Carrier Dynamics in Single Luminescent Silicon Quantum dots Fatemeh Sangghaleh

PhD Thesis

Information and Communication Technology

KTH Royal Institute of Technology

Stockholm, Sweden 2015

TRITA-ICT 2015:09

ISBN 978-91-7595-665-7

KTH School of Information and Communication Technology SE-164 40, Kista, SWEDEN

A dissertation submitted to KTH Royal Institute of Technology, Stockholm, Sweden, in partial fulfillment of requirements for the degree of Teknologie Doktor (Doctor of Philosophy). The defense will take place on October 23 2015 at 10.00 a. m. at Sal C, KTH-Electrum, Kistagången 16, Kista.

© Fatemeh Sangghaleh, October 2015.

Printed by: Universitetsservice US-AB

Abstract

Bulk silicon as an indirect bandgap semiconductor is a poor light emitter. In contrast, silicon nanocrystals (Si NCs) exhibit strong emission even at room temperature, discovered initially at 1990 for porous silicon by Leigh Canham. This can be explained by the indirect to quasi-direct bandgap modification of nano-sized silicon according to the already well-established model of quantum confinement.

In the absence of deep understanding of numerous fundamental optical properties of Si NCs, it is essential to study their photoluminescence (PL) characteristics at the single-dot level. This thesis presents new experimental results on various photoluminescence mechanisms in single silicon quantum dots (Si QDs).

The visible and near infrared emission of Si NCs are believed to originate from the band-to-band recombination of quantum confined excitons. However, the mechanism of such process is not well understood yet. Through time-resolved PL decay spectroscopy of well-separated single Si QDs, we first quantitatively established that the PL decay character varies from dot-to-dot and the individual lifetime dispersion results in the stretched exponential decays of ensembles. We then explained the possible origin of such variations by studying radiative and non-radiative decay channels in single Si QDs. For this aim the temperature dependence of the PL decay were studied. We further demonstrated a model based on resonance tunneling of the excited carriers to adjacent trap sites in single Si QDs which explains the well-known thermal quenching effect.

Despite the long PL lifetime of Si NCs, which limits them for optoelectronics applications, they are ideal candidates for biomedical imaging, diagnostic purposes, and phosphorescence applications, due to the non-toxicity, biocompability and material abundance of silicon. Therefore, measuring quantum efficiency of Si NCs is of great importance, while a consistency in the reported values is still missing. By direct measurements of the optical absorption cross-section for single Si QDs, we estimated a more precise value of internal quantum efficiency (IQE) for single dots in the current study. Moreover, we verified IQE of ligand-passivated Si NCs to be close to 100%, due to the results obtained from spectrally-resolved PL decay studies. Thus, ligand-passivated silicon nanocrystals appear to differ substantially from oxide-encapsulated particles, where any value from 0 % to 100 % could be measured. Therefore, further investigation on passivation parameters is strongly suggested to optimize the efficiency of silicon nanocrystals systems.

iv

Acknowledgement

My journey as a PhD student will be over soon. Looking back, I see years full of curiosity, enthusiasm, learning, improvements, challenges, failures and success. Today I’m a person with new perspectives about science, and research. During such an amazing journey I received support and encouragements from great number of people whom I would like to thank.

First and Foremost, I would like to express my sincerest gratitude to my advisor Professor Jan Linnros, for his encouragement, support and deep knowledge in the research topic which motivated and guided me through the right path. Thanks Jan for giving me this opportunity to be part of nano-silicon group and such a fascinating project. I appreciate all your time and ideas that made my PhD experience productive and stimulating.

I would also like to thank Professor Ulf Karlsson, the former head of the Material’s platform, for his support and positive attitude. I was so motivated to be a better researcher by your valuable advice and great encouragement. My passion for Swedish language comes from the amazing people like you, who inspired me by bringing front my progress continuously. Tack så jätte mycket, Ulf.

I would like to express my deep appreciation to Dr. Ilya Sychugov whom I regard as my unofficial co-supervisor. Thanks Ilya for building positive group dynamics as well as the scientific advice, knowledge and insightful discussions. You were the primary source of my morning scientific questions. I learned from you, how to “think” and “act” in a more balanced way for being a better experimentalist, and not get disappointed by the first failures.

Benjamin, thank you for showing me how to get started with sample fabrication and PL characterization and helping me to catch up with the ongoing project. I learned a lot from you and I was so inspired by your different approach to research and your curiosity upon scientific problems.

Fede, thank you for all the scientific adventures we had, from shaking and backing the vacuum tube, and long hours of low temperature measurements, to one day “Paris” walking after EMRS conference. You may continue our project with spectacular results and great success.

Roody, thank you for not only be the best officemate but also my “PhD buddy”. I will always remember our interesting fundamental discussions (from electron entanglement to biological evolution impacts on human behaviors). Thanks for your

vi

support during up and downs and for all the great times we had together. Without you the late night and weekend works would be so boring and unbearable.

I would like to thank my colleagues in Nano-silicon group (former and present), Aki-Kimmo, Miao, Yashar, Karolis, Rikard, Torsten, Apurba and Anna, for all the fruitful discussions, mind refreshing coffee breaks, paper cake gatherings and inspiring lunch breaks we had.

Many thanks go to all the present and former members in Materials physics department. Prof. Mats Göthelid, Prof. Johan Åkermann, Prof. Oscar Tjernberg, and Assoc. Prof. Jonas Weissenrieder for contributing in the nice working environment in our unit. I have enjoyed the company of Karin, Fatjon, Magnus, Bastian, Alex, Luca, Viktor, Hamid, Sohrab, Sareh, Karolina, Stefano, Zahra, Dunja, Marcelo, Olof, Milad, Markus, Shun, and Tobias. Thank you all for keeping the warm and positive atmosphere in the department. Thank you, Anneli for being so considerate, friendly and for all your efforts to arrange amazing department activities.

A special thank goes to Madeleine Printzsköld, for her highly efficient and professional work. Thanks Madeleine for your constant support and guide through all the confusing paper work, contracts, documentations and travel arrangements.

I’m grateful to be around so many amazing people in Electrum. Thanks to Mohsen, Carl, Dennis, Elena, Miguel, Aziza, Reyhaneh, Mounir, Anderson, Mahdi, Hossein, Ahmad, Reza Sanatinia, and Reza Nikpars for the nice fika times and small inspiring chats here and there in the building.

I appreciate Prof. Anders Hallen, my second supervisor, for his support and helps, Prof. Anand Srinivasan, Prof. Saulius Marcinkevicius, Assoc. Prof. Sergei Popov, and Assoc. Prof. Henry Radamsson for good advice. My deepest gratitude to Prof. Carl-Mikael Zetterling, and Prof. Ana Rusu for helping me through the difficulties of PhD studies.

Sincere thanks to Prof. Minuru Fujii for the inspiring discussions and our great running session in Tossa. Thanks to Prof. Jan Valenta, for his valuable discussions.

I would like to thank my friends and classmates in short period of being part of the Nanotechnology master program at KTH. Shabnam, Pooria, Sam and Arash for boosting my days with talks and laughters. I would like to thank Shabnam M. and Shabnam J. who tolerated (and survived?) all the crazy projects and adventures in my path. Your friendship is invaluable! Many thanks, to Anders, for being a great and considerate friend.

Last but certainly not least, my family, especially my parents, for their endless love and support, for their big hearts and always being there for me. Thanks to my siblings Ali, Mahshid, Mojgan, Reza for their constant encouragement and support to follow my dreams. So many thanks to Kamyar, Kiana, Aida and Mohammad, Ali N and

vii

Hossein. I love you all and without you I was not who I’m and where I’m today. Ayyub, Negar, Pedi, Saeid, Madeleine, Noella and Kaspian thanks for all your support, especially at first difficult months in Sweden, without you life would be hundred times tougher.

Chances are that I did not mention everybody. Thank you all for contributing to my

work and life in different ways during the past years and hopefully during the future.

Mahtab (Fatemeh) Sangghaleh Stockholm, September 2015

viii

ix

Abbreviations

EBL Electron beam lithography EQE External quantum efficiency FWHM Full width at half maximum HF Hydrofluoric acid IQE Internal quantum efficiency NC Nanocrystal NW Nanowire PL Photoluminescence QD Quantum dot QE Quantum efficiency QY Quantum yield RIE Reactive ion etching RT Room temperature SEM Scanning electron microscope Si Silicon TEM Transmission electron microscope

x

Contents

Abstract ............................................................................................................ iii

Acknowledgement ............................................................................................. v

Abbreviations ................................................................................................... ix

Appended publications .................................................................................. xiii

Other publications ......................................................................................... xiv

Summary of appended papers ........................................................................ xv

Chapter 1 Introduction ..................................................................................... 1

1.1 Introduction ............................................................................................. 1

1.2 Thesis structure ........................................................................................ 3

Chapter 2 Background and Theory ................................................................... 5

2.1 Semiconductor band structures ............................................................... 5

2.2 Low-dimensional semiconductors .......................................................... 6

2.3 Quantum dots .......................................................................................... 7

2.4 Optical properties of QDs ........................................................................ 9

2.4.1 Photoluminescence process ............................................................... 9

2.4.2 PL Emission bandwidth .................................................................. 10

2.4.3 Blinking ............................................................................................ 11

2.4.4 PL quantum efficiency .................................................................... 12

2.4.5 Optical absorption cross-section ..................................................... 13

2.4.6 PL intensity and higher excitations ................................................ 14

2.4.7 Electron-hole exchange interaction .................................................15

2.5 Silicon quantum dots ............................................................................. 16

Chapter 3 Experimental methods ................................................................... 19

3.1 Fabrication ............................................................................................. 19

3.1.1 Oxide-passivated single Si QDs ........................................................ 20

xi

3.1.2 Chemical synthesis .......................................................................... 21

3.2 Photoluminescence measurements ....................................................... 22

3.2.1 PL imaging and spectroscopy .......................................................... 23

3.2.2 PL decay measurements .................................................................. 26

3.2.3 Low-temperature PL measurements .............................................. 30

Chapter 4 Results and discussion ................................................................... 31

4.1 Oxide-passivated single silicon quantum dots ...................................... 31

4.1.1 General structural and optical characteristics ................................. 31

4.1.2 Photoluminescence .......................................................................... 33

4.1.3 Optical absorption cross-section ..................................................... 36

4.1.4 Temperature dependence of the PL ................................................ 38

4.1.5 High-excitation regime: biexciton creation versus Auger process? 46

4.2 Ligand-passivated silicon nanocrystals ................................................. 47

4.2.1 General structural and optical characterization .............................. 48

4.2.2 Spectrally-resolved PL decays ......................................................... 49

4.3 Internal and external quantum efficiency of silicon quantum dots ...... 52

Chapter 5 Conclusions .................................................................................... 57

Appendix A: System detectivity and QE estimation ....................................... 61

REFERENCES ................................................................................................ 65

xii

xiii

Appended publications

I. Fabricating single silicon quantum rods for repeatable single dot photoluminescence measurements B. Bruhn, F. Sangghaleh, J. Linnros, Physica Status Solidi A, vol. 208, 2010.

