Silicon Nanosheets: Optical Properties,Light Confinement in Multilayer

Waveguides, and Lateral ElectricalInjection and Luminescence

by

Han G. Yoo

Submitted in Partial Fulfillmentof the

Requirements for the Degree

Doctor of Philosophy

Supervised byProfessor Philippe M. Fauchet

Department of Physics and AstronomyArts, Sciences and Engineering

School of Arts and Sciences

University of RochesterRochester, New York

2009

ii

Curriculum Vitae

The author was born in Seoul, Republic of Korea in 1979. He received dual

Bachelor of Science degrees in applied mathematics and physics from the Univer-

sity of Rochester in 2002. He enrolled in a Ph. D. program in the Department of

Physics and Astronomy at the University of Rochester. He was granted a Mas-

ter of Arts degree in physics in 2004. He received a Department of Education

GAANN Award from 2002 until 2004 by the Department of Physics and As-

tronomy. Since 2004, he studied nanocrystalline silicon-based light source under

Professor Philippe M. Fauchet’s guidance. He is a member of MRS, IEEE and

SPIE.

iii

Acknowledgments

I would like to express my sincere gratitude to my advisor Professor Philippe M.

Fauchet for his guidance and support. I am indebted to him for the opportunity

to interact with and learn from him throughout my time in his group. I also

enjoyed his good sense of humor and having several interesting conversations not

related to research. Thank you, sir.

I am very thankful to Professor Yongli Gao for his guidance throughout my

graduate years. I have been encouraged by his genuine desire to see me succeed

not only in my research effort but also in whatever endeavor I may undertake in

the future.

I am also grateful to Professor Gary W. Wicks for the numerous occasions

when he generously set aside his time to answer my questions with gentleness. I

benefitted a lot from his clear teaching and lucid explanations. I would like to

express my appreciation to Professor Yonathan Shapir and Professor Andrew N.

Jordan for their time to review my thesis work.

I thank Professor Jung H. Shin of the Korea Advanced Institute of Science and

Technology for his guidance and many inspiring insights for my research. I am

very much indebted to him for helping me succeed in my research effort. It was

also my pleasure to get to know his family and have many engaging conversations

with him on variety of topics besides physics and engineering.

My appreciations go to my former and present colleagues in my group: Chris

Striemer, Rishi Krishnan, Jinhao Ruan, Mikhail Haurylau, Huimin Ouyang, Sharon

iv

Weiss, Ashutosh Shroff, Wei Sun, Hui Chen, Jidong Zhang, Mindy Lee, Jeff Clark-

son, Sean Anderson, Yijing Fu, Maryna Kavalenka, Xi Liu, Jonathan Lee, David

Fang, Krishanu Shome, Joshua Winans, Elisa Guillermain and Adam Heiniger.

My discussions with them have been very insightful throughout my research.

I would like to express my sincere appreciation to the administrative staff at the

Department of Physics and Astronomy and Department of Electrical Computer

Engineering. Throughout my graduate program, Barbara Warren has supported

and encouraged me through the ups and downs and was always on my side. She is

indeed a good advisor and advocate for graduate students. I am thankful for Vicki

Heberling in our group not only for her numerous efforts to work out the research

logistics smoothly but also her laughters. I am also very grateful to Janet Fogg-

Twichell who encouraged and supported me through the undergraduate program.

It meant a lot to me when she let me borrow textbooks from her stock semester

after semester knowing I was not able to have my own copies.

Paul Osbourne and James Lindner have been tremendous help in machining

and designing instrument parts. It was fun to share laughters and to observe

interesting projects undergoing in their shop. I want to also say thanks to Brian

McIntyre for his training and assistance with electron microscopy.

Grateful recognition goes to the Laboratory for Laser Energetics for letting

me use a couple of valuable instruments. I am particularly thankful to Dr. James

Oliver at the Optical Manufacturing Group for the spectroscopic ellipsometer and

Dr. Lawrence Iwan at the Optical and Imaging Sciences for the prism coupler.

I found the staff at Cornell NanoScale Science & Technology Facility to be not

only superb in their expertise but also very understanding and accommodating.

Michael Skvarla and Paul Pelletier often went out of their way to provide me

assistance with designing and fabrication.

Above all, I am truly indebted to my extended families—mother and my two

brothers Michael and Joey and Michael’s wife Winnie—all of whom sacrificed

v

part of their lives for each other. Such sacrifices never turn out to be futile. I am

grateful for my father who saw a potential in me and encouraged me to take a

scholarly pursuit. He passed away 16 years ago but I still have vivid memories of

him teaching me advanced level mathematics. I am sincerely thankful to you all.

I would like to express a genuine appreciation for my in-laws, especially mother-

in-law, all of whom were very supportive and understanding of me, my wife and

our children.

My children Katelyn, Isaac and Noah—all of whom were born during my

graduate program—are such a joy and blessing to me and my wife. Your mother

and I love you dearly. Most importantly I am blessed to have Christina as my wife

and my best friend. You made so much sacrifices for me to successfully complete

this program and you made it possible. I love you and am eager to continue to

journey together with you in whatever future may lie before us.

vi

Abstract

It has been discovered that the photoemission from erbium (Er) atoms in an

oxide host with silicon nanocrystals (nc-Si) is markedly enhanced by the energy

contribution from the neighboring nc-Si. It is thus of great interest to fully un-

derstand the photoemission mechanism of nc-Si sensitized Er atoms and develop

an optimal fabrication process and sample structures that would maximize the

optical gain.

The dielectric function of ultra thin c-Si films was obtained at various film

thicknesses (14 nm to 3.5 nm) using variable angle spectroscopic ellipsometry. The

dielectric constant at long wavelength (1.7 µm) was found to be decreasing as the

film thickness decreases. The reduction of the dielectric constant quantitatively

and qualitatively agreed with the most applicable theory, which is based on the

surface polarization effect.

The birefringence in a stratified multilayered film consisting of alternating

high- and low-index layers was predicted by simulations and experimentally con-

firmed by m-line measurements. The simulations followed the Abeles matrix

method, which is also known as the characteristic or transfer matrix method,

and it showed that the mode indices (characteristic propagation constant) for TM

polarized modes were substantially lower than those for the TE modes. This bire-

fringence is evidence for higher light confinement in the low-index layers (e.g. SiO2)

than in the high-index layers (e.g. a-Si or nc-Si film) for TM polarized modes at

infrared wavelengths (1.55 µm). The effect of lower dielectric constant at smaller

vii

film thickness, as mentioned above, is also observed in the m-line measurement,

which showed lower mode indices.

Injecting electrical charge carriers laterally along the Si layers of a multilay-

ered film was explored. A sample was fabricated by etching trenches in heavily

doped P- and N-type regions separated by an un-doped region and depositing

electrically conductive pads onto the trenches, forming a P-“I”-N diode. When a

bias voltage is applied, electrons and holes injected laterally along the Si layers

recombine to produce photons as evidenced by electroluminescent spectroscopy.

The slow transient change in electroluminescent intensity when the bias voltage

was abruptly modulated between various levels indicated a thermal effect due to

the current. Changes in modal indices were observed in m-line measurements at

various bias voltages, which resulted from the Si layers’ refractive index change

caused by the thermo-optical and free carriers-optical effects. These two effects

were also evidenced in the transmission m-line measurements, where an external

1.55-µm light was coupled into the multilayer film waveguide and its transmitted

intensity was measured as the bias voltage was modulated abruptly. It was found

that the thermo-optical effect influences the real part of the refractive index but

not the absorption coefficient noticeably, whereas the free carriers-optical effect

alters the absorption coefficient but not the real part of the index.

viii

Table of Contents

Curriculum Vitae ii

Acknowledgments iii

Abstract vi

List of Tables x

List of Figures xi

1 Introduction 1

1.1 Silicon Photonics . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Pursuit of Silicon Laser . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Bibliography 8

2 Size-Dependency of Dielectric Function of Si Nanostructures 9

2.1 Introduction & Motivation . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Experiment & Analysis . . . . . . . . . . . . . . . . . . . . . . . . 17

ix

2.4 Results & Comparison . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Bibliography 29

3 Birefringence and Optical Power Confinement In Horizontal Si /

SiO2 Multilayer Waveguides 32

3.1 Introduction & Motivation . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Results & Comparison . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Bibliography 47

4 Electroluminescence and Free Carrier Absorption in Si / SiO2

Multilayer Films by Lateral Electrical Injection 50

4.1 Introduction & Motivation . . . . . . . . . . . . . . . . . . . . . . 50

4.2 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Results & Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Bibliography 67

5 Summary & Future Outlook 71

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2 Future Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Bibliography 75

x

List of Tables

2.1 Various fit parameters used in the theoretical calculations based on

quantum confinement effect. . . . . . . . . . . . . . . . . . . . . . 14

xi

List of Figures

1.1 nc-Si as sensitizers for Er ions. a Energy in nc-Si is transferred to a

nearby Er atom. b Energy bands are shown for silicon nanocrystals

and Er ions embedded in an oxide matrix. After Fig. 2 of Ref. [8] 4

2.1 Electron energy ε vs. k for an isotropic three-dimensional nearly

free electron model. The solid curve represents the “continuous”

electron energies in a bulk structure, whereas the solid dots the

discrete energies a spherical nanodot structure. After Fig. 1 of

Ref. [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Plots of the several size-dependent static dielectric constants ε(a)

vs. the radius a of the silicon sphere in A. After Fig. 2 of Ref. [13]. 15

2.3 Ratio between the bare electric field Eb and the screened one E

in Si layers submitted to a constant electric field. After Fig. 2 of

Ref. [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Permittivity profiles along the [100] direction for Si(100) slabs with

H-terminated surfaces. The numbering refers to the slab size in

terms of Si planes. After Fig. 3 of Ref. [17]. . . . . . . . . . . . . 15

xii

2.5 Ratio between the bare electric field Eb and the screened one E

vs. the distance to the center in a 2.5-nm Si spherical nanocrystal.

The bare field is due to a charge +q at the center and a charge

−q uniformly spread on the surface of the sphere. After Fig. 4 of

Ref. [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6 (a) Permittivity of a Si slab as a function of thickness d; local

permittivity in the central Si plane (circles) compared to the overall

slab permittivity (disks). (b) Band gap of a Si slab as a function of

thickness d (squares). The horizontal line indicates the band gap

of a slab of infinite thickness (0.62 eV). After Fig. 4 of Ref. [17]. . 16

2.7 Fabrication procedure for the samples and bare Si pieces. When

further thinning down the samples’ top Si layer, the following se-

quence was repeated: (a) removal of oxidized Si by BOE etching,

(b) ellipsometry measurement, (c) dry oxidation in a flowing argon

and oxygen environment at either 600◦C or 650◦C for 5 minutes,

(d) ellipsometry measurement. The bare Si pieces did not undergo

step (b) after BOE etching. . . . . . . . . . . . . . . . . . . . . . 17

2.8 Ellipsometric angles Ψ and ∆ of both measured and fit data sets

at the incident angle of 65◦ for a 3.5-nm-thick Si layer of sample

C. The filled squares and circles represent the measured Ψ and ∆,

respectively. The solid and dotted curves represent the fitted Ψ

and ∆, respectively, generated by fitting the measured data with

two T-L oscillators. The fit matches the measured data very well

over the entire spectrum. . . . . . . . . . . . . . . . . . . . . . . . 21

2.9 (a) sample structure used in theoretical calculations. (b) actual

sample structure in experiment. (c) simplified sample structure

used in ellipsometric analysis. . . . . . . . . . . . . . . . . . . . . 22

xiii

2.10 Measured εR and εI over the entire spectrum vs. layer thickness

from 13.1 to 3.2 nm for sample B, incorporating no SR layer in the

fit. The oscillatory functions used in the fit are T-L and Gau. . . 23

2.11 Measured and theoretical ε for nanoslab as a function of the inverse

slab thickness. For clarity, the data from only sample B are shown

for the measurement, but the solid line represents a linear fit to all

the measured εNormalized for all three samples. Each ellipsometric

data (Ψ, ∆) was evaluated with 5 A of surface roughness layer using

the two different oscillator sets: a set of T-L and Gau (triangles)

and a set of two T-L oscillators (squares). The two resulting fits

(ε, 1/T ) are grouped together. The dashed lines are the theoretical

values calculated in Refs. [13], [14] and [17]. All ε are linearly scaled

such that their respective bulk values are 12. . . . . . . . . . . . . 25

2.12 Comparison of theoretical calculations and measurement evaluated

with a 0-, 5- and 10-A thick SR layer. . . . . . . . . . . . . . . . . 27

3.1 (a) Coordinate system and notation of the number of the films for

the present stratified multilayered film system. The film structure is

sandwiched between the incident (0) and substrate (m + 1) phases.

After Fig. 1 of Ref. [20]. (b) Decomposition of the refractive index

n along x and z directions. (c) The convention for the positive

direction for s (TE) and p (TM) polarizations. After Fig. 4.1 of

Ref. [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

xiv

3.2 (a) SEM of a structure made of alternating a-Si and SiO2 layers.

