Φ(SiF4)

Φs(XeF2)(6.3)

with Φs(XeF2) the impinging flux on the sample and Φ(SiF4) the product flux leaving

the sample. The production coefficient or etching efficiency is defined such that δ = 1

corresponds to the full conversion of reactant into products. The etch rate of silicon at

the sample is given by

d[Si]

dt=

δ

2Φs(XeF2) (6.4)

which reflects that we need two reactant molecules to form a product molecule. By

inserting the thickness aSi = 0.138 nm/ML of a monolayer of Si, the Si etch yield YSi

(nm) is related to the total dose D(XeF2) (ML) of reactant delivered to the surface, as

given by

YSi = aSiδ

2D(XeF2). (6.5)

This relation allows tracking of the total amount of Si removed during our experiments.

Further details concerning the mass spectrometer and the product analysis have been

reported in the past.9–11

6.3 Amorphization of c-Si

The production of the amorphized (a-Si) layer by Ar+ ions will be described briefly, since

ellipsometry has never been performed on Ar+ sputtering with ion energies in the range

of 1.0-2.5 keV. Furthermore, this information is required to described the XeF2 etching

in the following section. A more elaborate treatise will be published elsewhere.26

6.3.1 Model

In Fig.6.2 an ellipsometry measurement of the Ar+ etching of c-Si is shown (connected

dots). The large dot represents the model values of Ψ and ∆ of a clean c-Si sample,

i.e. no native-oxide layer, roughness or amorphized Si layer. At t = 0 the c-Si sample is

covered by a thin native oxide layer. By matching the simulation of an increasing native

oxide layer thickness on top of a c-Si bulk layer (Fig.6.3(a)) to the measured Ψ and ∆

the native oxide layer thickness is obtained. In this case the native-oxide layer thickness

is found to be 2.1 nm. The refractive indices required for the simulations are listed in

Tab. 6.1.

Next, Ar+ ions with an energy of 0.5 keV and a flux of 0.011 ML s−1 (= 7.5×1012

cm−2 s−1) are switched on resulting in an increase of Ψ and ∆. The ions initially remove

the native-oxide layer. Simultaneously the ions generate an a-Si layer with a rough layer

6.3. Amorphization of c-Si 61

3 6 9 12140

160

180

200

21

2.52.01.51.0

3

2

0

dr (nm)

dSiO2 (nm)

da-Si (nm) 01

t =0

t

0.5

1

Eion(keV)

Fig. 6.2: Ψ,∆-plot of a measurement of Ar+ sputter etching (connected dots). The drawn linesare simulations on the basis of Fig. 6.3. The large dot represents (Ψ,∆) for a clean c-Si sample.At t = 0 the c-Si is covered by a 2.1 nm native oxide layer. When Ar+ ions are switched on steadystate (Ψ,∆) situations are reached for the various ion energies. A corresponding amorphizedlayer thickness da−Si and a rough layer thickness dr is found by matching the simulations to themeasurement.

on top, eventually going to a steady state values of Ψ and ∆. Subsequently the ion

energy is increased with steps of 0.5 keV up to 2.5 keV keeping the ion flux constant. The

ellipsometric parameter Ψ increases with increasing ion energy whereas little variation

can be observed for ∆. At each energy a steady state situation is reached.

Next, a multi-layer model is required to obtain a-Si layer thickness da−Si and rough

layer thickness dr in which the rough layer is constituted from 50% void and 50% a-Si via

the Bruggemann equation Eq.2. The complex refractive index used for a-Si is mentioned

in Tab. 6.1 and has been determined in a more extensive study.26 Note that the values for

n and k used here are in good agreement with the values reported by Fried et al.18 (See

Tab. 6.1), although they used 20 keV Ar+ ions to amorphize a Si sample. The simplest

SiO2

c-Si bulk

(a)

dSiO2

(b)

c-Si bulk

a-Sida-Si

dra-Si void50%

50%

Fig. 6.3: Layer models used in the ellipsometry simulations for (a) the bare sample with a nativeoxide film on top and for (b) the Ar+ ion sputter etching. The model for the Ar+ ion sputtersimulation consists of an a-Si layer and a rough layer on top, which is a mixture of 50% void and50% a-Si .


Tab. 6.1: Numerical values of the refractive indices for the various layers assumed for data analysisand for reference.

Used for Material Assumed nmodelling Crystalline silicon (c-Si) 3.88 - 0.02 j ∗

SiO2 1.46 †

Amorphized silicon (a-Si) 4.58 - i 0.72 ‡

reference Amorphized silicon (a-Si) 4.63 - i 0.76 §

Rough SiFx 1.6 ¶

SiCl 1.66 ‖

∗ Ref.27, † Ref.28, ‡ Ref.26, § Ref.18, ¶ Ref.29, ‖ Ref.30

model to describe the measurement is shown in (Fig.6.3(b)). Two simulations by means

of this model are shown in Fig.6.2. Both simulations result from increasing the a-Si layer

from 0 to 15 nm keeping the rough layer thickness constant at 0 and 1 nm, respectively.

The following sections will show that this multi-layer model gives a good description of

the Ar+ etching of c-Si.

6.3.2 a-Si layer thickness

The a-Si layer thickness is determined by matching measurement and simulation at the

steady state Ψ and ∆ for each ion energy. The resulting a-Si layer thickness as a function

of ion energy is shown in Fig. 6.4. The errors are derived from 10 measurements on 10

different samples. The a-Si layer thickness for 1.05 keV Ar+ ions determined by Buckner

et al.15 is also included. Buckner used the complex refractive index determined by Fried

et al.18( see Tab. 6.1). The difference between his result and ours is an indication of the

difference in a-Si layer thickness resulting from the difference in complex refractive index.

With increasing ion energy the a-Si layer thickness increases, because the ions pene-

trate deeper into the silicon sample. Note that the a-Si layer thickness is in fact an effective

layer thickness, since the amorphous to crystalline transition is not discrete but gradual.19

A comparison with, e.g., SRIM17 is therefore not straightforward. Here, a comparison

is made by looking at the distribution of vacancy-causing collisions (vacancies/nm/ion)

as a function of depth. The solid line in Fig.4 represents the depth in SRIM that corre-

sponds to a level of vacancy-causing collisions equal to 0.1 vacancy/nm/ion, which is in

good agreement with the measured effective a-Si layer thickness. These conditions clearly

define the depth of the effective discrete transition from a-Si to c-Si.

6.3.3 Roughness

The rough layer is simulated using the Bruggemann effective medium approximation

(Eq. 6.2) using a mixture of 50% voids and 50% a-Si. The rough layer thickness is

6.3. Amorphization of c-Si 63

0.0 0.5 1.0 1.5 2.0 2.50

2

4

6

8

10

12

14

d a-S

i (n

m)

Ion energy (keV)

Buckner et al.

SRIM sim.

Fig. 6.4: a-Si thickness as a function of Ar+ ion energy (•) including SRIM simulations (straightline) and a result obtained by Buckner et al. (¥).

on the order of 0.65 ± 0.05 nm and shows no clear dependence on the ion energy. A

similar degree of roughness caused by ion etching was reported by various authors not

only on Si16,20,21 but also on other materials.31,32 The minor differences can be easily

related to the difference in diagnostic tool or experimental conditions such as ion angle of

impingement, ion flux, ion dose, and ion energy differences. Note that here the ions are still

switched on when the roughness is determined. Surface probe measurements (AFM/STM)

afterwards might give a different roughness due to surface relaxation once the ions are

switched off. More importantly, surface probe measurements give a different measure for

surface roughness (root-mean-square roughness σ) than the rough layer thickness from

ellipsometry which makes a quantitative comparison not straightforward.

The rather low roughness result can be explained by surface smoothing.31 After impact

of the energetically incident ions, a heat spike of 1 ps melts the surface locally, allowing

the surface to relax. One would expect this surface smoothing process, thus also the

surface roughness, to be ion energy dependent. Here, the surface roughness shows no

clear dependence on the incident ion energy. The energy deposited at the surface by the

impinging ions with energies between 0.5 and 2.5 keV results in lowering of the binding

energy of surface atoms and consequently in an improvement of the sputter yield. A higher

sputter yield may lead to a higher roughness. But simultaneously more energy is available

for surface relaxation. Apparently, the two effects cancel out. Hence, a pronounced ion

energy dependence of the surface roughness is not observed.

To conclude, the ion damage layer thickness and surface roughness obtained with

ellipsometry can be explained and the results are in good agreement with literature. This

insight in the amorphization process provides the necessary information to study the


(a)

dr

(b)

c-Si bulk

(100-x)%

void

c-Si bulk

a-Sida-Si

dra-Si void50%

50% x %

c-Si

Fig. 6.5: Layer models used in the ellipsometry simulations for (a) short term and for (b) longterm XeF2 etching.

chemical XeF2 etching of a 2.5 keV Ar+ created, 12 nm a-Si layer and subsequently the

underlying c-Si bulk.

6.4 Chemical XeF2 etching

In this section the ellipsometric characterization of the XeF2 etching of a 12 nm a-Si

layer and the underlying c-Si bulk sample will be addressed. The different models used

to analyze the ellipsometry data are discussed, elaborating on the approximations made.

The evolution of the roughness in time will be compared to AFM measurements and the

amorphous-to-crystalline transition region will be discussed in detail.

6.4.1 Model

To obtain the surface roughness, again (multi-)layer models describing the surface are

required. The used models are shown in Fig. 6.5. In time, the a-Si layer will be etched

away and in the process the roughness increases (Fig. 6.5 (a)). When the a-Si layer is

completely removed, the etching continues on the underlying bulk c-Si (Fig. 6.5 (b)). In

general, a ratio of 50% void/50% material is used to model the roughness. Here, the

percentage void x is used as an additional fit parameter.

These models lack the presence of a SiF reaction layer contribution. The question

therefore is whether this is a valid representation of the surface layers. In literature no

reference can be found on the optical properties of SiF except for a complex refractive

index for a rough SiF layer of n=1.6 determined by Oehrlein.29 Layadi and coworkers30

determined a complex refractive index for a SiCl layer of n=1.66, which should be some-

what similar to SiF considering the nature of F and Cl. However, since the reaction layer

is known to be just a few monolayers thick,13 here a first approach will be to consider the

contribution of the SiF layer to be negligible in contrast to the surface roughness. Hence,

no SiF contribution will be incorporated in the layer models.

6.4. Chemical XeF2 etching 65

3 6 9 12 15 18

50

100

150

200

dr, c-Si

dr, a-Si (nm)t = 0

(b)

5

( o )

( o )

da-Si 02t

(a)

Fig. 6.6: Ellipsometry trace of the XeF2 etching of first the a-Si layer followed by etching of theunderlying c-Si bulk (thick line). In region (a) the model in Fig. 6.5 (a) is used (thin line). Therough layer thickness dr, a−Si is set at a fixed value, whereas the amorphized layer thickness da−Si

is varied. In region (b) the model in Fig. 6.5 (b) is used (dashed line), which is shown here for aconstant void percentage x = 50 % (50% void / 50% c-Si) and a variable rough layer thicknessdr, c−Si. By matching the simulations to the measurement the rough layer thickness as a functionof time is derived.

3 6 9 12 15 18

50

100

150

200

%void / %c-Si

70/30

30/7020/80 60/4050/50

( o )

( o )

40/60

t = 0

dr, c-Si t

(b)

(a)

Fig. 6.7: Simulations and measurement of the long term XeF2 etching of the c-Si bulk resultingfrom the layer model in Fig. 6.5 (b). For three %void / %c-Si ratios the rough layer thicknessdr, c−Si is varied, resulting in the (gray) lines from point dr, c−Si=0 (dot). For the two (gray) crosslines the %void/%c-Si ratio has been varied in the range of 20%/80% to 70%/30% for dr, c−Si=15 nm and 20 nm, respectively. Matching the simulation to the measurement gives dr, c−Si andthe corresponding %void / %c-Si ratio as a function of time.


dr

c-Si bulk

etch direction

a-Si

Fig. 6.8: Representation of a cusp-like surface roughness. A lower void percentage with respectto the c-Si percentage for the rough layer implies a cusp-like shape.

6.4.2 Results ellipsometry

In Fig. 6.6, simulations are shown in which the rough layer is assumed to have a certain

thickness and the thickness of the underlying a-Si layer has been varied (along each thin

line). At a given point in time, the measurement matches a specific simulation. In this

way, the rough layer thickness and a-Si layer thickness can be obtained. Eventually, the

a-Si is fully removed, leaving only a rough c-Si layer on top of the bulk c-Si (Fig. 6.5

(b)). A simulation of this model with a 50% void/50% c-Si as a function of rough layer

thickness can be seen in Fig. 6.6 (dashed line). A fair agreement with the long term

behavior can already be observed.

In Fig. 6.7, the measurement (thick line) and simulations for three %void/%c-Si ratios

are shown as a function of the rough layer thickness dr,c−Si, originating in the point

dr,c−Si=0 (dot). For the two cross lines the %void/%c-Si ratio has been varied in the

range of 20%/80% to 70%/30% for dr,c−Si= 15 nm and 20 nm, respectively. By matching

the simulation to the measurement, the rough layer thickness as a function of time can

be derived. Note, that for Ψ between 6 and 9, the measurement comes close to the

simulation with a 40% void/60% c-Si ratio, then going back to the 50% void/50% c-Si

simulation. A 40%/60% ratio for %void/%c-Si can be seen as a surface that has a cusp-

like shape as is illustrated in Fig. 6.8. Such a rough layer can only arise from a process that

etches faster in the direction parallel to the etch direction than in the lateral direction,

perpendicular to the etch direction.

6.4.3 Evolution of roughness

The recorded ellipsometry trace in (Ψ,∆)-space for the XeF2 etch process in time is shown

in Fig. 6.6 (thick line). At t = 0 the etch process starts. First both Ψ and ∆ decrease as

a function of time (region (a)) followed by a region (region (b)) where Ψ increase again

but ∆ keeps decreasing. In Fig. 6.9 the results of the analysis of the ellipsometry data

as a function of the dose D(XeF2) of the impinging reactant flux is shown. On the left

hand side, the thickness dr of the rough layer is shown and on the right hand side, the


102 103 104

1

10

30

102 103 1040.01

0.1

(b)

d r (n

m)

D(XeF2) (ML)

(a)

Fig. 6.9: Rough layer thickness dr (left axis) and the simultaneously monitored SiF4 productioncoefficient δ (right axis) as function of XeF2 dose.

measured SiF4 production coefficient δ is shown. The letters (a) and (b) corresponds to

which model from Fig. 6.5 has been used for curve-fitting the data. Initially, the roughness

slowly increases followed by an intermediate phase starting at D(XeF2)≈2×103 ML, in

which the roughness shows a rapid increase. Finally, at D(XeF2)≈ 1.2×104 ML, the

roughness increases slow again. In the initial and final phase an increase dr ∼ D(XeF2)β

with β ≈ 0.2 is observed, whereas in the intermediate phase a strong anomalous increase

is observed, corresponding to β ≈ 1.5. The two completely different models show clearly a

convergence, which is a first indication that the models are indeed a good representation

of the XeF2 etch process and that the silicon-fluoride reaction layer can be considered

transparent to the ellipsometer.

The production coefficient or etch efficiency δ first shows an increase proportional to

D(XeF2)0.1 up to a dose 5×103 ML of XeF2. Next, a switch to an increase δ ∼ D(XeF2)

0.7

can be seen, which then levels off at D(XeF2) ≈ 1.2×104 ML. By etching through the

amorphous to crystalline transition the total surface area increases significantly. A sig-

nificantly larger surface area would imply that more sites are available to the incoming

etchant. Etch products can be created more easily, hence the etch rate goes up.

6.4.4 AFM data

To have an independent measurement of the surface roughness, samples are prepared for

various XeF2 doses and are analyzed ex situ with an atomic force microscope (NT-MDT

Solver P47) in non-contact mode. Here, the AFM results are compared to the ellipsometry

results. In Fig. 6.10 both the rough layer thickness from ellipsometry and the roughness σ

from the AFM measurements are shown as a function of the XeF2 dose. Two series of AFM


103 104

0.1

1

10dr (ellipsometry)

roug

hnes

s(n

m)

D(XeF2) (ML)

(AFM)

Fig. 6.10: Roughness as a function of XeF2 dose in terms of rough layer thickness dr fromellipsometry and root-mean-square roughness σ from AFM measurements. All samples have beenmeasured twice, resulting in the two series of points

measurements are shown, taken at different positions of the sample with 1×1 µm scan

size. Both show a similar trend in roughness evolution. Comparing AFM and ellipsometry

measurements is not straightforward since the measure for roughness is defined differently

for both diagnostics. The root-mean-square roughness σ (or interface width w) measured

by AFM is the standard deviation of the heights measured in the rough layer, whereas

ellipsometry measures the total thickness of the rough layer dr. An illustration of the two

measures is shown in Fig. 6.11.

