Optical Properties of Si-SiO2 Interfaces by Linear and Nonlinear Optical Techniques

ABSTRACT

WANG, JIH-FU TREVOR. Optical Properties of Si-SiO2 Interfaces by Linear and Nonlinear Optical Techniques. (Under the direction of Professor D. E. Aspnes. ) The objective of this research is to understand the physics of (001)Si-SiO2 interfaces by noninvasive, nondestructive optical techniques, that is, linear optical reflectance difference spectroscopy (RDS) and nonlinear optical second harmonic generation (SHG). The approach is to apply RDS and SHG to study optical anisotropy and interfacial bonding properties at the vicinal (001)Si-SiO2 interfaces respectively. Miscutting (001)Si samples toward (111) introduces atomic bonding asymmetry, leading to interesting linear and nonlinear optical responses. Optical responses from semiconductor are sometimes hard to interpret and understand. However, the linear and nonlinear optical probes general obtain information that complements one other. A close examination of these responses helps us to further understand the nature of the interface and to interpret optical responses unambiguously.

OPTICAL PROPERTIES OF Si-SiO2 INTERFACES BY LINEAR AND NONLINEAR OPTICAL TECHNIQUES

By

JIH-FU TREVOR WANG

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of Doctor of Philosophy

PHYSICS Raleigh

2001

APPROVED BY:

Dr. Gerald Lucovsky Dr. Robert J. Nemanich

Dr. Carlton M. Osburn Dr. John E. Rowe

Dedication

Biography

Jih-Fu Trevor Wang was born in Chang-hwau, Taiwan, R. O. C. to Chai

Chang and Shih-Shing Wang. He grew up with his three lovely sisters and two caring brothers sharing the joy as well as ups and downs of life in his early childhood. His parents taught him the importance of love, diligence,

indepen-dence, and discipline at a very young age. At fifteen, he left his home town to attend Taichung First Senior High School in the biggest city in central Taiwan, where he aspired to be a scientist and also acquainted himself with many gifted

and talented intellectuals, who often become the elites of society.

After completing his high school education, he went to attend Tunghai

University, where he majored in physics and was determined to pursue further study in physics in the future. He graduated with honors in his class. After

two-year compulsory military service as an Army Logistics officer, he went back to school to work as a university laboratory instructor before he came to the United States to pursue his dream to be a scientist. He was then admitted to physics

master program at the University of Oregon in 1990. In 1992 he earned a Master of Science in Physics. In 1992 he enrolled in the Electrical Engineering master

program at the University of North Carolina at Charlotte. In 1995 he earned his Master of Science in Electrical Engineering. During the time that he was an engineering student, he excelled in the discipline but never lost enthusiasm for

In 1994 he was selected to attend the atomic, molecular, and optical physics

summer school at Los Alamos National Laboratory to study H₂+ _{spectroscopic}

properties of excited electronic states using their Cray supercomputer. This experience was a turning point in his life. He then decided to come back to pursue his original plan to be a scientist. In 1995 he moved to Raleigh to study

physics and obtained a Ph.D. degree at North Carolina State University. After completing his Ph.D. degree, his next career move will bring him to the new frontiers of IR optics at Vanderbilt University. He always looks forward to new

Acknowledgements

It would not have been possible to finish the journey of graduate study

without the administrative and technical assistance and friendship of many

people. Here I would like to thank them all. First of all, I would like to express my

great appreciation to my advisor David E. Aspnes for his guidance and financial

support over the past few years. His dedication to science, keen insight

regarding problems, and care of his group set an excellent example for me.

I am also grateful to my committee members, Professors Gerald Lucovsky,

John E. Rowe, Robert J. Nemanich, and Carlton M. Osburn for their precious

time and for valuable suggestions. Each has made impressive achievements in

different areas of science, engineering, and industry, which have motivated me to

work hard to follow in their footsteps.

It has been quite interesting to have seen our research group grow from one

generation to another. I would like to acknowledge each, since they have given

me great and profound memories. I had many great times with both the first

generation, including Kim Bell, Ginger Edwards, Martin Ebert, Lucymarie

Mantese, Gary Powell, and Sang Duk Yoo, at the time when I was the youngest

in the group, and with the current generation, which consists of Muharrem Asar,

Klaus Flock, Sungjin Kim, and guest member Nicholas Stoute in alphabetical

order. I will never forget the friendships that we have built, and will cherish these

Without excellent administrative assistance I would not have finished my

research and completed my degree requirements. I would like to express my

gratitude to all, including in alphabetical order Jennifer Allen, Margaret Johnson,

Robert Eagler, Wilma Gill, Dianne Greene, Ina Lunney, Leslie Moon, Joan

O’Sullivan, Becky Savage, Cecilia Upchurch, and Nadine Ward.

Finally, I would like to express my great appreciation to my undergraduate

faculty as well as my junior high school mentors Mr. Chow and Mr. Chen, for their

endless LOVE and encouragement to me, and in particular for making an

TABLE OF CONTENTS

LIST OF FIGURES……….. ix

Chapter 1. Introduction 1

1.1 Overview……….. 1

1.2 Outline of this Dissertation……… 3

1.3 References………... 5

Chapter 2. Reflectance Difference Spectroscopy 6

2.1 Introduction……….. 6

2.2 Optical Anisotropy of Vicinal Si-SiO2 Interfaces: Evidence for Step Phase Transitions……….. 9

2.2.1 Samples and Sample Preparation……… 10

2.2.2 Experimental Configuration and Principles of RDS…… 11

2.2.3 RDS of Vicinal Surface-General Considerations……… 13

2.2.4 Experimental Results and Discussion……….. 16

2.3 Acknowledgements……… 33

2.4 References…..……… 34

Chapter 3. Second Harmonic Generation……….. 49

3.1 Introduction………. 49

3.2 Theory………. 54

3.2.1 Mathematical Formalism……… 54

3.2.2 SHG Response from the Interface:Analytic Forms of SHG

………. 57

3.3 Experiment……….. 63

3.4 Azimuthal Dependence of SHG Intensity for a 90 Vicinal (001)Si-SiO2 Interface……….. 65

3.5 Discussion of SBHM: Comparison to Previous Treatments… 69 3.6 Conclusions ……… 73

3.7 References.………. 75

Chapter 4. Summary and Conclusions……… 86

4.1 Summary, Conclusions, and Future Study……… 86

APPENDICES……….. 91

Appendix A:……….. 91

A.1 RDS Experimental Set-up……… 91

Appendix B:………..100

LIST OF FIGURES

2.1 ∆r / r spectra for thermally unannealed vicinal (001)Si-SiO2 interfaces…. 40

2.2 ∆r / r spectra for thermally annealed vicinal (001) Si-SiO2 interfaces…….. 41