(b) Schematic of sample structure with P periods of LSi thick a-Si

and LSiO2 thick SiO2 layers on a 5-µm thick thermal oxide layer.

(c) Sample structure as viewed by the prism coupler for m-line

measurement. The multilayer film is replaced by a single film with

an effective material index of nFilm and thickness LFilm = P (LSi +

LSiO2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 (a) Schematic of m-line measurement. (b) Graph of reflected light

intensity as a function of the modal index for a multilayer film of 34

periods of 15.2 a-Si and 19.7-nm SiO2. The arrows show the modal

indices greater than 1.44 at which a bound mode is established

(2.43, 2.16 and 1.75 for TE; and 1.74 and 1.55 for TM). Modal

indices between 1.8 and 1.9 were not measurable because of the

two prisms used. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4 First and second order modal indices versus SiO2 / a-Si layer thick-

ness ratio for both polarizations. The curves represent the calcu-

lation for 1.00-µm thick film and the dots represent the measured

values for film thicknesses ranging from 0.93 to 1.19 µm. . . . . . 42

3.5 Measured (dots) and calculated (curves) modal index difference

between the fundamental TE and TM modes as a function of layer

thickness ratio for total film thicknesses between 0.4 and 0.9 µm.

The maximum difference of ∼ 0.8 is obtained if the thickness ratio

is around 0.5 and 0.6. . . . . . . . . . . . . . . . . . . . . . . . . . 43

xv

3.6 The power profile of the first order TE and TM modes in a 0.60-µm

thick film consisting of 10 periods of alternating 30-nm thick a-Si

and SiO2 layers. The SiO2 substrate layer is positioned below the

0.0-µm mark and the air above the 0.6-µm mark. The shaded areas

represent the SiO2 layers. For TM polarization, the transverse E-

field component in the low-index nL region is greater by a factor of

nH2/nL

2 than that in the high-index nH region immediately across

the interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.7 The power confinement factor in the SiO2 layers for first order TM

mode as a function of layer thickness ratio at various total film

thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.8 The linear relationship between the total film thickness and its

optimum layer thickness ratio. The shaded area represents the

region where only one TM mode exists. . . . . . . . . . . . . . . . 45

4.1 (a) Longitudinal (vertical) injection scheme. (b) Lateral (horizon-

tal) injection scheme. . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 (a) Brief sequence of fabrication process: <1> RF magnetron de-

position of a-Si and SiO2, followed by rapid thermal annealing;

<2> ion implantation of P and B ions; <3> reactive ion etching

of trenches; <4> deposition of Ti on the trenches. (b) Plan view

showing the implantation (1 mm × 5 mm) and trench area (0.3 mm

× 4 mm) dimensions. The contact pad areas are colored orange and

their dimensions are 0.6 mm × 4.5 mm. (c) Finished sample. . . . 52

4.3 (a) IV measurement. (b) Spectroscopic electroluminescence mea-

surement at three different bias voltages: 45, 50 and 55 V. The

inset shows the integrated intensity as a function of the electrical

power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

xvi

4.4 (a) Plots of luminescence intensity, applied bias voltage and result-

ing current vs. time. For the first ∼ 70 S, the voltage modulated

between 0 and 35, 40, 45, 50 and 55 V. For the latter 70 S, the

voltage decreased by every 5 V from 55 to 35 V and down to 0 V

then increased back to 55 V. The duration of the current transient

segments lasted less than 0.25 seconds. (b) Plot of luminescence

intensity vs. time when the bias voltage switched from 55 to 50 V

(between 71 and 84 S). After the bias voltage was changed to 50 V,

the estimated time for the current to settle to its new level is 3.5 S. 55

4.5 (a) m-line measurement in the reflectance configuration at the bias

voltage of 0 V. The 2nd-order TE at 1.481 and 1st-order TM at

1.569 guided modes are shown along with the evanescent modes.

(b) m-line measurement in the reflectance configuration for the TE

polarization at various bias voltages for the 2nd-order guided and

1st-order evanescent modes. . . . . . . . . . . . . . . . . . . . . . 57

4.6 Temperature change as a function of electrical power for the 2nd-

order TE and 1st-order TM. The fit lines are for guides to eye. . . 59

4.7 m-line measurements in the reflectance and transmittance configu-

rations at 0 and 55 V for (a) the 1st-order guided TE mode (mea-

sured with the Si prism) and (b) 1st-order guided and evanescent

TM modes (GGG prism). The transmittance intensity is scaled

such that the 0 corresponds to the no transmittance. The modal

index values at 0 V as obtained in the reflectance configuration are

marked with purple vertical lines. . . . . . . . . . . . . . . . . . . 61

xvii

4.8 (a) Profile of the normalized field intensity for the three guided

modes inside the slab waveguide with respect to position. The

light blue region below 0.0 µm represents the air cladding layer,

whereas the region above ∼ 0.4 µm the thermal oxide layer. The

sputtered SiO2 layers are highlighted light yellow and the Si layers

white. (b) Transmittance intensity, bias voltage, current vs. time

for the 1st-order guided TE mode. Zero reading on the intensity

scale corresponds to no transmitted light intensity. . . . . . . . . . 62

4.9 ∆αSi and ∆NSieh vs. current (mA) using intensity- and energy

density-based modal confinement factors in the two Si layers. The

currents 0.0, 23.6, 38.7 and 56.6 mA correspond to 0, 45, 50 and

55 V of bias voltage. The fit lines are for guides to eye. . . . . . . 64

5.1 A rib waveguide consisting of the capping 1-µm wide oxide layer

on top of the multilayer film with electrical connections. . . . . . 73

5.2 A rib resonator with distributed Bragg reflectors. After Fig. 4.9

of [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

1

1 Introduction

1.1 Silicon Photonics

Silicon has been the dominant semiconductor material in the microelectronics

industry, primarily due to, not its own properties, but those of its native oxide-

an insulator (SiO2). Besides its oxide’s superb insulating property, silicon pos-

sesses other significant advantages over rival semiconductor materials (e.g., Ge

and GaAs), including its abundance, easy mass production with near perfect crys-

tallinity in large scale and sustainability of its properties in high temperature [1].

These prevailing qualities of silicon, along with integratability and economy of

scale, compelled the microelectronic industry to build its enormous fabrication

infrastructure around silicon.

The insatiable demand to achieve a smaller yet faster microelectronic chip

has led the industry to ever increase the transistor density and its operating fre-

quency, following Moore’s Law. An obvious way to attain such a chip is to reduce

the transistor size. However, reducing the chip size inevitably entails confronting

the limits of such technology, namely on fundamental, material, device, circuit

and system levels [2]. Among many components within a chip, particularly the

electrical interconnects between chips or even within a single chip are reaching the

2

device scaling limit, becoming a major bottleneck in chip performance. The scal-

ing down of the interconnects unfortunately results in not only higher resistance

and inductance and higher capacitance—all of which pose a detrimental effect on

chip’s operation speed-but also higher power consumption and heat dissipation.

Moreover, the proximity of the interconnects within themselves invites potential

problems of electromigration effect and of signal integrity degradation due to elec-

tromagnetic interference [3]. It is therefore essential to find an alternative to the

electrical interconnects and one of good candidates is optical interconnects.

Given the well-established fabrication infrastructure for silicon processing, op-

tical interconnects made with silicon seem to be an attractive solution for silicon-

based microelectronic chips. A successful hybridization of silicon technology with

optics would certainly open, and has opened, a whole new promising field in op-

toelectronics. Nevertheless, because of silicon’s very limited optical functionality

due to its indirect band gap and absence of Pockels electro-optic effect [4], it

had been considered as a practically nonviable choice of material in the optoelec-

tronics field. However, the discovery of bright luminescence from porous silicon

nanostructure in 1990 [5] prompted a re-evaluation of silicon as a promising op-

toelectronic material candidate, this time not in the bulk form but in nano-sized

structures. Silicon may never outperform optoelectronics made with expensive

and exotic materials, such as GaAs [6]. But if it can perform suitably well as

chip-to-chip interconnect components at a much lower cost, silicon’s legacy would

certainly continue in the optoelectronics era.

1.2 Pursuit of Silicon Laser

Analogous to electronics, the basic building blocks in photonics include optical

source, amplifier, transmission line, modulator, buffer, storage, detector, etc. De-

spite significant advancements overall in silicon-based photonics, a major challenge

3

still remains in developing optical sources (particularly lasers) and amplifiers fully

compatible with current silicon microelectronics fabrication. In order to create

a silicon laser, not only silicon must function as an amplifying medium but also

a resonant cavity made of silicon is needed for coherent light output. Since the

discovery of photoluminescence from porous silicon [5], silicon in various nanos-

tructures (e.g., nanodots) has been found to have higher luminescence efficiency

than bulk. Yet, there have been no reports of optical gain in silicon nanostructures

until 2000, when evidence was presented for optical gain from nc-Si fabricated by

ion implantation in a silicon oxide film [7]. This report prompted intensive research

on nc-Si and propelled an optimistic outlook that the silicon-based optoelectronics

is ever more feasible.

Among various forms of nc-Si host structures (e.g., disc, ring and sphere), nc-Si

embedded in a stratified film are of particular interest due to its straight-forward

fabrication process. Effort to attain optical gain from erbium atoms has been

expanded to investigating the infrared emission from Er-doped nc-Si embedded

films. If a low-cost laser made of such Er-doped films can be fabricated, it can not

only replace the expensive and exotic Er-based telecommunication devices but also

it can be used as the light source for optical interconnects in microelectronic chips,

as its emission wavelength falls below the Si absorption onset and consequently

would not inadvertently interfere with neighboring Si components.

The vast majority of research in Si-based light sources has been conducted

so far using optically pump schemes. In an optically pump scheme, an external

high-intensity laser with high photon energy (e.g., 488-nm from Ar laser) strikes

a test device, thus “optically pumping” the nc-Si’s inside the device to higher

electronic energy levels. The excited electrons then non-radiatively decay rapidly

into lower but stable excited energy levels, from which they undertake a radiative

recombination process and thus producing photons. If Er atoms are embedded

close to the nc-Si’s, electrons in the stable excited energy levels can decay back to

4

Figure 1.1: nc-Si as sensitizers for Er ions. a Energy in nc-Si is transferred to a

nearby Er atom. b Energy bands are shown for silicon nanocrystals and Er ions

embedded in an oxide matrix. After Fig. 2 of Ref. [8]

the ground energy level by non-radiatively transferring its energy (i.e., photon-less

energy transfer) to the adjacent Er atoms and the excited Er atoms luminesce at

their signature wavelength of ∼ 1550 µm (cf., Fig. 1.1).

Given the ample amount of reported research findings based on optical pump-

ing schemes, there has been growing research interested in employing electrical

pumping scheme in an effort to achieve a battery-powered light source. In an

electrical pumping scheme, a battery is connected to a pair of conductive contact

pads on a device, into which electrons and holes are injected when the battery

voltage is applied. The injected electrons and holes then recombine in the Si

regions, “electrically pumping” the nc-Si’s. This recombination would produce

photons or heat, or excite neighboring Er atoms if they are present. There are

two proposed injection schemes for a device based on a stratified multilayered film

of alternating nanometer-thick Si and insulating (e.g., oxide or nitride) layers. In

transverse injection method, electrons and holes are injected across (perpendicular

to) the layer orientation; in the longitudinal injection method, electrical charges

5

are injected along (parallel to) the layer orientation. By employing the lateral elec-

trical injection method on multilayer films of alternating nanometer-thin Si and

Er-doped insulating layers, electrically powered Er-doped Si-based light sources

are expected to play a critical role in overcoming the bottleneck in microprocessor

performance.

1.3 Thesis Overview

This thesis is constituted of three research topics. The first topic discusses the

size dependency of silicon nanostructures’ dielectric function. It is very impor-

tant to know the dielectric function of a material since it determines many of the

material’s optical and electrical properties. It has been theoretically predicted

that the dielectric function of silicon nanostructures (e.g., dots, wires and slabs)

differs from that of the bulk due to quantum confinement or surface polarization

effect. We measured the dielectric constant of a silicon nanoslab as a function

of its thickness and found that the dielectric value is reduced as the slab thick-

ness decreases in the visible and longer wavelength region, in agreement with the

surface polarization model.

The second topic deals with light confinement in a stratified multilayered film

consisted of alternating layers of a-Si and SiO2. The nc-Si clusters that act as

sensitizers for the Er atoms are fabricated by depositing an a-Si / SiO2 multilay-

ered film, that is then subjected to a high temperature annealing process. The Er

atoms in the SiO2 host, which emit at the telecommunication wavelength, gen-

erate higher luminescence intensity than in the nc-Si host. On the other hand,

the light from the Er atoms experiences optical loss when encountering the nc-Si

due to free (or confined) carrier absorption. Hence it is imperative that most of

the Er emission light be confined in the SiO2 host, which has a lower refractive

index than nc-Si or a-Si. We have completed an ab initio simulation on high- and

6

low-index multilayered films, which reveals unambiguously that the infrared light

in the TM polarization is more confined in the SiO2 layers than in Si layers. We

also have carried out an m-line measurement on such films, which showed a much

lower modal index for TM polarization than for TE, confirming the simulation

result. If the simulation uses the reduced dielectric value for ultrathin Si layers

instead of the bulk value, as discussed in the first topic, the simulation matches

even closer with the measurement.