II. Exciton lifetime measurements on single silicon quantum dots F. Sangghaleh, B. Bruhn, T. Schmidt and J. Linnros, Nanotechnology vol. 24, p 225204, 2013.

III. Optical absorption cross-section and quantum efficiency of a single silicon quantum dot F. Sangghaleh, I. Sychugov, B. Bruhn and J. Linnros, Proceeding of SPIE, Nanotechnology VI, 2013.

IV. Non-radiative decay in Si/SiO2 quantum dots in transition from dark to bright states F. Sangghaleh, B. Bruhn, I. Sychugov and J. Linnros, in manuscript, 2015.

V. Near unity internal quantum efficiency of silicon nanocrystals with ligand passivation F. Sangghaleh, I. Sychugov, Z. Yang, J. G. C. Veinot and J. Linnros, ACS Nano, vol. 9, p 7097‒7104, 2015

VI. Blinking statistics of silicon quantum dots B. Bruhn, J. Valenta, F. Sangghaleh, J. Linnros, Nano Letters, vol. 11, p 5574‒5580, 2011

xiv

VII. Effect of X-ray irradiation on the blinking of single silicon nanocrystals F. Pevere, B. Bruhn, F. Sangghaleh, Y. Hormozan, I. Sychugov and J. Linnros, Phys. Status Solidi A, 1‒4, 2015

VIII. Biexciton Emission as a Probe of Auger Recombination in Individual Silicon Nanocrystals F. Pevere, I. Sychugov, F. Sangghaleh, A. Fucikova and J. Linnros, Journal of Physical Chemistry C, vol. 119, 2015.

Other publications

IX. Oxidation of nanopores in a silicon membrane: self-limiting formation of sub-10 nm circular openings M. Zhang, T. Schmidt, F. Sangghaleh, N. Roxhed, I. Sychugov and J. Linnros, Nanotechnology, vol. 35, 2014

X. Absorption of Visible Light by a Si Nanocrystal: Energy Structure and Enhancement to Bulk Values I. Sychugov, F. Pevere, F. Sangghaleh, B. Bruhn, J.-W. Luo, A. Zunger, J. Linnros, under preparation 2015

xv

Summary of appended papers

Paper I.

This paper provides a three step recipe for fabricating well-separated individual silicon quantum dots, resolvable by single dot spectroscopy. The recipe consists of electron beam lithography, reactive ion etching and self-limiting oxidation resulting in undulating silicon nanowalls. The paper demonstrates a controlled fabrication procedure that results in the formation of single or double silicon quantum dots. Contribution: PL spectral measurements, involved in the related discussions, and involved in writing the manuscript.

Paper II.

This paper presents, for the first time, photoluminescence decays of excitons in single silicon quantum dots. The decays from several single dots were extracted from time-resolved PL images recorded by a gated image intensifier equipped CCD camera. In contrast to PL decay studies on ensembles of silicon quantum dots, where only an overall lifetime characteristics of the assembly is assessable, the dot-to-dot variation of the decay time was reported in the current study. Unlike ensemble studies, the PL decay of individual silicon quantum dots were of mono-exponential character with a lifetime between ~ 5‒45 µs. In this paper, the origin of the stretched exponential decay observed for silicon quantum dot ensembles is proved to be due to the lifetime variation of individual quantum dots. Contribution: Time-resolved PL decay measurements (all measurements), major part of the data analysis, and writing the manuscript.

Paper III.

This article presents direct measurements of the optical absorption cross-section of a single silicon quantum dot. The PL lifetime and rise time of the dot under various excitation fluxes were measured using time-resolved photon counting and based on the temporal shape of the PL intensity the absorption cross-section value was

xvi

obtained ( ~ 1.4× 10-14 cm2). Contribution: Time-resolved photon counting measurements, data analysis, and writing the manuscript.

Paper IV.

The paper provides the temperature dependence of optical characteristics (PL emission spectra, PL intensity and decays) of single silicon quantum dots fabricated by e-beam lithography and oxidation. Based on the results, carrier dynamics of the PL at low and high temperature regimes were studied. The origin of the thermally activated, non-radiative recombination channel with a typical decay time of microseconds was suggested to be resonant tunneling of the excited carriers to the adjacent trap sites. At very low temperatures, on the other hand, the decay time increases by an order of magnitude due to the “dark” triplet state of emission. Contribution: PL characterization consisting of time-resolved PL decay measurements, emission spectra and PL intensity measurements at various temperatures, data analysis and writing the manuscript.

Paper V.

This paper presents near 100% internal quantum efficiency of silicon nanocrystals with different oxide passivation and preparation methods. The Si nanocrystals were prepared by chemical synthesis and were measured in a suspension of toluene. A spectrally-resolved decay technique was used to measure the lifetime of such nanocrystals at various detection energies. The paper suggests a mathematical approach to extract the size-selected PL decay rates of silicon nanocrystals. The measured mono-exponential decays, as well as the coincidence of the extracted total decay rates with radiative rates reported in the literature were presented as a proof of almost 100 % internal quantum efficiency. The measured quantum yield on the other hand, varying in the range 30–70 % from sample to sample was explained as the fraction of bright to dark nanocrystals. The concepts of internal quantum efficiency and external quantum efficiency (quantum yield) related to silicon nanocrystals systems as well as various non-radiative and radiative decay channels were discussed in depth.

xvii

Contribution: Spectrally-resolved and time-resolved PL decay measurements and corresponding data analysis and processing, writing major part of the manuscript.

Paper VI.

This article presents blinking statistics, such as on- and off-time distributions and extracted blinking frequency of individual silicon quantum dots and the excitation flux dependency of these characteristics. In contrast to studies of direct bandgap quantum dots such as CdSe nanocrystals, where power law dependencies of the on- and off-time distributions were reported, in this work a purely exponential character with no statistical aging was observed. Furthermore, the obtained linear dependency of the blinking frequency on the excitation power in this work was explained by a single photon absorption process resulting in a direct trapping of the excited carriers without the need of an Auger process as in high-excitation flux conditions. Contribution: PL blinking measurements, involved in the related discussions.

Paper VII.

This paper studies the impact of X‒ray irradiation on the blinking of single silicon quantum dots. It is shown that the general optical properties of single quantum dots such as PL decay time, emission energy and linewidth were not substantially influenced by the X‒ray irradiation, unlike for direct-bandgap quantum dots for the same irradiation dose. Hence, it was concluded that compared to CdSe, silicon quantum dots were more radiation tolerant. The observed on- and off-time distributions of the blinking remains mono-exponential however no clear correlation was observed between the blinking parameters and the radiation dose. Contribution: Time-resolved PL decay and spectral measurements, data analysis. Involved in the related discussions and involved in writing the paper.

xviii

Paper VIII.

This paper presents the detection of biexciton emission and evaluation of the related quantum efficiency by performing time-resolved single-dot PL decay experiments at room and at cryogenic temperatures. No second peak in the emission spectrum, as a proof of biexciton creation, was observed at low-temperature spectroscopy. In addition, due to the very low efficiency obtained for the biexciton emission (~10‒20 times less than that of exciton emission), it is concluded that Auger recombination is dominant at high pumping regimes. This paper shows saturation of the PL intensity at high photon flux of single silicon quantum dots fabricated by two different methods, as the complementary evidence of suppression of the biexciton emission. Contribution: Contributed partly in time-resolved PL decay measurement and data analysis, contributed in related discussions and partly in writing the paper.

1

Chapter 1 Introduction

1.1 Introduction

Silicon as the main component of the integrated circuit technology has had an enormous impact on our daily lives through microelectronics and the information revolution. Enhancing the functionality as well as reducing energy consumption by implementing higher number of transistors in integrated circuits, in accordance to Moore’s law, led to shrinkage of the size of silicon-based components down to nano-scales. By reducing the size of devices, quantum mechanical effects become observable and may even dominate the device behavior and sometimes impose serious problems such as electron tunneling through the gate oxide in transistors. In contrast, silicon owes its enhanced optical properties to such nano-miniaturization.

The efficient light emission of nano-sized silicon was first discovered in porous silicon at the beginning of the 1990’s.1,2 Porous silicon has a sponge-like porous structure and consists of islands of silicon nanowires and therefore it is considered as a two dimensional confined system. However, the undulating width of the nanowires brings a confinement also along the nanowires resulting in the three dimensional confinement. It was shown that the carrier confinement in two dimensions widens the bandgap of the bulk silicon appreciably and transforms its continuous band structure to discrete energy states. Moreover, quantum confinement introduces an indirect-to-quasi-direct bandgap modification, resulting in a more efficient optical transition.3 The alterations of the band structure of silicon induced by size reduction are schematically illustrated in figure 1.1.

Further confinement of the silicon, results in spherical nano-sized confined structures in three dimensions and hence are called silicon nanocrystals. Throughout the ensuing decades, photoluminescence (PL) characteristics of silicon nanocrystals such as absorption and emission states, spectral features and carrier dynamics have been vastly studied on ensemble of silicon nanocrystals.4,5 Furthermore, numerous studies have been focused on the engineering of the size/shape and dispersion of nanocrystals as well as controlling the surface/interface chemistry of the passivation, via various fabrication methods.

Despite the successful syntheses of uniform, mono-dispersed silicon nanocrystals and quantitative characterization of the optical properties of such assemblies (in addition to the efforts carried out to explain the observed characteristics based on various physical models), the physics behind several fundamental aspects in silicon

2

Figure 1.1 Transformation of the continuous band structure of bulk silicon (left) to discrete energy states in a silicon nanocrystal (right). As a result of the quantum confinement effect, the bandgap of silicon at nano-scales increases and the carrier wave functions become spread in k-space, leading to the formation of quasi-direct band structures with more efficient optical transitions.

quantum dots is not well understood yet. In this sense, sufficient research on silicon nanocrystals with different passivation molecules specifically at single-dot level is still missing. In this regard, several important questions remained to be answered:

• Single dot photoluminescence decay character: What is the PL decay

character of single silicon quantum dots? What is the origin of stretched exponential decay of ensemble of silicon nanocrystals?

• Carrier dynamics of the luminescence in single silicon quantum dots: what is the share of the radiative and non-radiative recombination of the total PL decay?

• Photoluminescence absorption: what is the absolute value of the absorption cross-section and is it shape dependent?