2.3 Normalized RD lineshape versus crystal miscut angle before and after

thermally annealed treatment……… 42

2.4 RD amplitude at 3 eV versus miscut angle for UHV vicinal Si(001)……… 43

2.5 Step RD amplitude at 3eV versus miscut angle for UHV vicinal Si(001)… 44

2.6 Normalized E1 peak versus miscut angle for thermally annealed vicinal

(001)Si-SiO2 interfaces……… 45

2.7 Normalized E2 peak versus miscut angle for thermally annealed vicinal

(001)Si-SiO2 interfaces……… 46

2.8 Normalized E1 peak versus miscut angle for thermally unannealed vicinal

(001)Si-SiO2 interfaces……… 47

2.9 Normalized E2 peak versus miscut angle for thermally unannealed vicinal

(001)Si-SiO2 interfaces……… 48

3.1 SHG p-p, p-s, s-p, s-s data versus azimuth angle for vicinal 50 (111)Si

toward (11-2)-SiO2 interfaces……… 80

3.2 SHG p-p, p-s data versus azimuth angle for vicinal 90 (001)Si toward (111)-

SiO2 interfaces………..……….. 81

3.3 Schematic silicon bond picture for Si(111) and Si(001) ……….. 82

……….. 83

3.5 Vicinal 60 Si(001) SHG data-uannealed sample……….. 84

3.6 Vicinal 60 Si(001) SHG data-annealed sample...……….. 85

Appendix A Fig. 1a shows the principle of RDS works………..… 92

Fig. 1b Schematic diagram of a reflectance difference spectrometer………… 93

Fig. 2 Schematic diagram of a polarizer-photoelastic-modulator-analyzer RDS spectrometer……… 94

Fig. 3 a. Pure terrace Si(001) RDS spectrum and b. RDS Spectra of vicinal Si(001) surfaces……… 95

Fig. 4 Step RDS spectra from Fig. 2 and Fig. 3……….. 96

Fig. 5 UHV Si vicinal stepped surface ………. 97

Fig. 6 The first oxide layer at Si-SiO2 interface………... 98

Fig. 7 Neaton’s Si-SiO2 interface model………... 99

Chapter 1. Introduction

1. Overview

The current trend of semiconductor technology demands faster signal

processing speed, less heat dissipation, higher density of devices per chip, lower

defect concentrations for large volume manufacturing, lower leakage currents,

higher time-dependent breakdown voltages, more uniform oxide thicknesses

over larger wafer sizes, more functionality, better performance, and higher

reliability for each device. One simple approach at present is to continue to

reduce the gate dielectric (SiO2) thickness in metal-oxide field-effect transistors.

However, this scheme will no longer work once the gate oxide thickness reaches

the fundamental physical limit of ultralarge-scale-integrated (ULSI) device scaling

of 5 atomic distances by the year 2012.[1-3] At this scale the electrical and

optical properties of the thin oxide become quite different from what one would

expect on the basis of thicker oxides[4], hence a comprehensive understanding

and exact control of the interface become crucial.

Although many scientists and engineers around the world are trying to

circumvent these technological and scientific challenges, investigating for

example the use of high-k dielectrics as a possible replacement for SiO2 or other

types of transistors[4], these approaches have not yet been successful. Also,

although the Si-SiO2 interface has been studied for many decades, many

structure at the interface? Despite many efforts to answer these questions, there

has been no clear resolution of these issues and they are still under debate.

The main goal of the present work is to evaluate various vicinal (001)Si-SiO2

interfaces following various heat treatments by remote, invasive,

non-destructive linear and nonlinear optical techniques and to understand the optical

responses of these interfaces. Our results will help to further characterize these

interfaces by optical means in the future. Specifically, we apply reflectance

difference spectroscopy (RDS) and second harmonic generation (SHG) to study

the optical anisotropy of these interfaces and their interfacial bonding structures,

respectively, and correlate the RD and SHG results. Vicinal Si(001) substrates

introduce local bonding asymmetries at the interface leading to interesting linear

and nonlinear optical responses. From the optical responses arising from these

interfaces we obtain a better understanding of the linear and nonlinear optical

responses of steps, both single and double atomic height. We also obtain a

better understanding of single- and double-domain terraces, which cannot be

distinguished easily using the conventional truncated Fourier series or

complicated tensor-coefficient approaches.

Using the simplified bond hyperpolarizability model (SBHM) of SHG, which

we introduce to describe the anisotropy of SHG intensities, we quantitize and

characterize the interfacial properties in a more precise way and gain further

physical insight about these interfaces. This approach uses four complex

interfacial silicon bonds, to describe the nonlinear polarization of the interfaces

induced by the incoming electromagnetic field to gain physical insight from

azimuth-dependent SHG intensity data and to identify SHG absorption as well as

to obtain information about the origin of SHG. In fact, since some bonds are

equivalent, fewer than four complex hyperpolarizabilities are needed. In contrast,

the conventional phenomenological tensor approach employs a large number of

components to express nonlinear effects, even though symmetry consideration

causes some of the components to vanish. The fact that the tensor approach

also expresses SHG signals as complicated lengthy tensor functions means that

considerable useful information is buried and much of the physical insight that we

can gain from SHG data is lost. As part of the present work we obtain information

about thermal annealing and rapid thermal annealing (RTA) techniques that are

standard industrial methods to reduce defect density, roughness, and strain at

the interfaces. SHG p-p and p-s data indicate interesting changes of complex

hyperpolarizabilities as a result of this processing. The details of these results

will be described in this work and are planned to be published elsewhere.