Here, dr is assumed twice the 3σ interval of heights distribution, hence

dr ≈ 6σ. (6.6)

This definition is based on the statistical statement that a height data point outside the

3σ interval is most probably erroneous.33 This way the statistically relevant part of the

height distribution function is taken into account. Thus, by plotting the rough layer

thickness against the corresponding root-mean-square roughness σ a comparison on basis

of Eq. 6.6 can be made (Fig. 6.12).

The comparison seems valid for the long dosed samples. However, at short-term and

mid-term (a-Si to c-Si transition) the measurements show dr >> 6σ. This is related to

the way the roughness develops. If the roughness develops more rapidly in etch direction

but lateral dimension ξ stays smaller or is on the order of the AFM tip radius (ξtip= 10

nm), the AFM is not able to sample the surface properly (Fig. 6.13). The consequence

is an underestimation of the roughness obtained with the AFM. In the long term, the

lateral dimension ξ grows and becomes larger than the AFM tip radius ξtip, which results


dr

Fig. 6.11: Representation of rough layer thickness dr and root-mean-square roughness σ. TheAFM measures a distribution of heights relative the mean height. The roughness from AFMmeasurements is given by the standard deviation or root-mean-square σ of the heights distribution.Ellipsometry measures the total width of the heights distribution dr. Statistically relevant are theheights between plus and minus 3σ. Therefore, dr ≈ 6σ.

1

10

100

0.1 1 10

6

4

20

AFM (nm)

Ellip

som

etry

dr (

nm)

XeF 2-dose

Fig. 6.12: Rough layer thickness dr from ellipsometry as a function of the corresponding root-mean-square roughness σ from AFM measurements. Lines with dr = 20σ, 6σ and 4σ are shown.As a consequence of AFM tip size ξtip, defined in Fig. 6.13, the σ is an underestimation of theroughness, thus dr 6 20σ. In the long term limit the AFM tip size is small compared to thesurface roughness; dr ≈ 6σ is a good quantitative comparison between ellipsometry and AFM.Note that dr remains well above the 4σ line.


dr

c-Si bulk

AFM tip etch direction

ξ

dr,AFM

ξtip

Fig. 6.13: Underestimation of the roughness occurs when AFM tip radius ξtip is larger or on theorder of lateral dimension ξ and ξ < dr. Consequently the sampled roughness dr, AFM is smallerthan the real roughness dr.

in a proper sampling of the surface by AFM, hence the comparison on basis of Eq. 6.6

shows a good agreement with the experiments. In addition, a dr∼= 4σ comparison line

is added, which merely illustrates how sensitive the comparison on basis of Eq. 6.6 is.

6.4.5 Anomalous roughening

All independent diagnostics for the surface roughness, i.e the ellipsometry data, the AFM

data and the etch efficiency show anomalous behavior roughly centered at the transition

from the a-Si top-layer to the c-Si bulk. Here, an attempt is done to qualitatively ex-

plain this behavior. First, a simple plot to define the extent of the transition region is

introduced. The average thickness of the layer removed by etching is given by the integral

version of Eq. 6.5, equal to

YSi(t) =1

2aSi

∫ t

0

δ(t′)Φs(XeF2)dt′ (6.7)

where t′ = D(XeF2; t′) / Φs(XeF2).

In Fig. 6.14 the Si etch yield YSi is shown as a function of D(XeF2) for easy comparison

with our earlier plots. Additionally, plots of the functions Ymax = YSi + dr/2 and Ymin =

YSi - dr/2, which represent the upper and lower bounds of the structures on the roughened

surface. The dose (or point in etching time) where Ymax=12 nm, the thickness of the a-Si

layer at t=0, represents the time where the first c-Si patches start to become ‘visible‘

to the reactant. Conversely, the dose where Ymin=12 nm, determines the point in time

where the last cap of a-Si disappears from the sample. These two values D(XeF2)1 =

4×103 ML and D(XeF2)2 = 8×103 ML determine the region where both a-Si and c-Si

have to be considered, the transition region. The anomalous behavior of roughening is

contained in this transition region. In this region the shape of the structures, i.e. the

surface morphology, changes.

To conclude, in the analysis of the ellipsometry data with model Fig. 6.5 (b) in this

transition region the best description is obtained for a 40% void/60% c-Si ratio, while a

6.5. Roughness in reaction layer models 71

102 103 104

1

10

100

initial a-Si thickness

D(XeF2)2D(XeF2)1

Y min

YSi (n

m)

D(XeF2) (ML)

(a) (b)

transition regionY max

Fig. 6.14: Si etch yield YSi as a function of XeF2 dose D(XeF2) (•). The lines Ymax = Ysi + dr/2and Ymin = Ysi−dr/2 cross the initial a-Si layer thickness at D(XeF2)1 and D(XeF2)2, respectively.These boundaries define the a-Si to c-Si transition region.

50%/50% ratio is relevant for the final phase of pure c-Si etching for D(XeF2) > 1.2×104

ML. This suggests a cusp-like shape of the pits in the surface in the transition region.

Both features suggest that the remaining a-Si patches on the surface effectively act as a

capping layer which causes the growth of deep and narrow trenches in the bulk c-Si. As

a result the number of surface sites, i.e. the total surface area, increases. More sites are

available to the incoming etching and, hence, the etch rate increases. The ellipsometry

data on the roughness are corroborated by the AFM data, where in this transition region

the measured variation σ of the height distribution function is way too small as compared

to the thickness dr. This again suggests narrow and deep surface pits that cannot be

tracked by the AFM tip in the transition region. Fig. 6.15 illustrates the full etch process

in the three phases.

6.5 Roughness in reaction layer models

A severe surface area increase will have consequences for the kinetic reaction dynamics

models that have been proposed in the past. Some issues concerning the reaction layer

during XeF2 etching, such as the ’real’ or local reaction layer thickness, are still open

for debate, hence a discussion in the following section is an attempt to explain the local

reaction layer thickness on basis of surface area increase due to roughening.

The local reaction layer thickness is the reaction layer thickness at the atomic scale,

which is the parameter of most interest. However, when the surface area increases sig-

nificantly, the reaction layer thickness obtained with almost all diagnostics tools is an


(initial phase)

c-Si bulk

a-Si

(final phase)

c-Si bulk

c-Si

(transition phase)

c-Si bulk

c-Si

Fig. 6.15: Initial (a), transition (b) and final (c) phase of the XeF2 etch process.

area-integrated layer thickness. Therefore, this measure is no longer equal to the local

reaction layer thickness dlocal, but is an effective reaction layer thickness deff.,

deff = ρ dlocal. (6.8)

where ρ is the ratio of the area along the ragged peaks and valleys of the rough surface as

compared to the effective area by looking at the bulk of the sample. Thus ρ is the relative

increase in available surface sites due to the roughening.

Some experiments in the past have lead to the interpretation that the SiF reaction layer

should be several monolayers (up to 10 ML) thick in order to explain the observations(2).

However, Lo et al.13 concluded from XPS measurements that the SiF layer thickness is

only 1.7 ML and the observed thick reaction layer is a consequence of surface roughness

and not as suggested due to fluorine diffusion into the silicon.2 Vugts et al. arrived at the

same conclusion by estimating the roughness on the basis of accurate TDS measurements

with a mass spectrometer.11 In this report, the surface roughness has been characterized;

all information is present to review the available reaction layer models.

A simple but adequate model for XeF2 etching of Si, the bilayer model,11,13 is used

here for the discussion. A fast fluorination of Si-Si∗ surface sites results in Si-SiF and

Si-SiF2 species. Next the Si-Si back-bonds are broken, leading to SiF3 species at the

surface. Then, the last bond can be broken leading to SiF4 etch products. Basically, a

simple description to visualize the reaction layer is a subsurface monolayer of SiF and SiF2

species (partially) covered by a layer of SiF3 species. The rate equations for the bilayer

6.5. Roughness in reaction layer models 73

100 101 102 103 1040.01

0.1

1

4long term

measured

[SiF1,2

]

XeF2-dose (ML)

calculated

[SiF3]

short term

Fig. 6.16: Surface area increase ρ, SiF1,2 and SiF3 surface coverage (in ML) and SiF4 productioncoefficient δcalculated resulting from the bilayer model, as well as the measured δmeasured, as afunction of XeF2. For a XeF2 dose less than 103 ML, ρ is equal to 1 and the SiFx coverages followfrom matching δcalculated with δmeasured by determining the back bond breaking probability kb

and etching probability ke. For XeF2 dose above 103 ML, the increase ρ in surface area is the onlyvariable used to match δcalculated with δmeasured.

model are as follows:

∂[SiF1,2]

∂t= kfΦs(XeF2)

(1− [SiF1,2]

ρN0

)(6.9)

∂[SiF3]

∂t= kbΦs(XeF2)

([SiF1,2]

ρN0− [SiF3]

ρN0

)− keΦs(XeF2)

([SiF3]ρN0

)(6.10)

in which kf is the fluorination probability, kb is the back-bond breaking probability and

ke the etch probability. Here, [SiF1,2] and [SiF3] are the surface concentrations of the

corresponding species in ML on a flat surface. The parameter N0 is the Si surface concen-

tration for a flat surface (ρ=1, N0 = 1 ML). The formation of etch products is expressed

in δ as

δ = 2ke[SiF3], (6.11)

which has already been shown in Fig. 6.9. With the proper parameter values for ρ, kf ,

kb, ke and N0, the value of δ can be calculated and fitted to the measured δ. In Fig. 6.16

again δ is shown as a function of XeF2 dose, together with ρ and coverage of SiF1,2 and

SiF3 species (ML).

A discrimination is made between short term and long term parameter values. The

bilayer model simulations are obtained as follows. For a XeF2 dose below 103 ML ( =

short term) the surface area increase ρ is assumed to be close to 1. The true reaction layer

growth can be observed. The SiF1,2 species first start to generate a monolayer coverage.


Tab. 6.2: Bilayer model parameters used for short term and long term simulations, including theindication whether the parameter is used as fit parameter or as fixed value.

Parameter short term values long term valueskf 0.03 (fixed)∗ 0.03 (fixed)∗

kb 0.03 (fit) 0.03 (fixed)ke 0.03 (fit) 0.03 (fixed)N0 1 ML (fixed) 1 ML (fixed)ρ 1 (fixed) var. (fit)Φs(XeF2) 0.9 ML s−1 0.9 ML s−1

∗ from Ref.11

This layer gets covered for about 50% by SiF3 species leading to the steady state reaction

layer. To perform the simulations, kf is taken from Vugts et al.,11 ρ and N0 are fixed,

whereas kb and ke are used to fit the calculated δ to the measured δ. The fixed and

fitted parameter values are listed in Tab. 6.2. For a XeF2 dose above 103 ML due to

the etch process the roughness increases, which results in an increase of the surface area.

Therefore, kf , kb, ke and N0 are kept fixed to their values derived from the short term fit

to the measured δ. Only ρ is used to fit the increase in the measured δ. The concentration

of SiF1,2 species grows with the same factor as the surface area increase, thus also more

sites are available to harbor SiF3 species. Hence, more SiF3 species are available for SiF4

etch product formation, which translates into an increase in δ. The increase in δ implies

a factor of two increase in surface area. The corresponding [SiF1,2] is in this case about

2 ML with still a 50% SiF3 coverage: [SiF3]=1 ML. The local reaction layer thickness is

1.5 ML, but the effective thickness is 3.0 ML, if one assumes that the stoichiometry of

1 ML SiF-layer to be equivalent to SiF2 coverage. The local reaction layer thickness of

1.5 ML is in very good agreement with the 1.7 ML reported by Lo et al.,13 who used

XPS to measure the local reaction layer thickness. It also shows that the effective layer

thickness is twice the local reaction layer thickness, since the surface area has increased

with a factor of two.

The effective thickness is basically the measure usually reported in literature, because

almost every diagnostic gives the area integrated layer thickness instead of the local layer

thickness. It’s therefore questionable whether the assumption made by various authors

that a rather thick reaction layer is created in the etch process due to fluorine diffusion, is

in fact a 1.5 ML thick reaction layer stretched out along a rugged and rough surface profile.

Thus, the assumption that the SiF-layer contribution to the ellipsometry measurement can

be considered negligibly small is valid. Even when the effective layer thickness becomes 3

ML, the roughness is such that the SiF-layer contribution is much smaller than the surface

roughness. It should be noted that the roughening, thus also surface area increase, may

be related to experimental conditions such as Si crystal orientation, doping level, etchant

nature (XeF2, F2, F, Cl2, Cl ) and flux, sample history and maybe many more experimental

6.6. Surface morphology 75

dr

(a) 3-D geometry (b) unit cell

γ

ξ

Fig. 6.17: Geometrical model for the rough layer (a) and corresponding unit cell (b). The roughlayer thickness dr is the peak-to-peak height difference and ξ is the peak-to-peak lateral dimension.The average surface-slope angle is the angle γ as defined in figure (b).

parameters. The reported SiF reaction layer of several monolayers (up to 10 ML) thick

in past observations (2) may well be explained by an increase in surface area, depending

on the specific experimental conditions.

6.6 Surface morphology

With the rough layer thickness dr obtained from ellipsometry and the surface area increase

ρ obtained from the product coefficient δ, a detailed description of the surface morphology

can be derived. A 3-dimensional geometric representation for the rough layer is required.

The chosen geometry is a repetitive pattern (Fig. 6.17 (a)) of the unit cell, which is

constructed of a pyramid pointing upwards and a pyramid pointing downwards (Fig. 6.17

(b)). Now, the surface area increase ρ can be geometrically calculated by:

ρ =

√1 +

d2r

ξ2(6.12)

in which dr is the peak-to-peak height difference. Dimension ξ equals the peak-to-peak

lateral dimension. Actually, this formula is valid for both the 3-dimensional and 2-

dimensional case. Thus, the lateral dimension ξ here is equal to ξ defined in Fig. 6.13.

Since ρ and dr have been experimentally determined the lateral dimension ξ can be cal-

culated.

At the beginning of the transition (D(XeF2)1= 4×103 ML, Fig. 6.14) ξ is found to

be equal to 6.6 nm with dr=5.9 nm and at the end of the transition (D(XeF2)2 = 8×103

ML, Fig. 6.14) ξ= 12.9 nm with dr=18.7 nm. In the transition phase ξ becomes smaller

than dr and is smaller than the AFM tip radius ξtip = 10 nm. Again this substantiates

the fact that this type of surface roughness can not be properly tracked with the AFM.

In the final phase at D(XeF2)= 2×104 ML, the value of ξ is found to be 15 nm with dr =

27.8 nm. Here, ξ is significantly larger than the ξtip, hence the roughness can be tracked

properly.

Now, the average surface-slope angle can be determined, as given by the angle γ as

defined in Fig. 6.17 (b). For D(XeF2)= 2×104ML the angle is found to be 62. At 54


with respect to the Si(100) crystal plane lies the Si(111) plane, which is close to the 62

that is found here. This suggests that the roughness growth in the final phase has arrived

at a steady-state, i.e. surface area increase remains constant, which is governed by the

etching of the Si(111) plane.

6.7 Conclusions

Single wavelength ellipsometry has been successfully employed to characterize the surface

roughness caused by physical Ar+ etching and chemical XeF2 etching. The proposed ellip-

sometry layer models give a good representation of the etch process. Preliminary results

with spectroscopic ellipsometry show a similar behavior. Thus, for the Ar+/XeF2/c-Si

system single wavelength ellipsometry has proven to be a good tool to monitor surface

roughness. For XeF2 etching of the a-Si layer and subsequently the c-Si bulk sample, the

roughness evolution shows an anomalous roughening. When etching through the amor-

phous to crystalline transition the roughness increases proportional to D(XeF2)1.5 and,

simultaneously, the etch rate shows an increase. Since etching is faster in the direction

parallel to the etch direction than in the lateral direction, the surface shows a cusp-like

shape and hence the surface area increases severely. Presently, studies are devoted to

answer the question why the etching goes faster in the etch direction as opposed to the

lateral direction. In the a-Si to c-Si transition region the remaining a-Si patches act as a

capping layer, which might suggest an etch rate difference between a-Si and selected crys-

tal faces of c-Si. A comparison with AFM measurements substantiates the anomalous

roughening. On the basis of the bilayer model for XeF2 etching of silicon an estima-

tion of the surface area increase yields an increase of a factor of 2. The resulting local

reaction-layer thickness of 1.5 ML is in agreement with the 1.7 ML reported by Lo et al.13

Such a thin SiF reaction layer can be considered transparent to the ellipsometer and can

therefore be disregarded in the ellipsometry layer models. Due to surface area increase

this SiF layer becomes effectively 3 ML, but this is still negligibly small in comparison

to the roughness. These separate studies of Ar+ and XeF2 etching will facilitate a basis

for studying the surface roughness caused by the Ar+ ion assisted XeF2 beam etching of

silicon.


Authors wish to acknowledge J.A.C.M. v.d. Ven and L.H.A.M. v. Moll for the technical

support and W.M.M. Kessels and M.C.M. v.d. Sanden for the supporting discussions.

This research is supported by The Netherlands Foundation for Fundamental Research on

Matter (FOM: 99TF24).