The last topic discusses the lateral electrical injection scheme for nc-Si / SiO2

multilayered films and its thermal and free carrier absorption effects. In an effort

to build an electrically powered light source that can be incorporated in micro-

processors, it is critical to do away with an external high-intensity, high-photon-

energy light source required in an optical pumping scheme. It is thus imperative

to explore and accomplish electrical pumping, where electrons and holes are di-

rectly injected into nc-Si’s, rather than being indirectly generated by an external

light source. For the multilayered film structure, a widely used scheme is to de-

posit electrical contact pads on the two most outer layers of the film and to inject

electrons and holes across (perpendicular to) the layer orientation. In this lon-

gitudinal / transverse method, the electrical charges are recombined in Si layers

after penetrating through multiple insulating layers, naturally resulting in a high

turn-on voltage. On the other hand, if the charge carriers are injected into the Si

layers along (parallel to) the layer orientation, as done in the lateral / horizontal

method, the turn-on voltage is expected to be lower. To laterally inject charges, a

multilayer film on a thick thermal oxide layer undergoes ion implantation to create

heavily doped P- and N-type regions separated by an un-doped region, forming

a P-“I”-N diode. Using reactive ion etching, a trench is carved out across the

multilayer film in each doped region. A conductive pad is thermally deposited

onto each trench, electrically shorting the Si layers of the film together. To test

out this injection scheme, we have fabricated a multilayered film of 3 pairs of al-

7

ternating 69-nm nc-Si and 63-nm thick SiO2 layers on a 5-µm thick thermal oxide

layer with the 5-mm long doped regions and 3-mm wide region-to-region sepa-

ration. Current-voltage measurement shows the sample to be a very poor diode

with a very low break-down voltage. The electroluminescence spectroscopic mea-

surement shows a broad spectrum above 1.3 µm at 55 V. We also measured the

electroluminescent intensity as the bias voltage changed from one level to another.

The luminescence intensity showed a slow transient effect, indicating that the elec-

trically generated heat affects the electroluminescence. This heat also affects the

modal indices of the multilayer film, as confirmed by m-line measurement, since

it causes Si’s refractive index to increase. Free carrier absorption was verified in

the experiment where 1.55-µm light was coupled into the multilayer waveguide

using a prism coupler and the transmitted light intensity was measured as the

bias voltage was changed.

8

Bibliography

[1] A. Fowler, “On some modern uses of the electron in logic and memory,” Phys.

Today 50, 10, 50 (1997).

[2] J. Meindl, “Special issue on limits of semiconductor technology,” Proc. IEEE

83, 223 (2001).

[3] H. Chen, “Towards a nanocrystalline silicon laser,” Ph.D. dissertation, Uni-

versity of Rochester (2007).

[4] G. Reed, “The optical age of silicon,” Nature 427, 595 (2004).

[5] L. Canham, “Silicon quantum wire array fabrication by electrochemical and

chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046 (1990).

[6] S. Moore, “Intel makes a silicon laser,” IEEE Spectrum,

http://spectrum.ieee.org/jan05/2912, Jan. 2005, retrieved 22 Oct. 2007.

[7] L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical

gain in silicon nanocrystals,” Nature 408, 440 (2000).

[8] A. Polman, “Teaching silicon new tricks,” Nature Mater. 1, 10 (2002).

9

2 Size-Dependency of Dielectric

Function of Si Nanostructures

2.1 Introduction & Motivation

Silicon nanostructures have attracted a lot of attention because of their various

potential uses, from memory elements to light sources [1–4]. When designing de-

vices that incorporate Si nanostructures, it is often important to precisely know

their dielectric functions ε or indices of refraction n (ε = n2), since they deter-

mine many of their electrical and optical properties. For example, the dielectric

function affects the charging and discharging of silicon nanocrystals (nc-Si) with

free carriers and also the light confinement in a waveguide constituted of nc-Si in

the core.

There have been numerous experimental reports on the size dependence of ε

for various semiconductor nanostructures such as PbSe nanodots [5], but only a

few have been reported for Si nanostructures [6–10]. In those few studies, the

nanostructures were Si nanocrystals (nc-Si) embedded in a SiO2 film or either

a single [6–8] or multiple [9] polycrystalline films. The value of ε was obtained

through spectroscopic ellipsometry [6–9] and C-V measurement [10]. However all

the measurements except the one published in Ref. [6] were performed at only one

particular average size and therefore these studies could not confirm any particular

10

theory on static dielectric constant over a range of sizes. In Ref. [6], the size of

nc-Si ranged from 1.25 down to 0.6 nm but the lowest energy at which ε was

measured was ∼ 3 eV for 0.6-nm-wide nc-Si.

In this work, we instead systematically measured the size-dependent ε of crys-

talline Si (c-Si) nanoslabs, which are much simpler structures than the nc-Si

structures, of different thicknesses from ∼ 14 to 3.2 nm. We used a variable angle

spectroscopic ellipsometer with an adjustable retarder for high accuracy over the

spectral range of 0.73 (1.7) to 4.58 eV (0.27 µm). The experimentally obtained

values of ε are then compared to the theories that have been presented so far.

2.2 Theories

Several theoretical studies [11–17] have predicted a reduction in ε as the nanostruc-

ture size decreases. However these models propose different physical mechanisms

for the reduction and arrive at different reduction factors. In one model, the re-

duction is due to quantum confinement effects [11–13], which increases the band

gap energy compared to the bulk value. In a more recent model, the decrease of

ε was not attributed to the opening of the band gap, but instead to breaking of

polarizable bonds on the surface—a surface polarization effect [14–17].

2.2.1 Quantum Confinement Effect

Given that bulk Si crystal can be approximated as a linear isotropic medium, the

electric polarization P in the crystal is linear to the net electric field E in the

crystal

P = ε0χeE, (2.1)

where χe is electric susceptibility. The displacement field D then becomes,

D ≡ ε0E + P = εE, (2.2)

11

where

ε = ε0(1 + χe) (2.3)

is the electric permittivity and ε/ε0 = 1 + χe is known as the dielectric constant.

Since the polarization is defined to be the sum of all dipole moment p per unit

volume, Eq. (2.1) can be rewritten as

P ≡∑

V olume

p = ε0χeE. (2.4)

It is to be noted that this relation is derived based on macroscopic description of

the charge distribution in the crystal, ignoring the microscopic variation of the

field in each dipole. Hence the terms ε0 and χe in Eq. (2.4) should be considered

as average over a dipole.

Another expression relating the polarization and electric field can be obtained

from a microscopic relation between the dipole moment and polarizability of an

atom. Assuming that the four valence electrons of a Si atom are independent of

each other, they experience the spatially harmonic force exerted by the Si ion if

they are displaced from their equilibrium positions. The equation of motion for

such a bound electron acted on by a temporally harmonic electric field E(x, t) =

E(x)e−iωt is

∑F = mx = FDriving + FDamping + FRestoring

= −eE(x)e−iωt − rx− kx, (2.5)

where r and k are damping and harmonic force constants, respectively. For

simplicity, the local and external driving electric fields are taken as the same.

Otherwise the FDriving term should be replaced by FLocal = FExternalDriving +

FPolarizationInduced, which renders the derivation too complicated to deduce an in-

tuitive formula [18]. By rearranging the terms and substituting γ = r/m and

ω02 = k/m into the above Eq. (2.5), it becomes

m

(x +

r

mx +

k

mx

)= m

(x + γx + ω0

2x)

= −eE(x)e−iωt. (2.6)

12

The above equation is an expression for a damped, driven harmonic oscillator and

its solution x(t) has two terms, corresponding to the transient and steady states.

To obtain the expression for the dipole moment strength of a single electron-ion

oscillator, we only need to find the complex amplitude for the steady state term,

which is,

x = − e

m

1

ω02 − ω2 − iωγ

E. (2.7)

Hence the oscillator’s dipole moment is

p = −ex =e2

m

1

ω02 − ω2 − iωγ

E. (2.8)

If the Si atom’s electron-ion pair is further approximated as an undamped oscil-

lator with only one resonant energy at hω0 = 4 eV (instead of two at 3.4 and 4.3

eV), the total dipole moment of the N number of Si electrons in the volume of a

unit cell—polarization—is

P ≡∑

V olume

p =Ne2

m

1

ω02 − ω2

E. (2.9)

The above approximation renders the Si’s indirect band gap of 1.1 eV irrelevant,

since the Si atoms are considered to have a resonant oscillation energy εg = hω0

of 4 eV [13].

From Eqs. (2.4) and (2.9), the frequency dependent dielectric constant ε(ω)/ε0

can be obtained as the following:

ε0χeE =Ne2

m

1

ω02 − ω2

E

ε(ω)

ε0

= 1 +Ne2

ε0m

1

ω02 − ω2

= 1 +ωp

2

ω02 − ω2

= 1 +h2ωp

2

ε02 − h2ω2

, (2.10)

where ωp is called the plasma frequency of the Si electron gas in the unit volume

and ε0 oscillation energy. For static dielectric constant for bulk size εB (i.e., when

ω = 0), the above Eq. (2.10) reduces to

εB =ε(0)

ε0

= 1 +

(hωp

ε0

)2

, (2.11)

13

where the subscript “B” is denoted to emphasize the derived ε is the bulk value

and ε0 is set to 1 from here on for simplicity.

Figure 2.1: Electron energy ε vs. k for an isotropic three-dimensional nearly free

electron model. The solid curve represents the “continuous” electron energies in

a bulk structure, whereas the solid dots the discrete energies a spherical nanodot

structure. After Fig. 1 of Ref. [13].

Following the discussion in Ref. [13], the collection of the Si valence electrons

can be approximated as an isotropic three-dimensional nearly free electron system,

where the crystal potential energy is assumed to be very small and the electrons

fill up to the Fermi energy level εF . Figure 2.1 shows the electron energy ε as

a function of the k quantum number of its spherical Bloch function. In a bulk

structure, the difference between two adjacent k’s is so small that the relation

ε(k) vs. k is practically continuous; on the other hand, the difference in k (thus

in ε as well) becomes large and discrete in a nanostructure. Therefore the energy

separation ∆ε around kF becomes

∆ε =h2

2m

(k2 − k′2

)=

h2

2m(k + k′)(k − k′), (2.12)

where k and k′ are the quantum numbers immediately adjacent to the Fermi

quantum number kF . Solving the three-dimensional spherical Bessel function for

14

Table 2.1: Various fit parameters used in the theoretical calculations based on

quantum confinement effect.

Plot α l

[11] 0.69 1.37

[12] 0.92 1.18

[13] 0.54 2.00

k and k′ gives k − k′ = π/2a, which is substituted into Eq. (2.12), resulting in

∆ε(a) =πεF

kF a, (2.13)

in which εF = h2kF2/2m and k + k′ = 2kF .

In the presence of crystal’s periodic potential energy, the bandgap energy εg

is not that of nearly free electron model Eq. (2.13), but becomes [19]

εg ≡ ε+ − ε− =

√[∆ε(a)]2 + εg

2, (2.14)

Substituting Eq. (2.14) into Eq. (2.11), the size-dependent ε(a) is

ε(a) = 1 +(hωp)

2

(∆ε)2 + εg2

= 1 +(hωp/εg)

2

1 + (∆ε/εg)2 = 1 +

εB − 1

1 + (∆ε/εg)2

= 1 +εB − 1

1 + (α/a)2 . (2.15)

Rooted in Eq. (2.15), the theoretical calculations based on quantum confine-

ment effect use

ε(a) = 1 +εB − 1

1 + (α/a)l, (2.16)

with εB, α and l as the fit parameters. Table (2.1) shows some of the calculations

with their corresponding fit parameters.

2.2.2 Surface Polarization Effect

The theoretical calculations based on surface polarization effect [14–17] attribute

the nanostructure’s dielectric constant reduction to the breaking of polarizable

15

Figure 2.2: Plots of the several size-dependent static dielectric constants ε(a) vs.

the radius a of the silicon sphere in A. After Fig. 2 of Ref. [13].

Figure 2.3: Ratio between the bare electric field Eb and the screened one E in Si

layers submitted to a constant electric field. After Fig. 2 of Ref. [14].

Figure 2.4: Permittivity profiles along the [100] direction for Si(100) slabs with

H-terminated surfaces. The numbering refers to the slab size in terms of Si planes.

After Fig. 3 of Ref. [17].

16

Figure 2.5: Ratio between the bare electric field Eb and the screened one E vs.

the distance to the center in a 2.5-nm Si spherical nanocrystal. The bare field is

due to a charge +q at the center and a charge −q uniformly spread on the surface

of the sphere. After Fig. 4 of Ref. [14].