1.2 Outline of this Dissertation

In Chapter 2 we describe the application of RDS to study the linear optical

anisotropy of vicinal Si(001)-SiO2 interfaces and describe our results. We

compare our results to those obtained by others on clean surfaces in UHV,

cases. From these analogies we are able to take advantage of the

double-domain nature of these interfaces to study SHG at these interfaces using the

SBHM. The results show that a single- to double-height step phase transition

exists at the Si-SiO2 interface as well as on clean surfaces in UHV. We conclude

the chapter with the theory explaining possible step driving mechanisms.

In Chapter 3 we describe our application of SHG to study the chemical

bonding at these interfaces. First we show that the SBHM can describe SHG

anisotropies at the (111)Si as well as the (001)Si cases, and compare the two

cases. The results show that optical responses can also be understood as

classical dipole radiation of induced effective linearly and nonlinearly polarizable

Si bonds. We explain the origin of SHG anisotropy at the interface and the

implications of the unusual one- and three-fold symmetries associated with

atomic steps at the vicinal (001)Si-SiO2 interfaces.

Chapter 4 summarizes our conclusions and lists suggestions for future

1.3 Reference

1. Semiconductor Industry Association: National Roadmap for Semiconductor

71-81 (Sematech, 1997).

2. D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. Evans-Lutterodt, and

Timp, Nature 399, 758 (1999).

3. M. Schulz, Nature 399, 729 (1999).

Chapter 2. Reflectance Difference Spectroscopy

2.1 Introduction

The Si-SiO₂ interface has been intensively studied for many decades, but

fundamental questions remain. These questions gain importance since, from a

technological point of view, the gate oxide thicknesses of transistors are

expected to arrive at the fundamental physical limit of ultralarge scale integration

(ULSI) device scaling of 5 atomic distances by the year 2012. To achieve

expected device performance, functionality, and reliability under such conditions,

exact control of interface properties will become critical, and inevitable.[1-3]

We therefore require a more precise and comprehensive understanding of

the properties of specifically the (001)Si-SiO₂ interface at the atomic scale, since

this is the orientation used in technology. In addition to its technological

importance, from a scientific point of view an improvement of our understanding

can lead to further advances in topics such as chemical reactivity, interface

reconstructions, and step phase transitions, as well as providing information

about clean-surface topics such as adatom diffusion, nucleation, film growth, and

heteroepitaxy including the growth of III-V semiconductors on Si for

optoelectronic applications.[4-9]

This work is a comprehensive study of interfaces formed on vicinal (001) Si

simplified bond hyperpolarizability model (SBHM), discussed in detail in Section

3.2, was a direct collaboration involving Powell. However, two distinctions need

to be made. First, (001) Si is the orientation used in technology, and hence is in

principle of considerable more interest to problems currently faced by technology.

Second, (001) is a much more difficult Si orientation to deal with, since in

contrast to the (111) surface, (001) Si exhibits two domains on a macroscopic

scale, and thus the intrinsic terrace contributions are much more difficult to study.

As a result the present investigation deals with the response of vicinal (001)

samples, and is restricted to oxidized interfaces rather than a combination of

oxidized and nitrided interfaces as investigated by Powell.

In this work we are particularly interested in steps, which by entropy occur

on a statistical basis on nominally flat surfaces but can be generated in controlled

densities through the use of vicinal samples, i.e., by deliberately cutting and

polishing surfaces misoriented by various amounts with respect to the (001)

direction. One motivation for studying steps is that they affect electron and hole

channel mobilities in FET structures.[5,6] A second motivation is that, although

step transitions have been studied in great detail on atomically clean surfaces in

ultrahigh vacuum (UHV), essentially no studies have been made concerning

steps at interfaces. These factors prompted us to probe steps and investigate

phase-transition mechanisms, if they exist, at (001)Si-SiO2 interfaces. Optical

techniques in general offer several advantages over conventional surface

investigation mainly by providing a simple, fast, noninvasive way of accessing

steps beneath transparent overlayers. In particular, owing to its sensitivity to

steps, reflectance-difference (-anisotropy) spectroscopy (RDS/RAS) is ideal. We

show here that RDS is not only “step-specific” but also “sub-step-specific”.

Our results are of interest for several reasons. First, our RDS data show

that the oxidized vicinal (001) Si-SiO₂ interface exhibits a single-to-double-height

step phase transition near 4° with increasing vicinal angle, which is quite similar

to that observed in ultrahigh vacuum (UHV) and by now well understood

theoretically. However, the UHV transition is driven by localized strain resulting

from Si terrace dimers, which do not exist, or at least do not exist in the same

form, at Si-SiO₂ interfaces. We argue that, as in the UHV case, the phase

transition is also due to strain, although details will have to wait until calculations

of the step structure are available. To our knowledge such calculations do not

exist for steps on the Si-SiO₂ interface.

Second, we have performed extensive studies of these samples using

second-harmonic generation (SHG), which also reveal the step-phase transition

and in addition are used to provide an additional critical test of the SHBM, which

was previously investigated only for the (111) Si-dielectric interface. Comparing

the results obtained with the two orientations shows distinct differences and also

provides new insight concerning the origin of SHG signals at these interfaces.

angle of incidence and observation of 12°, as opposed to 29° as determined for

(111)Si-dielectric interfaces. This implies that the SHG signal arises at the Si

side of the (001) interface, as opposed to the oxide side for the (111) orientation.

We have also performed spectroscopic ellipsometric (SE) measurements of

these interfaces, but the results are not discussed here since the data were

obtained mainly to verify that the interface widths were small and the sample

properties measured therefore not dominated by interface-roughness effects.

Our results show interesting and unexpected effects that should provide

theorists with an incentive to consider the (001)Si-SiO₂ interface in more detail.

This is a goal certainly worth encouraging given the technological importance of

this materials system.

Regarding the rest of Sec. 2.2, Sec. 2.2 describes sample preparation,

experimental apparatus, and methods of analysis, while Sec. 2.3 presents and

discusses the results.

2.2. Optical Anisotropy of Vicinal Si-SiO₂ Interfaces: Evidence for Step Phase

Transitions

As discussed in the Introduction, we have investigated the Si-SiO₂ interface

by performing a series of linear-optical and SHG measurements on vicinal

(001)Si-SiO2 samples. Specifically, our set consists of (001) samples with offcut

experimental details regarding sample preparation and RD data acquisition, and

how the results are analyzed.