References 77

References

1 J. W. Coburn and H. F. Winters, J. Appl. Phys. 50, 3189 (1979).




5 M. J. M. Vugts, L. J. F. Hermans, and H. C. W. Beijerinck, J. Vac. Sci. Technol. A 14, 2138 (1996).

6 M. J. M. Vugts, L. J. F. Hermans, and H. C. W. Beijerinck, J. Vac. Sci. Technol. A 14, 2820 (1996).






12 M. J. M. Vugts, G. L. J. Verschueren, M. F. A. Eurlings, L. J. F. Hermans, and H. C. W. Beijerinck,J. Vac. Sci. Technol. A 14, 2766 (1996).


14 V. S. Aliev, V. N. Kruchinin, Surf. Sci. 442, 206 (1999).

15 J. L. Buckner, D. J. Vitkavage, E. A. Irene and T. M. Mayer, J. Electrochem. Soc. 133, 1729 (1986).

16 A. C.-T. Chan, G.-C. Wang, Surf. Sci. 414, 17 (1998).

17 J. F. Ziegler, J. P. Biersack, and U. Littmark, The stopping range of ions in solids (Pergamon, Oxford,1985).

18 M. Fried, T. Lohner, E. Jaroli, Gy. Vizkelethy, G. Mezey, J. Gyulai, M. Somogyi, and H. Kerkow,Thin Solid Films 116, 191 (1981).

19 D. B. Graves, D. Humbird, Appl. Surf. Sci. 192, 72 (2002).

20 R. Petri, P. Brault, O. Vatel, D. Henry, E. Andre, P. Dumas, and F. Salvan, J. Appl. Phys. 75, 7498(1994).

21 J. G. C. Labanda, S. A. Barnett, L. Hultman, J. Vac. Sci. Technol. B 16, 1885 (1998).



24 G. M. W. Kroesen, G. S. Oehrlein, E. de Fresart, M. Haverlag, J. Appl. Phys. 73, 8017 (1993).

25 A. H. M. Smets, D. C. Schram, and M. C. M. van de Sanden, J. Appl. Phys. 88, 6388 (2000).


26 A. A. E. Stevens, W. M. M. Kessels, M. C. M. van de Sanden, and H. C. W. Beijerinck, submitted toJ. Vac. Sci. Technol. A.

27 E. D. Palik, ed., Handbook of optical constants of solids (London : Academic Press, 1998), vol. I, pp.547–569.

28 E. D. Palik, ed., Handbook of optical constants of solids (London : Academic Press, 1998), vol. I, pp.749–736.

29 G. S. Oehrlein, J. Vac. Sci. Technol. A 11, 34 (1993).

30 N. Layadi, V. M. Donnely, J. T. C. Lee, and F. P. Klemens, J. Vac. Sci. Technol. A 15, 604 (1997).

31 C. Casiragh, A. C. Ferrari, R. Ohr, A. J. Flewitt, D. P. Chu, and J. Robertson, Phys. Rev. Lett. 91,226104 (2003).

32 Dae Won Moon and Kyung Joong Kim, J. Vac. Sci. Technol. A 14, 2744 (1996).

33 H. M. Wadsworth Jr., Handbook of Statistical Methods for Engineers and Scientists (London :McGraw-Hill, 1990).

Chapter 7

Roughening during XeF2 etching of Si(100) through

interface layers: H:Si(100) and a-Si/Si(100)

Abstract

Real-time spectroscopic ellipsometry has been applied in situ in an Ar+/XeF2 beam etch-ing experiment to study the roughening of Si(100) etched by XeF2 at room temperature.The role of initial surface conditions has been examined. For the etching of hydrogen-terminated (H:)Si(100), the roughness evolution as a function of XeF2-dose can be charac-terized by an initially fast roughening phase followed by a slower, final roughening phase.Similar behavior is observed when etching through an amorphous silicon (a-Si) layer ontop of crystalline Si(100) bulk as obtained by sputter-cleaning of Si(100) substrates. BothH-termination and a-Si lead to patch formation on the surface where etching is impededand, hence, high aspect-ratio etch pits develop. The quantitative differences in rougheningare caused by the duration and timing of their influence on the etch process until H-bondedSi surface atoms or a-Si are totally removed from the surface. Surface area increase dueto the roughening is responsible for observed trends and differences in etch rates, reactionlayer thickness and composition as a function of etch time which has been reported byseveral authors.

7.1 Introduction

Fundamental studies of dry etching of silicon are of great interest considering its role

in semiconductor fabrication. Key issue in the chemical processing of silicon surfaces

is to produce well-defined, low-damage surfaces. Better understanding of the atomic-

scale reaction dynamics between halogens and Si(100) surfaces can aid in meeting these

technological demands for next generation semiconductor devices.

Initial surface conditions prior to processing can be of significant importance for

the etch process, whether the surface is clean and reconstructed, hydrogen-terminated,

sputter-cleaned by ion bombardment or contaminated.1–4 Furthermore, spontaneous chem-

ical etching is an isotropic etch process in which roughening of the surface is a major con-

cern. Often, roughness has been used as an argument in literature to explain some not

well understood experimental observations.2,5–7 Insight into the fundamentals of roughen-

79

80 Chapter 7. Roughening during XeF2 etching of Si(100) through interface layers: H:Si(100) and a-Si/Si(100)

ing of surfaces and the influence of initial surface conditions in etch processing is required

to increase the understanding of the microscopic etch mechanisms.

In a first study we have already shown that surface roughening is severe when etching

sputter-cleaned Si(100) with XeF2 using single-wavelength ellipsometry.3 Here, the rough-

ening mechanism of silicon etched by XeF2 has been studied by applying in-situ, real-time

spectroscopic ellipsometry (SE) in a Ar+/XeF2 beam-etching apparatus for various initial

surface conditions: XeF2 etching of (a) hydrogen-terminated Si(100) (H:Si(100)) and (b)

Ar+ sputter-cleaned, amorphous silicon (a-Si) on top of a c-Si(100) bulk (a-Si/Si(100)).

In this way we can study how initial surface conditions may have an impact on the

roughening mechanism and, additionally, by using spectroscopic ellipsometry instead of

single-wavelength ellipsometry we may obtain more detailed information on the roughness

characteristics.

First, some aspects of the XeF2 etch mechanism of silicon will be addressed (Sec.7.2)

Next, the experimental details are discussed (Sec.7.3), followed by a description of the

multi-layer dielectric models that have been used to analyze the SE measurements (Sec.7.4).

Then, two case studies will be described: (a) the etching of H:Si(100) in Sec.7.5, includ-

ing a comparison with atomic-force-microscopy measurements, and (b) the etching of

a-Si/Si(100) in Sec.7.6. Differences and similarities between the two cases as well as

implications for the XeF2/Si etch mechanism will be discussed in Sec.7.7.

7.2 XeF2/Si etch mechanism

Surface roughness and initial surface conditions might be responsible for some of the con-

flicting experimental observations within the framework of the XeF2/Si etch mechanism.

A brief overview of key elements of the reaction mechanism at room temperature will be

presented here, including the issues of initial surface conditions and the potential influence

of surface roughness.

7.2.1 Initial reaction steps

In the case of a clean Si surface, an F-atom is abstracted from the XeF2 molecule by

a reactive site, i.e. dangling bond, without energy barrier, whereby the complementary

XeF scatters off the surface.8 As a result, the surface layer consists initially primarily of

SiF for most reconstructed Si(100) and Si(111) surfaces with possibly some SiF2 at step

edges. Once dangling bonds are passivated, the next reaction step requires breaking of

Si-Si back-bonds which is an activated process with a much smaller reaction probability.

Since F is known to be very electronegative, bond charges will reside preferentially close

to the F atom, leading to an effective charge separation between the Si (δ+) and F (δ−).9

The back-bonds are weakened by this phenomenon and, hence, back bonds are suscep-

tible to subsequent F-atom insertion which is supplied by physisorbed XeF2 molecules.

7.2. XeF2/Si etch mechanism 81

Tab. 7.1: Reaction layer thicknesses and SiFx-species distributions as reported in the literature.The silicon surfaces were all (2×1)-reconstructed prior to processing unless mentioned otherwise.

species coverage total XeF2

Initial surface Ref. ratios coverage doseSiF : SiF2 : SiF3 (ML) (ML)

Si(100), 10 Ωcm 11 3.00 : 1 : 0.28 1.13 50Si(100) 12 2.00 : 1 : 0.25 1.40 50sputtered Si(100), 10 Ωcm 11 1.25 : 1 : 0.25 1.13 50Si(111)-(7×7) 1 Ωcm 7 2.78 : 1 : 1.56 0.95 103

Si(111)-(7×7) 1 Ωcm 7 1.78 : 1 : 1.95 1.75 >104

H-term. Si(111), 10 Ωcm 2 3.25 : 1 : 5.50 - >104

n-&p-doped Si(111), 0.1 Ωcm 13 1.58 : 1 : 3.71 - >104

n-doped Si(111), 0.001 Ωcm 13 1.74 : 1 : 4.07 - >104

p-doped Si(111), 0.001 Ωcm 13 1.67 : 1 : 4.37 - >104

Subsequent steps of F-atom attachment to SiFx surface species leads eventually to the

formation of SiF4 molecules, which are volatile and can desorb from the surface as the

main etch product at room temperature:

Si+F−−→ SiF

+F−−→ SiF2+F−−→ SiF3

+F−−→ SiF4(g) (7.1)

The silicon-fluoride reaction layer thickness remains this way typically 1.5 mono-layer (ML

),10 composed of a surface layer of SiF and SiF2 species (partially) covered by a layer of

SiF2/SiF3 species. Table 7.1 lists a selection of literature reports on species coverages and

reaction layer thicknesses. Clearly, some variations in observations are visible, possibly

because of different XeF2 exposure times, preparation method, and doping level of the Si

substrates. After a low (50 ML) XeF2 dose, surfaces are primarily SiF, whereas SiF3 is a

minority species. Hence, SiF4 products are not easily produced and the etch rate/reaction

probability is very low.12 After 50 ML of dose the surface is still flat, since relatively little

etching has occurred. Lo et al. show that it takes about 103 ML of XeF2-dose to reach an

intermediate, steady-state reaction layer consisting of primarily SiF followed by SiF3 and

a minor amount of SiF2.7 Hence, the experiments and simulation remaining far below 103

ML of XeF2-exposure may still be categorized as being in the process of reaction layer

build-up despite the fact that during this process etching may already have occurred.

Continued exposure to XeF2, beyond a 103 ML dose, shows an increase in all species

and the increase is most pronounced in the SiF3 species coverage, which becomes by far

the most abundant species.7 Due to the removal of Si in the etch process, the surface

is believed to roughen and, hence, the total amount of SiFx species increases. One can

argue that surface area increase due to roughening allows more SiF3 to be present on the

surface, whereas on flat surfaces only a small amount is allowed due to steric hinderance.

Thus, defining a reaction layer composition seems to be arbitrary if the total XeF2-dose

and/or the surface morphology are not known.


7.2.2 Influence of initial surface

Initial surface conditions have also a significant effect on both the initial reaction of F

with Si and on the etch process on longer times scales. Morikawa et al. observe similar

trends and ratios in species coverage as a function of XeF2-dose as reported by Lo et al.,

although in this case the initial surface is H-terminated.2 The SiFx growth occurrence on

H-terminated Si(100) shows, however, a delay for about 0.5·103 ML. The H-terminated

surface is apparently stable for a prolonged period of time. The fact that Si(100) is not

etched in hydrofluoric acid (HF) treatment and leads to H-terminated Si(100) is already

an indicator for the fact that H-terminated Si(100) is an energetically favorable and more

stable surface state than F-terminated Si(100).14 The hydrogen is not replaced by F, but

needs to be removed by SiHxFy product formation. The F-atoms need to be inserted into

the subsurface back-bonds of the first Si layer to achieve this. Now, once a SiHxFy is

released at a certain position on the surface, SiF species in the next layer can be exposed

to incoming XeF2 molecules, and the regular etching can start. The observation of H-Si

bonds even after exposure to XeF2 above ∼104 ML substantiates the fact that H is not

easily removed from the Si surface.2

A different initial surface condition can be obtained by sputter-cleaning. A sputter-

cleaned Si(111) shows already a totally different reaction layer after 50 ML of XeF2 dose

as compared to a (2×1)-reconstructed Si(111) surface (Table 7.1), possibly because of the

amorphous surface structure. Initial reaction of F with surface atoms is not hampered, a

reaction layer is formed and the etching can start immediately. Next, the a-Si is being

removed, resulting in a gradually increasing roughness.3 Once the etching arrives at the

a-Si/c-Si interface, at some positions on the surface the c-Si is going to be etched while

at other positions a-Si remains as patches on the surface. For this case, we showed that

roughening of the surface is in fact an important aspect of the etch process and, also,

that the etch rate is enhanced as a result of surface morphology changes.3 Furthermore,

it was shown that the buried amorphous-crystalline interface plays a major role in the

roughening dynamics.

The real-time SE experiments presented in this paper should be able to show the

implications of roughening and initial surface conditions on some of the experimental

observations for the etching of silicon with XeF2.


The experimental setup used in this study has been described extensively in previous

publications. Figure 7.1 shows a cross section of the setup. The new feature is the

addition of a spectroscopic ellipsometer (Woollam M-2000U with an infrared extension)

covering the photon energy range of 0.75-5 eV (250-1700 nm). The angle of incidence is

typically 74.3 with respect to the surface normal and the light is focused onto a 1 mm2


Magnetic

linear drive

loadlock

UHV chamber

detector

chamber

2

11. Sample rotator

2. XeF2 source

3. Ar+ -ion source3

P light source

A R

C

D

Fig. 7.1: Experimental setup in horizontal cross-section. Samples can be exchanged between arotatable sample holder and the sample storage in the load lock with a linear magnetic drive.The sample is mounted in a rotatable sample holder (1) that can be operated manually via anexternal drive. The XeF2 source (2) and Ar+-ion source (3) are at 52 and 45 from surfacenormal, respectively. Etch products are detected in a separate detector chamber perpendicular tothe sample surface. The spectroscopic ellipsometer is incident at 74.3 from the surface normal.The SE consists of a broadband light source, polarizer(P), rotating compensator(RC), analyzer(A)and a fiber-coupled CCD-array detector(D).

area of the sample. Each measured spectrum is an average over typically 200 spectra

recorded by the ellipsometer resulting in a time resolution of typically 10 s, which is more

than sufficient for the experiments described in this paper. The spectroscopic ellipsometry

data are analyzed with WVASE32r software. All measurements have been performed at

room temperature.

Simultaneously with the ellipsometry measurements, etch products are monitored with

the mass spectrometer. At room temperature the only etch product for the etching of

Si(100) with XeF2 is SiF4.6,15 The SiF+

3 -signal is a measure for the SiF4 etch product flux

and is converted in the production coefficient δ,3 which is defined as

δ =2 Φ(SiF4)

Φs(XeF2)(7.2)

with Φs(XeF2) the impinging flux on the sample and Φ(SiF4) the product flux leaving

the sample. The production coefficient or etching efficiency is defined such that δ = 1

corresponds to the full conversion of reactant into products.

For the H-terminated c-Si etching experiments the native oxide is removed by dipping

10×10 mm2 Si(100) substrates in a 2 % hydrofluoric acid (HF) solution for 2 minutes

after ultrasonic cleaning with ethanol at 40C and rinsing in purified water. This leads to

a mono-, di- and trihydride-terminated Si substrates with mostly dihydrides.14 Further-

more, SE shows an initial roughness/steps of typically six mono-layers (ML) and ∼0.15


layer #

2

N

x1

x2

xN

c-Si

d1

d2

dN

1

void fraction xi

(1-x1)

(1-x2)

(1-xN)

layer

thickness

Si fraction

(1-xi)

Fig. 7.2: Multi-layer roughness modeling. Layer i with thickness di has a void percentage xi, whichis always larger than the void percentage xi+1 of the lower lying layer i + 1. Using this model, themorphology details of the rough layer can be included in the analysis of the experimental results.

nm root-mean-square roughness measured with atomic force microscopy (NT-MDT Solver

P47) in non-contact mode (scan size: 1.5×1.5 µm).

For the a-Si/c-Si transition etch experiment, the samples are ultrasonically cleaned

with ethanol at 40C, rinsed with purified water and in-situ bombarded with 1 keV Ar+

ions to remove the native oxide and create a 6.4 nm a-Si top layer. The Si(100) used in

this study is phosphorus-doped n-type Si with a resistivity of 10-30 Ωcm.

7.4 Multi-layer dielectric model

Two, differently prepared Si(100) samples have been etched with XeF2: a H-terminated

Si(100) sample and a sputter-cleaned Si(100) sample. To obtain information from SE

measurements, different multi-layer dielectric models for the substrates have to be used,

as described next.

7.4.1 H-terminated Si(100)

The multi-layer dielectric model for the substrate consists of a stack of layers on top

of the c-Si-bulk substrate, with different dielectric functions for the materials in the

various layers. For c-Si the dielectric functions described by Jellison et al.16 are used.