Figure 2.6: (a) Permittivity of a Si slab as a function of thickness d; local permit-

tivity in the central Si plane (circles) compared to the overall slab permittivity

(disks). (b) Band gap of a Si slab as a function of thickness d (squares). The

horizontal line indicates the band gap of a slab of infinite thickness (0.62 eV).

After Fig. 4 of Ref. [17].

17

bonds on its surface, which in turn reduces the number of polarizable bonds per

unit cell and thus the overall dielectric constant value. The local dielectric value

at each location (i.e., each crystal plane in a slab) is calculated as a function of

the distance from the center of the nanostructure. As shown in Figs. 2.3, 2.4 and

2.5, the dielectric value at the center is equal to the bulk value but is reduced

at the surfaces. It naturally follows that the overall dielectric value of the whole

nanostructure would decrease as the structure size gets smaller (Fig. 2.6).

2.3 Experiment & Analysis

2.3.1 Fabrication and Data Acquisition

Figure 2.7: Fabrication procedure for the samples and bare Si pieces. When fur-

ther thinning down the samples’ top Si layer, the following sequence was repeated:

(a) removal of oxidized Si by BOE etching, (b) ellipsometry measurement, (c) dry

oxidation in a flowing argon and oxygen environment at either 600◦C or 650◦C

for 5 minutes, (d) ellipsometry measurement. The bare Si pieces did not undergo

step (b) after BOE etching.

The Si nanoslabs were made of small pieces of a silicon-on-insulator (SOI)

18

wafer—100 nm of (100) c-Si separated from the Si wafer by 200 nm of SiO2

(buried oxide)—providing large refractive index contrast desirable for ellipsometry.

The top c-Si layer thickness was first reduced to 13.8 (sample A), 13.1 (sample

B) and 11.4 nm (sample C) by a wet thermal oxidation followed by removal

of the top SiO2 layer in 20:1 BOE (buffered oxide etchant). To further reduce

the remaining top c-Si layer by small step size (between 1.1 to 1.9 nm), the

samples repeatedly underwent dry oxidation for 5 minutes in a flowing argon

and oxygen ambient inside a tube furnace at either 650◦C (sample A) or 600◦C

(samples B and C) followed by BOE etching, producing nano-sized Si slabs on

the thick SiO2 layer (Fig. 2.7). Spectroscopic ellipsometry was carried out in

between each etching step (i.e., at different thicknesses) on the same location

for each sample. AFM measurements were performed on sample A when its

thickness was 5.6 nm and surface profilometry was performed on sample B at 3.2

nm. To minimize the growth of native oxide, the 40-minute long ellipsometry

measurement was done within 10 minutes after the BOE etching in air at room

temperature and the samples were kept in a vacuum desiccator whenever they

were not under measurement. In order to check the amount of ultra-thin thermal

oxide growth including possible native oxide, a bare (100) c-Si piece of size similar

to each sample was placed alongside during each oxidation and its oxide growth

was measured by ellipsometry afterward.

A variable angle spectroscopic ellipsometer (J. A. Woollam Vertical VASE)

was used over the spectral range of 0.73 to 4.58 eV. The measurements were

performed in steps of 0.05 eV at three different incident angles (65◦, 70◦ and 75◦).

To attain a high accuracy, each ellipsometric angle (Ψ, ∆) was acquired with a

total of 50 analyzer revolutions with an adjustable retarder placed in between

light source polarizer and sample, which enabled accurate measurement of ∆ over

the entire range of 0◦ to 360◦ [20]. It is imperative to ensure that the acquired

ellipsometric angles were accurate for every layer thickness, down to ∼ 3 nm.

19

Since the wavelength of interest is 1.7 µm, the length scale of the thinnest layer

thickness to the wavelength is about 0.0018 and the required phase resolution

is 360◦ × 0.0018 ≈ 0.6◦. The phase resolution of the ellipsometer was better

than 0.6◦, hence the acquire ellipsometric angles were accurate throughout the

spectrum and the all thicknesses down to ∼ 2.5 nm. A Xenon light source with a

monochrometer provided the incident beam of a circular shape with diameter of

∼ 4 mm. The probed areas on the samples, therefore, were of an elliptical shape

with the lengths of about 10, 12 and 15 mm along the lateral axis at 65◦, 70◦

and 75◦ incident angles, respectively. The measurements were taken on the same

spot on each sample so as to avoid any errors due to possible SiO2 layer thickness

fluctuations.

Surface roughness and the possible presence of small pinholes were investi-

gated over different length scales. First, three dimensional surface profiles were

acquired by a profilometer with a lateral resolution of 0.9 µm. For sample B

with 3.2 nm thickness, the profilometer showed a few micron square pinholes and

pillars over 349 µm × 262 µm scanned areas with ∼ 0.2% of surface area hav-

ing the pinholes/pillars. The surface rms roughness was ∼ 0.5 nm. In addition,

AFM measurements with ∼ 40-nm resolution were performed on a ∼ 5.6-nm-thick

nanoslab of sample A. The 10 µm × 10 µm scan showed a very smooth surface

with ∼ 0.1% of area occupied by a handful of small pits and pillars with lateral

sizes less than 425 nm. The AFM measurement found the surface rms roughness

to be ∼ 0.4 nm, which was in good agreement with the profilometry data.

2.3.2 Ellipsometry Data Analysis

When analyzing the data, the thin Si layer was modeled by different combinations

of Kramers-Kronig consistent parametric oscillatory functions: Tauc-Lorentz (T-

L) and Gaussian (Gau) [20–22]. These functions generated εI (ε = εR + iεI) with

no absorption below the band gap energy of Si (1.1 eV). The combinations of

20

the oscillatory functions that yielded a good match with the measured data were

(1) a set of one Gau and one T-L and (2) a set of two T-L’s. The two different

oscillatory function sets would output slightly different values for thickness and ε

for the same ellipsometric data, thus providing a rough idea for the error range.

The fitted variables were oscillators’ parameters and layer thickness. For each

sample, the model layer thickness for the buried oxide was kept fixed (e.g. 198.6

nm) for all scans as it was not expected to be changed by the oxidation and etching

processes. Likewise its ε was fixed to the bulk value.

Since ellipsometry acquires Ψ and ∆, which are function of the product of

thickness and ε, it is imperative that the measured thickness (and/or ε, if possi-

ble) be verified separately, in order to confirm that the measured ε is reliable. As

discussed above and shown in Fig. 2.7, along with each sample a bare Si piece

of similar size underwent the identical oxidation-etch iteration. The amount of

thermal oxide growth on the bare piece was measured by the spectroscopic ellip-

sometry, and it ranged between 2.1 and 2.6 nm for sample A (oxidized at 650◦C)

and between 1.7 and 2.4 nm for samples B and C (oxidized at 600◦C). The es-

timated Si reduction amount on the sample was then calculated based on the

oxide growth on the bare piece, since it was expected that the same amount of

oxide would grow on the sample. For all the three samples and oxidation-etch

iterations, the estimated and actual reduction amounts were consistent with each

other, hence confirming that the samples’ Si nanoslab thickness values as obtained

from the ellipsometry were reliable.

Since ellipsometry is a model-based technique, the resulting best-fit model

must be evaluated for fit error and physical meaningfulness. In terms of fit statis-

tics, a fitted model was counted in the final analysis if the mean square error

(MSE) was ∼ 10 or less, the error bars for all fit parameters were less than 10%

of the fit values and all parameters were uncorrelated with one another. The

energy peaks of the fitted Si layer’s εI were also checked to verify that they were

21

Figure 2.8: Ellipsometric angles Ψ and ∆ of both measured and fit data sets

at the incident angle of 65◦ for a 3.5-nm-thick Si layer of sample C. The filled

squares and circles represent the measured Ψ and ∆, respectively. The solid and

dotted curves represent the fitted Ψ and ∆, respectively, generated by fitting the

measured data with two T-L oscillators. The fit matches the measured data very

well over the entire spectrum.

22

between 3 and 5 eV—close to the energy peaks for bulk 3.4 and 4.2 eV—as quan-

tum confinement or surface polarization effect was not expected to change the

peak position outside this range. Fig. 2.8 illustrates the quality of the fits. Since

the fit matches the measured data very well over the entire spectrum, the ε and

thickness values deduced from the fit represent the measurement accurately.

Figure 2.9: (a) sample structure used in theoretical calculations. (b) actual sample

structure in experiment. (c) simplified sample structure used in ellipsometric

analysis.

The possible influence of surface roughness (SR) in the ellipsometric data anal-

ysis was considered by including an SR layer. The dielectric function of the SR

layer was modeled using an effective medium approximation (EMA) with 50%

of void and 50% of the ultra-thin Si layer [20]. The model for the sample then

consisted of c-Si substrate, SiO2 layer, the ultra-thin Si layer and the SR layer, all

with perfectly uniform thicknesses (Fig. 2.9(c)). After fitting the model against

measured data, the best fit yielded an SR layer’s thickness of between 0 and 0.5

nm.

2.4 Results & Comparison

Since Si is transparent in the spectral range below its bandgap energy of 1.1

eV, the ε measured at 0.73 eV (the lowest spectral energy available from the

23

Figure 2.10: Measured εR and εI over the entire spectrum vs. layer thickness from

13.1 to 3.2 nm for sample B, incorporating no SR layer in the fit. The oscillatory

functions used in the fit are T-L and Gau.

24

ellipsometer) was selected to be compared to the static ε predicted by the theories.

At 0.73 eV, εR is not affected by a possible broadening of the two electronic

transition resonances near 3.4 and 4.2 eV. Fig. 2.10 shows the measured εR and

εI for sample B (without an SR layer in the fit) over the entire spectrum at its

various thicknesses from 13.1 down to 3.2 nm. It shows the absolute values of εR

and εI decrease overall as the thickness decreases.

The known value for εBulk at 0.73 eV is 12 [23]. Our ellipsometric measure-

ments performed with a layer thickness of ∼ 13.5 nm yielded a value of ∼ 11.5,

which was taken as the measured εBulk. The theoretical models predicting the be-

havior of ε as a function of size used different values for εBulk (10.4 [11], 10.6 [14],

11.3 [13] or 11.4 [12]). To compare the theoretical predictions and our measure-

ments, we decided to normalize both to εBulkNormalized = 12. The rescaling of

the measurements or theoretical predictions was performed using the following

expression:

εNormalized = 1 +εBulkNormalized − 1

εBulk − 1(εUnnormalized − 1) (2.17)

where εUnnormalized is the measured or calculated value for a given size and εBulk

is the value measured for 13.5-nm-thick films or the bulk value used in the calcu-

lations.

Between the two competing theories, the quantum confinement effect theories

for nanodots [11–13] are based on the generalized Penn model (GPM), expressed

as

ε(R) = 1 +εBulk − 1

1 + (α/R)l(2.18)

where R is the radius of the nanodots. On the other hand, the surface polarization

effect theory [14–17] considers a nanostructure to have two regions—surface and

core—with different dielectric values. The surface region of depth dSurface (or

equivalently volume VSurface) has the dielectric value of εSurface, whereas the rest

of the region (core) that of εBulk. The dielectric value of an isolated nanoslab

25

of thickness T with two surface regions (one on each surface) as a whole then

becomes1

ε(T )=

1

εBulk

− (1

εBulk

− 1

εSurface

)2dSurface

T, (2.19)

from which the expression for ε(T ) can be obtained as, with use of geometric

series,

ε(T ) ≈ εBulk − (εBulk − εSurface)εBulk

εSurface

2dSurface

T. (2.20)

It is to be noted that the two competing theories both exhibit 1/Size dependence.

Figure 2.11: Measured and theoretical ε for nanoslab as a function of the inverse

slab thickness. For clarity, the data from only sample B are shown for the mea-

surement, but the solid line represents a linear fit to all the measured εNormalized

for all three samples. Each ellipsometric data (Ψ, ∆) was evaluated with 5 A of

surface roughness layer using the two different oscillator sets: a set of T-L and

Gau (triangles) and a set of two T-L oscillators (squares). The two resulting fits

(ε, 1/T ) are grouped together. The dashed lines are the theoretical values calcu-

lated in Refs. [13], [14] and [17]. All ε are linearly scaled such that their respective

bulk values are 12.