2.2.1 Samples and Sample preparation.

Our experiments were performed on P-doped n-type nominally (001) Si

wafers with resistivities of about 10 Ω-cm and vicinal angles from 1o to 9o

oriented toward the nearest (111) axis. The samples were prepared by a

modified oxide growth technique that is also used to prepare gate

dielectrics.[10,11] The procedures are as follows. First, 100 Å sacrificial oxides

were thermally grown on the Si substrates at a temperature of 900 o_{C after RCA}

chemical cleaning. Next, these oxides were removed immediately after growth in

dilute (1:500) HF. Finally, immediately after stripping 30 Å thermal oxides were

grown at 800 o_{C. Half of these samples were annealed in N2 at 900} oC for 20

min., and half were saved for control purposes.

Different oxide preparation methods and processing sequences lead to

significantly different degrees of roughness at these interfaces. The variety of

conclusions in the literature are at least partly a consequence of the neglect of

these factors. Accordingly, we paid particular attention to sample preparation.[12]

The micro-roughness of the interface is generally related to the presence of

(SE). The SE-determined interface widths of our samples are about 5Å or less,

indicating that our interfaces are essentially atomically smooth. Hence we rule

out the possibility of artifacts due to rough interfaces.

2.2.2 Experimental Configuration and Principles of RDS

RD data were obtained using a spectrometer with a range of 1.5 to 5.5 eV,

as described elsewhere.[7] Specifically, the configuration consists of a Xe arc

lamp, a focusing mirror, a folding mirror, a quartz Rochon prism, the sample, a

photoelastic modulator operating at 50 kHz, an quartz Rochon analyzer prism, a

condensing mirror, a folding mirror, a 0.1 m focusing-grating monochromator,

and an end-on photomultiplier as shown in appendix A. The output of the

photomultiplier was converted to a voltage, which was used to regulate the

photomultiplier voltage to maintain 10 µm average anode current at the output to

normalize the signals despite a considerable variation in detected intensity over

the 1.5 to 5.5 eV spectral range. The output of the photomultiplier was also

routed to two phase-sensitive detectors operating at 50 and 100 kHz to obtain

the spectral dependences of the relative phase and amplitude, respectively, of

the anisotropy of the near-normal-incidence reflectance of the sample. However,

only the relative amplitudes are used here. At mid-range the configuration can

achieve a signal-to-noise ratio of about 1 part in 105_.

incidence with the samples in air. The relative angles of polarizer and modulator

were adjusted to give a zero reading on the 100 kHz phase-sensitive detector

prior to measurement. However, owing to the small signals involved data were

obtained at 4 azimuth angles, nominally 0, 45, 90, and 135°, and subsequently

combined by Fourier analysis first, to ensure that at least one azimuth angle

existed at which a true null could be obtained and second, to eliminate as far as

possible instrument artifacts, since these contribute equally to all spectra

regardless of sample azimuth. The determination of a true null signal at some

azimuth ensures that there exists only one contribution to the optical anisotropy

of the sample, or more accurately no contributions with principal axes at surface

orientations different from that of the main anisotropy arising from the steps.

The optical anisotropy of the samples can be expressed in terms of the

complex normal-incidence reflectance as

∆ ~r / r~ =

+ − R R ~ ~

= ∆ r / r + i ∆θ

R~₋ = (r~_α −~r_β), R~₊ =

2 1

) ~ ~ (r_α +r_β

where r~_α and r~_β are the complex reflectances for incident light linearly

polarized along the principal axes α andβ, respectively, of the sample. In our

r

r / ~

~

∆ data, α is defined to be the along the [1 1 0] direction (parallel to the

According to the Fresnel three-phase model, ∆ r~ / r~ can be written in terms of

the interface (or surface) dielectric anisotropy (

ε

∆ r~ / r~ = λ πid

4

(

1

− −

s ε

ε ε_{α β}

)

where ε_s is the bulk dielectric function of the substrate and ε_αd and ε_βd are the

interface (or surface) dielectric responses along the α and β axes, respectively,

λ is the incident wavelength, and d is the thickness of the interface.[13] Since Si

is cubic, the linear anisotropy arising from the bulk is negligible, and since the

SiO₂ overlayer is amorphous, its linear anisotropy is also negligible. Hence the

observed anisotropy originates entirely from the interface, and is expressed as

the effective two-dimensional dielectric response (ε −_α ε_β)d.

2.2.3 RDS of a Vicinal Surface – General Considerations.

In general, as with clean surfaces the optical anisotropy of the Si-SiO₂

interface is expected to arise in principle from a combination of step and terrace

contributions, and thus can be written as

∆r / r = Ft (∆r / r)terrace + Fs (∆r / r)step 2.1

where (∆r / r)terrace and (∆r / r)step are the RD signals from the terraces and steps,

terrace orientations exist, since the Si lattice consists of two chemically identical

interpenetrating fcc lattices rotated with respect to each other by 90°.[see

Appendix A ] If one could create a primitive surface or interface, i.e., one where

all atoms were drawn from only one of the two inequivalent sublattices, the (001)

surface should exhibit twofold rotation symmetry as a consequence of the fact

that the outermost plane of atoms has two bonds upward to the oxide. For

materials such as Si and Ge that crystallize in the diamond structure, the two

sublattices are chemically identical, so it is impossible to chemically distinguish

them and prepare a singular surface through the use of chemistry as is the case

of III-V compound semiconductors. Thus for (001)Si-SiO₂ interfaces that are not

deliberately miscut by a sufficiently large angle any macroscopic surface area,

such as that covered by an incident optical beam, must consist of statistically

equal areas of interface atoms drawn from each of the two different sublattices,

although the individual domains themselves will exhibit twofold rotational

symmetry. Thus a macroscopic region of the (001)Si-SiO₂ interface will exhibit

overall fourfold rotation symmetry, which will not be detected by linear-optical

probes since the linear-optical response is described by a second-rank tensor.