Often, a single roughness layer is included in multi-layer models with 0.5 void-fraction

and 0.5 material-fraction. The Bruggemann approximation is then used to calculate

the effective dielectric functions for the roughness layer.17 As will be discussed below,

we have chosen to model the roughness using a two-layer roughness model to fit the

ellipsometry measurements, with 0.75 void/0.25 c-Si fractions in the top-layer and 0.25

void/0.75 c-Si-fractions in the bottom-layer, as shown in Fig. 7.2. Measured pseudo-

dielectric functions 〈ε1(ω)〉 and 〈ε2(ω)〉, as derived from the measured ellipsometric angles

7.4. Multi-layer dielectric model 85

0 1 2 3 4 5 6

-20

-10

0

10

20

30

40

0

10

20

30

40

50

c-Si

ε 1

photon energy (eV)

a

bc

f

c-Si

f

c

b

ε 2

XeF2 -dose (ML)

a. 270

b. 725

c. 1200

d. 2050

e. 4810

f. 11970

a

Fig. 7.3: Measured pseudo-dielectric functions (solid lines) after increasing exposure of H:Si(100)to XeF2 using the two-layer roughness model. The arrows indicate the change of the various partsof the spectra as a function of XeF2-exposure time. For reference the dielectric functions of c-Siare also shown (dashed lines).

Ψ(E) and ∆(E) 18 assuming a two-phase (ambient/substrate) layer model, have been

plotted in Fig. 7.3. Typical root-mean-square experimental errors are σε1=σε2=0.05. For

reference, the dielectric function of silicon is shown. The absolute 〈ε1(ω)〉 shows a gradual

decrease over the full spectra range. Below E(ω)=2.5 eV, the function 〈ε2(ω)〉 shows

an increase with increasing XeF2 dose; above E(ω)=2.5 eV, the function 〈ε2(ω)〉 shows

an decrease with increasing XeF2 dose. Fit optimization with the two-layer roughness

model is done by minimizing the χ2 between experimental and calculated pseudo-dielectric

functions. The value of χ2 for the fits gradually increases from χ2=4 for the initial H-

terminated Si substrate up to χ2=12 for long XeF2-exposure times.

Including multiple layers for the roughness is necessary because of the structure de-

pendence of the rough layer during etching. This was already observed in an earlier study

using single-wavelength ellipsometry,3 where the void fraction in a single-roughness layer

modeling was used to properly model the ellipsometry measurement. To further support

the multi-layer roughness modeling approach, a fit analysis for a set of multi-layer models

of a H:Si(100) sample after exposure to 1.2·104 ML XeF2 has been performed and is sum-

marized in Table 7.2. Large disagreement between measured and simulated SE spectra

was observed when using a single roughness layer, with either a fixed or a fitted void


Tab. 7.2: Multi-layer roughness modeling results (shown in Fig. 7.2) for the pseudo-dielectricfunctions measured after 1.2·104 ML XeF2-dose on H:Si(100). The void fractions shown are thexi from top layer to bottom layer and dr is the weighted rough layer thickness. If the voidfractions are included as fit variables in the SE analysis it is mentioned in the void fraction column.Corresponding χ2-values and the 90% confidence interval for dr are a measure for the quality ofthe least squares curve fit. The simulation labeled (c) corresponds to the model chosen for theanalysis of the real-time SE measurements.

sim. # layers N void fraction xi

∑i di dr χ2 90% conf.

no. (top/../bottom) (nm) (nm) int. (nm)(a) 1 0.50 17.8 17.8 83 0.2(b) 1 0.57 (fit) 17.4 15.0 64 0.1

(c) 2 0.75/0.25 29.4 14.7 12 0.1(d) 2 0.75/0.22 (fit) 31.0 14.5 11 0.2

(e) 3 0.90/0.50/0.10 44.2 18.3 8 0.3(f) 3 0.93/0.57/0.13 (fit) 43.5 17.0 5 0.8

(g) 4 0.90/0.60/0.40/0.10 41.6 17.1 5 0.3(h) 4 0.93/0.66/0.25/0.04 (fit) 52.7 16.1 4 1.4

(i) 5 0.90/0.70/0.50/0.30/0.10 40.6 17.8 5 1.0(j) 5 0.96/0.68/0.48/0.22/0.03 (fit) 58.4 16.4 3 10

fraction in the top layer, as can be concluded from the large χ2 >60. Hence, including

the void-fraction in the fits is not sufficient in the SE measurements. A dramatic decrease

in χ2 can be observed when choosing two roughness layers. The χ2-value is further re-

duced when choosing more layers and fitting the void fraction simultaneously. Choosing

more layers and including void percentage fitting also implies having more fit parame-

ters available. A larger number of fit parameters can result in better fits in terms of χ2,

but may not be reliable due to correlations between fit parameters, which is reflected in

an increase in the 90% confidence interval value. Furthermore, the sum of the separate

roughness layer thicknesses∑

i di increases with increasing number of layers.

Increasing the number of roughness layers included in the modeling results in capturing

finer details of the rough layer, i.e., higher peaks and deeper valleys. Due to this effect,

a weighting method of the separate layers is introduced to be able to make a comparison

between fit results with multiple layers. The weighting method translates the multi-layer

thicknesses into a single-layer thickness, as follows:

dr =N∑

i=1

gi di (7.3)

where the weighting factor gi is related to the void-fraction xi

gi = 1− |1− 2xi|, (7.4)

7.5. H:Si(100) etching 87

such that the contribution of layers situated far from the mean heights, i.e. tails of the

total height distribution, is reduced. This weighting method results in a weighted layer

thickness dr approximately equal and independent of the number of layers for all multi-

layer fits, as is shown in Table 7.2.

In conclusion, the use of the multi-layer roughness model is validated, where the

weighted rough layer thickness is comparable to the thickness of the rough layer obtained

assuming a single roughness layer model, with the difference that specific morphology

changes are accounted for as is necessary in this particular study. As the optimum choice

for minimizing both the value of χ2 and the number of parameters in the curve fit, we

have chosen the two-layer model with fixed void fractions, 0.75 for the top-layer and

0.25 for the bottom layer. It should also be noted that the observed time-dependence of

the roughening as presented below was found to be independent of the number of layers

included in the modeling. The weighted rough layer thickness is used in the presentation

and discussion of the results.

7.4.2 a-Si/Si(100)

For the analysis of the a-Si/Si(100) etch experiments two separate multi-layer models

are used. The layer model used to fit the SE data is initially a single roughness layer of

0.5 void/0.5 a-Si on top of a a-Si layer with a c-Si substrate underneath. This model will

fail to fit the data properly once most a-Si is removed from the surface and predominately

the underlying c-Si bulk is being etched. This is the point where the two-layer roughness

model described above is used to fit the long term etching. To be able to quantitatively

compare the rough layer thickness for the two models, the weighted rough layer thickness

is again used. For a-Si the dielectric model is a Tauc-Lorentz model, which is commonly

used for modeling amorphous materials.19 This layer modeling approach is similar to the

modeling approach of the single-wavelength ellipsometry experiments.3

7.5 H:Si(100) etching

The real-time SE data fitted with the two-layer model and for fixed void percentages leads

to the (weighted) rough layer thickness dr of the XeF2 etched H:Si(100) as a function of

XeF2-dose, as shown in Fig. 7.4(a). The thickness of the separate layers dtop and dbottom

is shown as well. Figure 7.4(b) shows the production coefficient δ, which is proportional

to the SiF4-product flux. An impinging XeF2-flux of 0.8 ML s−1 has been used. For

about 500 ML of XeF2-dose mass spectrometry does not show any product formation

at all, accompanied by no observed change in roughness. The H-terminated surface is

apparently stable to the incoming XeF2-molecules and etching is not allowed to start

immediately. Next, the rough layer thickness shows an initial rapid increase in roughness.

Simultaneously, the production coeffient increases rapidly. After ∼2·103 ML of XeF2-dose


0.0 0.5 1.0 1.50

5

10

15

20

25

0.0 0.5 1.0 1.50.0

0.1

0.2

dr

dtop

laye

r thi

ckne

ss (n

m)

dbottom

(a)

(b)

XeF2-dose ( ·104 ML )

Fig. 7.4: (a) Rough layer thickness dr (solid line) as a function of XeF2-dose of an initiallyH:Si(100) sample. Also shown are the top-layer thickness dtop (dashed line) and the bottom-layerthickness dbottom(dotted line) from the two-layer roughness model, which add up to dr, followingthe weighting formulism presented in Sec. 7.4. (b) Production coefficient δ as a function of XeF2-dose, as measured by mass spectrometry simultaneously during the ellipsometry measurement.

the roughening slows down appreciably, accompanied by a slowly decreasing production

coefficient. In the beginning, the top-layer is thinner than the bottom-layer but increases

more rapidly. The top-layer even becomes thicker than the bottom-layer for a certain

period of time. Beyond 3·103 ML of XeF2-dose, the bottom-layer is again thicker than

the top-layer.

This behavior can be explained qualitatively as follows. The H-termination prevents

etching to start immediately. This implies that H is not replaced by F. First, H has to be

removed, presumably through SiHxFy product formation. The F-atoms have to insert into

Si-Si back-bonds for etching to take place. The SiHxFy product formation is apparently

difficult and delays the start of etching. The SiF4 product formation at Si sites, which

have been cleared from H, is no longer hampered and the etching can begin. This will lead

to preferential etching in depth at H-free areas on the surface, i.e. SiFx surface patches,

hence the roughness grows rapidly. The size of the SiFx-patches grows less rapid than

the rough layer thickness, which leads to pitting of the surface. If the lateral dimensions

of the pits grow slower than the depth, i.e. dr, a significant increase of the number of

surface sites where XeF2 can react is to be expected. As a result SiF4 product formation

increases rapidly. Slowly the remaining H-terminated surface area is being removed and

etch pits start merging. The pit-like surface eventually changes into a surface with cusp-

7.5. H:Si(100) etching 89

0.0 0.5 1.0 1.50

5

10

15

20

0.0 0.5 1.0 1.50

5

10

d r (nm

)

(n

m)

XeF2-dose ( x 104 ML )

Fig. 7.5: Rough layer thickness dr (solid line) as function of XeF2-dose compared with the root-mean-square roughness σ (open circles) obtained from AFM measurements on 10 H:Si(100)-samplesexposed to various XeF2-doses. Note the factor of two difference in the scale for dr (left) and σ

(right).

like roughness features. Characteristic for such a surface is a bottom-layer thickness larger

than the top-layer thickness, as can be seen in the long term roughness evolution, i.e., the

steady-state roughness growth, as shown in Fig. 7.4(a). The slowly decreasing δ after the

initial rapid increase is not fully understood. A similar dose dependence of δ has been

been observed by Vugts et al.6 It is most likely related to a slight decrease of the surface

area after the initial rapid increase of surface area associated with the influence of surface

H-atom. The H-termination has forced the surface morphology into a state which is not

alike the natural, stochastic roughness evolution for XeF2 etching of clean Si(100). Once

the influence of surface H-atoms has disappeared, the etch process may strive to restore the

surface morphology natural for XeF2 etching of Si(100). Also, SiF+3 -signal assumed to be

caused by SiF4 etch products may partially be originating from SiF3H etch products, which

require less F-atoms to create volatile etch products. The latter is however not likely the

reason for the overshoot and decrease in δ. From the integration of δ the Si etch yield can

be determined.3 The etch yield related to SiF3Hy should then be equal to the area under

the δ-curve which exceeds the steady-state (=long XeF2-exposure) level of 0.09±0.02. The

Si etch yield related to this area is ∼80 ML and is therefore much larger than, at most,

2 ML of Si etch yield related to SiF3H-products. Figure 7.5 shows a comparison between

the weighted rough layer thickness and atomic-force-microscopy measurements. As can be

seen, the SE roughness dr shows a similar trend as the AFM root-mean-square roughness

σ. For long XeF2-exposure time the SE roughness is approximately a factor of two larger

than the AFM roughness. However, for shorter exposure time, more than a factor of two

difference can be observed. Here, AFM tip-size effects are believed to underestimate the

roughness in contrast to the SE roughness.3 This, in fact, gives support to the proposed

roughening mechanism as described above. If the lateral dimensions of the etch pits are


below a critical size the AFM tip may not be able to properly track the surface height

fluctuations.

The influence of crystal structure was verified in an experiment subjecting a H:Si(111)

(n-type, 4-16 Ωcm) to XeF2. No quantitative difference in roughening and in produc-

tion coefficient was observed between H:Si(100) and H:Si(111), which indicates that the

roughening does not depend on crystal structure at room temperature.

7.6 a-Si/Si(100) etching

The etching of an a-Si layer on top of the c-Si bulk has been studied earlier by means

of single-wavelength ellipsometry.3 Here, we present a similar experiment, however with

two differences: (a) spectroscopic ellipsometry is used to measure the etch process instead

of single-wavelength ellipsometry, and (b) here a 6.4 nm a-Si layer is prepared by 1

keV Ar+-ion bombardment instead of a 12 nm a-Si layer prepared by 2.5 keV Ar+-ion

bombardment. An impinging XeF2-flux of 2.2 ML s−1 has been used. In Fig. 7.6(a) the

a-Si/Si(100) roughening is shown together with the product formation (Fig. 7.6(b)) as

a function of XeF2-dose. The dotted, vertical line indicates where the layer modeling

is switched from the a-Si, single-layer roughness model to the c-Si, two-layer roughness

model. As can be seen, the weighted rough layer thickness dr is continuous, despite the

fact that two totally different layer models are used to analyze the initial and long term

SE measurements. Initially, the roughness shows a slow increase on the a-Si. Gradually

the roughening speeds up and crosses over to a final, slower roughening phase. The

production coefficient shows a low value of 0.03 when etching the a-Si, but increases to

a final value of 0.11. The increase in the production coefficient coincides with the fast

roughening phase and, thus, with the transition from a-Si to c-Si etching. The reactive

a-Si surface allows immediate bonding of F-atoms. A reaction layer is created and hence

the etching starts immediately. Etch product formation is observed and the roughness

slowly increases. When going into the transition region, the absolute value of the rough

layer thickness becomes larger than in the H:Si(100) case. Here, the valleys of the rough

a-Si reach the underlying c-Si bulk earlier than the hills. A preferential etching of c-Si

over a-Si results in a large increase in dr as etch pits are created in the c-Si. The rough

layer thickness grows in a rapid pace until all a-Si is removed. During this phase the

production coefficient increases, partly because the number of surface sites where etching

can occur increases on the walls of the etch pits and, partly, because of the increase of the

c-Si surface fraction with a larger δ than is the case for a-Si. Finally, δ levels off when

only c-Si is being etched and the final, slower roughening phase is reached.

The spectroscopic ellipsometry result does not differ from the single-wavelength ellip-

sometry result in Ref.3, except for the fact that the absolute thickness after long XeF2-

exposure is higher in the single-wavelength ellipsometry measurements. In the single-

7.7. Roughening, initial conditions and reaction layer 91

0 1 2 3 40

5

10

15

20

25

0 1 2 3 40.0

0.1

0.2

c-Si

d r (nm

)

(a)a-Si

(b)

XeF2-dose ( ·104 ML )

Fig. 7.6: (a) Rough layer thickness dr of a-Si(6.4 nm)/c-Si(100) as a function of XeF2-dose. (b)Production coefficient δ as a function of XeF2-dose, as measured by mass spectrometry simultane-ously during the ellipsometry measurement.

wavelength experiment a thicker amorphous silicon layer was initially created using 2.5

keV Ar+-ions, resulting in an a-Si layer thickness of 12 nm. Thus, the moment at which

the transition region will be reached, is shifted in time and more roughness will have

accumulated on the a-Si. More a-Si roughness, i.e. the distance between hills and val-

leys, prior to entering the transition leads to thicker a-Si patches that have a longer

lasting influence on the roughening in the etching of the a-Si/c-Si-interface. Hence, the

absolute rough layer thickness will be larger when a thicker a-Si layer is etched. The

single-wavelength ellipsometry results reported in Ref.3 are therefore in accordance with

the SE results presented here and with the influence of the a-Si/c-Si-interface on the

roughening behavior.

7.7 Roughening, initial conditions and reaction layer

The cartoons in Fig. 7.7 summarize the roughening mechanism discussed for the two

studies presented. On H:Si(100) the initial reaction is delayed (a), etch pits are created at

surface positions where H is removed, resulting in a rapid increase in rough layer thickness

(b)-(d) and goes into the final, slow roughening phase once all H is removed (e). On a-Si

the roughness slowly increases (a), until valleys reach the underlying c-Si (b). A rapid

increase in rough layer thickness is caused by preferential etching of c-Si (c)-(d), until the

a-Si patches are fully removed and the final, slow roughening phase is reached (e).