• Quantum efficiency: Optically, how efficient could a silicon quantum dot system be?

• High-excitation regime: What is the dominant PL mechanism under high excitations?

• Emission intermittency/blinking (switching between on and off state): what is the mechanism behind blinking of silicon nanocrystals?

3

The questions above have been set as the main target of the current study. By performing PL spectral and decay measurements on single Si QDs, embedded in a thick oxide shell at various temperatures, carrier dynamics of the PL was studied in detail. Moreover, through PL decay experiments, under different excitation power densities, the origin of the PL was clarified and the absorption cross-section absolute value of such single QDs was measured directly. Accordingly, the quantum efficiency was determined at a single-dot level. The quantum efficiency is further investigated on ensemble of ligand-passivated silicon nanocrystals by applying spectrally-resolved PL decay experiments. The concepts of external quantum efficiency sometimes referred to as quantum yield (QY) and internal quantum efficiency (IQE) were discussed and determined for such nanocrystals.

Clarifying the items above is a significant step towards exploiting Si NCs in various applications. For example, silicon as a non-toxic, biocompatible and abundant material is an ideal candidate for biomedical imaging and diagnostic applications.6,7

1.2 Thesis structure

A summary of the theory and background, essential to understand experimental results and discussions is given in chapter 2. The first and second sections briefly introduce the band structure of bulk and low-dimensional semiconductors, respectively. In section three, based on the quantum confinement of carriers, the concept of the quantum dot is formulated and presented. Section four is devoted to the discussion of various optical properties of indirect bandgap semiconductor nanocrystals and the physical models for the corresponding characteristics. A brief background on the silicon nanocrystals as the subject of this thesis is given in section five.

Chapter 3 is dedicated to the experimental details related to the current study. Fabrication of single Si QDs, embedded in SiO2 based on the method developed in a previous project,8 is shortly explained in section 1. Additionally, a brief description of syntheses of ensemble of silicon nanocrystals with ligand passivation (prepared in the Department of Chemistry at University of Alberta, following a collaborative project with the group of Prof. Jonathan Veinot), is given in the same section. In section 2, the experimental setup and techniques applied throughout the current work is reviewed.

In chapter 4, section 1, the results of the PL spectroscopy and time-resolved PL

4

decay measurements of single silicon quantum dots at various temperatures are presented. Moreover, the results of spectrally-resolved decay studies of ensembles of ligand passivated silicon nanocrystals are shown in section 2. In chapter 5, the thesis is concluded followed by a short summary and outlook.

5

Chapter 2 Background and Theory

2.1 Semiconductor band structures

As the name implies, “semi-conductors” refer to materials with electrical conductivity character between a metal (conductor) and an insulator. As elements they belong to group IV in the periodic table (e. g. Si and Ge), and as compounds to combinations of group III-V (e. g. GaAs) or II-VI (e. g. ZnO). The crystalline structure of semiconductors introduces a periodic potential resulting in the formation of particular band configuration in k-space, consisting of the valence band (VB), conduction band (CB) and the energetically forbidden zone called the bandgap. The bandgap is ‘direct’ if the lowest energy state of the CB and the highest energy state of the VB have the same crystal momentum (k-vector) in the Brillouin zone; otherwise it is referred to as ‘indirect’ bandgap. Figure 2.1 shows band structures of GaAs and Si, as direct and indirect bandgap semiconductors, respectively.

Figure 2.1 The band structure of indirect and direct bandgap semiconductors, GaAs (left) and Si (right), respectively, adopted from Marvin, et al.9 In GaAs the recombination is direct band-to-band while in Si phonon-assisted transitions are necessary to conserve the momentum.

6

The maximum energy level occupied by electrons in a material at 0K is called the ‘Fermi level’ which is determined by the Fermi-Dirac distribution at thermodynamic equilibrium (in which the Pauli Exclusion Principle is taken into account). In metals, the Fermi level lies within the allowed energy bands while in semiconductors it is often located in the forbidden energy zone. In highly pure semiconductors, at zero temperature, electrons occupy the valence band fully while the conduction band is empty. In contrast to metals, where the overlap of the bands let the delocalized carriers move freely and hence they are inherently conductive, in semiconductors only excited electrons in the conduction band (or the opposite charge carriers, “holes” in the valence band) are involved in the conductivity. This is the principle behind operation of diodes/transistors.

Semiconductors are optically luminescent, if the excited carriers in the conduction band release their excess energy as propagating electromagnetic waves through the recombination process with “holes” in the valence band, as a consequence of energy conservation. Based on the excitation source, different terminologies are used to describe the luminescence process. High energy electron beam (102‒103 eV), electric field, exothermic chemical reactions, and light are excitation sources in cathodoluminescence, electroluminescence, chemiluminescence and photoluminescence processes, respectively.

Taking into account momentum conservation, the PL absorption/recombination mechanism occurs via direct band-to-band or phonon assisted band-to-band transitions. Phonons, or quanta of lattice vibrations, are quasi-particles that are capable of interacting with photons. In direct bandgap semiconductors carrier annihilation occurs via direct band-to-band transitions since CB and VB are at the same point in k-space. In contrast, in indirect bandgap semiconductors, direct band-to-band transition is of extremely low probability. Since photon momentum is negligible, a third particle (phonon) with a suitable k- momentum is needed to obey the k-conservation rule.

2.2 Low-dimensional semiconductors

Typically, bulk metal consist of ~ 1023 atoms per cm3. In single isolated atoms, the electrons occupy orbitals and form discrete energy levels. In proximity of other atoms, the degenerate energy states of individual atoms are perturbed and split into continuous energy bands. However, by reducing the number of perturbing atoms, or spatial size shrinkage, this continuity transforms into a set of discrete levels. The

7

spatial confinement of materials in 1, 2 or 3 dimensions, forming quantum well (QW), quantum wire (Qwire) and quantum dot (QD), respectively. Such confinement applies boundary conditions to the wave functions and corresponding quantum numbers and results in a change in the density of states (DOS). Figure 2.2 show the density of states for a bulk semiconductor, which has continues parabolic dependence on energy and for a confined semiconductor in three, two and one dimensions. The transformation of continues energy bands of bulk into discrete energy states and size dependency of the bandgap of confined material is called “quantum confinement effect”.

Figure 2.2 Density of states (DOS) of bulk semiconductor, quantum well (QWell) confined in one dimension, QW confined in two dimensions, and QD confined in three dimensions, from left to right respectively. The continuous DOS of bulk semiconductor becomes discrete atomic-like states in the QDs.

2.3 Quantum dots

Semiconductors confined in three spatial dimensions down to nano-scale are called nanocrystals (NCs). More general, any three dimensional confined potential, or quasi-zero dimensional structures are referred to as quantum dots (QD). They are also

8

termed “artificial atoms” as their energy states mimic that of atoms with similar quantum numbers. The energy of the localized states of NCs is obtained based on the particle in box model and by solving the Schrödinger equation in a spherically symmetric potential (assuming an infinite barrier) as below:

𝐸𝑛𝑛 = ℏ2

2𝑚�𝜒𝑛𝑛𝑅�2 (2.1)

where 𝜒𝑛𝑛 stands for the n th root of the l st order spherical Bessel function. The strength of the quantum confinement is scaled by the Bohr exciton radius (ab) which is the typical size of an exciton (a quasi-particle consisting of an electron-hole pair bound by the Coulomb potential) in a bulk semiconductor in analogy with a hydrogen atom.

𝑎𝑏 = 𝜀ℏ2

𝜇𝑒2= 𝜀𝑚0

𝜇 (2.2)

where the reduced mass (µ) is defined as: 1

µ= 1

𝑚𝑒

+ 1

𝑚ℎ

. Accordingly based on the

Hamiltonian of a hydrogen-like atom, the exciton Rydberg energy is 𝑅𝑦∗ = 𝑒2

2𝜀𝑎𝑏 . If

the radius of a QD is larger than its Bohr exciton radius (𝑎 > 𝑎𝑏), the system is referred to as being in the weak confinement regime and if it is smaller (𝑎 < 𝑎𝑏) it is in the strong confinement regime (figure 2.3).

Consequently the exciton energy states of weak and strong confinement conditions are obtained as below, respectively:

𝐸𝑛𝑚𝑛 = 𝐸𝑔 −𝑅𝑦∗

𝑛2+ ℏ2𝜒𝑚𝑛

2

2𝑀𝑅2 (2.3)

𝐸𝑛𝑛 = 𝐸𝑔 + ℏ2

2µ𝑅2𝜒𝑛𝑛2 (2.4)

where 𝜒𝑚𝑛 are the roots of the spherical Bessel functions (m‒number of the root, l‒order of the function).

9

2.4 Optical properties of QDs

2.4.1 Photoluminescence process

By exciting QDs with energies higher than their bandgap energy (Eexc>Eg), electrons from the valence band are excited to the conduction band. If the absorption energy is higher than the CB edge, the excess energy is released by emitting phonons when electrons from thermodynamically non-equilibrium states relax to the band edge. Finally, through radiative recombination the electron annihilates with the corresponding hole in the valence band and emits a photon. The QD is practically transparent for excitation energies smaller than the corresponding bandgap energy. Another possible scenario is that instead of band-to-band radiative recombination, the excited electron relaxes to available defect levels, and finally resumes to its original energy state in the valence band by releasing phonons, which is considered as a non-radiative recombination path. In a more general point of view, if the excess energy of the electron is released in other forms than photons, it is referred to as a non-radiative transition.

Figure 2.3 (a) An electron and a hole pair bound by Coulomb potential referred to as an axciton, (b) weak (R>ab) and strong (R<ab) confinement regimes. The energy states are more distinct for smaller nanocrystals. (c) Radiative band-to-band transition, relaxation process from higher states to the band edge and non-radiative defect related transition (from left to right, respectively).

10

In indirect bandgap bulk semiconductors, a direct band-to-band transition has extremely low probability and several emission peaks are found in the spectrum due to phonon assisted radiative transitions. Phonons have momentum and their interaction with photons make the indirect optical transitions possible by satisfying the momentum conservation rule.