For clean, on-axis surfaces in UHV this double-domain behavior leads to

combined symmetries of type (2×1) or (1×2) as observed by reflection

high-energy electron diffraction (RHEED). These symmetries result from the

directions. While the exact microscopic nature of (001)Si-SiO₂ interfaces is

clearly more complicated than that of the clean surface and is still under debate

(see below), a given single domain should still be optically anisotropic. Thus a

primitive interface should yield an anisotropy contribution for all miscut angles

down to and including zero. However, given the strength of the Si-O bond and

therefore the energy difference between bonding and antibonding orbitals, it is

not clear that any terrace optical anisotropy will be particularly strong in our

accessible spectral range of 1.5 to 5.5 eV. The early reflectance measurements

of Chiarotti et al. certainly suggest that any such anisotropy will be relatively

featureless in this spectral range at best.

Step contributions may be different, but are complicated by the fact that at

least four types of step reconstructions, two single-height and two double-height,

can occur. Each of these can run in orthogonal directions across the surface.

Even though no models so far have been proposed to describe the detailed

atomic structure of steps at Si-SiO₂ interfaces, given the strong binding energy of

the Si-O bond it is clear that the bonding configurations will be entirely different

from those on clean surfaces. The driving force here should be to maximize the

number of nominally “dangling” bonds-oxygen deficient bonds- (those that at the

interface involve oxygen atoms) rather than minimizing them, and also to satisfy

interface energy minimization.[32] As a result it is not clear that an interface

anisotropy analogous to the surface-state anisotropy observed on clean surfaces

above. Nevertheless, by geometric arguments any step contribution should be

optically anisotropic, although if this arises from strain or lifetime effects it may

not be possible to distinguish one type of step from another in the spectral data.

Since the different step configurations are expected to have different

formation energies, for sufficiently large vicinal angles we would expect one type

of step to be preferred, with its enthalpy overcoming the entropy-driven

production of single-height steps that is expected to occur for small vicinal

angles. This is well known in the case of clean surfaces in UHV, where the

step-phase transition occurs at miscut angles of about 3 to 4° and is driven by the

lower energy of a particular double-height step. The response of the oxidized

interface with increasing vicinal angle should therefore be qualitatively similar to

that of the clean surface: a small, possibly vanishing anisotropic response for

small vicinal angles and a more rapidly increasing one at larger angles. Thus the

general behavior expressed by Eq. (2.1), which has been shown to be valid for

the UHV case, is expected to apply here as well.[12]

2.3 Experimental Results and Discussion.

To determine the optical anisotropy of vicinal silicon interfaces, we obtained

RD spectra of oxidized vicinal interfaces prepared and measured as described

above. A representative set of data is plotted in Figs. 2.1 and 2.2 for the

spectra are calculated as a Fourier transform of four spectra each taken at

azimuth angles separated by 45° and with an averaging time of 2 s per data

point. The inversion angle of the Fourier analysis was first chosen to obtain a

null spectrum if possible (not shown), and a spectrum corresponding to the

maximum signal. The purpose of this approach was to ensure that null spectra

could be realized, i.e., that only one type of optical anisotropy was effectively

present. This was observed to be the case for all data except those taken on

unannealed 3 and 7° samples, which showed small residual structures at the

(E0’, E1) and E2 spectral features near 3.4 and 4.2 eV, respectively, for reasons

that are not clear.

The spectra are shown for increasing vicinal angle and are offset for clarity.

These spectra show two general features, one related to the (E0’, E1) complex

and the other to the E2 transitions. It is clear from these data that to within our

signal-to-noise capability these lineshapes remain essentially constant and

simply increase in magnitude with increasing miscut angle as shown in Figs

2.6-2.9 . This is consistent with our strain argument given above. Thus unless all

possible contributing processes have exactly the same lineshape to within our

ability to determine it, not a likely occurrence, these data indicate that only one

mechanism is responsible for the observed anisotropy of these interfaces from 1°

To begin, analysis can therefore be reduced to examining the behavior of

these amplitudes with miscut angle. We first assume that all lineshapes are

equivalent to that shown for the annealed 9° sample in Fig. 2.2 with the possible

exception of baseline offsets, then use a least-squares fitting procedure to

determine the magnitude of the 9° component in each of the other spectra.

Since baselines vary somewhat from spectrum to spectrum, the baseline

(assumed to be a constant) and the scaling amplitude were both treated as

adjustable parameters in this analysis. The amplitudes so determined are shown

in Fig. 2.3. The uncertainty of these magnitudes, as determined by repeating the

measurements on different areas of the wafers, is about 3% of the full-scale

value. While the amplitudes of the oxidized samples show a relatively smooth

linear increase, those of the annealed samples shows a distinct break at 4°. The

datum for the 3° sample is clearly anomalous. However, this is a real effect as

the unusual RD response was observed for several runs. A recheck of the

orientation of this sample showed that it was indeed 3°, and not 6° as might be

inferred from its value. We note that a similar anomaly at a miscut angle of 3°

was also seen in XPS measurements[23], suggesting the existence of coherence

effects in terrace widths and /or step configurations at “special” angles even in

interfaces, as previously noted in several similar investigations of clean surfaces

in ultrahigh vacuum (Ref Whitman, possibly Hoppe and Wijers). This

was interpreted as facet formation at the interface. [23] The mechanism is still not

clear and requires futher investigation.[23]

Figure 2.3 also shows that the interfaces are rough compared with the ones

after treatment and less ordered as indicated by data randomness before thermal

annealing treatment. It turns out that the trends do follow a straight line but with a

large fluctuation before thermal annealing. However, upon thermal annealing the

optical anisotropy becomes “linearly” proportional to the vicinal crystal miscut

angle as shown in Fig. 2.3. In particular, the RD trend before the annealing

treatment also implies that the interfaces are in the mixed stepped phase, which

will be explained by the theory in the following.

We now consider the implications of these results. Our analysis will follow

in part that of Jaloviar et al.[14] since RD data for clean vicinal (001)Si surfaces

in UHV show similar trends, and a comparison of the UHV and oxidized cases

will aid the understanding of both sets of data. The UHV data show a similar

lineshape invariance with respect to miscut angle, although the lineshape itself

exhibits some differences with respect to that obtained for the Si-SiO₂ interface.

One major discrepancy is the appearance of significant anisotropy below 3.4 eV

in the UHV case, which implies substantial surface absorption since Si is

essentially transparent in this spectral region. This low-energy absorption is due

to states that exist on the clean surface but are not expected to be present (and

higher-lying structures are similar in both clean-surface and oxidized-interface cases

and are expected to originate for similar reasons. Since all features increase

monotonically with increasing vicinal angle, we can consider these features to be

connected in some way to steps. This includes those features that are clearly

due to surface states. In principle this also includes terrace contributions, since

steps can cause one terrace orientation to be favored over another or vice versa.