H:Si(100) a-Si/Si(100)

Ha-Si

etc

h t

ime

(a)

(b)

(c)

(d)

(e)

Fig. 7.7: Schematic representation of various phases of the roughening process on H:Si(100) (left)and a-Si/Si(100) (right) as described in previous sections. On H:Si(100) the initial reaction isdelayed (a), etch pits are created at surface positions where H is removed, resulting in a rapidincrease in rough layer thickness (b)-(d) and going into the final, slow roughening phase once all His removed (e). On the a-Si the roughness slowly increases (a), until valleys reach the underlyingc-Si (b). A rapid increase in rough layer thickness is caused by preferential etching of c-Si (c)-(d),until the a-Si patches are fully removed and the final, slow roughening phase is reached (e).

In both cases the interface layer plays a major role in the roughening behavior. The

observed roughening indicates that Si(100) is preferentially etched over both H-terminated

Si atoms and Si atoms in the amorphous material. As a result, when etching the interface

layer, a fast roughening phase is observed. The absolute roughness prior to entering the

final, slower roughening phase depends on how long the interface remains presents. The

H:Si(100)-interface is on the order of a mono-layer thick and influences the etch process

immediately at the start of XeF2-exposure. The a-Si/Si(100)-interface is on the order of a

few to tens of mono-layers depending on the roughness accumulated while etching the a-

Si-layer. Hence, the time duration of the influence of the interface, but also the moment at

which the fast roughening phase occurs, is determined by the thickness of the amorphous

silicon after sputter-cleaning. The observed absolute roughness before entering the final

roughening phase is the lowest for the H:Si(100)-interface and increases from the buried

a-Si(6.4 nm)/Si(100)-interface in this study to the a-Si(12 nm)/Si(100)-interface in the

single-wavelength study of Ref.3.

The dose dependence of the production coefficient δ is shown to be most likely related

to surface area changes for H:Si(100)-etching, although the slow decrease after the initial

rapid increase is not well understood. It is probably related to a restoration of the surface

area increase, caused by the influence of surface H-atoms, to a more natural surface

morphology. For the a-Si/Si(100)-etching the dose dependence of δ is partly related to

surface area increase and partly by an etch rate difference between a-Si and c-Si. The

7.8. Conclusions 93

observed δ after long XeF2-exposure times is δ=0.09±0.02 for H:Si(100) and 0.11±0.02 for

a-Si/Si(100), which supports the fact that the surface area increase after long exposure

times is larger in the latter case. The exact surface area can be estimated if the (average)

lateral dimension of the roughness features would be known. This information is however

not available at present.

The observation of preferential etching of crystalline Si(100) over amorphous silicon is

in contradiction with molecular dynamics (MD) simulations. MD suggest that a-Si etches

more easily than c-Si.20 If amorphous silicon is etched more easily than the crystalline sil-

icon, it should lead to a delay, or even a decrease, of the roughening when etching through

the amorphous-to-crystalline interface. The preferential etching of crystalline Si(100) over

amorphous silicon, as concluded from the roughening behavior and production probabil-

ity δ, is also observed under SF6/O2 plasma etch conditions by Zijlstra and coworkers.21

They ascribed the etch rate difference to a higher oxygen content in the a-Si surface.

In our case oxygen is not significantly present during the etching and can therefore not

be held responsible for an etch rate difference here. To prove the preferential etching of

crystalline Si(100) over amorphous silicon, the etching of a clean Si(100)-sample should

to be measured. Preparing clean Si(100) is however currently not possible in our setup.

In Sec. 7.2 we have discussed experimental observations of reaction layer thickness and

composition. Furthermore, we have established that roughening of the surface occurs on

time scales on the order of 0.5·103 to 10·103 ML of XeF2-dose with specific influence of the

preparation of the silicon substrates. The SE and QMS study on H:Si(100) shows good

agreement with the observations by Morikawa et al.. First, the etch process is delayed by

the H-termination. Second, the observed roughening dynamics implies the creation of high

aspect-ratio etch pits and, thus, an increase in the total number of surface atoms (=surface

area increase). The fast roughening phase can be seen on identical XeF2-exposure times as

the increase and change in composition of SiFx-species observed in XPS measurements.2,7

We conclude that the surface morphology is an important aspect when measuring the

reaction layer thickness and composition. Furthermore, the reaction layer thickness and

composition may vary depending on the preparation method of the silicon substrates and

the duration of XeF2-exposure. Different roughening behavior as a function of XeF2-dose

has been observed and explained in relation to sample preparation.

7.8 Conclusions

Spectroscopic ellipsometry has been applied to characterize surface roughening as a result

of XeF2 etching of interface layers on Si(100), in particular H:Si(100) and a-Si/Si(100).

The roughening shows in both cases initially a fast roughening followed by a slower rough-

ening phase. The initial conditions of the surface prior to the etching, whether the sur-

face is prepared by HF-treatment or sputter-cleaning by ion bombardment, have an im-


portant influence the roughening dynamics as a function of XeF2-exposure time. The

H-terminated Si(100) surface is stable to the XeF2, which delays the onset of the etch-

ing. Consequently, surface regions where H-atoms have been removed, are preferentially

etched. This leads to a rapid increase in rough layer thickness. Once all surface H-atoms

are removed, the roughening shows a slower, final roughening phase. A similar scenario is

observed when etching the amorphous-to-crystalline silicon interface. Preferential etching

of crystalline over amorphous silicon when etching through the a-Si/Si(100)-interface re-

sults in a fast roughening phase. The roughness accumulated when etching the a-Si layer,

which is proportional to the thickness of the initial a-Si layer, determines the duration

of preferential etching and, thus, the absolute rough layer thickness at the end of the

fast roughening phase. These roughening mechanisms lead to high-aspect ratio etch pits

and, as a result, a significant increase of the number of Si surface atoms, i.e. surface area

increase. The corresponding surface morphology changes are of major influence on the

SiF4 product formation, i.e. etch rate, and the observed SiFx reaction layer thickness and

composition as measured with XPS.2,7







References

1 D. Chen and J. J. Boland, Phys. Rev. B 70, 205432 (2004).







8 R. C. Hefty, J. R. Holt, M. R. Tate, D. B. Gosalvez, M. F. Bertino, and S. T. Ceyer, Phys. Rev. Lett.92, 188302 (2004).

9 R. Q. Zhang, Y. L. Zhao, and Boon K. Teo, Phys. Rev. B. 69, 125319 (2004).

References 95

10 One mono-layer (ML) of silicon-fluoride is the equivalent of 1 ML of Si atoms with two F-atoms perSi-atom.

11 F. R. McFeely, J. F. Morar, N. D. Shinn, G. Landgren, and F. J. Himpsel, Phys. Rev. B. 30, 764(1984).

12 David Humbird and David B. Graves, J. App. Phys. 96, 791 (2004).

13 J. A. Yarmoff and F. R. McFeely, Phys. Rev. B. 38, 2057 (1988).



16 G. E. Jellison, Jr. and F. A. Modine, J. Appl. Phys. 76, 3758 (1994).



19 A. A. E. Stevens, W. M. M. Kessels, M. C. M. van de Sanden, and H. C. W. Beijerinck, submitted toJ. Vac. Sci. Technol. A.

20 D. Humbird and D. B. Graves, J. Vac. Sci. Technol. A 23, 31 (2005).

21 T. Zijlstra, E. van der Drift, M. J. A. de Dood, E. Snoeks, and A. Polman, J. Vac. Sci. Technol. B17, 2734 (1999).

Chapter 8

Spectroscopic second-harmonic generation during

XeF2 etching of H-terminated Si(100)

Abstract

Real-time and spectroscopic second-harmonic generation (SHG) has been applied to studysurface Si-Si bonds in XeF2 etch dynamics of Si(100). On a fully fluorinated Si(100)surface the SH spectrum reveals two surface resonance contributions with SH photonenergies 3.27 eV and 3.46 eV during XeF2 exposure in the 2.7-3.5 eV second-harmonic(SH) photon energy range. The former resonance is related to bulk-like E′

0/E1 Si-Si inter-band transitions modified by the bonding to F-atoms. The SH dynamics observed duringXeF2 etching of H-terminated Si(100) can be explained in terms of a change of the surfaceelectronic states from a H-terminated to a F-terminated Si(100) surface. After terminationof the XeF2-exposure, a change in SH spectrum is observed which is potentially relatedto reconstruction within the silicon-fluoride reaction layer.

8.1 Introduction

Dry etching of silicon plays an essential role in semiconductor technology. Key issue in the

etch processing of silicon surfaces is to produce well-defined, low-damage surfaces. Bet-

ter understanding of the atomic-scale reaction dynamics between halogens and Si(100)

surfaces can aid in meeting the technological demands for next generation semiconduc-

tor devices. Second Harmonic Generation (SHG) has the potential to directly measure

the electronic states related to surface Si-Si bonds as has been demonstrated on clean

and hydrogen-terminated silicon surfaces,1–3 native oxide (NO) on silicon,1,4–6 and silicon

surfaces exposed to halogens.7,8 In this report, we investigate XeF2 etching of hydrogen-

terminated (H:)Si(100) using SHG both spectroscopically, in SH photon energy range

between 2.7-3.5 eV, and in real-time. In this SH photon energy range, surface Si-Si

bonds are probed and have been characterized in real-time, during etching of silicon in

an Ar+/XeF2 beam etching experiment.9–11

Etching of H:Si(100) with XeF2 has a complex dynamic behavior involving the tran-

sition from H:Si(100) to a fluorinated (F:)Si(100) surface with simultaneous roughening

97

98 Chapter 8. Spectroscopic second-harmonic generation during XeF2 etching of H-terminated Si(100)

of the surface. Also, the start of etching of H:Si(100) is delayed as hydrogen termina-

tion results in a fairly stable surface and the removal of all H requires long exposure to

XeF2 (∼104 ML XeF2-dose).12 The fact that H:Si(100) is a stable surface, is also known

for oxidation of H:Si(100) in ambient air.13 This delay in etching has been corroborated

with mass spectrometry (QMS) and spectroscopic ellipsometry (SE) measurements in our

experiment.11 The SE experiments also showed that XeF2 etching leads to significant

roughening of the surface. SHG could in principle elaborate on issues such as the stabil-

ity of H:Si(100) to XeF2-exposure, the influence of chemisorbed F-atoms on surface Si-Si

bonds, the transition from a H-terminated to a F-terminated surface during XeF2-etching.

Within the electric-dipole approximation, SHG is described by a second-order nonlin-

ear polarization ~P (2)(2ω) in a medium induced by an incident electric field ~E(ω),

~P (2)(2ω) = ε0 χ(2)(2ω) : ~E(ω) ~E(ω), (8.1)

where χ(2)(2ω) is the nonlinear susceptibility tensor. SHG is forbidden in the bulk of

centro-symmetric materials, such as c-Si, as in these media symmetry considerations im-

ply χ(2)=0. However, at a surface or interface the symmetry is broken and χ(2) is non-zero,

thereby making the technique of SHG particularly surface and interface sensitive. Micro-

scopically, SHG is the conversion of two photons with energy ~ω into a single photon with

energy 2~ω. The process of SHG is resonantly enhanced when the photon energy of either

the fundamental or the SH radiation coincides with the energy of an electronic transition

in the material, resulting in a sum of one or more resonance features in SH spectra. Con-

sequently, SHG is a technique that is potentially sensitive to both the symmetry and the

electronic states of surfaces and interfaces.

To be able to distinguish the various contributions to the SH signal and, thus, identify

the microscopic origin of the various resonance contributions, the SH intensity spectra

I(2ω) can be reproduced with a coherent superposition of critical-point-like (CP) reso-

nances: 1,4,6,14,15

I(2ω) =

∣∣∣∣∣∑

L

∑

αβγ

AL,αβγ(ω, θ) χ(2)L,αβγ(2ω)

∣∣∣∣∣

2

I2(ω), (8.2)

where the nonlinear nonlinear susceptibility tensor element χ(2)L,αβγ can be approximated

by a sum of CP-resonances with excitonic line shapes, defined as:

χ(2)L,αβγ(2ω) =

∑p

χ(2)L,αβγ,q(2ω; ωq, hq, Γq, φq) =

∑p

hq eiφq

2ω − ωq + iΓq

, (8.3)

with resonance amplitude hq, excitonic phase φq, frequency ωq and line width Γq. The

subscript L denotes the spatial, macroscopic origin (e.g. L = S for surface and L = I

for interface), αβγ denotes the specific element of the nonlinear susceptibility tensor

χ(2)(2ω) and q denotes the specific CP-resonance contribution χ(2)L,αβγ,q(2ω; ωq, hq, Γq, φq).

8.2. SHG in beam etching 99

The complex functions AL,αβγ(ω, θ) represent the linear propagation of the fundamental

and SH radiation through the system including absorption, refraction and interference

from multiple reflections for the fundamental and SH photon energy in the system. The

propagation depends on the angle of incidence θ, the radiation frequency ω and the specific

element of the nonlinear susceptibility tensor χ(2), and is obtained by assessing the fresnel

coefficients in an interface region between two media, which is treated as a polarized sheet

placed in an infinitesimal vacuum gap between the two media, where the SH radiation is

generated.14,16,17

For the study presented here, SH intensity spectra have been measured for p-polarized

fundamental and SH radiation (pin, pout). For The SH spectra measured for this polar-

ization combination have been analyzed with the assumption that the SH signal arises

from χ(2)S,zzz(2ω) for which the fresnel coefficients are much larger than for other tensor

elements in our configuration as follows from the assessment of the propagation functions

AS,αβγ(ω, θ). Here, the subscript L, αβγ = S, zzz is further ignored and, hence, the SH

spectra have been reproduced by a simplified version of Eq. 8.2:

I(2ω) =

∣∣∣∣∣A(ω, θ)∑

q

χ(2)p (2ω; ωq, hq, Γq, φq)

∣∣∣∣∣

2

I2(ω). (8.4)

Using this model to analyze SH spectra we have identified the contributions to the

SH signal, as listed in Tab. 8.1. SH spectra measured on H:Si(100) and on NO-Si(100)

showed good agreement with literature.1,6 Recently, we have also shown that during Ar+-

ion bombardment of Si(100), the SH spectra can be reproduced by a coherent sum of one

surface and one interface resonance contributions.14 Here, we present the spectroscopic

SHG results on H:Si(100) and F:Si(100) (in Sec. 8.3). Next, the real-time SHG at dif-

ferent probe wavelengths during XeF2 etching of H:Si(100) will be described in Sec. 8.4.

The observed SH dynamics has been modeled by assuming a time-dependent change in

surface resonance contributions related to the disappearance of H:Si(100) and the ap-

pearance of F:Si(100) resonances. Finally, the macroscopic and microscopic origin of the

resonance contributions to the SH measurements presented in this work will be reviewed

and discussed (Sec. 8.5). First, in Sec. 8.2 we described the experimental details.

8.2 SHG in beam etching

8.2.1 high-vacuum setup

The experimental setup has been described extensively in previous publications.9,10,18 Fig-

ure 8.1 shows a cross section of the setup. The main processing chamber has a background

pressure of 10−8 Torr. The setup is equipped with a load-lock system for sample storage

(p <10−8 Torr) and easy sample exchange. A single-wavelength ellipsometer (SWE) to


Tab. 8.1: Overview of the χ(2)q (2ω; ωq, hq,Γq, φq)-resonance contributions to the SH signal derived

from modeling of SH spectra measured for polarization combination (pin, pout) on the varioussystems studied in the SHG configuration described in this report. The analysis of SH spectra hasbeen performed in all case with the assumption that the SH signal arises from χ

(2)L,zzz(2ω). The

subscript q denotes the specific CP resonance contribution. The macroscopic origin L is given inthe last column. The phase factor φq denotes a phase difference between resonances when morethan one resonance is present, otherwise φq=0. The error margins in the resonance parameters aretypically ∆ωq= 0.001 eV/~, ∆hq=0.01 (a.u.), ∆Γq=0.002 eV/~ and ∆φq=0.03 rad.

system χ(2)q (2ω; ωq, hq, Γq, φq)-resonances macroscopic origin L

native oxide on Si(100) χ(2)NO1(2ω; 3.34, 0.052, 0.094, 0) + Si(100)/SiO2-interface

χ(2)NO2(2ω; 3.53, 0.040, 0.091, 4.96) Si(100)/SiO2-interface

a-Si/c-Si ∗ χ(2)S (2ω; 3.36, 0.25, 0.5, 0) + a-Si-surface

χ(2)I (2ω; 3.53, 0.19, 0.11, 3.95) a-Si/Si(100)-interface

H:Si(100) † χ(2)H (2ω; 3.33, 0.052, 0.13,0) H:Si(100)-surface

F:Si(100), XeF2 on † χ(2)F1(2ω; 3.27, 0.008, 0.07, 0) + F:Si(100)-surface

χ(2)F2(2ω; 3.46, 0.027, 0.08, 1.57) F:Si(100)-surface

F:Si(100), XeF2 off † χ(2)F1(2ω; 3.27, 0.006, 0.04, 0) + F:Si(100)-surface

χ(2)F2(2ω; 3.46, 0.019, 0.10, 2.36) F:Si(100)-surface

∗ Ref.14† this work

measure roughness and layer thicknesses and a mass spectrometer (QMS) to monitor etch

products can be employed simultaneously with the SHG measurements.