However, as a consequence of the quantum confinement effect and due to Heisenberg uncertainty principle, (Δ𝑥Δ𝑝 ≥ ℏ/2) when the size of a semiconductor decreases, in other words electrons become more localized (smaller Δx), their wave functions (their momentum) spread across the k-space (larger Δp) widely. Hence, size shrinkage results in a significant overlap of the wave functions of electrons and holes and therefore a relaxation of the k-conservation in indirect bandgap nanocrystals and consequently no-phonon assisted transitions become possible.3,10

The characteristics time takes for the excited electrons to lose their excitation energy and go into the ground state called “lifetime” or the PL “decay time” (τ) and its exact distribution is of mono-exponential. Consequently, the rate of the transition to the ground state is given by 1/τ in which both radiative and non-radiative transitions probability contribute. Therefore the total decay rate is defined as below:

1𝜏

= 1𝜏𝑟

+ 1𝜏𝑛𝑟

(2.5)

where τr and τnr are radiative and non-radiative lifetimes, respectively. The total PL decay of direct bandgap QDs are in the range of ~ ns while in QDs with indirect bandgap it is much longer in the range of ~ µs.11

2.4.2 PL Emission bandwidth

For an ideal band-to-band transition of a single quantum dot at cryogenic temperatures, one might expect the emission spectra of δ-function with a very narrow spectral bandwidth. Ideally, this linewidth is set by the lifetime through Heisenberg’s

uncertainty relation ∆𝐸~ ℏΔt

~ ℏτ where τ is the decay time. From studies of single

quantum dots, however, it has been found that peak shifts the “spectral diffusion” may occur randomly in time. Thus, the spectral linewidth is affected by such spectral shifts in the PL position. Such effect probably caused by interaction with the local environment11 which shifts the energy states as well as altering the oscillator strength

11

of optical transitions. Although in practice, at low temperatures, the measured linewidth of single dots are narrow enough to be far below the thermal energy as a proof of the atomic like discrete energy levels in single nanocrystals.12

At room temperatures due to the thermal broadening the spectral bandwidth of single nanocrystals are relatively broad referred to as “homogenous” linewidth broadening effect. In ensembles the size distribution of nanocrystals implies additional widening to the bandwidth known as “inhomogeneous” linewidth broadening. The line width of ensemble of QDs therefore, is a convolution of

homogenous Γhom and inhomogeneous Γinh broadening (Γ = �Γℎ𝑜𝑚2 + Γ𝑖𝑛ℎ2 ).

2.4.3 Blinking It has been observed that single nanocrystals sometimes do not emit light continuously under continues excitations but instead they exhibit a random switching between a bright and a dark state, referred to as ON and OFF states, respectively. This phenomenon is called “PL intermittency” or “blinking”. The observed ON/OFF durations are changing between the range of ~ ms intervals to very long times (hours).13 The PL intermittency is ascribed to the Auger mechanism, in which nanocrystals become charged and the excitation energy is given to a third electron or hole relaxing by a non-radiative process (figure 2.4).

Figure 2.4 Schematic illustration of a nanocrystal (consisting of the core and shell) in its OFF (left) and ON (right) state. The corresponding recombination procedure is shown under each schematic.

12

2.4.4 PL quantum efficiency

The quantum efficiency (QE) of silicon nanocrystal is defined as the probability of radiative transitions versus the total recombination probability:

𝑄𝐸 = 1/𝜏𝑟1/𝜏𝑟+1/𝜏𝑛𝑟

(2.6)

If the radiative transition is more efficient than non-radiative transitions (e. g. the

radiative rate is much faster than non-radiative rate 𝜏𝑟 ≪ 𝜏𝑛𝑟) the efficiency approaches unity and 𝜏 ≅ 𝜏𝑟. However in reality most of the nanocrystals contain surface/interface/shell defects, which provide non-radiative recombination channels and result in less than 100% efficient optical transitions. Obviously decay rates of such non-radiative transitions involved in the QE are comparable to radiative rates. QE is also referred to as internal quantum efficiency (IQE) to emphasize that it is different than the quantum yield (QY). For ensemble of nanocrystals quantum yield (QY) is usually determined as the ratio between numbers of emitted photons to the number of absorbed photons. This quantity, sometimes referred to as external quantum efficiency (EQE) and is typically measured in an integrating sphere.14

Figure 2.5 A schematic diagram to simply visualize the definition of quantum yield and the internal quantum efficiency in ensembles of NCs (left and right, respectively). Various processes are involved in the quantum yield, while in internal quantum efficiency only bright NCs are taken into account.

13

Therefore QY includes all possible processes inside the NC ensemble. As an instance, nanocrystals might release their absorbed energy in the form of lattice vibration which degrades the QY value. These NCs are known as “dark” NCs and characterized by very efficient non-radiative recombination because of the presence of defect centers. Furthermore, blinking dots in the OFF states15 are considered as dark nanocrystals. Unlike the IQE which is only influenced by non-radiative decays comparable with radiative ones (bright NCs or blinking ones, in their ON state), QY is affected by various types of non-radiative decay rates. This is shown in the simple schematic of the definition of QY and IQE of ensemble of NCs in figure 2.5.

QY can be expressed mathematically based on the IQE of individual nanocrystals and the time fraction of ON state (blinking duty cycle δ) as below:

𝑄𝑄 =∑ 𝛿𝑖𝐼𝑄𝑄𝑖𝑁𝐵𝐵𝑖=1

(𝑁𝐵𝐵+𝑁𝐷𝐷𝑟𝐷) (2.8)

NBR and NDark are the number of bright and dark nanocrystals.

2.4.5 Optical absorption cross-section

The optical absorption cross-section (σ) is representative of the efficiency of the photoluminescence excitation process in the sense of interaction of incoming photons with nanocrystals. Hence, determining the absorption cross-section of nanocrystals is of great importance in order to exploit them in devices. Absorption cross-section is dependent on the effective density of states and the oscillator strength.16 Considering an excitation pulse (typically shorter than the exciton lifetime in NCs) with the energy of E and excitation frequency of υ, the number of excitation photons in an area of A is n= E/hυA. Accordingly the mean number of created e-h pairs per nanocrystal after the excitation pulse will be:

< 𝑁 >= 𝑛𝑛 (2.7)

where σ is the absorption cross-section of the nanocrystal. Hence absorption cross-section value could be determined quantitatively in this way.

14

2.4.6 PL intensity and higher excitations

The PL intensity of nanocrystals under continuous excitation can be modeled according to a set of differential equations. In this model nanocrystals are considered to be in different excitation states containing i=0,1,…number of excitons. The rate equation of the states’ occupation probabilities is as below:16

𝑑𝑝𝑖𝑑𝑑

= 𝜙𝑒𝑒𝑛(𝑝𝑖−1 − 𝑝𝑖) −𝑝𝑖𝜏𝑖

+ 𝑝𝑖+1𝜏𝑖+1

(2.8)

where 𝑝𝑖 is the number of occupation probability of the ith-state, 𝜙𝑒𝑒 excitation photon flux and 𝜏𝑖 total decay time of the transition from the state of i to i-1. Due to the dominance of fast Auger processes the creation of triple or higher exciton populations are negligible and therefore is excluded in the formula. Nanocrystals are considered to be in three different states with 0, 1 and 2 excitons.

The absolute PL intensities of exciton and biexciton (two pairs of bounded electron-holes) are given by 𝐼1 = 𝑝1 𝜏1𝑟⁄ and 𝐼2 = 𝑝2 𝜏2𝑟⁄ where 𝜏1𝑟 and 𝜏2𝑟 are the respective radiative decay times. By substituting the steady-state condition (dpi/dt=0) in which the PL intensity after the initial increase becomes constant under continuous excitation, in the eq. (2.8) the exciton and biexciton intensities will be:

𝐼1 = 𝑄𝑄1𝜙𝑒𝑒𝜎

1+𝜏1𝜙𝑒𝑒𝜎+𝜏1𝜏2𝜙𝑒𝑒2 𝜎2 (2.9)

𝐼2 = 𝑄𝑄2𝜏1𝜙𝑒𝑒2 𝜎2

1+𝜏1𝜙𝑒𝑒𝜎+𝜏1𝜏2𝜙𝑒𝑒2 𝜎2 (2.10)

where QE1 and QE2 are the corresponding exciton and biexciton quantum efficiency values.

According to eq. (2.9), under weak excitation conditions (𝜙𝑒𝑒στ < 1), where only one exciton per nanocrystal is generated, the PL intensity increases linearly by the excitation power. At high excitations, however, the PL saturates.

Using the population rate equations, also the temporal shape of the PL intensity of an exciton under pulsed excitation is obtained:17

𝐼1(𝑡) = 𝐼0 �1 − 𝑒𝑥𝑝 �−�𝑛𝜙𝑒𝑒 + 1𝜏1��� (2.11)

15

According to this formula the absorption cross-section value can be measured directly from the slope of the 1/τ1 versus excitation flux plot.

2.4.7 Electron-hole exchange interaction

In quantum mechanics when wave functions of two indistinguishable fermions overlap, according to Pauli exclusion principle, their perturbed wave function should be either symmetric (singlet) or asymmetric (triplet) with respect to each other. The corresponding energy states are called “singlet” and “triplet” states, and considering

the Hamiltonian independent of spin as 𝐻� = 𝑃1�2+𝑃2�

2

2𝑚+ 𝑉(𝑥1,𝑥2) it can be shown that

the average energy of the interaction for the symmetric condition is higher than that of the asymmetric one. The energy difference between singlet and triplet states is called the “exchange splitting energy”. In a quantum dot the energy states are subject to exchange interaction of electron and holes. As the overlap is higher (the quantum dot is smaller) the exchange energy is larger. Theoretically it is shown that the splitting energy scales with nanocrystal size as 1/R3.18

This aspect of quantum dots is proven by studying the temperature dependency of the decay times. Transitions from the triplet state are parity forbidden and the low recombination rate of photoluminescence intensity is ascribed to populating of the triplet state at cryogenic temperatures.19

According to this model and considering thermal equilibrium of singlet and triplet states, temperature dependency of the radiative decay rate is obtained as below:

Γ𝑟 =3Γ𝑇+Γ𝑠exp (− Δ

𝐷𝐵𝑇)

3+exp (− Δ𝐷𝐵𝑇

) (2.12)

where Γ𝑇 and Γ𝑠 are decays rates of triplet and singlet states, respectively, Δ denotes exchange splitting energy and 𝑘𝐵𝑇 is thermal energy.

16

2.5 Silicon quantum dots

Silicon as bulk semiconductor is an inefficient light emitter, even at liquid He temperatures, due to its indirect bandgap nature. It was in 1990 when strong room temperature visible emission was reported on porous silicon.1,2 Porous silicon has a sponge like structure consisting of networks of nano-sized silicon entities. Historically the discovery of porous silicon goes back to 1956 when Uhlir described etching of silicon by using hydrofluoric acid under anodic bias.20 However the interest in the research society did not raise until 30 years later when its amazing optical properties were discovered, and consequently the efforts focused on fabrication and characterization of silicon nanocrystals.