On Fig. 2.11, the measured εNormalized are plotted along with theoretically cal-

culated εNormalized as a function of the reciprocal of the nanoslab thickness [14,17]

26

or nanodot diameter [13]. For clarity the measured values for only sample B

are shown, but the solid straight line represents a linear fit to all the measured

εNormalized for all three samples A, B and C combined. Since each measured

ellipsometric data (Ψ, ∆) were fitted with two different sets of oscillatory func-

tions, there are for each data two slightly different fitted values for thickness and

εNormalized. The triangles represent the fit with T-L and Gau oscillators and the

squares designate the fit with two T-L oscillators. These two fit results for the

same ellipsometric data are grouped together, giving a general clue to the data’s

error range. For all three samples’ data, the value of ε is only weakly dependent

of the choice of the parametric oscillatory functions. Given the surface rough-

ness obtained from the AFM and surface profilometry, the fits were evaluated

with a 0.5-nm SR layer. The trend is that of a clear reduction when the thick-

ness decreases below 10 nm. Since there were no theoretical calculation based on

quantum confinement effect for slabs, a rough estimate for a slab was obtained by

taking two-thirds of the ε reduction amount shown in Ref. [13]. The calculated

ε shown in Fig. 3 of Ref. [14] was found to be in error [24]. The effective dielec-

tric constant of a slab should have been obtained by averaging 1/ε(z), where z is

monolayer position, rather than ε(z) and the revised theoretical values are plotted

in Fig. 2.11. The measurement agrees both qualitatively and quantitatively with

the theoretical calculations based on surface polarization.

Experimental observation of the surface polarization effect is highly suscep-

tible to surface conditions, one of which is surface roughness. It is essential to

distinguish the ε reduction due to the purported surface polarization effects as

proposed in Ref. [14] from the decrease simply due to surface roughness. As

mentioned above, the possible influence of surface roughness was evaluated by

including an SR layer above the Si slab, which was modeled by EMA with 50%

of εV oid and the ε of the Si slab. As revealed by the profilometry and AFM mea-

surements, the upper bound for the SR layer thickness can be estimated to be

27

Figure 2.12: Comparison of theoretical calculations and measurement evaluated

with a 0-, 5- and 10-A thick SR layer.

∼ 0.5 nm. To get a better idea on how the SR layer thickness affects the ε and

thickness, the ellipsometric data were re-evaluated with 0, 1, 1.5 and 2 nm of SR

layer for comparison. As the SR layer thickness increases, the nanoslab thickness

becomes smaller and ε of the slab larger. For SR layer thicknesses beyond 0.5 nm,

the MSE of the fit rises; beyond 1 nm, ε becomes higher than the bulk value to

compensate for the arbitrarily decreased nanoslab thickness. Hence the best fit is

obtained for a 0.5-nm-thick SR layer. The different trends with varying SR layer

thicknesses are shown in Fig. 2.12. If a 0.8-nm-thick SR layer were incorporated

in the fitting, the resulting ε trend would match that of the theoretical plot. As

discussed above the quality of the fit degrades if the SR layer thickness is greater

than 0.5 nm, therefore the fit with a 0.5-nm-thick SR layer is compared against

the theoretical prediction.

28

2.5 Conclusion

In conclusion, the dielectric function of ultra-thin Si nanoslabs has been measured

by variable angle spectroscopic ellipsometer as their thicknesses decreased from 14

to 3.5 nm. The dielectric value at 0.73 eV is reduced by ∼ 13% (from 12 to 10.4)

compared to the bulk value. The data are in both qualitative and quantitative

agreement with theories based on the surface polarization effect for an isolated Si

slab.

29

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silicon nanocrystals based memory,” Appl. Phys. Lett. 68, 1377 (1996).

[2] A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic,

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“Silicon-based visible light-emitting devices integrated into microelectronic

circuits,” Nature 384, 338 (1996).

[4] L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical

gain in silicon nanocrystals,” Nature 408, 440 (2000).

[5] Z. Hens, D. Vanmaekelbergh, E.S. Kooij, H. Wormeester, G. Allan, C.

Delerue, “Effect of quantum confinement on the dielectric function of PbSe,”

Phys. Rev. Lett. 92, 026808 (2004).

[6] H.V. Nguyen, Y. Lu, S. Kim, M. Wakagi, and R.W. Collins, “Optical Proper-

ties of Ultrathin Crystalline and Amorphous Silicon Films,” Phys. Rev. Lett.

74, 3880 (1995).

[7] D. Amans, S. Callard, A. Gagnaire, J. Joseph, G. Ledoux, and F. Huisken,

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93, 4173 (2003).

30

[8] M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, M. Cerqueira, E.

Alves, and M. Stepikhova, “Dielectric function of nanocrystalline silicon with

few nanometers (< 3 nm) grain size,” Appl. Phys. Lett. 82, 2993 (2003).

[9] K. Lee, T. Kang, H. Lee, S. Hong, S. Choi, T. Seong, K. Kim, and D. Moon,

“Optical properties of SiO2 / nanocrystalline Si multilayers studied using

spectroscopic ellipsometry,” Thin Solid Films 476, 196 (2005).

[10] C. Ng, T. Chen, L. Ding, Y. Liu, M. Tse, S. Fung, and Z. Dong, “Static

dielectric constant of isolated silicon nanocrystals embedded in a SiO2 thin

film,” Appl. Phys. Lett. 88, 063103 (2006).

[11] L. W. Wang and A. Zunger, “Dielectric constants of silicon quantum dots,”

Phys. Rev. Lett. 73, 1039 (1994).

[12] M. Lannoo, C. Delerue, and G. Allan, “Screening in semiconductor nanocrys-

tallites and its Consequences for porous silicon,” Phys. Rev. Lett. 74, 3415

(1995).

[13] R. Tsu, D. Babic, and L. Ioriatti, “Simple model for the dielectric constant

of nanoscale silicon particle,” J. Appl. Phys. 82, 1327 (1997).

[14] C. Delerue, M. Lannoo, and G. Allan, “Concept of dielectric constant for

nanosized systems,” Phys. Rev. B 68, 115411 (2003).

[15] C. Delerue and G. Allan, “Effective dielectric constant of nanostructured Si

layers,” Appl. Phys. Lett. 88, 173117 (2006); ibid. 89, 129903 (2006).

[16] F. Trani, D. Ninno, and G. Iadonisi, “Role of local fields in the optical prop-

erties of silicon nanocrystals using the tight binding approach,” Phys. Rev.

B 75, 033312 (2007).

[17] F. Giustino, and A. Pasquarello, “Theory of atomic-scale dielectric permit-

tivity at insulator interfaces,” Phys. Rev. B 71, 144104 (2005).

31

[18] John D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

[19] Richard L. Liboff, Introductory Quantum Mechanics, 4th ed. (Addison Wes-

ley, 2002).

[20] H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry (Springer, 2005).

[21] A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins,

X. Deng, and G. Ganguly, “Optical properties of ultrathin crystalline and

amorphous silicon films,” J. Appl. Phys. 92, 2424 (2002).

[22] G. E. Jellison and F. A. Modine, “Parameterization of the optical functions

of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371

(1996); ibid. 69, 2137 (1996).

[23] E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

[24] C. Delerue, and G. Allan, Institut d’Electronique, de Microelectronique et de

Nanotechnologie, France (personal communication, 2008).

32

3 Birefringence and Optical

Power Confinement In

Horizontal Si / SiO2

Multilayer Waveguides

3.1 Introduction & Motivation

The goal of achieving optical gain at the telecommunication wavelengths using a

silicon platform is driving research on erbium incorporation in CMOS-compatible

host materials and structures. Erbium luminescence at 1.55 µm is especially strong

if the Er ions reside in a silicon oxide host and are excited by energy transfer

from silicon nanocrystals (nc-Si) placed in close proximity [1–6]. An attractive

structure is a stratified multilayer film of alternating thin layers of nc-Si and Er-

doped SiO2 [3,4]. One of the major hindrances to achieving lasing using Er is the

confined (or free) carrier absorption by nc-Si and thus there has been a marked

interest in minimizing this type of loss [7, 8].

One of the possible ways to minimize loss is to tailor the Er light distribution

in the film such that the light interacts with Er in the SiO2 layers only and avoids

the nc-Si layers. Simulations have shown that for a waveguide consisting of ultra-

33

thin slots of low refractive index nL (e.g., SiO2) embedded between high refractive

index nH regions (e.g., Si), the intensity of TM-polarized light—the direction of its

H-field parallel to the slot—can be enhanced in the slots [9,10]. Power confinement

factors in the slot(s) of ∼ 30% for a single-slot vertical waveguide [10, 11] and ∼56% for a three-slot horizontal waveguide [12] have been reported. This high power

confinement in the low-index regions is due to the D-field continuity across the

interface. Since the E-field strength differs by a factor of nH2/nL

2 immediately

across the interface between the two regions, the larger the material index contrast

is, the stronger the power confinement in the low-index region is. This effect has

been verified by measuring the effective modal index via thermo-optic coefficient

measurements [13], angle-resolved attenuated total reflectance [14] and cladding

field intensity measurements [15].

Reported in this chapter are simulations and experiments on horizontal multi-

layer films consisting of alternating nanometer-thin amorphous Si (a-Si) and SiO2

layers. Since the material index of nc-Si is similar to that of a-Si overall [16], our

results are also applicable to multilayer films of alternating polycrystalline Si and

SiO2 layers, which can be formed by post-deposition thermal annealing [17, 18].

Simulations show that a birefringence of up to 0.8 and a power confinement of

up to ∼ 85% can be achieved. It ought to be noted that these effects should also

be observable in any multilayer film made of alternating ultra-thin layers with a

large material index contrast, not just for Si / SiO2 multilayer films.

3.2 Simulation

3.2.1 Derivation

The simulation technique used in this project was Abeles’ matrix method, which

is also popularly known as the characteristic or transfer matrix method [19,21,22].

34

Figure 3.1: (a) Coordinate system and notation of the number of the films for

the present stratified multilayered film system. The film structure is sandwiched

between the incident (0) and substrate (m + 1) phases. After Fig. 1 of Ref. [20].

(b) Decomposition of the refractive index n along x and z directions. (c) The

convention for the positive direction for s (TE) and p (TM) polarizations. After

Fig. 4.1 of Ref. [23].

35

For a stratified multilayer film of m layers as shown in Fig. 3.1(a), the harmonic

electric wave with angular frequency ω in each layer is expressed as

exp[ik · x− iωt] = exp[ik0(βx + αz)− iωt], (3.1)

where the spatial vector x ≡ xx + yy + zz and k ≡ nk0k = k0(βx + γy + αz) as

shown in Fig. 3.1(b). Due to the translational invariance of the structure in the y

direction, the amplitude does not vary along the y direction (but its phase does)

so γ = 0 and thus the y component is not present in Eq. [3.1]. Given a complex

angle of incidence θ, the transverse (α) and longitudinal (β) components of the

complex refractive index n are expressed as

α = n cos θ

β = n sin θ(3.2)

Following from Snell’s law, the longitudinal component of n must be the same for

all layers, i.e.,

βj−1 = βj

nj−1 sin θj−1 = nj sin θj

(3.3)

for all j-th layers. Since β is the same for all layers, the wave amplitude in Eq. [3.1]

at a given xx location depends only on the zz location, i.e., the amplitude along

z direction is proportional to exp[+k0α(z)z].

As shown in Fig. 3.1(a), there are two harmonic waves in each layer: inci-

dent (forward-propagating) and reflected (backward-propagating) waves. With

the superscripts + and − denoting forward- and backward-propagating waves, re-

spectively, the amplitudes of these two waves at position z in the j-th layer are

E+(z) = E+j exp[+k0αj∆z]

E−(z) = E−j exp[−k0αj∆z],

(3.4)

where E+j and E−

j denote the field amplitudes at the j-th interface, αj is the α in

the j-th layer and ∆z is the distance from the j-th interface, ∆z = z −∑j−1i hi.

36

It is evident from Eq. [3.4] that the field amplitudes at any zz location can

be calculated once the field amplitudes at the interfaces are known. The Abeles’

matrix method provides a matrix equation that relates the amplitudes among all

interfaces: E+

0

E−0

=

(1∏

j=m+1

Cj

) E+

m+1

E−m+1

=

a b

c d

E+

m+1

E−m+1

, (3.5)

where the matrix product must be multiplied in the order from m + 1 down to 1

and

Cj =1

tj

exp[−iδj−1] rjexp[−iδj−1]

rjexp[iδj−1] exp[iδj−1]

(3.6)

is the propagation or characteristic matrix for the j-th layer and tj and rj are the

Fresnel transmission and reflection coefficients, respectively, between the (j − 1)-

th and j-th layers. The quantity δj−1 denotes the change of phase between the

(j − 1)-th and j-th interfaces and defined to be

δ0 ≡ 0

δj−1 ≡ αj−1hj−1.(3.7)

The Fresnel coefficients for s (TE) and p (TM) polarizations can be expressed as

rjs =nj−1 cos θj−1−nj cos θj

nj−1 cos θj−1+nj cos θj

tjs =2nj−1 cos θj−1

nj−1 cos θj−1+nj cos θj,

(3.8)

for s polarization and

rjp =nj−1 cos θj−nj cos θj−1

nj−1 cos θj+nj cos θj−1

tjp =2nj−1 cos θj−1

nj−1 cos θj+nj cos θj−1,

(3.9)

for p polarization (cf., Ref. [20]).

Since a bound guided mode is established in the film by total internal reflection

at the cladding-film and film-substrate interfaces, there is no forward-propagating

wave in the cladding and backward wave in the substrate, i.e., E−m+1 = 0 and

37

E+0 = 0. These field conditions require the matrix element a in the Eq. [3.5] to be

a = 0.