The XeF2 source positioned at a 52 angle with respect to the surface normal. The

temperature of a storage vessel containing XeF2 crystals is controlled between 0C and

25C. This way the vapor pressure of the XeF2 and, ultimately, the XeF2 sample flux can

be controlled. From the vessel the XeF2-vapor flows through a flow resistance (0.17 mm

diameter, 10 mm length) to a multichannel array (16 µm diameter, 450 µm long channels

in stainless steel) to ensure a wide dynamic range of fluxes and an extremely narrow, 3

mm FWHM, beam of XeF2 molecules. The XeF2 flux can be varied this way between

0.06 and 3.6 mono-layers per second (ML s−1).9 In this study a XeF2 flux of 1 ML s−1

has been used.

8.2.2 Si(100) samples and preparation

The silicon samples used in this study are n-type Si(100) with a resistivity of 10-30 Ωcm.

The 10×10 mm2 Si substrates are pre-treated to remove the native oxide in a 2 % hy-

drofluoric acid (HF) solution for 2 minutes after ultrasonic cleaning with ethanol at 40C.

This leads to a mono-, di- and trihydride-terminated Si substrates with mostly dihydrides

and with an initial roughness of typically 0.6-1.0 nm measured with spectroscopic el-

8.2. SHG in beam etching 101

Magnetic

linear drive

loadlock

UHV chamber

detector

chamber

2

11. Sample rotator

2. XeF2 source

3. Ar+-ion source3

lens

polarizer

filter

Ti:Sapphire

~90 fs, 80 MHz

920 - 710 nm, 1.35 - 1.75 eV5 W cw

532 nm

lens

prism PellinBroca

slit

photomultiplier

filter

polarizer

pinhole

compensator

ω

ω

2ω2

Nd:YVO4

Fig. 8.1: Horizontal cross section of the ultra high vacuum chamber and the optical setup. Thesamples are placed in a rotatable sample holder (1) and can be replaced using a load lock. TheXeF2 source (2) and the Ar+-ion gun (3)(Nonsequitur Technologies, customized version of ModelLEIG-2, Eion=10-2000 eV) are positioned at 52 and 45 with respect to the sample surfacenormal. The fundamental laser radiation, provided by a Ti:Sapphire laser, and the generated SHGradiation propagate through the setup at 74 angle of incidence with respect to the sample surfacenormal. Detection of the SH radiation takes place by a photomultiplier tube connected to photoncounting electronics.

lipsometry (SE) and ∼0.15 nm root-mean-square roughness measured with atomic force

microscopy (NT-MDT Solver P47) in non-contact mode (scan size: 1.5×1.5 µm). The Si

samples are mounted on sample holders and are placed in a storage system. The storage

system with the samples is transferred into the load lock, which is then evacuated. This

procedure takes about 10 minutes, which is sufficient to prevent renewed oxidation of the

H-terminated silicon (H:Si).19 The samples are oriented at an azimuthal angle of 45 with

respect to the [001] crystal axis. All experiments presented here have been carried out at

room temperature.

8.2.3 SHG optical setup

A Ti:Sapphire oscillator (Spectra Physics (SP) Tsunami) with broadband optics, which is

pumped by an intra-cavity doubled continuous-wave Nd:YVO4 laser (SP Millennia Vsj),

is used to generate the fundamental laser radiation. The laser pulses have a pulse duration

of ∼90 fs, a repetition rate of 80 MHz and the photon energy is tunable between 1.35


- 1.75 eV (920-710 nm). The laser beam is guided to the sample in the high-vacuum

setup with broadband silver coated mirrors (New Focus (NF) 5103). A variable wave

plate (NF 5540) and a Glan-Thompson polarizer (NF 5525) have been used to select the

desired polarization of the fundamental radiation and to set the power of the laser beam

at the sample to typically 50 mW. Any radiation at the second-harmonic (SH) wavelength

generated in the laser or in optical components in the beam path is suppressed using a color

filter (Schott OG 570). The fundamental beam enters and leaves the vacuum chamber

through stress free fused silica view ports at 74 angle with respect to the sample surface

normal. The fundamental radiation is focused onto the sample using a BK7 lens (CVI

PLCX 25.4-103.0-C) to a spot with an estimated radius of 100 µm, which leads to a typical

fluence of 2 µJ/cm2 per pulse. The reflected beam passes a second polarizer (Thorlabs

GL10A) to select the desired polarization of the second-harmonic radiation. Two color

filters (Schott BG40) are used to suppress most of the fundamental radiation. Next,

the beam is focused with a lens (CVI PLCX 25.4-64.4-C) onto a slit placed in front of a

photomultiplier tube (Hamamatsu R585). Before passing the slit, a 90 prism and a Pellin

Broca dispersion prism spatially separate the remaining fundamental radiation from the

SH radiation and the slit is positioned such that only the SH radiation is allowed to pass

and to be detected by the photomultiplier tube. The photomultiplier tube is connected to

photon counting electronics to record the SH signal. The dark count rate of this detection

scheme was below 4 Hz.

Spectroscopic SHG measurements are performed by tuning the fundamental radiation

wavelength of the Ti:Sapphire laser. The laser pulse width is set to a FWHM of ∼12 nm

(0.02-0.03 eV) for each laser wavelength using a spectrometer (Ocean Optics USB2000).

Next, the power is set and the SH intensity is recorded. The measurement of a SH

spectrum takes typically 1-1.5 hour by this procedure.

All results presented here are obtained at p-polarized fundamental and SH radiation.

This polarization setting resulted, in this case, in at least 40× higher SH intensities

as compared to other polarization configurations. The 74 angle of incidence is mostly

responsible for this as it results in a large electric field component in the z-direction,

perpendicular to the surface. Consequently, the fresnel coefficients of the χ(2)zzz-element of

second-order nonlinear susceptibility tensor of the Si(100)-surface 20 are much larger than

the fresnel coefficients of all other tensor elements.

The SH intensity I(2ω) has been calculated from the measured SH signal after cor-

rection for the laser intensity and the response of the optical system. The response of

the optical system has been determined using independent transmission measurements

of polarizers and filters, and the wavelength dependent detection efficiency of the photo-

multiplier tube. The resulting sum response of the optical system was then verified by

measuring the SH spectrum on z -cut α-quartz sample. Quartz is often used as a reference

in SHG experiments,21,22 as its SH signal should be independent of wavelength in the

8.3. Spectroscopic SHG from fluorinated Si(100) 103

2.6 2.8 3.0 3.2 3.4 3.60.0

0.1

0.2

0.3

2.6 2.8 3.0 3.2 3.4 3.60.0

0.2

0.4

0.6

0.8

1.0

Qua

rtz S

H s

igna

l (ar

b. u

nits

)


Nor

m. s

yste

m re

spon

se (-

)


Fig. 8.2: SH spectrum measured on single-side polished z -cut α-quartz (left ordinate) and thenormalized response of the optical system (right ordinate), which is obtained from independenttransmission measurements of filters and polarizers and the detection efficiency of the photomulti-plier tube. Correction of the quartz SH spectrum for optical response results in a nearly constantSH signal, independent of photon energy.

visible range.

Figure 8.2 shows the system response (line) and the SH spectrum measured on quartz

(circles) for p-polarized fundamental and SH radiation. Correction of the quartz-spectrum

for the optical response would lead to a SH spectrum almost fully independent of SH

photon energy with implies that no significant dispersion and/or diffraction-limitations

need to be accounted for. By keeping the measurement procedure for all the spectra

presented here identical, this calibration method allows us to correct the spectra for the

transmission characteristics of the optical elements and the detection efficiency of the

photomultiplier tube.

8.3 Spectroscopic SHG from fluorinated Si(100)

Spectroscopic SHG from H:Si(100) and F:Si(100) has been investigated to determine the

resonance contributions to the SH signal. SH spectra have been measured before, during

and after exposure to XeF2 as shown in Fig. 8.3. The H:Si(100) spectrum, measured

before XeF2-exposure, shows a symmetric peak at 3.33 eV, similar to what has been

reported in literature.1,4 The SH spectrum of F:Si(100) during XeF2-dosing is measured

after an exposure of the initially H:Si(100) surface to ∼104 ML of XeF2 to assure that

all H-atoms are removed from the surface in the etch process. While measuring the SH

spectrum during XeF2-dosing, the etching continues and the surface roughness increases

from 12 nm to 13 nm as measured by single-wavelength ellipsometry. The 1 nm increase

in roughness during the measurement is believed not to be of significant influence on the


2.6 2.8 3.0 3.2 3.4 3.60.0

0.2

0.4

0.6

0.8 H:Si(100) during XeF2 exposure after XeF2 exposure

SH

inte

nsity

(arb

. uni

ts)


Fig. 8.3: SH spectra measured on H-terminated Si(100) (triangles) and during (squares) and after(circles) XeF2-exposure of Si(100). The measurements are performed after long exposure of thesample to XeF2 to ensure the removal of all hydrogen from the intially H:Si(100)-surface. Thelines are fits to the measurements using two surface contributions in the CP-resonance model.

2.6 2.8 3.0 3.2 3.4 3.60.00

0.05

0.10

0.15

(2)F2

(2)F1

(2)H

|(2

)p|2


Fig. 8.4: Resonances obtained from fits with the CP-resonance model to the SH spectra in Fig. 8.3measured on H:Si(100) (dotted line) and on F:Si(100) during (solid lines) and after (dashed lines)XeF2 exposure. On F:Si(100) two surface resonances have been found: χ

(2)F1 with a resonance

energy 3.27 eV (thick lines) and χ(2)F2

with a resonance energy at 3.46 eV (thin lines).

measured spectrum.

The SH spectrum during XeF2 exposure shows two maxima with a minimum in SH

intensity at ∼3.30 eV. This is indicative for at least two resonance contributions to the

F:Si(100) spectrum. A phase difference between two resonance contributions can be re-

sponsible for the fact that the peaks in the measured SH spectrum of F:Si(100) appear

8.3. Spectroscopic SHG from fluorinated Si(100) 105

non-symmetric. Destructive interference between two resonances may result in a mini-

mum in the SH intensity, as is observed at ∼3.30 eV.

Next, XeF2-dosing is terminated and after 600 s again a SH spectrum is measured.

The SH spectrum after exposure to XeF2 shows only one maximum. Apparently, the

surface states that are being probed are different during and after exposure to XeF2.

To identify the resonance contributions to the SH signal, the SH spectra have been

reproduced with the model described in Sec. 8.1. For simplicity, we assume that the res-

onances in the measured spectra arise from 2ω-resonance features in the surface region.

The resonance parameters hq, ωq, Γq and phase φq are fit parameters. Two 2ω-resonance

contributions, χ(2)F1 and χ

(2)F2, have been used to fit the F:Si(100) spectra and one contri-

bution, χ(2)H , for the H:Si(100) spectrum. The fits are the lines through the data points in

Fig. 8.3. The resulting resonances χ(2)H , χ

(2)F1 and χ

(2)F2 are shown in Fig. 8.4. The resulting

fit parameter values are listed in Tab. 8.1. For H:Si(100) the CP resonance is located at

~ωH=3.33 eV. For both F:Si(100) spectra the resonance frequencies of the two resonance

contributions are found to be ~ωF1=3.27 eV and ~ωF2=3.46 eV. The primary difference

between the spectra during and after XeF2 is a phase difference change between the two

resonances, resulting in a destructive interference during XeF2-dosing and, thus, a min-

imum in SH intensity at 3.30 eV, and constructive interference after the XeF2-dosing

is terminated. Furthermore, the resonance amplitude of both resonances changes after

termination of the XeF2-dosing. The amplitude of hF1 increases and the amplitude hF2

decreases.

Clearly, the surface states that are being probed are different when hydrogen or flu-

orine, is chemisorbed on the surface. For H:Si(100) the observed resonance is located at

3.33 eV SH photon energy, which is close to bulk silicon E ′0/E1 direct inter-band tran-

sitions as known for the linear optical properties of Si.23 The microscopic origin of the

χ(2)H -resonance is related to the same direct inter-band transitions in Si-Si bonds, but is

slightly red-shifted due to the presence of the vacuum-H:Si(100) interface and chemisorbed

H-atoms.1 The microscopic origin of the two F:Si(100)-resonances is less clear. However,

the differences in the SH spectra that have been observed during and after XeF2-dosing is

a strong indication that both resonances are surface Si-Si states influenced by the presence

of chemisorbed F-atoms. The changes in amplitudes and the change in phase difference

could be related to a reconstruction within the silicon-fluoride layer after termination of

the XeF2-dosing. A reconstruction within the silicon-fluoride layer then changes the influ-

ence of chemisorbed F-atoms on the surface Si-Si bond states. Monitoring the real-time

SH signal at various SH photon energies during XeF2 etching of H:Si(100) could give more

insight into the microscopic origin of the F:Si(100)-resonances.


8.4 SHG during XeF2 etching of H:Si(100)

As mentioned in the introduction, XeF2 etching of H:Si(100) has a complex dynamic

behavior. The H-terminated Si(100) is fairly stable to XeF2. This results in a delay in the

start of etch product formation. Consequently, a slow transition from a fully H-terminated

to a fully F-terminated Si(100) surface can be expected. To investigate this behavior, the

SH signal has been measured on seven samples at different SH photon energies during

the XeF2 etching of H:Si(100). The start of the actual etching occurs at D0 =900 ML as

determined by mass spectrometry and ellipsometry. Variations in D0, i.e. the XeF2-dose

before the start of the etching, of 150 ML have been observed as a result of variations

in background XeF2 in the vacuum chamber between subsequent SH measurements on

different samples. The real-time SH signal as a function of XeF2 etch-dose D − D0 in

mono-layers (ML) is shown in Fig. 8.5 as measured at (a) 3.44, (b) 3.40, (c) 3.34, (d)

3.30, (e) 3.22, (f) 3.02 and (g) 2.76 eV SH photon energy. For each measurement a new

H:Si(100) sample is used.

Exposure of the H-terminated Si(100) surface to XeF2 results, between D = 0 and

D = D0, in a decrease in SH signal at SH photon energies above 3.35 eV, followed by an

increase in SH signal over the full SH photon energy range, as shown in Fig. 8.5. Once

the etching starts at D = D0, the SH signal decreases over the full SH photon energy

range. Above 3.30 eV the SH signal drops to zero and subsequently increases again at

longer exposure times. Below 3.3 eV the SH signal decreases slowly to lower values, with

a minimum SH intensity at 3.3 eV. A SH spectrum constructed from these real-time

measurements at a XeF2-dose of 2000 ML results in a SH spectrum consistent with the

spectrum shown in Fig. 8.3. First of all, the SH signal shows dynamics prior to the actual

etching (D − D0 < 0) of the H-terminated Si(100). Mass spectrometry does not show

etch products being created and ellipsometry does not show any surface change. SHG is,

however, already sensitive to surface changes upon XeF2-exposure prior to etch product

formation. The observation of a delay in the start of the actual etching and Si-H on the

surface even after long exposure to XeF2,12 suggests that the H:Si(100) is fairly stable to

XeF2. The fact that H:Si(100) is a stable surface, is also known for oxidation of H:Si(100)

in ambient air.13 We believe that the observed dynamics in the SH signal is related to

the initial reaction of F-atoms with H-terminated silicon surfaces. Due to the stability of

the H:Si(100) surface, F-atoms have to react with Si-Si back bonds or surface defect sites

which are more susceptible to F-atoms. The change in surface states by this reaction is

then the reason of the observed dynamics in SH response. Hence, the details of the initial

reactions of XeF2 with H:Si(100) can in principle be investigated by SHG. Here, we focus

on the dynamics occurring in the SH signal once the actual etching starts at (D−D0)> 0.

In an attempt to quantify the physical picture of a transition from H:Si(100)-related

surface states to F:Si(100)-related surface states, we have reproduced the observed SH

8.4. SHG during XeF2 etching of H:Si(100) 107

-1 0 1 2 3 40.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.00.0

0.5

1.0

0.0

0.5

1.0

D-D0 ( 103 ML)

p

(2)

p|2

SH

inte

nsity

(arb

. uni

ts)

(c) 3.34 eV

(b) 3.40 eV

(g) 2.76 eV

(f) 3.02 eV

(e) 3.22 eV

(d) 3.30 eV

(a) 3.44 eV

Fig. 8.5: Real-time SH signal of H:Si(100) as function of XeF2-dose D−D0 measured at (a) 3.44eV, (b) 3.40 eV, (c) 3.34 eV, (d) 3.30 eV, (e) 3.22 eV, (f) 3.02 eV and (g) 2.76 eV SH photon energy.XeF2-dosing of the H:Si(100) samples start approx. at D−D0=-900 ML (D0=900±150 ML) withsome sample-to-sample fluctuations. The actual etching of the H:Si(100) starts at D −D0=0 ML(=t0). The lines starting at D −D0=0 ML dose are results from simulations based on Eq. 8.5.

dynamics by making use of the three resonances χ(2)H , χ

(2)F1 and χ

(2)F2, as determined in

Sec. 8.3. In order to do so, we have assumed that the SH dynamics is described by a

coherent superposition of these resonance with different weights as a function of time.