The quantum confinement effect as well as the impact of the defects and dangling bonds on the emission were vastly studied in silicon nanocrystals passivated by oxide or ligand molecules and size tunable visible emission were clearly demonstrated.21–25 However, the physics behind many optical properties of silicon nanocrystals are not well understood yet. As an instance the origin of the PL emission of silicon quantum dots was controversial for a long time.26 The observed fast decaying blue emission (~ ns) was ascribed to dangling bonds while the red line with longer decays (~µs) attributed to quantum confined excitons and thus the corresponding PL emission energy is strongly dependent on the nanocrystal size. Several other origins responsible for various PL emission energies with different decay rates are introduced in the literature such as transitions through localized surface/interface levels, hot carriers, and direct band Γ‒Γ recombination.27

Another controversial field is the photoluminescence recombination mechanism and carrier dynamics of Si NCs. Ensembles of Si NCs exhibit “stretched exponential” PL decay line shapes, 𝐼 = 𝐼0exp �−(𝑡/𝜏)𝛽� where τ and β are lifetime and decay factor, respectively. The dispersion factor β represents the distribution of the lifetimes in the system and mathematically it shows the curvature of the decay plot. The PL lifetime of silicon nanocrystals at room temperature (~µs) are relatively long which is even longer at cryogenic temperatures (~ms)29–31 and the reported β values are in the range of ~ 0.4‒0.8.31 The physical origin of the stretched exponential of the PL decay was explained by various models such as tunneling through localized non-radiative decay centers32, migration of excitons33 and distribution of crystal shape for a given fixed volume.34

Despite of the strong light emission of Si NC, its slow radiative PL decay rate is a draw back. The reported QE for porous silicon at room temperature was ~ 8%,35 while improvements in fabricating mono-size dispersed silicon nanocrystals as well

17

as modifying passivation (e. g. annealing in hydrogen environment) resulted in values as high as ~ 40‒80%.36,37 Part of the waste of the absorption energy ending in the form of non-radiative transition with fast recombination rates compared to radiative channels, is believed to be due to dark nanocrystals. These nanocrystals absorb photons efficiently but do not necessarily contribute into recombination processes, due to permanent charge trapped states or temporarily OFF state of blinking. The ratio of dark to bright nanocrystals can be estimated according to the absolute value of the quantum yield (external quantum efficiency).

The properties mentioned were mainly studied in the ensemble of Si NCs. Silicon nanocrystals as assembly have different crystalline network configuration, surface passivation, and residual size and shape distribution. Therefore ensemble characterization only provides statistical information and doesn’t reveal individual behaviors. By the developments of single dot spectroscopy techniques, originally for single molecules,28 as well as single dot fabrication methods fundamental investigations of photo physics of individual dots have become possible.

Focusing mainly on single-dot spectroscopy, in the current project the photoluminescence decay of single Si QDs were measured and the corresponding recombination mechanism was studied. In addition the absolute values of absorption cross-section of single dots were determined, which results in the more precise estimation of internal quantum efficiency of single silicon quantum dots. We have discussed that the carrier diffusion mechanism proposed in the literature is not present in our silicon QD system since the single dots are isolated with no interaction or carrier migrations. Moreover a model for the thermally activated non-radiative processes degrading the efficiency of Si NCs, based on the resonant tunneling of the excited carriers to the adjacent trap sites have been proposed.

To study the impact of the passivation and local environment on the PL decay of silicon NCs, the PL decay of various ligand-passivated Si NCs in solutions were also studied. The spectrally-resolved measurements of Si NCs with different ligand passivation molecules and preparation techniques reveals near unity internal quantum efficiency of such NCs.

18

19

Chapter 3 Experimental methods

3.1 Fabrication

Si nanocrystals are fabricated via gas, liquid and solid phase approaches, which could be categorized into bottom-up and top-down techniques, as well. In the bottom-up method small building blocks (e. g. atoms) are put together to form structures in desired sizes, while in the top-down approach larger structures are partitioned into nano-sized dimensions. Some of the most common fabrication methods of Si NCs are as follows: decomposition of silane gas (SiH4) in different plasma reactors38,39 electrochemical dissolution of bulk silicon,40 solution reduction of SiCl4,41 ion implantation of Si into SiO2,42 thermal annealing of SiOx films deposited by CVD,17 sputtering,43 or vacuum evaporation,44 and laser ablation.45 The optical characteristics of silicon nanocrystals are very much dependent on the fabrication procedure and thus results from different types of surface/interface defects, dangling bonds, nanocrystals size and shape distributions. Therefore the choice of fabrication technique for particular type of studies is of a great importance.

In the current project, silicon nanocrystals were prepared via two approaches:

(1) Oxidation of silicon nanowalls in a self-limiting regime. Nanowalls were patterned and formed on silicon wafers by using electron beam lithography (EBL) and reactive ion etching (RIE), respectively. Such fabrication procedure which resulted in the formation of isolated, single Si QDs, was performed in the clean room of KTH Royal Institute of Technology, Stockholm, in continuation of the previous project focused on fabrication on single Si QDs.8

(2) Annealing of dried HSQ, followed by liberating hydride-terminated Si NCs using HF and passivating the obtained NCs with various ligand molecules through chemical processes. Through this method solutions of Si NCs in toluene were synthesized in Canada following a collaborative project with the group of Prof. Jonathan Veinot, (Department of Chemistry, University of Alberta).

20

3.1.1 Oxide-passivated single Si QDs

Single Si QDs with oxide passivation were fabricated in three steps using electron beam lithography (EBL), reactive ion etching (RIE) and self-limiting oxidation. The mentioned fabrication method was originally used to fabricate pillars of nano-sized silicon in the beginning of 1990-s.46 By a combination of EBL, Cr lift off and RIE columns of silicon were formed on a piece of silicon wafer, followed by oxidation to shrink the silicon core. By adjusting the oxidation parameters (e. g. the temperature of ≤ 900 oC) a self-limiting regime dominates where the oxidation rate of concave curvatures are faster than convex curvatures due to stress effects.47 Therefore the pillars oxidize faster in the center than at the top and nano-sized cores are formed close to the top of the columns. Later on it was shown that single silicon quantum dots were fabricated more easily by oxidation of silicon nanowalls instead of pillars.48

Figure 3.2 Scanning electron microscope images of (a) array of silicon pillars, and (b) a typical EBL pattern after dry etching and before oxidation, consisting of undulating silicon nanowalls shown in more details in the zoomed image.

That is because in pillars a slight fluctuation in oxidation parameters, for instance the oxidation duration, may lead to a total consumption of the silicon core and formation of silicon dioxide instead. In the other hand, in the case of nanowalls, due to the continuation of the walls, quantum dots can be formed all along the walls with less spatial limitation. Formation of the quantum dots is more controllable by oxidizing undulating silicon nanowalls in different thicknesses, as it was stablished in the

21

previous project8,48 and used in the current study as well. The fabrication procedure started by oxidizing silicon wafers at 900 °C for 30 min

and spinning a layer of an ordinary optical resist followed by hard baking in order to protect it against dust and damage before dicing. Then the resist and the oxide layer were removed in an ultrasonic acetone bath (5 min) and hydrofluoric acid wet etch bath (60 sec), respectively. The completion of the oxide removal can be confirmed by the hydrophobicity of the surface, since a pure silicon surface is strongly hydrophobic. Before starting the EBL process an oxygen plasma cleaning step (RIE. 20 sscm O2, 100 mTorr, 10 W, 3 min) was also applied to clean the samples. Contrary to the pillar fabrication where a positive resist was used and thus a metal lifting process applied subsequently, in order to prepare matrices of silicon nanowalls the negative resist of HSQ 2% was utilized. The resist were spun on the samples with the speed of 6000 rpm for 40s and backed at ~ 150 °C for 10 min. A liquid bath of MF-CD26 was used as the developer for 1 min after the EBL exposure.

An EBL pattern consisting of four rectangular fields including pillars (figure 3.2a), straight and undulating walls, and several test structures in an area of 100 × 100 µm2 (figure 3.2b) were designed by using related EBL software (Raith). After the EBL exposure and developing procedure, the nano-meter sized patterns were etched down (depth of ~ 200 nm) through reactive ion etching based on HBr chemistry. Subsequent oxidations at 900 °C (normally for ~ 30 minutes) led to the formation of individual silicon cores inside the nanowalls. The nanowalls were defined in three different thicknesses of thin, medium and thick, so that by altering the oxidation duration one can have control over the formation of the nano-cores inside different parts of the walls. For more details about the EBL mask design and fabrication procedure we refer to the doctoral thesis dealing with the above mentioned process.8

3.1.2 Chemical synthesis

Solutions of Si NCs functionalized with various ligand molecules were synthesized through a well-established chemical process.49

First the solvent was removed from commercial HSQ solution (Fox-17, 74 wt % solution in methyl isobutyl ketone from De Corning). Then it was annealed at 1100 oC in a 5% H2 and 95% Ar atmosphere for 1h. The obtained powder was mechanically ground into finer powder and suspended again into distilled water. Then by HF treatment, nanocrystals were liberated and transferred into toluene.50 Different passivation methods such as radical assisted hydrosilylation using

22

azobisisobutyronitrile (AIBN) as radical initiator, thermal initiator and photo-chemically initiated hydrosilylation, as well as a number of ligand molecules (e. g. hexyl, dodecyl, and methyl undecanoate) were used to functionalize the hydro-terminated surface of nanocrystals. Figure 3.1b shows the original HSQ compound after solvent removal. Luminescent Si NCs with different sizes produced by the above mentioned process directly after the HF treatment before the surface functionalization are shown in figure 3.1c and 3.1d.

Figure 3.1 (a) HSQ chemical structure, (b) HSQ powder (after solvent removal), (c) and (d) hydride-terminated Si NCs under UV excitation (after HF treatment before functionalization), The samples and photos were prepared by Dr. Anna Fucikova.

3.2 Photoluminescence measurements

Photoluminescence spectroscopy is a technique in which a luminescent material is excited by light and emitted photons are dispersed into different wavelengths to form spectrum. For this purpose, the emitted light from the sample is collected by objectives and guided to a spectrograph. A simple schematic of a typical PL setup is demonstrated in figure 3.3. Inside the spectrograph an entrance slit with adjustable width pictures the light on a concave mirror (mirror 1 in figure 3.3) which collimates and images the light onto a dispersive element such as a grating. The emitted photons are then dispersed by grating into various spectral wavelengths at slightly different angles which is focused and imaged onto a detector by a second concave mirror (mirror 2 in figure 3.3). Finally, the incoming photons are detected by a detector such as charged coupled device (CCD) camera and converted into electrons, and the digitalized signal then is translated into the pixels in detector by corresponding

23

software. The outcome will be a linear dispersion of light in wavelengths versus the actual position of the luminescent object. Many optical aspects of Si QDs can be studied through the as mentioned technique. Among them the optical bandgap and quantum confinement effect, nanocrystal size distribution, optical absorption and recombination mechanism, PL intensity and corresponding excitation power dependency, and phenomena such as PL intermittency (blinking) or Auger process could be specified.