Following the convention set in Refs. [23, 24] for field direction in Cartesian

coordinate system,

Ex(z) =[E+

p (z) + E−p (z)

]αj

nj

Ey(z) = E+s (z) + E−

s (z)

Ez(z) =[−E+

p (z) + E−p (z)

]βj

nj.

(3.10)

It is to be noted that only the real components of the field must be used in

calculating the energy density and power [22]:

S = Re(E)× Re(H)

u = 12(Re(E) · Re(D) + Re(B) · Re(H)).

(3.11)

3.2.2 Field Continuity Across Interface & Field Enhance-

ment

Across the interface between two dielectric materials with no free charge density

and different permittivity values ε1 and ε2, the E and D field continuity require-

ments are

E‖1 = E

‖2 (3.12)

and

D⊥1 = D⊥

2 . (3.13)

Hence, in a multilayer film, the E field is continuous across the interfaces for TE

mode (Eq. [3.12]). On the other hand, for TM mode the transverse component of

the D field is continuous (Eq. [3.13]), which in turn means

ε1E⊥1 = ε2E

⊥2 , (3.14)

because D = εE. If ε1 < ε2, then E⊥1 is greater than E⊥

2 by a factor of ε2/ε1.

In other words, the field E1 in the lower index (n1) material is enhanced by a

38

factor n22/n

21 compared to the field E2 in the higher index (n2) material right in

the vicinity of the interface. The enhanced E1 field however rapidly decreases

at location further from the interface. If the layers in the multilayer film are

substantially small compared to the wavelength, the light can be confined more in

the lower-index layers than in the high-index layers for TM mode. This might at a

quick glance seem contrary to the principle of total internal reflection, which shows

that light is confined in high-index region. The principle is valid for multilayer

films with layer thicknesses comparable or greater than the wavelength for both TE

and TM polarizations. For the case of ultra-thin layers and for TM polarization

only, field is enhanced in the low-index region.

3.2.3 Parameters

For the refractive index of the deposited and thermal oxide layers and that of a-

Si, we used the values of 1.44 and 3.44 obtained from variable angle spectroscopic

ellipsometric measurements at 1.55 µm. The layer thicknesses were also obtained

from the ellipsometric measurements.

3.3 Experiment

3.3.1 Fabrication

Films containing layers of a-Si and SiO2 were deposited by computer-controlled

reactive ion RF magnetron sputtering at room temperature on Si substrates cov-

ered by a 5-µm thick thermal oxide layer (Fig. 3.2). The layer thicknesses LSi

and LSiO2 of the two materials varied from ∼ 3 to ∼ 40 nm and the number of

periods P ranged from 13 to 160, to keep the total film thickness LFilm close to 1

µm, ensuring the presence of multiple guiding modes. Two sets of five films were

39

Figure 3.2: (a) SEM of a structure made of alternating a-Si and SiO2 layers.

(b) Schematic of sample structure with P periods of LSi thick a-Si and LSiO2

thick SiO2 layers on a 5-µm thick thermal oxide layer. (c) Sample structure

as viewed by the prism coupler for m-line measurement. The multilayer film is

replaced by a single film with an effective material index of nFilm and thickness

LFilm = P (LSi + LSiO2).

40

fabricated: in one set the thickness ratio LSiO2/LSi was kept close to 1, whereas

the ratio in the other set ranged between 0.7 and 11.5.

3.3.2 Experimental Methods

Figure 3.3: (a) Schematic of m-line measurement. (b) Graph of reflected light

intensity as a function of the modal index for a multilayer film of 34 periods of

15.2 a-Si and 19.7-nm SiO2. The arrows show the modal indices greater than 1.44

at which a bound mode is established (2.43, 2.16 and 1.75 for TE; and 1.74 and

1.55 for TM). Modal indices between 1.8 and 1.9 were not measurable because of

the two prisms used.

To experimentally verify the higher power confinement in the lower index lay-

ers (slots)—defined as the ratio of the power in the low-index layers to the total

power—the modal indices were obtained using a prism coupler instrument (Met-

ricon 2010) via the m-line measurement [25]. The indices were measured at 1.55

µm. A 1/2 waveplate and a linear polarizer were employed to select the po-

larization (TE or TM). As shown in Fig. 3.3(a), the incident light was coupled

evanescently into the multilayer film through a prism, establishing a bound guid-

ing mode at certain incident angles. A germanium detector measured the intensity

of the reflected light from the interface between the sample and prism base. The

film’s modal indices were evaluated by treating the multilayer stack as a single

41

film with an effective material index nFilm sandwiched between the 5-µm thick

thermal oxide and air.

Figure 3.3(b) shows the reflected light intensity as a function of modal index

for a multilayer film consisting of 34 periods of 15.2- a-Si and 19.7-nm thick SiO2.

For this sample, a total of three TE modes and two TM modes were found. When

a bound mode is established, the reflected light intensity becomes significantly

smaller, as marked with arrows on the figure. Two prisms were used to cover a

wide range of effective modal indices—one covering 1.0 ∼ 1.8 and the other 1.9 ∼2.9.

3.4 Results & Comparison

3.4.1 Modal Indices & Birefringence

Our simulations indicated that as long as the multilayer thickness is less than 8%

of the wavelength, the modal indices for a fixed thickness primarily depend on

the SiO2 / Si thickness ratio and little on the number of periods or the individual

layers’ thicknesses.

Figure 3.4 compares the calculated and measured modal indices of the first and

second order TE and TM modes as a function of the layer thickness ratio for a 1-

µm thick film. As the fraction of SiO2 increases, the modal index decreases and the

second order TM mode is no longer supported. The experiments and calculations

are in good agreement. The deviations between the measurement and calculation

are primarily due to variations in the actual film thickness between 0.93 to 1.19

µm. Simulations performed with actual film thicknesses resulted in less than 2%

of discrepancy.

As expected, the TM modal indices are substantially lower than the TE ones,

indicating a strong birefringence. Figure 3.5 shows the modal index difference

42

Figure 3.4: First and second order modal indices versus SiO2 / a-Si layer thickness

ratio for both polarizations. The curves represent the calculation for 1.00-µm thick

film and the dots represent the measured values for film thicknesses ranging from

0.93 to 1.19 µm.

between the fundamental TE and TM modes as a function of layer thickness ratio

at various total film thicknesses. A maximum difference of ∼ 0.8 is obtained over

a wide range of layer thickness ratios and total film thicknesses.

3.4.2 Power Profile

To determine whether the lower effective mode indices of the TM polarized light

is simply due to a higher evanescent field intensity in the air and substrate layer,

we calculated the power profile for both polarizations. Figure 3.6 shows that the

TM-polarized light intensity is highly localized in the SiO2 layers and that power

in the cladding is small in all cases. Hence the modal index disparity between

the two polarizations is due to the higher field confinement in the SiO2 layers. As

explained in Ref. [10], the higher field concentration in the lower index regions for

TM modes due to the continuity of the transverse D-field component across an

43

Figure 3.5: Measured (dots) and calculated (curves) modal index difference be-

tween the fundamental TE and TM modes as a function of layer thickness ratio

for total film thicknesses between 0.4 and 0.9 µm. The maximum difference of ∼0.8 is obtained if the thickness ratio is around 0.5 and 0.6.

interface is possible if the light wavelength is substantially greater than the layer

thicknesses.

3.4.3 Confinement Factor & Optimum Layer Thickness

Ratio

In Fig. 3.7, the power confinement factor in the SiO2 layers for the fundamental

TM mode is plotted as a function of layer thickness ratio for various total film

thicknesses. At any given layer thickness ratio, the confinement factor in the

SiO2 layers rises as the total film thickness increases, approaching the absolute

maximum of ∼ 85% (' nH2/nL

2

1+nH2/nL

2 ), which can be reached for 0.90-µm or thicker

films provided that the thickness ratio is greater than 1.72.

Furthermore, the figure shows that for each film thickness there is an optimum

layer thickness ratio at which the confinement in the SiO2 layers is maximum.

44

Figure 3.6: The power profile of the first order TE and TM modes in a 0.60-

µm thick film consisting of 10 periods of alternating 30-nm thick a-Si and SiO2

layers. The SiO2 substrate layer is positioned below the 0.0-µm mark and the

air above the 0.6-µm mark. The shaded areas represent the SiO2 layers. For

TM polarization, the transverse E-field component in the low-index nL region is

greater by a factor of nH2/nL

2 than that in the high-index nH region immediately

across the interface.

45

Figure 3.7: The power confinement factor in the SiO2 layers for first order TM

mode as a function of layer thickness ratio at various total film thicknesses.

Figure 3.8: The linear relationship between the total film thickness and its opti-

mum layer thickness ratio. The shaded area represents the region where only one

TM mode exists.

46

The confinement factors for thicker films reach their maxima at higher thickness

ratios than for thinner films. The optimum layer thickness ratio for a given film

thickness follows an empirical linear relationship (Fig. 3.8). For example, if the

film thickness is 0.50 µm, then the optimum ratio is ∼ 0.83. The shaded region in

Fig. 3.8 denotes the layer thickness ratio and total film thickness where only one

TM mode exists. If a film is to be a single-mode waveguide for TM polarization

and to provide the highest SiO2 confinement, then its thickness should be set to

0.80-µm. This thickness is larger than the one producing the largest birefringence

(Fig. 3.5).

Finally, we note that for large SiO2 / Si thickness ratios, the confinement factor

decreases. This decrease is the result of the increasingly large evanescent tails in

the air and the SiO2 substrate, which are produced by the decreasing effective

refractive index of the multilayer.

3.5 Conclusions

Simulations and experiments have shown that multilayer films with high contrast

material indices exhibit a high birefringence and confine more TM-polarized light

in the low-index layers than in the high-index layers. For a given total thickness,

there is an optimum SiO2 / Si layer thickness ratio that yields the maximum

light confinement in the SiO2 layers. This optimum ratio is linearly proportional

to the total film thickness. This demonstrates that using TM polarization it is

possible to reduce the confined carrier absorption loss in a nc-Si / Er-doped SiO2

multilayer film via modal profile shaping such that most of the light is confined

in the Er-doped SiO2 regions.

47

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self-organization in nanocrystalline silicon,” Nature 407, 358–361 (2000).

[19] J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of

planar multilayer waveguides and reflection from prism-loaded waveguides,”

J. Opt. Soc. Am. A 1, 742–753 (1984).

[20] K. Ohta and H. Ishida, “Matrix formalism for calculation of electric field

intensity of light in stratified multilayered films,” Appl. Opt. 29, 1952–1959

(1990).

[21] O. S. Heavens, Optical Properties of Thin Solid Films, 2nd ed. (Dover, 1991),

Chapter 4.

[22] H. Angus Macleod, Thin Film Optical Filters, 3rd ed. (Taylor & Francis,

2001).

[23] R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North

Holland, 1987), Chapter 4.

[24] Constantine A. Balanis, Advanced Engineering Electromagnetics (Wiley,

1989).

[25] R. Ulrich and R. Torge, “Measurement of thin film parameters with a prism

coupler,” Appl. Opt. 12, 2901–2908 (1973).

50

4 Electroluminescence and Free

Carrier Absorption in Si /

SiO2 Multilayer Films by

Lateral Electrical Injection

4.1 Introduction & Motivation

Figure 4.1: (a) Longitudinal (vertical) injection scheme. (b) Lateral (horizontal)

injection scheme.

The effort to incorporate a nc-Si-based light source within a microprocessor as

an optical interconnect component has driven intensive research into developing an

efficient mechanism to excite the nc-Si’s. Most research so far has focused optical

pumping mechanisms [1, 2], for it employs an easier experimental set-up than

51

electrical mechanisms to study their characteristics. However to integrate the light

source in a microprocessor, it is imperative to explore and actualize an efficient

mechanism to excite the nc-Si’s electrically [3–7], doing away with a high-intensity,

high-photon-energy external light source required in optical pumping techniques.

For multilayer film structure, which emerges as one of the best suitable nc-Si-

based waveguide structures [8], there are two schemes to inject charge carriers:

longitudinal (across) to the layer orientation and lateral (along), as shown in

Fig. 4.1. In longitudinal scheme, electrically conductive pads are deposited on

both of the two outer-most layers of the multilayer film and the electrons and

holes are injected across the layer orientation. This naturally results in a high

turn-on voltage as the charge carriers must penetrate through multiple insulating

layers (e.g. SiO2). In lateral scheme, on the other hand, conductive pads are

deposited on trenches at two opposite edges of the film and charges are injected

along the semiconducting layers (e.g. Si). Published recently are a couple of

reports on lateral electrical contact technique for solar cell application [9, 10],

where impinging photons generated electrons and holes that traveled laterally to

their respective conductive pads. Contrastingly, an efficient mechanism to inject

electrons and holes to generate photons is sought after in optical interconnect

application.