Hence, initially the surface state is described by χ(2)H and at the end, when all H-atoms

have been removed from the surface, the surface state is described by χ(2)F1 and χ

(2)F2. Then,

in the coherent superposition of all three resonances, the weight of χ(2)H has to decrease


and the weights of χ(2)F1 and χ

(2)F2 have to increase as a function of time. In the simulation,

the resonance amplitudes hH , hF1 and hF2 have been used as the weights of the various

resonance contributions.

However, when the etching starts, the surface is already a mixture of H and F bonded

Si surface atoms, as mentioned above. To be able to quantitatively described the SH

intensity at D0, we need an additional resonance at 3.54 eV. This resonance is assumed

to be χ(2)F2 with its resonance parameters, as listed in Tab. 8.1, except the resonance

position is 3.54 eV SH photon energy instead of 3.46 eV. Hence, at D0 the SH intensity

is described with resonance χ(2)H and χ

(2)F2 with the new resonance position 3.54 eV and

a phase difference φH of 1.57 rad. This phase difference has been taken equal to the

phase difference between χ(2)F1 and χ

(2)F2 and, thus, the phase difference between χ

(2)H and

χ(2)F1 is assumed to be 0. Without phase difference between χ

(2)H and χ

(2)F1 the resonances

will not destructively interfere, which was necessary to obtain a good agreement between

measured and simulated SH dynamics below 3.30 eV SH photon energy.

In summary, the resonance amplitudes represent the weights of the three resonance

contributions, for which hH(D0) = 0.052 → hH(D →∞) = 0 and

hF1(D0) = 0 → hF1(D →∞) = 0.008. The resonance amplitude hF2 remains constant,

instead the resonance frequency is allowed to red-shift:

ωF2(D0) = 3.54 eV/~→ ωF2(D →∞) = 3.46 eV/~. The phase differences between the

resonances is given by φH = φF1 = 1.57 rad and φF2 = 0. Then, by incorporating these

assumptions in Eq. 8.4, the SH dynamics is simulated by:

I(2ω) = |A(ω, θ)|2 | χ(2)H (2ω; ωH , hH(D −D0), γH , φH) +

χ(2)F1(2ω; ωF1, hF1(D −D0), ΓF1, φF1) +

χ(2)F2(2ω; ωF2(D −D0), hF2, ΓF2, 0) |2 I2(ω),

(8.5)

where the parameters hH(D−D0), hF1(D−D0) and ωF2(D−D0) are the only parameters

that change as a function of etch-dose D −D0 with exponential functions:

hH(D −D0) = 0.052 exp (−(D −D0)/∆τ ) (8.6)

hF1(D −D0) = 0.008 (1− exp (−(D −D0)/∆τ )) (8.7)

ωF2(D −D0) = 3.46 (1 + 0.08 exp (−(D −D0)/∆τ )) eV/~ , (8.8)

where the 1/e constant of the exponential functions ∆τ=825 ML has been kept the same

for all three parameters and has been optimized to reproduce the real-time SH measure-

ments as accurately as possible. The results from the simulations for the various SH

photon energies are shown in Fig. 8.5.

The simulation result presented here may not be unique, since a lot of parameters can

potentially change. However, various simulation attempts showed extreme sensitivity for

the choice of resonance parameters and their values that are allowed to change in time.

One example that gave similar simulation results is a simulation where χ(2)H gradually

8.5. Discussion on microscopic origin of SHG 109

changes into χ(2)F1 and χ

(2)F2 changes in the same fashion as described above, i.e. a red-

shift in ωF2. For this simulation also fH , γH , and ωH were allowed to change in time

to the values corresponding to the parameter values of resonance χ(2)F1. This implies that

resonance χ(2)H and χ

(2)F1 have probably the same microscopic origin. Resonance χ

(2)F1 located

at 3.27 eV is, therefore, most likely also related to bulk-like E ′0/E1 surface Si-Si states.

The microscopic origin of resonance χ(2)F2 will be discussed in Sec. 8.5.

The straightforward and simple simulation based on a physical picture as presented

here uses only three parameters and shows a very good quantitative agreement with the

measured SH dynamics during XeF2 etching for all SH photon energies. This simulation

implies that the observed SH dynamics is in fact related to the transition from a H:Si(100)

surface with a single resonance to a F:Si(100) surface with two resonances. The H:Si(100)

is fairly stable to XeF2 molecules, which delays the start of the etching. The F-atoms

is believed to react initially with Si-Si back bonds or defect sites on the surface that are

susceptible to F-atoms. Eventually, H-atoms are removed through SiFxHy etch product

formation. In time, this leads to the decrease in H-terminated surface and the increase

in F-terminated surface. The total SH signal then arises from the coherent sum of SH

signals generated by χ(2)H , χ

(2)F1 and χ

(2)F2 resonance sources with different weights and their

phase differences. A minimum in the real-time SH signal has been observed above 3.30 eV

SH photon energy as a result of destructive interference when the χ(2)H and χ

(2)F2 generate

SH signal with similar weights. Once the surface is fully fluorinated the SH signal arises

only from χ(2)F1 and χ

(2)F2 resonance contributions. As a result the SH intensity saturates at

constant values for the various SH photon energies.

From the simulation it can be estimated that steady-state F:Si(100) is achieved after

(D −D0)≈5·103 ML, which is on the order of the observed timescale for the removal of

all H-atoms from the surface.12 In other words, a dose of 5000 ML XeF2 is required to

remove all H-atoms from the surface. If we now assume that 1 ML of H-atoms is present

on the initial surface which is removed in SiF2H2 etch products, we can estimate an etch-

product formation probability of ∼10−4 for SiF2H2 etch products. For comparison, the

etch-product formation probability of SiF4, which is the only etch product during room-

temperature XeF2 etching of clean Si(100) is much larger, typically 10−1.24 The delay in

the start of the etching was found to be approximately 900 ML of XeF2-dose, hence, at

the start of the etching about 10−1 surface sites are occupied by F-atoms.

8.5 Discussion on microscopic origin of SHG

The SH spectra have revealed resonances related to H:Si(100) and F:Si(100). For the

H:Si(100)-surface one 2ω-resonance has been identified at 3.33 eV SH photon energy,

which is close to bulk silicon E ′0/E1 electronic inter-band transitions as known for linear

spectroscopy.23


The microscopic origin of the χ(2)H -resonance is related to bulk-like E ′

0/E1 inter-band

transitions in Si-Si bonds with red-shift in resonance energy due to the presence of the

vacuum-H:Si(100) interface and chemisorbed H-atoms.1 The χ(2)F1-resonance of F:Si(100)

was argued to have the same microscopic origin in Sec 8.4. Resonance χ(2)F1 is however more

red-shifted from the bulk E ′0/E1-resonance than χ

(2)H , which suggest a stronger weakening

of surface Si-Si bonds when bonded to F-atoms with respect to bonding to H-atoms.

The microscopic origin of the χ(2)F2-resonance at 3.46 eV is however not well understood.

Similar to SHG from native oxide (NO) on Si(100) (see Tab. 8.1 and Refs.1,6), the F:Si(100)

spectrum shows two resonances. Considering the similarity in the two-resonance structure

of the SH spectra of F:Si(100) and NO-Si(100), the microscopic origin of both χ(2)F2 and

χ(2)NO2 could very well be similar. The resonance energy of χ

(2)F2 (3.46 eV) is however lower

than χ(2)NO2 (3.52-3.70 eV). Bergfeld et al. assigned this NO-Si(100)-resonance to a specific

Si-SiOx bonding complex at the Si-SiO2-interface.1 Here, the same may be valid for the

χ(2)F2-resonance observed on the F:Si(100)-surface.

In general, the differences between the H:Si(100), NO-Si(100) and F:Si(100) resonance

contributions, such as the resonance energies ωq, suggests an influence of the nature of

the chemisorbed species on the surface Si-Si bond states, e.g., the amount of H/F/O

atoms adsorbed per surface/interface Si and the bonding complexes that are formed. The

differences in the SH spectra that have been observed during and after XeF2-dosing is a

strong indication that both resonances are related to surface Si-Si states influenced by

the presence of chemisorbed F-atoms. A reconstruction within the silicon-fluoride layer

could lead to a change in the total F-atom coverage or a change in the SiFx-species

distribution(x = 1, 2, 3), i.e., a change in the Si-SiFx bonding complexes. In that case,

the influence of chemisorbed F-atoms on the surface Si-Si bond states will be altered and,

subsequently, the SH spectra will be different during and after XeF2-dosing.

Whether some of the contributions in our SH spectra are electric-field-induced-second-

harmonic (EFISH) related 4 is at present difficult to prove or rule out, but it does not

change the conclusions of the SHG experiments presented here.

8.6 Conclusions

Real-time and spectroscopic second-harmonic generation has been demonstrated for XeF2

etching of H:Si(100). A fluorinated Si(100) surface the SH spectrum reveals two surface

contributions with resonance frequencies 3.27 eV and 3.46 eV during XeF2 exposure. The

microscopic origin of the former resonance is related to bulk-like E ′0/E1 inter-band tran-

sitions in Si-Si bonds. The microscopic origin of resonance at 3.46 eV is however not

fully clear. Once the XeF2 exposure is terminated the spectrum shows a phase differ-

ence change between the two surface contributions and a change in both the resonance

amplitudes, which is indicative for a reconstruction within the silicon-fluoride reaction

8.7. Acknowledgements 111

layer. A reconstruction within the silicon-fluoride layer could lead to a change in the total

F-atom coverage or a change in the SiFx-species distribution(x = 1, 2, 3), i.e., a change in

the Si-SiFx bonding complexes. Also, the SH dynamics observed during XeF2 etching of

H-terminated Si(100) has been explained. The physical picture of a slow transition from a

H-terminated Si(100) to a F-terminated Si(100) surface has been implemented in a time-

dependent coherent superposition of resonance contributions. With this model a good

quantitative agreement with the measured SH dynamics of XeF2 etching of H:Si(100) has

been obtained. We presented a clear demonstration of how the SHG observed during the

etching of Si(100) can provide detailed information regarding the etch dynamics. The SH

dynamics simulation only incorporates the change of the surface states where roughening

might be of influence.11 By ignoring the possible influence of roughening of the surface

and still obtaining a good description of the SH dynamics, implies that roughening is

believed not to be extremely important in these SHG experiments.

In general, the SHG studies of Ar+-ion bombardment 14 and XeF2 etching presented

here have demonstrated that SHG is a surface/interface specific diagnostic tool with the

potential to aid in a better understanding of the surface Si-Si bond states in future etch

dynamics studies of ion-assisted (Ar+/XeF2) etching of Si(100).







References

1 S. Bergfeld, B. Braunschweig, and W. Daum, Phys. Rev. Lett. 93, 097402 (2004).

2 U.Hofer, Appl. Phys. A 63, 533 (1996).

3 K. Pedersen and P. Morgen, Phys. Rev. B 52, R2277 (1995).

4 J. I. Dadap, Z. Xu, X. F. Hu, M. C. Downer, N. M. Russel, J. G. Ekerdt, O. A. Aktsipetrov, Phys.Rev. B 56, 13367 (1997).

5 Z. Xu, X. F. Hu, D. Lim, J. G. Ekerdt, M. C. Downer, J. Vac. Sci. Technol. B 15, 1059 (1997).

6 G. Erley, W. Daum, Phys. Rev. B 58, R1734 (1998).

7 S. Haraichi, F. Sasaki, S. Kobayashi, M. Komuro, T. Tani, J. Vac. Sci. Technol. B 13, 745 (1995).

8 S. Haraichi, F. Sasaki, S. Kobayashi, M. Komuro, T. Tani, J. Vac. Sci. Technol. B 15, 871 (1997).




11 A. A. E. Stevens, W. M. M. Kessels, M. C. M. van de Sanden, and H. C. W. Beijerinck, to bepublished.


13 D. Bodlaki and E. Borguet, J. Appl. Phys. 95, 4675 (2004).


15 G. Erley, R. Butz, W. Daum, Phys. Rev. B 59, 2915 (1999).

16 B. Koopmans, A. Anema, H. T. Jonkman, G. A. Sawatzky, and F. van der Woude, Phys. Rev. B 48,2759 (1993).

17 V. Mizrahi and J. E. Sipe, J. Opt. Soc. Am. B 5, 660 (1988).



20 P. Haleri, ed., Photonic probes of surfaces (Elsevier, Amsterdam, 1995), chap. 9, by G. A. Reider andT. F. Heinz.

21 C. Flueraru, C. P. Grover, Appl. Opt. 42, 6666 (2003).

22 Lu R., Wang H. F., Chin. Phys. Lett. 20, 1269 (2003).


24 M. J. M. Vugts, G. L. J. Verschueren, M. F. A. Eurlings, L. J. F. Hermans, and H. C. W. Beijerinck,J. Vac. Sci. Technol. A 14, 2766 (1996).

Chapter 9

Surface roughness and subsurface ion-damage layer

in Ar+-ion assisted XeF2 etching of Si(100):

preliminary results

Abstract

Spectroscopic ellipsometry has been applied to investigate surface roughness and ion-damage layer thickness for ion-assisted etching of Si(100) in an Ar+/XeF2 beam etchingexperiment. The surface roughness shows a decreasing trend for increasing Ar+-to-XeF2-flux ratio R = ΦAr+/ΦXeF2 and shows virtually no dependence on the ion energy in therange of 100-2500 eV. The underlying ion damage layer thickness shows the oppositetrend. If the etching is more chemical of nature, i.e., for ΦXeF2 >> ΦAr+ , the roughnessincreases, whereas if the etching becomes more physical of nature, i.e., for increasing ΦAr+

with respect to the ΦXeF2 , results in a polishing of the surface. These observations arein agreement with earlier reports on the severe roughening for spontaneous XeF2 etchingand the smoothness observed for Ar+-ion bombardment.

With the shrinking of IC and MEMS devices, surfaces and interface become more

and more important. Etching of silicon by means of plasmas causes roughening of the

surface and results in the creation of a subsurface ion damage layer. In Chapters 5, 6

and 7 we have described the separate studies Ar+-ion bombardment and XeF2 etching on

Si(100). These studies demonstrated that Ar+-ion bombardment leads to a subsurface

damage layer with a very low surface roughness (5-15A), whereas XeF2 leads to severe

roughening of the surface. Here, we have combined the two to study the roughening and

subsurface damage layer in an Ar+-ion assisted XeF2 etching situation using spectroscopic

ellipsometry (SE). This allows us to investigate the ion energy dependence and the ion-

to-neutral flux ratio dependence of surface roughness and subsurface ion damage layer.

As known from previous work, ion-to-neutral flux ratio and ion energy are the main

parameters that described the etch mechanism of silicon with Ar+ and XeF2.1,2

The SE measurements have been analyzed with a multi-layer model as shown in

Fig. 9.1. For the dielectric functions of the damaged layer, a Tauc-Lorentz function

model of amorphous silicon (a-Si) is used as determined in Chapter 4. For the crystalline

silicon literature dielectric functions have been used.

113

114

c-Si bulk

a-Si

da-Si

dra-Si void50%

50%

c-Si bulk

dr

a-Si

voidx%

y%

100-x-y% c-Si

(a) (b)

Fig. 9.1: (a) Multi-layer model that has been used to analyze the SE measurements. A roughlayer consisting of 50% voids and 50% a-Si on top of a fully amorphous layer and the semi-infinitec-Si bulk layer. (b) Once the first model fails, a multi-layer model consisting of a rough layer ontop of the c-Si-bulk with a mixture of voids, a-Si and c-Si could be used.

It should be noted that the measurements presented here are limited to the Ar+-

to-XeF2-flux ratio R = ΦAr+/ΦXeF2 and Eion parameter space for which the multi-layer

modeling presented in Fig. 9.1(a) is still valid. Once the rough layer thickness becomes

larger than the underlying a-Si layer, the multi-layer model probably needs to be ad-

justed. In this regime the a-Si layer will probably lay as a thin sheet following the surface

roughness on top of the crystalline bulk. This can be modeled, e.g., with varying c-Si,

a-Si and void percentages, representing the rough, top layer, as shown in Fig. 9.1(b).

In Fig. 9.2 the resulting steady-state a-Si layer thickness da−Si (a) and the rough

layer thickness dr (b) have been shown for a number of ion energies as a function of

flux ratio. With increasing ion energy da−Si becomes larger as can be expected since the

penetration depth of ions with higher energy is larger. For increasing flux ratio, da−Si

increases, whereas dr decreases. Then, above a certain flux ratio, da−Si and dr seem to

saturate to values in agreement with the a-Si and rough layer thickness as observed for

ion-bombardment only (Chapter 4). Furthermore, almost no ion energy dependence in

the roughness is observed. For the lower ion energy (100-300 eV) measurements it can be

seen that the a-Si thickness goes to zero at R ∼10−1. This means that for R <10−1 the

multi-layer model will have to be changed into the more complex multi-layer model.