Figure 3.3 A schematic of the micro-PL setup used in the current study for a typical room temperature PL spectroscopy, consisting of a laser diode as UV excitation source (405 nm), an inverted microscope, a spectrograph, avalanche photo detectors and an EMCCD camera.

3.2.1 PL imaging and spectroscopy

A home-built, micro-PL setup adjusted for various photoluminescence experiments, were engaged in the current study (figure 3.3). The excitation source were an Omicron PhoxX laser diode (λex=405 nm) applied in continuous wave (cw) and pulse mode. To ensure a monochromatic excitation, a notch filter was used after the laser. The preferred excitation wavelength range is far above the bandgap of silicon to

24

ensure good absorption. Moreover the components of microscope made of fused silica have negligible scattered light under such excitation range and thus less stray light would influence on the signal. The laser beam impinges onto the sample either through the Zeiss inverted microscope (bright mode) or from the side path, with a relatively shallow angle of ~ 20° with respect to the sample surface, in a dark field configuration. Contrary to the bright field mode where the excitation and collection are along the same path, in the dark field configuration less excitation stray light will be scattered into the microscope objective lens. For typical room temperature PL imaging and spectroscopy, a Zeiss 10x objective lens with numerical aperture (NA) of ~ 0.25 and a 100x Nikon with NA ~ 0.7 were used to collect the light. The collected photons then are guided through the microscope to a spectrograph (Andor-Shamrock 500i) and detected by an Andor-iXon3-888 electron multiplying CCD camera (thermoelectrically cooled down to ~ ‒100 °C). Higher numerical aperture 100x objectives were impossible to utilize in the dark field configuration in practice due to the extremely small focal distance, which did not allow the passage of the excitation beam from the side.

The samples of Si QDs embedded in SiO2 were fabricated on 1 × 1 cm2 silicon substrates and therefore were placed upside-down on the microscope stage for PL measurements. A reflection and PL image of a typical sample containing single Si QDs taken under white light and UV illumination are shown in figure 3.4a and b, respectively.

Figure 3.4 (a) Reflection and (b) PL images of undulating silicon nanowalls taken under white light and UV illumination, respectively. The area with dense luminescence Si QDs (the upper section of images) relates to the silicon nanowalls with two different thicknesses, while the area with the more scattered luminescent Si QDs (the lower section of images) corresponds to the silicon nanowalls with three different thicknesses. The scale bar indicates 25 µm.

25

The upper section of the images represents Si QDs formed by oxidizing undulating silicon nanowalls with two different thicknesses. Accordingly the area comprise a dense number of luminescent single Si QDs compared to the lower part consisting of silicon nanowalls with three different thicknesses which results in the formation of Si QDs further apart from each other.

For single dot PL spectroscopy, the entrance slit of the spectrometer should be adjusted to observe single quantum dots along a line (figure 3.5 a and b) and the spectrograph should be set in the wavelength dispersive mode, so the emitted light is dispersed onto the detector chip. Thus the x-axis will be converted to a wavelength scale while the position along the slit enables observation and spectral recordings of all quantum dots originally positioned within the slit. Two different gratings with spectral resolutions of 0.9 and 0.08 nm (200 µeV in the nanocrystal emission range) are available. The outcome will be the PL intensity versus emission wavelength all along the real vertical coordinate (figure 3.5 c and d), and therefore each spectrum can be ascribed to a certain dot.

Figure 3.5 PL images of single Si QDs, formed by oxidizing various types of silicon nanostructures, (a) with an open slit, and (b) closed slit (width ~ 100 µm) targeted to the specified line with white rectangle, (c) PL spectra image of the single dots along the specified line, and (d) the PL spectrum of a single Si QD marked by a red arrow in all the figures. The linewidth is relatively broad (full width at half maximum ~ 150 meV) due to homogenous broadening, at room temperature.

26

3.2.2 PL decay measurements

The photoluminescence lifetime of silicon nanocrystals is referred to the time it takes for excited carriers to release their excess energy, and relax to the original energy states via radiative or non-radiative transitions, after the excitation cessation. Hence adjusting the excitation flux, duty cycle and pulse duration is of great importance to address various absorption and recombination mechanisms appropriately. For time-resolved studies the PL intensity must normally reach the steady-state condition, well before the laser cessation, when the generation and recombination rate are in equilibrium. Moreover the laser frequency range should be scaled in accordance to the lifetime of the system under investigation (see figure 3.7).

For a typical room temperature time-resolved measurement, an excitation frequency, on time duration and excitation power density of ~ 5 kHz, 100 µs, and 20 Wcm-2 were used respectively, taking into account that the PL decays of Si NCs are in the range of ~ µs. The as mentioned parameters were altered depending on the kinetic properties of the samples.

PL decays of individual silicon quantum dots with oxide passivation (Si QD/SiO2) as well as ensemble of ligand-passivated silicon nanocrystals were studied. For this aim, time-resolved and spectrally-resolved PL techniques were applied using an image intensifier (Hamamatsu C7245) and an avalanche photo diode (ID Quantique) with maximum temporal resolution of 165 picoseconds per time channels. The experimental details of such studies are explained as below in three parts.

(i) The first series of experiments relate to the PL decay measurements of

single Si QD with thick SiO2 shell. For this purpose an image intensifier with adjustable gate width were used between the microscope and the CCD camera.

An image intensifier is a vacuum tube consisting of a photo cathode, multichannel plates (MCP) and an anode in the form of phosphor screen which intensifies the low luminescent emission of Si QDs and reflects brighter images of the objects on the detector. The MCP is an array of electron multiplier channels which multiplies the number of electrons based on the secondary emission. A schematic of a microchannel and an image intensifier is shown in figure 3.6a and b, respectively. The emitted photons from the sample are converted to electrons in the photocathode and the amplified photoemission signal is accelerated towards the phosphor screen output by the electric field. Finally the emitted photons

27

Figure 3.6 Schematic of (a) a microchannel, and (b) an image intensifier. The incoming photons are converted into electrons by the photocathode and multiplied by the microchannel plate (MCP) in the image intensifier.

are temporally sampled by the image intensifier and guided to the CCD camera. Through such a technique, sequences of PL images of single Si QDs taken at different delays after the excitation pulse were recorded and eventually the corresponding PL decay curves were extracted as the intensity profile of particular single Si QDs. An example of PL images taken at various times after the laser cessation and a schematic of the related excitation pulse and the decay curve is shown in figure 3.7. For statistical studies of PL lifetimes of single Si QDs, using an image intensifier is an appropriate choice, since all the quantum dots are measured at once by taking PL images. However, low signal-to-noise ratio as well as the time consuming post processing procedure are disadvantages.

(ii) The second set of experiments was devoted to single-dot, time-resolved PL decay measurements of single Si QDs with thick oxide passivation, based on single photon counting technique. For this purpose an avalanche photo diode (APD) with the temporal resolution of picosecond was used. APDs are highly sensitive semiconductor photodiodes including a depletion region where the electron multiplication occurs. Incident photons create electron hole pairs in the depletion region accelerated towards the respective PN junction in an inverse bias and collide with the atoms of crystal lattice. Hence numbers of electron hole pairs are generated via ionization in an avalanche manner (figure 3.8). The sensitive area of the APD utilized in the current study (ID Quantique) has an active area diameter of 20 µ𝑚 which is equal to ~ 4 pixels on the CCD.

28

Figure 3.7 Schematic of time-resolved PL imaging of single Si QDs using an image intensifier with an adjustable time window width, (a) excitation pulse and the corresponding PL rise and decay curve of a single Si QD, (b) PL images taken at 0, 5, 9, 15, and 60 µs delay times. The extracted PL intensity profile of the single Si QD specified with red empty rhombs are plotted as red data points in (a).

The produced dark counts (~ 3 counts/sec) are negligible compared to the counts collected from single Si QDs (~ 60 counts/sec under excitation power density of ~ 20 W/cm2). The APD was connected to the right port of the inverted microscope via a -0.5x magnifying lens (figure 3.4), in order to focus the emitted light on the small area of the APD chip. Photon counting measurements using an APD can be performed only on a single QD at a time. However the reasonable detected counts from single Si QDs and in situ recorded decays are beneficial. Pre-adjusting the APD chip position with respect to the EMCCD is necessary. This procedure was carried out by using an isolated bright object and tracking its coordinate based on the counts read by the APD. The count level was checked time by time during the measurements in order to compensate any shifts in APD position due to thermal expansion/compression or instability of the mechanical setup. Experimental parameters set for the single dot PL decay measurements using the APD, such as the excitation frequency and duty cycle as well as the number of detection channels after the laser cessation, varied depending on the sample under study and the experimental conditions.

29

Figure 3.8 Schematic of an avalanche photo detector (APD) and the impact of the ionization avalanche charge resulting in electron/hole multiplication.

In order to improve the signal-to-noise ratio post binning were applied to the measured data and the background was subtracted. No deconvolution was performed since the setup has a sub-nanosecond response function and therefore the microsecond time scales of the decay could be resolved. The PL decay data then were fitted by mono-exponential function. In the case of a high pumping regime, the initial fast transient was excluded from the fitting.

(iii) The third series of PL lifetime studies were dedicated to spectrally- resolved PL decay measurements of ensemble of Si NCs with various ligand passivation molecules and preparation parameters using the avalanche photo diode. For this purpose, the APD was placed after the spectrometer (figure 3.4) and the 10x objective lens was used to collect the emitted photons. The APD chip position and the spectral window determined by the spectrograph slit were calibrated using atomic lines of a Hg-Ar lamp. The spectral resolution was of Δλ ≈ 3 nm. The solutions of ligand-passivated Si NC were measured in Suprasil quartz cuvettes under excitation of 2 W/cm2, with excitation pulse and frequency altered between 100‒500 µs and 0.5‒10 kHz, respectively depending on the selected detection energy. Post binning was applied to the measured data in order to improve the signal-to-noise ratio.

30

3.2.3 Low-temperature PL measurements

An Oxford instrument liquid flow cryostat operated with liquid nitrogen/helium was used to perform low-temperature (down to ~ 2K) PL spectroscopy and decay measurements of single silicon quantum dots. The cryostat was evacuated continuously (~ 10-7‒ 10-6 mbar) and therefore is thermally insulated and samples were fixed on its cold finger by using silver paste. The main challenge was the mechanical instability of the instrument in long exposures and blockage of tubes due to condensation. Instability of the mechanical components was modified using vibration dampers and in the case of blockage, the tubes were cleaned by utilizing compressed air.