Beyond showing such lateral electrical injection scheme is possible, discussed

in this report are thermal and free carriers-optical effects observed in a slab waveg-

uide due to the injection scheme. By employing the m-line measurement technique

in transmission configuration for 1.55-µm wavelength, the injected charge carriers

were found to generate heat and free carrier absorption that reduced the light

intensity in the waveguide. This finding therefore points to a need to minimize

not only free carrier absorption [8,11,12] but also the required amount of current

and voltage for luminescence.

Additionally, the free carrier absorption coefficients were measured for both

52

1st-order guided TE and TM modes at various bias voltage and current. The

absorption coefficients for the TM mode was smaller than that of the TE by a

factor of 2, confirming that the light confinement factor in the Si layers is smaller

for the TM than TE polarization [8]. The light confinement factors can be based on

electric field intensity (|E|2), energy density (u), strength (|E|) and displacement

field strength (|D|). Since it is important to which confinement factor metric

to use when estimating the free carrier concentrations based on the absorption

coefficient, the ratios between the TE and TM modes’ confinement factors in the

Si layers are also compared.

4.2 Fabrication

Figure 4.2: (a) Brief sequence of fabrication process: <1> RF magnetron deposi-

tion of a-Si and SiO2, followed by rapid thermal annealing; <2> ion implantation

of P and B ions; <3> reactive ion etching of trenches; <4> deposition of Ti on

the trenches. (b) Plan view showing the implantation (1 mm × 5 mm) and trench

area (0.3 mm × 4 mm) dimensions. The contact pad areas are colored orange and

their dimensions are 0.6 mm × 4.5 mm. (c) Finished sample.

As illustrated in Fig. 4.2, a total of three pairs of 69-nm thick a-Si and 62.5-nm

thick SiO2 were deposited by reactive ion RF magnetron sputtering in a UHV at

room temperature on a 1-mm thick Si substrate with a 5-µm thick thermal oxide

53

layer. The a-Si layers were subsequently crystallized by rapid thermal annealing

at 1000 ◦C, forming polycrystalline layers [13,14]. Following Stopping and Range

of Ions in Matter (SRIM) calculations, B and P ions were implanted (forming

a P-“I”-N diode) at three different energies and doses to achieve the same ion

concentration among all three nc-Si layers—1.2× 1015 for B and 3.3× 1014 cm-2

for P ions. The wafer underwent a rapid thermal annealing at 1000 ◦C for 30

seconds to cure the implantation-induced damage. Before the RIE step to carve

out trenches in a CF4 plasma environment, the 4-inch wafer was partitioned into

16 mm × 16 mm dies. For a third of those dies their trenches were etched through

all three pairs of the nc-Si / SiO2 layers; another third dies were etched through

only the top two pairs and the last third only the top one pair. A 230-nm thick

Ti layer was deposited on the trenches by E-beam thermal evaporator and rapid

thermal annealing at 600 ◦C for 45 seconds, followed by 750 ◦C for 45 seconds,

was performed to form titanium silicide [15–17]. After dicing the wafer, electrical

wires were attached to the Ti contact pads on each die by silver epoxy. Based on

the current-voltage and electroluminescence measurements, only one out of about

ten dies at the center of the wafer passed enough current to emit luminescence

and the depth of this die’s trench is two pairs deep.

4.3 Results & Analysis

4.3.1 Current-Voltage & Spectroscopic Electroluminescence

The IV measurement shown in Fig. 4.3(a) indicated a poor P-“I”-N diode. The

field strength across the “intrinsic” junction was about 183 V / cm at 55 V. Given

that only two out of three 69-nm thick Si layers were connected to the metal

contacts and the length of the implanted regions was 5 mm, the current density

at 55 V came out to be around 9 kA / cm2. Over the course of 8 weeks, the

54

Figure 4.3: (a) IV measurement. (b) Spectroscopic electroluminescence mea-

surement at three different bias voltages: 45, 50 and 55 V. The inset shows the

integrated intensity as a function of the electrical power.

current at the bias voltage of 55 V had decreased from 87 to 51 mA, more rapidly

so in the 8th week, indicating a degradation. Therefore the value of the current is

listed along with its corresponding bias voltage in this report.

Using a microscope objective lens mounted to an NIR photomultiplier tube

module, electroluminescence from the diode edge was measured over between the

wavelength of ∼ 1.0 and 1.7 µm at three different bias voltages (Fig. 4.3(b)). A

broad spectrum above 1.3 µm emerged when the bias voltage of 55 V was applied

across the junction, though its origin could not be concretely identified. The inset

in Fig. 4.3(b) shows the integrated intensity as a function of the electrical power,

which does not follow a linear relationship.

4.3.2 Thermo-Optical Effect: Modulation of Electrolumi-

nescence

With the diode mounted and pressed against a prism in a prism coupler set-up,

the luminescence intensity from the diode edge was measured as the bias voltage

modulated from one level to another (Fig. 4.4). At the onset of the voltage

55

Figure 4.4: (a) Plots of luminescence intensity, applied bias voltage and resulting

current vs. time. For the first ∼ 70 S, the voltage modulated between 0 and 35,

40, 45, 50 and 55 V. For the latter 70 S, the voltage decreased by every 5 V from

55 to 35 V and down to 0 V then increased back to 55 V. The duration of the

current transient segments lasted less than 0.25 seconds. (b) Plot of luminescence

intensity vs. time when the bias voltage switched from 55 to 50 V (between 71

and 84 S). After the bias voltage was changed to 50 V, the estimated time for the

current to settle to its new level is 3.5 S.

56

modulation, the luminescence intensity showed a slow transient effect, which was

substantially longer than the electric current transient duration of 0.25 second.

This slow transient time, as revealed in Fig. 4.4(b) clearly, alluded to an influence

on electroluminescence by the heat generated by the electrical current. When the

voltage alternated between 0 and 35 ∼ 55 (0 ∼ 70 S) and increased by every 5

V from 35 to 55 V (110 ∼ 140 S), the luminescence intensity settled down to

slightly lower levels than the initial levels at the onsets of the voltage changes.

This slow transient periods of settling-down indicated a luminescence-depressing

effect of thermal influx. A thermal outflux, on the contrary, would cause the

luminescence intensity to settle up to a higher level, as demonstrated when the

voltage decreased from 55 to 35 V (70 ∼ 105 S).

Based on the 3.5-S duration to reach a thermal equilibrium after the voltage

(current, power) switched from 55 (62, 3.42) to 50 V (45 mA, 2.24 W) as shown in

Fig. 4.4(b), the amount of temperature change can be estimated using the Joule

heating relation assuming negligible heat dissipation into the gadolinium gallium

garnet prism (specific heat capacity of 0.381 J g-1 K-1 from [18]) and the metal

pneumatic arm that was compressing the diode against the prism. Given the

diode size and the specific heat capacities of Si (0.713 J g-1 K-1 from [19]) and

SiO2 (0.740 J g-1 K-1 from [20]), the temperature reduction came out to be less

than 9.7 ◦C when the voltage decreased from 55 down to 50 V.

4.3.3 Thermo-Optical Effect: Modal Indices

Modal indices of the multilayer film were affected by the temperature change since

the refractive indices of Si (1.6 × 10−4 K-1 from [21]) and SiO2 (1.1 × 10−5 K-1

from [22]) are temperature dependent. Variations in the modal index (propagation

constant) can be determined accurately down to 1× 10−4 by m-line measurement

technique [8, 21]. With the TE polarization defined as the E-field pointing in

parallel to the layer orientation, the measurement revealed there were two guided

57

Figure 4.5: (a) m-line measurement in the reflectance configuration at the bias

voltage of 0 V. The 2nd-order TE at 1.481 and 1st-order TM at 1.569 guided

modes are shown along with the evanescent modes. (b) m-line measurement in

the reflectance configuration for the TE polarization at various bias voltages for

the 2nd-order guided and 1st-order evanescent modes.

TE modes at modal indices of 2.316 and 1.481 and one TM mode at 1.569. These

modal index values matched fairly well with the simulation results of 2.396 and

1.462 for the 1st and 2nd-order TE and 1.622 for the 1st-order TM, as obtained

by transfer matrix method [23]. In the simulations, the refractive indices set to

3.400 for the polycrystalline Si, 1.482 for the SiO2, and 1.435 for the thermal oxide

layers.

The diode was mounted and pressed against the gadolinium gallium garnet

(GGG) prism such that the incident 1.55-µm light was coupled into the prism

and then passed through the “intrinsic” junction between the two conductive

pads on the diode. Shown in Fig. 4.5(a) is the m-line measurement in reflectance

configuration for TE and TM polarizations at the bias voltage of 0 V, where the

guided modes were identified at 1.481 for the 2nd-order TE and at 1.569 for the

1st-order TM, along with evanescent modes. The shifts in modal indices at various

bias voltages and electrical powers are evidently demonstrated in Fig. 4.5(b) for

TE polarization. The 1st-order evanescent mode’s index was invariant of the

58

electrical power (and temperature), whereas that of the 2nd-order guided mode

increased as the power increased. The identical trend was also observed for the

TM polarization although with smaller modal index changes for its guided mode.

Incidently, when the diode was mounted against a Si prism instead for the 1st-

order TE mode, no modal index shift was observed because of the coincidence

that the dn/dT of the Si prism is the same as the dβ/dT of the 1st-order TE

mode.

Changes in the modal index can be attributed to the refractive index changes

for both Si and SiO2 layers due to thermo-optical (TO) and free carriers-optical

(FC) effects. Nevertheless, the thermo-optical coefficient dn/dT for Si is greater

than that of SiO2 by a factor of 15 and free carrier absorption is absent in the SiO2

insulating layers. Therefore, the shift in the modal index is predominantly due to

the refractive index change in the Si layers only: ∆n = ∆nTO + ∆nFC, where n

denotes Si’s refractive index. The term ∆nTO is positive as the temperature (thus

power) increases and ∆nFC negative as the free carrier concentration (i.e. current

and thus power) increases. To obtain ∆n, first the amount of the experimental

modal index change ∆βExp ≡ βfExp − β0

Exp was obtained from between the initial

bias voltage of 0 V (corresponding to P0 = 0 W) and the final voltage Vf (Pf ).

Simulations were performed over various Si’s refractive index values nSim between

3.40 and 3.41, in order to find nfSim which produced the same amount of modal

index change in the simulation, i.e. ∆βSim = ∆βExp. This method was taken

because, first, the simulated and experimental modal indices were not exactly

identical and, second, the simulated modal index is linearly proportional to the

Si’s refractive index over the small range between 3.40 and 3.41.

To get a rough estimate of the diode’s temperature change, the free carriers-

optical effect is assumed to be negligible compared to the thermo-optical effect:

∆n ' ∆nTO. Based on the change in the refractive index in the simulations

∆nSim, the temperature change ∆T was calculated using the Si’s thermo-optical

59

coefficient of 1.6× 10−4 K-1.

Figure 4.6: Temperature change as a function of electrical power for the 2nd-order

TE and 1st-order TM. The fit lines are for guides to eye.

Plotted in Fig. 4.6 is the temperature change as a function of electrical power

for the 2nd-order TE and 1st-order TM. Evidently shown is the discrepancy be-

tween the two polarizations in the temperature change rate by a factor of ∼ 2,

whose cause is presently under investigation. When the bias voltage was decreased

by 5 V (∼ 1.2 W) from 60 (∼ 3.7) to 55 (∼ 2.5), the temperature decrease came

out to be about 20 ◦C for TM polarization but 8 for TE. The TM polarization’s

temperature change rate of 8 ◦C / 1.2 W is in agreement with the one estimated

by Joule heating relation, where the temperature decreased by no more than 9.7

◦C when the power decreased by ∼ 1.2 W (5 V) from 3.42 (55) to 2.24 (50).

It must be noted that not only the real part of the (complex) refractive index

is dependent on the temperature but also the the imaginary part of the index,

and consequently, the absorption coefficient α. However α around the 1.55 µm

wavelength is practically 0 and dα/dT ' 0 [24–26]. Therefore the thermo-optical

60

effect influences only the real part of the refractive index.

4.3.4 Free Carriers-Optical Effect

In order to investigate the free carriers-optical effect, m-line measurements were

performed in both the transmittance and reflectance configurations. Figure 4.7(a)

shows such measurements for the 1st-order guided TE mode with the peaks of

transmittance and reflectance intensities coinciding with each other. Between the

two bias voltages of 0 and 55 V, no shift in the modal index was detected due

to the Si prism acting as a large heat sink for the diode. On the contrary, the

transmittance and reflectance peaks did not coincide for the 1st-order guided TM

mode (Fig. 4.7(b)), which was probably due to a slight off-angle alignment of the

detector with respect to the diode facet and measuring the intensity in the film

as well as in the cladding / substrate (cf. Fig. 4.8(a) and a further investigation is

underway). Consistent with the thermo-optical effect discussed in Sec. 4.3.3, the

modal index shifted to a higher value at the elevated bias voltage.