From spontaneous etch studies (XeF2 only) it is known that the roughness increases

as a function of XeF2-dose to values higher than dr=150 A and has a time dependent

behavior. Ion bombardment showed a steady-state roughness with dr ∼5-15 A, fully in

accordance with the smoothing behavior of ions. The ion-assisted roughness presented

here clearly shows the interplay between chemical and physical roughening: the more

chemical the etching is (low R), the higher the roughness becomes, whereas increasing the

physical-to-chemical ratio (≡ R) of the etch process results in a decrease of the roughness.

Also at low flux ratio chemical etching causes the underlying a-Si layer thickness to de-

crease to the expense of the rough layer thickness. In the limit case where ΦXeF2 >> ΦAr+

the roughness is expected to become fully chemical of nature and, hence, the roughening

is expected to become time-dependent.

115

10-3 10-2 10-1 1000

20

40

60

80

100

120

10-3 10-2 10-1 1000

10

20

30

40

50

60(b)

d a-

Si (Å)

Ar+ / XeF2

(a)

Ar+ / XeF2

Eion

(eV)10020030050010002500

d r (Å)

Fig. 9.2: (a) amorphous, ion damage layer thickness and (b) rough layer thickness as a functionof Ar+/XeF2 flux ratio for a number of ion energies.

To conclude, the surface roughness for ion-assisted etching is primarily Ar+/XeF2

flux ratio dependent and can be qualitatively described as an balance between chemical

etching, causing the surface to roughen, and smoothing by ion-bombardment.

References



117

Summary

An all optical diagnostics approach has been undertaken to reveal new insight into the

reaction dynamics of Ar+/XeF2 beam etching of silicon. As a first step separate studies

of Ar+-ion bombardment of Si and XeF2 etching of Si have been perfomed using real-time

and spectroscopic ellipsometry and second-harmonic generation.

Ion bombardment of Si(100) results in a damaged, amorphous Si (a-Si) layer. By

means of ellipsometry the thickness of the a-Si for Ar+-ion energies between 70 and

2000 eV has been determined. Good agreement has been found between the measured

layer thickness and model predictions from SRIM simulations and molecular-dynamics

(MD) simulations. Ion bombardment results in extremely smooth surfaces with typical

rough layer thicknesses of 0.5-1.0 nm. Also the dynamics of the creation process of the

amorphous layer upon ion bombardment and the relaxation dynamics after termination of

the ion bombardment has been resolved with spectroscopic ellipsometry. The Si-matrix in

the damaged layer is shown to be fully amorphous after exposing the initially crystalline

Si substrate to an equivalent of ∼30 mono-layers (ML) of Ar+-ions. It is suggested that

the relaxation is caused by defect-controlled relaxation in the bulk amorphous silicon.

Ellipsometry has also revealed that the spontaneous, XeF2 etching of hydrogen-terminated

Si(100) results in severe roughening of the surface. The roughness evolution as a func-

tion of XeF2-dose can be characterized by an initially fast roughening phase followed by a

slower, final roughening phase with rough layer thicknesses above 15 nm. Similar behavior

is observed when etching through an amorphous silicon (a-Si) layer on top of crystalline

Si(100) bulk as obtained by sputter-cleaning of Si(100) substrates. Both H-termination

and a-Si lead to patch formation on the surface where etching is impeded and high aspect-

ratio etch pits develop where the underlying crystalline Si(100) is being etched. Surface

roughening was already mentioned in several literature reports to be responsible for con-

flicting experimental results. Here, we have established that surface area increase due to

the roughening is in fact responsible for observed trends in etch rates and reaction layer

thickness and composition as a function of etch time.

Real-time and spectroscopic second-harmonic generation (SHG) has been applied in

the 2.7-3.5 eV second-harmonic (SH) photon energy range to study surface Si-Si bonds in

XeF2 etch dynamics of hydrogen-terminated Si(100). On a hydrogen-terminated Si(100)

a single 2ω-resonance in the SH spectrum is observed at resonance frequencies 3.33 eV.

However, a fully fluorinated Si(100) surface reveals two surface resonances in the SH

spectrum with resonance frequencies 3.27 eV and 3.46 eV during XeF2 exposure. The

former resonance is related to bulk-like E ′0/E1 Si-Si electronic transitions modified by the

bonding to fluorine. At present, the microscopic origin of the latter resonance remains

unknown. The SH dynamics observed during XeF2 etching of H-terminated Si(100) can

118

be explained in terms of a change of the surface electronic states from a H-terminated to

a F-terminated Si(100) surface. Once the XeF2 exposure is terminated a change in SH

spectrum is observed which could be related to reconstructions within the silicon-fluoride

reaction layer.

These separate ellipsometry studies of Ar+-ion bombardment and XeF2 etching of Si

have resulted in a solid basis for the employment of ellipsometry to study ion-assisted

etching. A first step has already been made to determine the subsurface ion-damage

layer and surface roughness during ion-assisted etching of Si(100). If the etching is more

chemical of nature, i.e., for ΦXeF2 >> ΦAr+ , the roughness increases, whereas if the etching

becomes more physical of nature, i.e., for increasing ΦAr+ with respect to the ΦXeF2 , results

in a polishing of the surface. These observations are in agreement with earlier observations

on the severe roughening for spontaneous XeF2 etching and the smoothing observed during

Ar+-ion bombardment. Similar to the observations by mass spectrometry, the roughness

seems to depend predominantly on the Ar+-to-XeF2 flux ratio.

119

Samenvatting

Om nieuwe inzichten te verwerven in de reactiedynamica van Ar+/XeF2 bundeletsen

van silicium, is een diagnostische aanpak met behulp van volledig optische meettechnieken

ondernomen. Als een eerste stap zijn aparte studies van Ar+ ionenbombardement op

Si en XeF2 etsen van Si uitgevoerd waarbij (spectroscopische) ellipsometry en tweede-

harmonische generatie zijn toegepast om het etsproces te monitoren.

Ionenbombardement op Si(100) resulteert in een beschadigde, amorfe Si (a-Si) laag.

Met behulp van spectroscopische ellipsometrie is de dikte van de laag gemeten voor

Ar+ ionenbombardement met ionenenergieen tussen 70 en 2000 eV. De gemeten amorfe

laagdikte komt goed overeen met voorspellingen uit SRIM simulaties en moleculaire-

dynamica (MD) simulaties. Ionenbombardement resulteert tevens in extreem gladde

oppervlakken met een dikte van de ruwe laag van 0.5-1.0 nm. Verder is de dynamica

van het creatieproces van de amorfe laag ten gevolge van ionenbombardement en de

relaxatie van de laag na ionenbombardement tijdsopgelost gemeten met spectroscopische

ellipso-metrie. De Si-matrix is volledig amorf na blootstelling van het initieel krystallijne

Si substraat aan een equivalent van 30 mono-lagen ionen. De relaxatie van de amorfe laag

kan geınterpreteerd worden als een defect-gedreven relaxatie in de bulk van de amorfe

laag.

Met behulp van ellipsometrie is tevens aangetoond dat spontaan, XeF2 etsen van

waterstof-getermineerd Si(100) sterk verruwd. De ruwheid vertoont een karakteristieke

ontwikkeling als functie van de blootstellingsduur aan XeF2 waarbij een initiele, snelle

verruwingsfase opgevolgd wordt door een uiteindelijke, langzame verruwingsfase met een

dikte van de ruwe laag groter dan 15 nm. Een soortgelijk verruwingsgedrag is gezien voor

etsen van amorfe lagen, verkregen door ionenbombardement, bovenop kristallijne Si(100)

substraten. Voor het etsen van H-termineerd Si(100) en a-Si lagen op Si(100) leidt het

etsen tot de vorming van gebieden op het oppervlak waar het etsen wordt bemoeilijkt

ten gevolge waarvan op gebieden, waar de onderliggende, kristallijne Si(100) reeds geetst

wordt, diepe en smalle putten ontstaan. Oppervlakteverruwing werd in menig literatuur-

referentie reeds genoemd in het geval dat de verschillende experimentele gegevens niet

met elkaar verenigbaar bleken. Hier hebben we laten zien dat oppervlaktevergroting ten

gevolge van de oppervlakteverruwing verantwoordelijk is voor de gerapporteerde trends

in etssnelheid en reaktielaag-dikte en -samenstelling als functie van de etsduur.

Tijdsopgeloste en spectroscopische tweede-harmonische generatie (SHG) is toegepast

in het 2.7-3.5 eV tweede-harmonische (SH) fotonenergiebereik om Si-Si bindingen aan het

oppervlak te bestuderen tijdens het XeF2 etsen van H-getermineerd Si(100).

Spectroscopische SHG op H-getermineerd Si(100) laat een enkele 2ω-resonantie zien met

resonantiefrequentie 3.34 eV. Een voledig gefluorineerd Si(100)-oppervlak, tijdens XeF2

120

etsen, laat daarentegen twee resonanties zien met resonantiefrequenties 3.27 eV en 3.46

eV. De eerste resonantie (3.27 eV) is gerelateerd aan bulk-achtige E ′0/E1 Si-Si directe

bandovergangen die beınvloed zijn door binding aan fluor. De oorsprong van tweede

resonantie (3.46 eV) is nog onbekend. De dynamica in het SH-signaal tijdens XeF2 etsen

van H-getermineerd Si(100) kan uitgelegd worden in termen van een verandering van

oppervlakte toestanden ten gevolge van een overgang van H-gebonden naar F-gebonden

Si-Si elektronische oppervlaktetoestanden. Zodra de blootstelling aan XeF2 wordt gestopt

verandert het SH-spectrum, wat mogelijk te verklaren is door een reconstructie van de

siliciumfluoride reactielaag.

De separate ellipsometriestudies van Ar+ ionenbombardement en XeF2 etsen vormen

een solide basis om iongeassisteerde etsen te gaan bestuderen met ellipsometrie. Een

eerste aanzet daartoe heeft geresulteerd in een beter inzicht van de door ionen beschadigde

Si-laag en oppervlakte ruwheid tijdens iongeassisteerd etsen van Si(100). Als het etsen

chemisch van aard is, d.w.z. als ΦXeF2 >> ΦAr+ , dan neemt de ruwheid toe, maar als het

etsen meer physisch van aard is, d.w.z. voor toenemende ΦAr+ in verhouding tot ΦXeF2 ,

leidt iongeassisteerd etsen tot het polijsten van het oppervlak. Deze observaties zijn in

overeenstemming met de sterke verruwing als gezien voor spontaan XeF2 etsen en de lage

ruwheid gezien voor Ar+-ionen bombardement. Overeenkomstig met massaspectrometrie-

metingen van de reactiewaarschijnlijkheid van XeF2 en produktiewaarschijnlijkheid van

etsprodukten laat de ruwheid een sterke afhankelijkheid van de Ar+/XeF2-fluxverhouding

zien.

121

Dankwoord / Acknowledgements

Aangezien meerdere mensen een grote bijdrage hebben geleverd aan de realisatie van

dit werk wil ik hen bij deze bedanken.

Ten eerste wil mijn mentoren bedanken. Herman Beijerinck dank ik niet alleen voor

de discussies, begeleiding en hulp, maar vooral ook voor de gezellig tijd. Je bent altijd

kritisch met commentaar op geschreven werk of presentatie, maar je aanwijzingen waren

dermate concreet dat met niet al te veel moeite het eindresultaat bereikt kan worden.

Uiteindelijk is het alleen maar ten goede gekomen van de kwaliteit van het werk. De

goede gesprekken met zo nu en dan een persoonlijk tintje tijdens besprekingen en tijdens

een aantal bezoeken in Boulder zijn leerzaam geweest en op momenten dat het nodig was

een ondersteuning geweest. Wat we er zeker in moeten houden is de rondjes golf waar

je, net als ik, erg van geniet en inmiddels uiterst bedreven in bent geraakt. Tevens gaat

mijn dank uit naar Erwin Kessels. Je hebt me door de jaren heen veel geholpen en ik heb

veel van je geleerd. Als je als promovendus dicht op de materie zit wil je nog wel eens

doordraven wat betreft interpretaties en daar wist je me altijd wel op de juiste manier

met de beide benen terug op de grond te zetten. Bij deze dank ik ook Richard van de

Sanden. Ook jij hebt door de jaren heen geregeld een momentje tijd gemaakt om je visie

en ideeen over het werk duidelijk te maken wat inspirerend heeft gewerkt. Naar mijn

mening hebben we samen een mooie stap voorwaarts gemaakt in het bundeletsonderzoek

met nieuwe inzichten en nog niet volledig uitgewerkte ideeen die een vervolg verdienen.

Een deel van de gepresenteerde metingen is tot stand gekomen met dank aan een

aantal stagaires, Gijsbert Vandeweerdt, Jan Pieter Chan en Simon Mathijssen, en in het

laatste jaar met dank aan afstudeerder Paul Gevers en collega-promovendus Joost Gielis.

Ik wens de laatste twee veel succes met de gezette koers wat betreft experimenten op

SCEPTER; erg mooi werk, heren. Met name Paul, die het werk op SCEPTER gaat

voortzetten komende 4 jaar, wens ik al het beste toe en ik hoop dat je net zo’n leuke tijd

zult hebben op dit project als ik. Verder dank ik de collegaas bij AQT en ETP voor de

discussies tijdens besprekingen en pauzes en de prettige werksfeer die ervoor gezorgd heeft

dat ik altijd met veel plezier naar het werk ben gekomen. Peter Vankan, Paul, Joost, Igor

Aarts, Erwin, Erik Langereis, Johan Hoefnagels en Arno Smets wil ik in het bijzonder

bedanken, niet alleen voor de discussies over werk-gerelateerde zaken maar ook voor de

gesprekken over de gewone, niet-werk-gerelateerde dingen des levens. Het persoonlijke

tintje aan onze samenwerking waardeer ik zeer. The same is true for you, Ina Martin. I

very much appreciate our friendship and all the things we’ve done together at the AVS

meetings and during my stay in Boulder.

Many thanks go out to Steven Cundiff and Elaine Li for the pleasant and wonderful

visit at JILA in Boulder. Despite the initial difficulties we still managed to get some

122

interesting results concerning high-Tc superconductors and SmB6. I wish both of you all

the best in your future career.

Niets blijft draaien zoals het draait zonder de ondersteuning van de technische staf

Louis van Moll, Jolanda van de Ven, Ries van de Sande, Jo Jansen, Bertus Husken en

Herman de Jong. Bedankt voor vaak snelle oplossingen van problemen en het meedenken

bij nieuwe ontwikkelingen. Ook Rina Boom-van der Velde en Jeanne Loonen wil ik zeker

niet vergeten voor de vele zaken die jullie voor ons allen regelen en organiseren; dank

hiervoor.

Tenslotte wil ik de mensen uit mijn prive-sfeer bedanken. Allereerst gaat mijn dank uit

naar mijn ouders, zus en schoonbroer. Jullie onvoorwaardelijke steun in welke vorm dan

ook is voor mij van enorm belang geweest om me te brengen waar ik nu ben. Tegen jullie,

Mark, Roy, Ralf, Dennis, Frank, Anouk en partners wil ik zeggen dat ik jullie vriendschap

zeer waardeer. Jullie zijn voor mij de beste vrienden die ik me kan wensen. Ondanks dat

ik met vlagen veel afwezig ben geweest gedurende de laatste jaren, waardeer ik het zeer

dat jullie er toch onvoorwaardelijk voor me zijn geweest. Wim en Toos wil ik bedanken

voor alle goede zorgen, in het bijzonder voor Bram. Elke middag of voor langere perioden

hebben jullie voor hem gezorgd, waardoor ik zonder problemen de nodige buitenlandse

avonturen heb kunnen ondernemen.

Tot slot, mijn twee belangrijkste maatjes. Nieke, je bent pas kort in mijn leven en

meteen krijg je te maken met iemand die veel afwezig is, met name in de laatste maanden.

Ik heb mijn frustraties en ergernissen altijd bij je kwijt gekund en je hebt me door de lastige

perioden gesleept. Je hebt het vast op vele momenten graag anders gezien. Een ding is

zeker: het zit er nu echt op. Ondanks dit alles hebben we elkaar gevonden in de periode

tot nu. Ik voel me dan ook bevoorrecht om met jou een ongetwijfeld mooie toekomst

tegenmoet te gaan, ongeacht waarheen die ons zal leiden. En als laatste natuurlijk Bram,

waar ik niet te veel woorden aan hoef te wijden, want dat doen we nooit. Wat er ook

is geweest of is gebeurd, er is een iemand die blij is als ik er weer ben en me de o zo

belangrijke afleiding en innerlijke rust biedt... en dat ben jij.

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Curriculum Vitae

18 februari 1977 : Geboren te Roermond

1989 - 1995 : Voortgezet Wetenschappelijk OnderwijsScholengemeenschap St. Ursula te Horn

1995 - 2002 : Studie Technische NatuurkundeFaculteit Technische NatuurkundeTechnische Universiteit Eindhovendoctoraal examen december 2001

2002 - 2006 : Onderzoeker-In-OpleidingFaculteit Technische NatuurkundeTechnische Universiteit Eindhoven

Shining a light on silicon etching - Technische Universiteit Eindhoven

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