Since the UHV lineshapes are also invariant, we plot without regard to the

actual mechanism giving rise to the anisotropy at a given energy, and therefore

without loss of generality, the amplitude of |∆_{r /r|uhv at 3 eV in Fig. 2.4. The}

trend is the same, general increases exhibiting a break in the slope with only the

lower-miscut line intersecting zero. Whether the 3° anomaly seen in Figs. 2.1

and 2.2 exists for clean surfaces in UHV is not established since Jaloviar et al.

did not report data on a sample miscut by 3°. Since in UHV the single- to

double-height phase transition occurs at a vicinal angle of about 4°, the implication is

that the contribution for the oxidized interfaces are also coming from steps.

As a result of STM measurements [20] considerable information is available

about the nature of clean vicinal surfaces in UHV. Below about 3o the surface is

essentially double-domain, terminated by a combination of (2x1) and (1x2)

surface becomes single-domain with the terraces separated by

double-atomic-height DB steps in the notation of Chadi [21]. At 3° the surface consists of a

coexistence of about 40% D_B steps and 60% S_B steps, leading to a gradual

structural phase transition regarding S_B and D_B steps. As known from the

previous studies[14], both SB and DB steps contribute significantly to RD signals.

In particular, the rebonding necessary to create a SA step does not perturb the

nearby terrace atoms, and therefore one would expect SA steps to have

negligible RD contribution. Rebonding effects on RD spectra have been

discussed in great detail in Ref. 14, and are supported by the first-principles

calculations of Schmidt et al.[18,19] In addition, the intersection point in Fig. 2.4

implies that DB and SB steps are coexistent and optically indistinguishable on the

samples miscut at 3o angle, which is in excellent agreement with the STM

results.[20]

A further close examination of RD step spectra reveal a straight line. These

are shown in Fig. 2.5, and clearly imply that there exist two “almost identical”

types of steps associated with optical anisotropies, and that the optical

anisotropy is “linearly” proportional to the crystal vicinality, in other words, step

density. If the straight line are extrapolated, it intercept the y-axis at a negative

value as the vicinal angle approaches zero. The negative value suggests that the

terrace effect was somewhat over-compensated in Ref. 14 as a result of the RD

spectrum. Besides, the higher intercept at lower vicinality is more evidence of

double-domain behavior. For clean surfaces in UHV, these two types of steps

( rebonded SB and DB ) [21] are almost identical except that the step height as

well as the nearest dimers on the terraces above and below the steps are

different. It is plausible that the intercept in Fig. 2.5 can be attributed to the

residual terrace contribution. The rebonded SB and DB steps to which we refer

were thoroughly illustrated and theoretically studied by D. J. Chadi.[21].

Nevertheless, it is quite legitimate to apply the same interpretation to the RD

trend in Fig. 2.3 as in Fig. 2.4. With this interpretation, double-domain

single-atomic height steps dominate at oxidized interfaces with miscut angle less than

4o while single-domain double-atomic height steps prevail at interfaces with

miscut angle greater than 4o. The agreement between the two sets of data shows

that optical anisotropies of both clean and oxidized surfaces are in part induced

by similar effects, although the atomic structures of steps, dimers, and terraces at

oxidized silicon surfaces are different from those at clean ones. Hence, we term

these structures as being due to quasi-steps, quasi-dimers, and quasi-terraces.

These structures can be approximately visualized by assuming that oxygen

atoms incorporate at bridge sites [24] that would correspond to dimers on the

clean surfaces (one oxygen atom incorporated between every two silicon atoms

in silicon tetrahedral structure unit).

structural model. However, despite enormous efforts to establish an accurate

model, the conclusions from various studies of many experimental techniques

are elusive. Nevertheless, most of these studies agree that there exist two

distinct interface regions. One is about 1 to 2 monolayers thick with Si atoms in

intermediate oxidation states, i.e, Si+1(Si2O), Si+2(SiO), and Si+3(Si2O3). The

other is a compressed region extending about 20 Å into the bulk amorphous α

-SiO2 layer. It is well established that core-level photoelectron spectroscopy (PES)

enables us to obtain the information about the density and distribution of these

intermediate oxidation states (suboxides) but no corresponding spatial

information of the suboxides.[12] On the other hand, reflection high energy

electron diffraction (RHEED), x-ray diffraction (XRD), grazing incident x-ray

scattering (GIXS), and transmission electron microscopy (TEM) can only give us

precise spatial information about the first layered suboxides, because the

amorphous nature of the nearby bulk SiO2 material limits the resolution that we

can obtain.

In order to construct a model, several criteria must be met. First, the

interface should exhibit minimum strain and be about 5 Å wide (the strain results

from the volume mismatch between Si and SiO2).[24] Second, the near-interface

structure should be aβ-tridymite-like interfacial crystalline phase, as shown by

GIXS,[24] XRD,[26] and TEM.[27,28] Third, nearest neighbors should exhibit

chemical shifts due to intermediate oxidation states, as observed by PES.[24]

interface (1 per 104 interface atoms) as shown by electrical measurements, such

as capacitance-voltage measurements.[29] Finally, the density and distribution

of the intermediate oxidation states should be that shown by PES[24]

Pasquarello, Hybertsen, and Car [24] proposed models that meet all these

criteria. However, it is not possible to choose uniquely among their models since

spatial information about the suboxides is not available. From an atomic orbital

bonding point of view, the silicon (oxygen) atomic bonding orbital is structurally

4-fold-symmetric (2-4-fold-symmetric). Several of their models meet the above

requirements.