For both polarizations, the depression in the transmitted light intensity is ev-

ident at the higher voltage. In the case of the 1st-order guided TE mode the

reduction is due to free carriers-optical effect only as the thermo-optical effect is

absent; whereas both of the effects were present for the TM mode. When esti-

mating the absorption due to the free carriers based on the reduced transmittance

intensity, it is imperative to distinguish the two origins to the weakened intensity:

the shift in the modal index and absorption due to free carriers. For the 1st-order

guided TE mode in Fig. 4.7(a), the intensity depreciation is due to the free carri-

ers only as the modal index did not vary between the two bias voltages. On the

contrary for the 1st-order guided TM mode in Fig. 4.7(b), since a clear transmit-

tance peak was absent at the modal index value, it is not possible to ascertain the

absorption amount due to the free carriers only.

61

Figure 4.7: m-line measurements in the reflectance and transmittance configura-

tions at 0 and 55 V for (a) the 1st-order guided TE mode (measured with the Si

prism) and (b) 1st-order guided and evanescent TM modes (GGG prism). The

transmittance intensity is scaled such that the 0 corresponds to the no transmit-

tance. The modal index values at 0 V as obtained in the reflectance configuration

are marked with purple vertical lines.

62

Figure 4.8: (a) Profile of the normalized field intensity for the three guided modes

inside the slab waveguide with respect to position. The light blue region below

0.0 µm represents the air cladding layer, whereas the region above ∼ 0.4 µm the

thermal oxide layer. The sputtered SiO2 layers are highlighted light yellow and

the Si layers white. (b) Transmittance intensity, bias voltage, current vs. time for

the 1st-order guided TE mode. Zero reading on the intensity scale corresponds to

no transmitted light intensity.

63

Figure 4.8(a) shows the normalized intensity profile of the three guided modes

in the slab waveguide as obtained from the simulation. For the 1st-order TE mode,

about 50% of the entire field intensity is confined in the Si and 30% in the SiO2

layers, with the remaining 12% in the cladding. On the other hand, for the 1st-

order TM mode, only 3% is in the Si but 59% in the SiO2 layers. The confinement

factors in terms of the field energy density [27] are 85% in Si and 12% in SiO2

for the TE, whereas 56% in Si and 14% in SiO2 layers for the TM polarization.

Consequently a larger absorption coefficient in the multilayer film is expected in

the TE than in TM polarization.

To observe free carriers-optical effect for 1st-order guided TE mode, an 1.55-

µm laser line filter (FWHM of 40 nm) was placed in between the diode facet

and detector to filtering out all the other wavelengths especially at the longer

wavelength (cf. Fig. 4.3(b)). As done in Sec. 4.3.2, the bias voltage modulated

between 0 and 55, 40 and 45 V and the transmittance intensity correspondingly

alternated as demonstrated in Fig. 4.8(b).

The light intensity variation was due to free carriers in the first two Si layers

closer to the air, since only those two out of the three Si layers in the film were

connected to the electrical pads. It must be noted the absorption coefficient of

the multilayer slab waveguide is not naught even at 0 V, i.e. αFilm0 6= 0, with

zero absorption coefficients for both Si and SiO2 materials, due to lossy layer-

to-layer interface roughness [28]. From the Beers-Lambart law, the transmittance

intensity I0 at the bias voltage of V0 = 0 V is expressed as I0 = IInc10−αFilm0 ·l, where

IInc is the incident light intensity in the waveguide and l is the diode junction

length of 0.5 cm. Similarly, If = IInc10−(αFilm0 +∆αFilm

f )·l at the bias voltage of Vf ,

where ∆αFilmf ≡ αFilm

f − αFilm0 . The ratio of the two transmittance intensities

then becomes If/I0 = 10−∆αFilmf ·l and therefore the change in the waveguide’s

absorption coefficient is ∆αFilmf = −log10(If/I0)/l.

In order to obtain the change in the Si’s free carrier absorption coefficient ∆αSi,

64

the modal confinement factor of the two Si layers must be taken into account.

The simulations showed that the two Si layers hold about 36% of the entire field

intensity and 61% of energy density when there is no absorption in the Si layers

at 0 V, i.e. ISi0 = CI0 where C denotes the confinement factor at the 0-V bias

voltage and is practically invariant of the absorption coefficient in the Si layers.

The waveguide’s absorption coefficient change is then ∆αFilmf = C∆αSi

f . Assuming

an identical concentration for electron (∆Ne) and hole (∆Nh) carriers, the carrier

concentration can be obtained from ∆αSif based on the free carriers-optical effect

[24]:

∆n = ∆ne + ∆nh = −[8.8× 10−22∆Ne + 8.5× 10−18(∆Nh)0.8]

∆α = ∆αe + ∆αh = 8.5× 10−18∆Ne + 6.0× 10−18∆Nh

(4.1)

Figure 4.9: ∆αSi and ∆NSieh vs. current (mA) using intensity- and energy density-

based modal confinement factors in the two Si layers. The currents 0.0, 23.6, 38.7

and 56.6 mA correspond to 0, 45, 50 and 55 V of bias voltage. The fit lines are

for guides to eye.

Figure 4.9 shows the ∆αSi and ∆NSieh as a function of current, assuming ∆Neh =

∆Ne = ∆Nh despite the different B and P dopant concentrations by a factor of 3

65

(1.2×1015 for B and 3.3×1014 cm-2 for P). If the modal confinement factor is based

on the energy density, the carrier volume density is about 1 × 1015 cm-3, where

as it is larger by a factor of 61%/36% ' 1.7 if the intensity-based confinement

factor is used. At these carrier concentrations, the change in the real part of the

Si’s refractive index ∆nSi came out to be about −1× 10−5, which is significantly

smaller than the ∆n = 1.6× 10−4K-1× 25K ' 4× 10−3 due to the thermo-optical

effect. Therefore it can be concluded that the free carriers-optical effect alters the

Si’s absorption coefficient only whereas the thermo-optical effect shifts only the

real part of the refractive index.

4.4 Conclusion

A lateral electrical injection scheme for Si / SiO2 multilayer film was devised

and implemented to observe electroluminescence and the thermo-optical and free

carrier absorption effects. High-dose B and P ion implantations were carried out

on a multilayer film consisting of three pairs of 69-nm thick polycrystalline Si

and 62.5-nm thick sputtered SiO2 layers to form a P-“I”-N junction. A reactive

ion etching was performed to etch a trench through the multiple layers in the

doped region and a Ti metal contact was deposited over the trench to electrically

short the Si layers together. The current-voltage measurement showed a diode-like

property and the spectroscopic electroluminescence pointed to two sources of the

luminescence: one below Si’s bandgap and another above 1.7 µm.

Due to the large electrical power of at least 0.3 W (35 V) that was required to

produce a measurable luminescence, the diode-waveguide experienced a thermo-

optical effect which increased the Si’s refractive index and consequently the modal

indices, as demonstrated by m-line measurements in the reflectance configuration.

The absorption due to the free carriers was observed in the 1st-order guided

TE mode by measuring the transmittance intensity as a function of voltage (and

66

current). Changes in the absorption coefficient and carrier concentrations for Si

layers were estimated based on the changes in the transmittance intensity. It was

found that the free carriers-optical effect varies the Si’s absorption coefficient but

not the real part of its refractive index, unlike the thermo-optical effect.

67

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[22] J. H. Wray and J. T. Neu, “Refractive Index of Several Glasses as a Function

of Wavelength and Temperature,” J. Opt. Soc. Am. 59, 774 (1969).

[23] K. Ohta and H. Ishida, “Matrix formalism for calculation of electric field

intensity of light in stratified multilayered films,” Appl. Opt. 29, 1952 (1990).

[24] S. Libertino and A. Sciuto, “Chapter 4. Electro-Optical Modulators in Sili-

con.” Optical Interconnects: The Silicon Approach. Ed. L. Pavesi, (Springer,

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[25] G.E. Jellison and H.H. Burke, “The temperature dependence of the refractive

index of silicon at elevated temperatures at several wavelengths,” J. Appl.

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[26] E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

[27] J. T. Robinson, K. Preston, O. Painter and M. Lipson, “First-principle

derivation of gain in high-indexcontrast waveguides,” Opt. Express 16, 16659

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[28] Y. Fu and P. M. Fauchet, “Optical loss due to interface roughness in multi-

layer films,” (in progress).

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5 Summary & Future Outlook

5.1 Summary

In Chap. 2, the dielectric value ε of a Si nanoslab was investigated as a function

of the slab thickness. Using variable angle spectroscopic ellipsometry, ε was ex-

perimentally verified to be diminishing as the thickness decreases, in agreement

with the theoretical calculation based on surface polarization effect. The dielectric

value at 0.73 eV (1.7 µm) was reduced by a factor of ∼ 13% (from 12 to 10.4)

when the thickness decreased from 14 to 3.5 nm. It is therefore appropriate to

use the reduced ε value for Si layers thinner than ∼ 5 nm.

Discussed in Chap. 3 was the form birefringence and optical power confinement

in horizontal Si / SiO2 multilayer slab waveguide. Multilayer films consisting of al-

ternating a-Si and SiO2 with various SiO2 / a-Si thickness ratios were deposited on

5-µm thick thermal oxide layer by RF magnetron sputtering system at room tem-

perature. The sputtered layers’s thicknesses were all substantially smaller than

the wavelength of interest 1.55 µm (less than 3%). With the TE polarization

defined to be the E-field direction pointing parallel to the layer orientation, the

films’ modal indices were measured using m-line technique and found to be differ-

ent between TE and TM polarizations, showing a form birefringence. Simulations

72

using Abeles’ matrix method were carried out and confirmed the birefringence as

observed experimentally, which was due to different field distribution within the

multilayer films between the two polarizations. The simulations showed that for

TM polarization up to 85% of its entire modal power are confined in the low-index

SiO2 layers. Therefore it is possible to significantly minimize the optical loss due

to free carrier absorption if the guided light in the films are TM polarized. As

mentioned above, if the Si layer thickness is less than ∼ 5 nm, it is necessary

to use the reduced dielectric value in order to obtain a more accurate result in

simulation.

Chapter 4 deals with a lateral electrical injection scheme for multilayer films,

where electrons and holes were injected laterally along the layer orientation. High-

dose B and P ion implantations were performed on the multilayer to form a P-“I”-

N junction. A trench was etched in each of the implanted regions and filled with

titanium silicide, connecting all Si layers together. The sample functions as both

an electrical diode and slab waveguide. A large amount of current of at least 10

mA at 35 V was needed to generate a measurable luminescence for an NIR photo

multiplier tube module. Because of the heat produced by the large electrical

power, the waveguide experienced a thermo-optical effect, which was observed

by m-line technique in both TE and TM polarizations. Also observed was the

absorption caused by the free carriers injected into the Si layers. Based on the

modal confinement factor and the amount of transmittance intensity reduction,

variations in the absorption coefficient and carrier concentrations in the Si layers

were estimated. Contrary to the thermo-optical effect, the free carriers-optical

effect was found to influence the absorption coefficient but not the real part of its

refractive index.

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Figure 5.1: A rib waveguide consisting of the capping 1-µm wide oxide layer on

top of the multilayer film with electrical connections.

5.2 Future Outlook

It is imperative to further explore the lateral electrical injection scheme for hori-

zontal multilayer waveguide structure in order to achieve an electrically pumped

nc-Si based light source that could be incorporated into microchip processors as

an optical interconnect component. The first step is to optimize the fabrication

process such that the diode would behave like a good P-“I”-N diode with a low

turn-on and large break-down voltages. The second step is fabricating diodes with

a smaller “intrinsic” junction width (e.g. ∼ 2 µm). This would lower the bias volt-

age (thus the power) needed to achieve a given current level in the junction and

consequently reduce the amount of heat generated by the electrical power.

Furthermore, to make an infrared light source, the lateral electrical injection

scheme can be employed on an nc-Si / Er-doped SiO2 multilayer film, where the

energy generated by recombination of injected electrons and holes is transferred

to the Er atoms in the SiO2 layers which then emit the desired 1.55-µm photons.

As illustrated in Fig. 5.1, an capping oxide layer on the slab waveguide would

confine a TM mode underneath [1], keeping the light from getting lost in the lossy

implanted regions.

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Figure 5.2: A rib resonator with distributed Bragg reflectors. After Fig. 4.9 of [2].

Going beyond developing a light source-waveguide structure, a set of dis-

tributed Bragg reflectors can be fabricated on the multilayer film to transform

it to a resonator. This structure is conducive to achieving a lasing source as the

resonator would produce coherent light. If an oxide capping layer is placed on

either end of the resonator, the coherent TM-polarized light from the resonator

can propagate along the rib waveguide with little loss to the doped regions and

to the free carriers in the nc-Si layers.

75

Bibliography

[1] J. H. Shin, M.-S. Yang, J.-S. Chang, S.-Y. Lee, K. Suh, H. G. Yoo, Y. Fu

and P. Fauchet, “Materials and devices for compact optical amplification in

Si photonics,” Proc. of SPIE 6897, 68970N (2008).

[2] H. Chen, “Towards a nanocrystalline silicon laser,” Ph.D. dissertation, Uni-

versity of Rochester (2007).