The incident excitation beam was adjusted carefully in the dark field configuration to get the minimum scattered light from the cryostat glass inside the objective lens (~ 45° with respect to the sample surface). A Zeiss 63x window-corrected objective lens with the NA of ~ 0.75 was used to collect emitted photons.

To measure the PL decay of single Si QDs at various temperatures many stable, bright dots were initially characterized and selected at room temperature and targeted. At various temperatures PL spectra of individual dots were re-measured to ensure the same dots were aimed for PL decay experiments. Some of the dots were in their dark states at particular temperatures and high condensation on the sample surface at particular temperatures (~220 K), restricted the number of dots under study and the selected temperatures.

31

Chapter 4 Results and discussion

4.1 Oxide-passivated single silicon quantum dots

4.1.1 General structural and optical characteristics

In transmission electron microscopy (TEM) images, single silicon quantum dots fabricated by EBL, RIE and self-limiting oxidation, were identified as disconnected spherical cores mainly at the upper parts of the walls.51 Under UV excitation, such silicon nano-cores referred to as silicon quantum dots might yield photoluminescence. The lower part of the walls, after short oxidation, does fully oxidize and some luminescent nanowires are formed. A TEM image of such wires in addition to nano-sized single silicon cores, broken apart from a wire, is shown in figure 4.1.

The spectral characteristics of these silicon quantum dots, primarily at room temperature, have been studied in detail in a previous project with the focus on the fabrication and characterization of single Si QDs with thick oxide passivation.8 Hence, in the current work PL spectroscopy was performed prior to various measurements, mainly as a probe to identify single silicon quantum dots. One should note that the PL emission of the background silicon nanowires are weak, broad and delocalized and therefore distinguishable from the corresponding Si QD’s PL emission and accordingly could be subtracted as a background signal.52

Figure 4.1 TEM image of silicon nanowires and Si QDs separated from the wire beneath, inside undulating nanowalls (taken by Ilya Sychugov).

32

Figure 4.2 (a) SEM image of an undulating silicon nanowall after RIE and before oxidation, (b) PL image of similar structures taken under UV excitation, (c) RT photoluminescence emission spectrum of the single Si QD specified with the red arrow in (b), under UV excitation of 8 Wcm-2 and Gaussian fits to the main (red) and satellite (blue) peak (d) PL intensity traces of the studied single Si QD and the corresponding histogram of blinking traces (one single blinking for this particular trace). Considering a threshold line two distinct ON and OFF states are identified.

The spatial separation of individual dots enables us to target the same single silicon quantum dot for various experiments. As it is shown in figure 4.2, the single Si QD specified with a red arrow in the PL image (figure 4.2 b) was targeted and its PL spectrum and blinking traces are shown in figure 4.2c and d, respectively.

Room temperature PL emission spectra of several single silicon quantum dot at room temperature exhibit a dot-to-dot variation in the spectral shape, with relatively broad FWHM (~ 150 meV) and the emission energy varying between ~ 1.6‒2.0 eV,

Figure 4.3 (a) On- and off-time distributions of a single silicon quantum dot under the excitation power density of 30 W/cm2 in semi-logarithmic scale and corresponding mono-exponential fits. (b) Blinking frequency as a linear function of excitation power density.53

33

for individual dots. According to the blinking statistics studies53 on- and off-time distributions of single silicon quantum dots exhibit a single exponential character. This is in contrast with the power law distribution for on- and off interval lengths in direct bandgap nanocrystals (e. g. CdSe).54,55 Although different models have been suggested to explain such distributions,56–59 the exact mechanism of the blinking is still controversial. Figure 4.3a shows on- and off-distributions of a single silicon quantum dot under excitation power density of 30 W/cm2.53

The linear blinking frequency dependence on the excitation power density observed for single Si QDs (figure 4.3 b) was attributed to a single photon absorption process. Therefore a model of direct trapping of excited carriers was suggested as the mechanism behind the blinking process in single silicon quantum dots.53

4.1.2 Photoluminescence

The PL decays of single silicon quantum dots were measured as the main focus of the current work to investigate the carrier dynamics of silicon nanocrystal systems. For ensembles of silicon nanocrystals as well as porous silicon, the PL decay has been reported to be of stretched exponential character with the dispersion factor β between 0.4‒0.8, and microsecond PL lifetime,31 which is much longer that the PL decay time of direct bandgap nanocrystals (~ns). This is due to the indirect bandgap nature of silicon. By performing single dot PL decay measurements however, here we obtained individual PL decay characteristics which were hidden in the results achieved by ensemble studies. First, the photoluminescence of single silicon quantum dots exhibits mono-exponential decay with a large dot-to-dot lifetime variation (~ 5‒45 µs). Figure 4.4 presents the PL decay data of single silicon quantum dots with slightly different emission energies (different sizes) and corresponding linear fits.

Second, considering theoretical calculations,3 and ensemble studies31 on the PL decay of silicon nanocrystals, it was expected to observe a PL decay time drop by the decrease of the nanocrystal size, however, to our surprise, no clear correlation between PL lifetimes and emission energies of single silicon quantum dots were found.

34

Figure 4.4 (a) PL decay of two single silicon quantum dots in semi-logarithmic scale and corresponding mono-exponential fits, under the laser power density of ~ 25 Wcm-2, (b) PL emission spectra of the identical single dots.

The spectral dependence of the PL lifetimes of a number of single Si QDs are shown in figure 4.5. The random distribution of PL lifetimes, in a relatively broad range, versus emission energies suggests a strong influence of other parameters than nanocrystal size. Parameters such as passivating molecules, geometrical shape, possible defect sites, etc. effect on the recombination rate of the PL in single Si QDs, as well. Different models have been proposed in the literature to explain the stretched exponential PL decay of ensembles of Si QDs. For example tunneling through possible localized carrier states,32 migration of excitons in a network of interconnected nanocrystals,33 and a distribution of the crystalline shape for a given volume of nanocrystals.34 Here, we prove that mathematical summation of widely different individual lifetime results in the stretched exponential PL decay of nanocrystal ensembles. The results of such a mathematical approach are shown in figure 4.6. The sum of the mono-exponential PL decays of a total of 35 single silicon quantum dots was well fitted by a stretched exponential function with a dispersion factor β of 0.68. As expected, for a limited number of single quantum dots with a narrow emission energy range of 1.73‒1.76 eV (gray dashed line in figure 4.5), the β value is higher (~ 0.76) as an evidence of a smaller variation of individual PL lifetimes and hence resulting in less stretched character of the decay.

35

Figure 4.5 Distribution of room temperature PL lifetimes of single silicon quantum dots versus emission energy (rhombus) at a laser power density of 25 Wcm-2. The spectral dependence of the ensemble of silicon nanocrystals and porous silicon,31 as well as theoretical calculations3 (red and green dashed lines, and black solid line, respectively) are plotted to compare.

Figure 4.6 Sum of the mono-exponential PL decay of single Si QDs (triangles) and the corresponding stretched exponential fit with the dispersion factor β of 0.68. The related lifetime distribution is presented in the inset. The sum of the mono-exponential PL decays of a limited number of single quantum dots (emission energy range ~ 1.73‒1.76 eV) is shown as the gray circle symbols and the related stretched exponential with β of ~ 0.78.

36

4.1.3 Optical absorption cross-section

While single quantum dot PL decay data provide valuable information on the PL recombination mechanism, the temporal shape of the PL rise can be used to investigate the absorption characteristics of single silicon quantum dots. The absorption cross-section σ is then obtained by taking into account the state filling equations in the low pumping regime.60 Hence, absorption cross-section σ values of single silicon quantum dots were found by measuring the rise time of the photoluminescence under different excitation flux below the saturation level (see section 2.4.6). Figure 4.7a presents the PL decay and rise time of a single quantum dot under various excitation power densities. The kinetics of the photoluminescence rise follows a mono-exponential function as shown by solid lines in figure 4.7a. The dependence of the luminescence rise rate on the excitation flux ϕ was verified to be linear (figure 4.7b), in accordance to the temporal shape of the luminescence formula (eq.2.11). Thus the slope of the linear curve of the PL rise rate versus the excitation flux ϕ yields an absolute value of ~ 1.46 × 10−14𝑐𝑚2 for the absorption cross-section, at the excitation wavelength of 405 nm. In total the obtained absorption cross-section values of three different single quantum dots were larger (~ by a factor of 10) than the values reported for ensemble of silicon nanocrystals for the same excitation energy.16,60

Figure 4.7 (a) PL decay and rise time of a single silicon quantum dot under various excitations, and (b) the corresponding extracted 1/τrise, the linear slope of the plot gives the absorption cross-section value.

37

Absolute values of absorption cross reported by Kovalev, et al.16 for ensembles of nanocrystals and our measured values for single Si QDs are shown in figure 4.8. Within such a narrow range it is not clear if there is any correlation between σ and the emission energy of single dots, however considering the results obtained from ensemble measurements a slow relative decrease of the absorption cross-section by size decrease would be expected. Larger absorption cross-section values of single Si QDs, compared to the ensembles, can be attributed to the structural geometry of such dots which appeared to be more elongated, nanorod-like (see figure 4.1a)61,62 with relatively thick oxide passivation. Considering the same volume of spherical Si nanocrystals and Si nanorods, shape difference applies a small variation on the density of states and hence, trivial impacts on the absorption cross-section. However, the strength of the excitation field involved in the absorption process is strongly geometry dependent.63,64 In general, the absorption cross-section can be estimated according to 𝑛 = 𝛼𝑉𝛼 for a randomly polarized excitation. α and V denote the bulk absorption coefficient and the object volume, respectively and 𝛼 is a factor including the field strength of the illumination inside the material. Hence, the increase in σ can be attributed to the stronger strength of the excitation field inside Si nanorods than Si nanodots. Note that our illumination can be considered as a randomly polarized source, in addition to the impinging angel of the beam on the silicon nanowalls in the dark excitation configuration as it was explained in the experimental section (3.2.1).

Figure 4.8 Absolute values of absorption cross-section values of ensemble of silicon quantum dots reported by Kovalev, et al.16 at different detection and excitation energies. Red data points are measured absorption cross-section values of single silicon quantum dots in this study. The dashed red line is for the eye guide.

38

4.1.4 Temperature dependence of the PL

4.1.4.1 Temperature dependence of the photoluminescence emission spectra

Room temperature PL spectroscopy includes thermally induced effects, e. g. homogenous linewidth broadening,12 thermally activated non-radiative processes,65 and PL emission bandgap shifts.66 Therefore, performing low-temperature PL spectroscopy is of great importance in order to study not only the inherent optical properties of silicon quantum dots but also the mechanism behind such thermally induced effects.