This situation changed recently with advances in electron energy loss

spectroscopy (EELS), since this has now made it possible to obtain localized

spatial information regarding suboxides and their electronic properties. Based on

the previous criteria and the new EELS spectra,[2,30] a new model was

proposed by Neaton, Muller, and Aschcroft. This is a hybrid of the models of

Pasquarello et al.[24] The Neaton et al. model in Appendix A predicts the same

theoretical unoccupied projected density of states of the oxygen atoms (O

p-UDOS) that is observed for the intensity profiles of the O Kedges measured by

EELS.[30]

In addition, Buczko et al. [31] and Tu et al. [32] applied first-principles ab

initio calculationsand quantum Monte Carolo simulations, respectively, to explore

fact, a 2x1 stripe phase terrace (row pattern of O bridges) as shown in Appendix

A.[31,32] This is consistent with X-ray diffraction[25] and RHEED data.[33] The

Neaton et al. model not only encompasses this aspect but also predicts many

interface properties that agree quite well with the previous experiments. These

studies indeed put a firm footing on the Neaton et al. model and the conclusions

about the structure of the first oxide layer.

Moreover, Ourmazd et al. [27,28] used TEM to demonstrate the presence of

a c-SiO2-like layer at the interface and a 90o (0o) rotation of the c-SiO2 layer

across a single (double) step on nominal Si-SiO2 samples. This suggests similar

atomic bonding structures exist at both clean and oxidized surfaces.

Furthermore, Rochet [34] et al. showed that double steps exist at the oxidized

surface with a 5o miscut angle even though their sample preparation was not

standard. Wantanbe et al. [29] and Cai et al. [30] used scanning tunneling

microscopy (STM) to investigate the local leakage current through ultrathin SiO₂

layers. Their STM images imply that B-type steps still exist even under thin oxide

films. All these evidences about steps and terraces underlie our interpretation of

the RD spectra of oxidized interfaces.

Since thermal oxidization transforms -Si-Si- bonds into -Si-O-Si- bonds, the

angle of the -Si-O-Si- bonds often varies slightly from one site to another.[24,31]

As a result the contributions from quasi-terraces are small compared with those

from quasi-steps because of the cancellation due to both double-domain and

Fig. 2.1 receives most of its contribution from steps rather than

quasi-terraces, especially at low crystal vicinality. On the other hand, the spectrum in

Fig. 2.5 is a pure step anisotropy calculated by removing the terrace contribution

from the RD spectra. The different slope constant ratios in Figs. 2.3 and 2.4

result from the fact that the electronegativity of oxygen upon incorporation leads

to similar but different polarizabilities that are responsible for most of the

anisotropies observed for both oxidized and clean silicon surfaces. It is very

likely that these RD signals arise from the region near the first oxide layer, since

this region still preserves Si crystalline order. Long-range order is lost only above

the first layer.

It should be noted that the step-driving mechanisms in both cases are

almost the same, since the common intersection point indicates the coexistence

of SB and DB steps that depend strongly on the atomic bonding structures in a

topological rather than a chemical manner. Rossow et al. [37,38] performed a

RDS study on RCA-cleaned vicinal Si(001) surfaces (H terminated) and found a

surprising similarity between H-terminated and our O-terminated lineshapes.

This implies that the observed optical anisotropy is more atomic-bonding

structure-specific than chemical-termination-specific.

To put it more directly in terms of the driving mechanism, one can apply a

thermodynamic formalism to describe surface morphology and the associated

thermody-showed that the thermodynamic states that dictate Si(001) surface morphology

can be described by the Hamiltonian.

_{H H SB E}

( )

( )

step +

+

= ( ) or

H =H(DB)+E_step

( )

( )

(

)

[

]

∑

= _{⊥ −}

i i i i c hihi

l h h

h SB

H( ) λ ₁ κ 2 2ε 1 δ _{, 1} 2.3

(

) (

)

[

]

∑

= _{⊥ −}

i i i c hihi hi l

h h DB

H( ) λ ₁ 2ε 1 δ _{, 1} λ_|| 1 δ _1,2 2.4

( )

E_strain(1)

(

) (

) (

[

) (

(

)

)

]

0 l λ l l πa πp

λ − _σ 2.5

( )

E_strain(2)

(

)(

)

[

(

)

(

) (

(

)

)

]

d

d λ λ π

λ − _σ 2.6

( )( )

( )

E_exstrain = , E_ex.strain(DB)=εσ_⊥, β =

( ) (

)

( )

E_step

(

)

( )

( )

( )

( ) (

)

(

(

)

)

( )

( )

max H E Sl E Sl E Sl

l T K Sl E Sl

F = _step − _b λ _SB + _strain + _strain + _exstrain

2.8

( )

( ) (

)

(

(

)

)

F = _step − _b λ _DB + _exstrain 2.9

The step phase boundary is given by F

( )

( )

where F is Helmhotz free energy per unit area and λ_maxis the maximum

calculated using the transfer-matrix method, [40-42]

where for Z_{H( )SB}

h

(

(

) (

[

)

]

)

(

[

]

)

(

[

(

)

]

)

' 2 1 2 exp exp 2

exp− β κ h−l −β λ_⊥ h−h −β ε_c −δ_hh

(

)

[

(

)

]

(

)

2

exp− β κ h −l _h'

where for Z_{H( )DB}

h

(

(

)

[

(

)

]

)

(

[

]

)

(

[

(

)

]

)

(

)

[

(

)

]

(

)

h

Here, H is the transfer-matrix element associated with H(SB) and H(DB)

respectively, h_i represents the fluctuation of the ith _{segment of the ledge front at}

a temperature T, λ_⊥ is the energy cost per unit length of a ledge created in the

perpendicular direction, λ_|| is the energy of breaking the DB step into a pair of SA

and SB steps, ε_c is the creation energy of a corner in a jagged ledge, and

β=

( ) (

)

the strain relaxation energy E_strain(1)

( )

( )

strain

) 2

( _{. It only applies to single}

(Sl) steps in that E_strain =0 for the double (Dl) stepped surface. E_strain

( )

reaches its minimum for a surface with steps equally spaced.

harmonic approximation [41] of E_strain

( )

[

( )

]

[

( )

]

16 3

8l a λ_d l a

λ

κ = _σ + where

( )

E_strain(1) _(E

( )

strain

) 2

( _{) is the first-order (second-order) strain relaxation energy.} 0

λ

is the creation energy per unit length of a domain wall due to dangling bonds,

local deformation, and other such factors, λ_σ is the coefficient of long-range

force-monopole interaction, which depends on the particular pattern of the stress

domain, the magnitude of anisotropy in σ_ij stress tensor, and the specific bulk

elastic constant. λ_d is the coefficient of the short-range force-dipole interaction,

which is significant for SA and SB steps.

The first term inE_strain(2)

( )

the second-order strain energy associated with the stress-domain

interaction.E_ex.strain is the external applied strain energy,ε = the external applied

strain, σ_|| (σ_⊥) is the stress tensor along (perpendicular to) the surface dimer

bond direction, λ_SA, λ_SB, and λ_DB are the step formation energies per unit length

for the S_A, S_B, and D_B steps, and a is a microscopic cutoff length of a Lorentian

broadening of the force density f_j

( )

( )

(

)

₍

₎

f_{j o}

0 0 1 Im δ ρ

Equation (9)* is a function of

(

)

(

)

step transition, which is only valid for the temperature range 3000-5000C.[42] The

external strain ε is applied to the surface, then the widths of alternating 2x1 (or

1x2) domains will become

(

)

(

)

tempera-ture is low or at absolute zero, the step thermal fluctuation energy in (2.9) is

negligible and free energy is dictated by the strain-domain relaxation,

force-mutipole interactions, and step formation energies. As a result, D_Bstepped

surfaces have a lower free energy than Sl stepped surfaces for l<l_c1(or θ >θ_c1).

On the contrary, D_B stepped surfaces have higher free energy than Sl stepped

surfaces for l >l_c2 (orθ <θ_c2). For l_c1 <l <l_c2( or 0 1 0

2 =2.5 < < c =3

c θ θ

θ ) mixed

stepped surfaces having lower free energy than either of them are favorable.[41]

As the temperature rises, the step thermal fluctuation energy is no longer

negligible, the range of critical vicinal miscut angle (θ_c2,θ_c1) becomes bigger, and

thus there occurs no distinct step phase transition above a certain temperature.

In other words, the step phase transition is gradual.[41] Although the theoretical

calculation of (θ_c2,θ_c1)[41] and the step formation energies are still not accurately

known, this model can account for most experimental results.It not only can be

applied to the UHV case but also to the “oxidized” one, except that all the

parameter values are different and λ₀ is the creation energy per unit length of a

domain wall due to oxygen-deficient bonds, local deformation, and other such

factors. Therefore the step driving mechanism for both cases are almost the

instance, there exists a localized strain[42] near the Si-SiO2 interface because

of lattice mismatch before thermal annealing treatment. The localized strain is

equivalent to the external applied strain at the interface, as a consequence,

leading to a larger (θ_c2,θ_c1) range. Therefore, the RD signals in Fig. 2.3 indicate

the presence of mixed stepped interfaces before the annealing treatment.

However, after the annealing treatment the localized strain is reduced[42] and

the (θ_c2,θ_c1) range becomes smaller, resulting in the distinct step phase

transition shown in Fig. 2.3.

At present, experimental techniques are still unable to provide us with better

step-image resolution, which hinders current progress in theoretical

first-principles calculations of step properties at buried interfaces. Nevertheless, the

atomic bonding topology plays a pivotal role in interface thermodynamics.

Consequently, we hope that the understanding obtained from RDS and other

techniques will further stimulate experimental and theoretical studies in a more

systematic way in the future although the structures and energies of oxidized

steps are presently unknown.

We conclude this section by noting that several of our interpretations are not

only consistent with various recent experiments but also with theories available in

the literature. Renaud et al.[25]and Tsu et al.[33] employed grazing incident x

ray scattering and RHEED techniques, respectively, to demonstrate that there

Tu and Tersoff applied a Monte Carolo simulation to determine Si-SiO2 interface

structures by minimizing interface energy. The optimal interface structure they

found consists of an ordered array of (2x1) -Si-O-Si- bridges with low strain

energy.[32] In summary, using RDS techniques, we are able to identify the

existence of the steps at the Si-SiO2 interfaces optically. Steps, in fact, consist of

domain single-atomic height steps as well as single-domain

double-atomic height steps, of which the density varies linearly with respect to the

vicinality of the silicon substrate. A “gradual” step phase transition was also

observed, which is in good agreement with recent experiments by other

techniques and theoretical predictions. [20,42]

In general the optical anisotropy of cubic semiconductors originates from

the local field effect, which is caused by the broken symmetry (or reduced

symmetry) of the interface and specifically of the difference in screening across

the interface. These effects are aided by bonding charge transfer near the

interface, which tends to minimize the interface energy thermodynamically, and

interface chemical termination as well as strain, which affects the electronic

polarizability of near-interface atomic bonding structures.[18,19,43,44] Although

the conclusions drawn here agree well with the studies reported in the literature,

a systematic theoretical investigation of optical anisotropy of the oxidized vicinal

silicon surfaces is still not available. In principle, interface (or surface) induced

and unambiguous interpretation of RDS lineshapes still relies entirely on the

systematic theoretical study based on first-principles calculations. The present

work is intended to pave the way for further progress in this direction.

The present study of steps at the interface should also shed light on

heteroepitaxy on silicon, which has been explored extensively since the 1980s.

The double steps at the interface can be used to avoid antiphase domains that

occur in heteroepitaxy.[48] Hence the better understanding of the atomic steps

will be of crucial importance in this application as well.

2.4. ACKNOWLEDGMENTS

It is a pleasure to acknowledge support of this work by the Office of Naval

Research under Contract No. 00014-93-1-0255 and by the Army Research Office

under Contract No. TCN 97-184, J. -F. T. Wang would like to thank Joan N.

O’Sullivan at the Microelectronics Laboratory of N. C. State University for her

assistance in sample preparation and also would like to thank committee

members Professor Gerald Lucovsky and Professor Carton M. Osburn for their

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2 3 4 5 0.0

0.5 1.0 1.5

3O

1O 9O

VICINAL (001)Si-SiO2 UNANNEALED

10

3 (

∆

R / R)

ENERGY (eV)

2 3 4 5 0.0

0.5 1.0 1.5

VIC IN AL (001)Si-SiO₂ AN N EALED

1o 9o

10

3 (

∆

R / R)

EN ER G Y (eV)

0 2 4 6 8 10 0.0

0.2 0.4 0.6 0.8 1.0 1.2

ANNEALED

UNANNEALED

VICINAL (001)Si-SiO

LIN

ESH

APE NORMAL

IZED FRACTION

VICINAL ANGLE (DEGREE)