Temperature dependent single dot PL spectroscopy was performed on several single Si QDs under the excitation power density of 20 W/cm2. The transformation of the PL spectral emission band of a single Si QD (labeled as Si QD‒2) by decreasing the temperature from 300K to 2K is shown in figure 4.9.

Figure 4.9 Normalized PL spectra of a single Si QD (labeled as Si QD‒2) at different temperatures, the featureless broad RT band reveals phonon-assisted energies at cryogenic temperatures. At 2K spectra comprise 4 peaks: zero-phonon line (ZPL), stretching mode (SM), transversal acoustic (TA) and optical (TO) phonon modes where the three latter have respectively 5, 16 and 60 meV distance to the ZPL.

39

It can be clearly seen that the room temperature (RT) broad homogeneous linewidth of the PL spectra narrows down at 2K (~ 5 meV). At low temperatures, in addition to linewidth narrowing, more spectral features related to phonon-assisted transitions (i. e. TA and TO phonon mode) and stretching modes (SM) are revealed. These peaks are placed at distances of 16, 60 and 5 meV, respectively toward lower energies as it is shown at the bottom of figure 4.9 for 2K. So far the presented results related to the temperature dependence of PL emission of single Si QDs have been a confirmation to what was obtained before in the previous project.8,52 Now novel achievements of the current study will be presented.

The PL emission peak position of Si QD‒2 versus temperature is shown in figure 4.10. Note that PL emission peak positions were extracted by fitting Lorentzian functions deconvoluted for the main peak (ZPL) taking into account other phonon replicas. Due to the broad linewidth of the RT emission spectrum and therefore impossible deconvolution of the ZPL, the corresponding peak position value was not extracted for room temperature.

The zero phonon line (ZPL) shifts to higher energies with respect to the RT peak position following the general temperature dependence of the semiconductor’s bandgap, based on Varshni’s model:67

𝐸𝑔𝑎𝑝(𝑇) = 𝐸𝑔𝑎𝑝,0 − 𝐴 ∙ � 2exp [ℏΩ 𝑘𝐵𝑇⁄ −1]

+ 1� (4.1)

where 𝐸𝑔𝑎𝑝,0 is the bandgap energy value at T=0 K, A is a temperature-

independent constant representing the electron-phonon interaction strength, kB is the Boltzmann constant and ℏΩ denotes the average phonon energy considering the Bose-Einstein distribution. The best fit to our experimental data (shown as a red solid line in figure 4.10) were achieved by considering three parameters of A ≈ 0.017, Egap,0 ≈ 1.70 eV and ℏΩ ≈ 15.3 meV.

The obtained average photon energy of single Si QDs is much lower, compared to the results reported for ensemble of silicon nanocrystals (A ≈ 0.019±0.005 and ℏΩ ≈ 30.2±6 meV for Si QDs size of 3.5±0.1 nm)68,69 and for bulk silicon (ℏΩ ≈ 32 meV ).70 Considering that the stretching mode is absent in bulk silicon, the lower average phonon energy can be justified by the existence of a stretching mode (SM) in single Si QDs with thick oxide passivation. In the case of ensembles of silicon nanocrystals, however, the impact of SM on the average phonon energy is not resolvable.

40

Figure 4.10 Temperature dependence of the PL peak position of zero phonon line (empty symbols) of Si QD‒2 fit by Varshni’s formula (see eq. 4.1) shown as red dashed line.

4.1.4.2 Temperature dependence of the photoluminescence decay: carrier dynamics

One of the powerful techniques to investigate the photoluminescence recombination mechanism is time-resolved PL spectroscopy,71 especially at various temperatures. Such studies have already been done for ensemble of silicon nanocrytstals as well as for porous silicon and various models have been proposed for the PL recombination path at low and high temperature regimes.16,19,72 Part of the results which will be presented in the current section could be predicted based on ensemble studies and theoretical calculations. However the novelty of this work, first relates to temperature dependent studies of the PL decay time of individual Si QDs, considering the experimental difficulty of these measurements (see section 3.2.3). Second, at high temperature regimes the origin of non-radiative decay channels with microsecond decay time have been investigated in details.

The PL decay of several single silicon quantum dots were measured under an excitation power density of ~ 20 W/cm2, at different temperatures. As it is shown in figure 4.11, the PL decay exhibits a mono-exponential character at all temperatures, as expected from the room temperature PL decay results already presented in section 4.1.2. However, a significant increase (≈ 100 times variation of PL lifetimes) in PL

41

decay

Figure 4.11 Temperature dependence of the decay time of several single silicon quantum dots under an excitation power density of ~ 20 Wcm-2. PL decays of single Si QD‒2 at various temperatures are shown in the inset in semi-logarithmic scale. The solid lines are the corresponding mono-exponential fits to the experimental data. A post binning procedure was applied to the measured data in order to improve the signal-to-noise ratio.

rates of single Si QDs at lower temperatures was observed. The absolute values of the PL decay time of Si QD‒2 are shown the inset of figure 4.13, in semi-logarithmic scale, as empty symbols and the corresponding exponential fit as solid lines. Note that the fast initial transient due to high-excitation pumping is excluded from the exciton decay. PL decay rates of a single silicon quantum dot (labeled as Si QD‒1) at various temperatures are shown in figure 4.13. The detailed information on Si QD‒1 can be found in paper IV appended to this thesis.

Figure 4.12 A simple schematic of singlet-triplet exciton states, with splitting energy of Δ. The triplet state is set as the zero level of energy in the calculations.

42

Figure 4.13 PL decay rates of the single Si QD‒1 at various temperatures (rhombus). The black dashed line is a guide for the eye. Experimental data are in agreement with the singlet-triplet model at low temperatures. The green dashed line is the best fit to the data based on this model.

In the low-temperature regime a well-established model has been proposed by Calcott, et al.19,73 for the temperature dependence of the radiative decay rates of silicon nanocrystals based on singlet-triplet exciton energy states (see section 4.2.7). A simple schematic of the singlet-triplet states with the exchange splitting energy Δ is shown in figure 4.12. According to this model, by temperature decrease the singlet state becomes depopulated while the triplet state begins to populate gradually. Hence the PL decay rate drops at low temperatures since the emission from the triplet state is parity forbidden. We have extracted the exchange splitting energy of the singlet-triplet states for several single Si QDs, as well as the radiative decay rates based on the corresponding model. Here, the experimental data related to Si QD‒1 (figure 4.13) is taken as an example to present the mathematical calculations.

In the low-temperature regime, according to the discussion presented by Kovalev, et al.4 PL decay is dominated by radiative transitions. Therefore:

Γ𝑑𝑜𝑑𝑎𝑛 = Γ𝑟𝑎𝑑 = Γ𝑆 + Γ𝑇 (4.2)

where Γ𝑑𝑜𝑑𝑎𝑛 is the experimental decay data and ΓS/T denote transition rates of singlet and triplet states.

43

In general, the transition rate from the ground to the singlet or triplet states could be estimated by the Fermi golden rule as:

Γ𝑆 = 𝑃𝑆 × Γ0𝑆 , and Γ𝑇 = 𝑃𝑇 × Γ0𝑇 (4.3)

where PS/T and Γ0S/0T denote population probability and inherent decay rates of the singlet/triplet states (temperature independent).

Considering the triplet level as the zero energy and based on the Boltzmann distribution, the population probability of the singlet and triplet states could be calculated from:

𝑃𝑠 =exp (− Δ

𝐷𝐵𝑇)

3+exp (− Δ𝐷𝐵𝑇

) , and 𝑃𝑇 = 3

3+exp (− Δ𝐷𝐵𝑇

) (4.4)

Finally, the temperature dependence of the radiative decay rate can be calculated

by taking into account the thermal equilibrium between populations of singlet and triplet states as:

Γ𝑟(𝑇) = 3Γ0𝑇+Γ0𝑆exp (−Δ/𝑘𝐵𝑇)3+exp (−Δ/𝑘𝐵𝑇)

(4.5)

where 𝑘𝐵𝑇 is the thermal energy and Δ represents the splitting energy.

Our experimental data could be fit by equation 4.5, using fitting parameters of Δ ≈ 10 meV and Γ0𝑆≈180 kHz, below 70 K (green solid line in figure 4.13). Note that the saturation of decay rates at very low temperatures reveals only the triplet state is occupied. Due to the spin-orbit interaction and geometry of the confinement potential, the decay rate of the triplet state becomes constant.34 Therefore the measured total decay rate at 2 K was considered as the inherent decay rate of the triplet state Γ0𝑇 ≈ 3.4 kHz. As it was expected, the inherent decay time of the triplet state is approximately 50 times longer than the singlet state, since the transition from the triplet state is parity forbidden.

Our experimental PL decay rate data are in good agreement with the singlet-triplet model and extracted splitting energy values (Δ ≈ 6‒12 meV), as well as radiative decays rates are in accordance with other studies.4,19,68,74

A drastic variation between the experimental total PL decay rates and the fitted function was observed for temperatures above 70 K. In order to estimate this deviation the fitted function was extrapolated to higher temperatures, as it is shown by green dashed line in figure 4.13. The dashed black line is a guide for eye. The

44

Figure 4.14 Non-radiative PL decay of several single silicon quantum dots at high temperatures (empty symbols) in semi-logarithmic scale. The dashed line is the best fit to the average data by Arrhenius function.

extrapolated fitting function becomes constant above 100 K, as it can be seen in figure 4.13. Since the radiative decay rate is constant in the high temperature regime and totally independent of temperature, the constant part of the extrapolated fitting function was considered as the radiative rate of Si QD‒1 and accordingly the non-radiative rate could be calculated in the high temperature regime. Figure 4.14 shows non-radiative decay rates of several single Si QDs extracted in a similar way. An activation energy is obtained by fitting the Arrhenius equation 𝑘 = 𝐴𝑒−𝑄𝐷 𝑘𝐵𝑇⁄ to the average of the extracted non-radiative decay rates resulting in Ea ~ 36 meV. The separation of the experimental data from the singlet-triplet model at high temperatures, can be interpreted as the contribution of a thermally activated non-radiative process in the exciton recombination of single Si QDs which was suppressed at cryogenic temperatures.65,72,75 However, the proposed models based on carrier migration75,76 to the neighboring quantum dots doesn’t explain our results, since here we have totally isolated single Si QDs with no interactions.

In the current study we propose a model for a thermally activated non-radiative decay process in single Si QDs, based on a resonant tunneling of excited carriers to adjacent trap sites. Accordingly, mathematical calculations were performed for Si QD‒1 with a diameter of approximately 3 nm to estimate the distance of such a trap site and consequently the feasibility of this model.

45

For this purpose: (i) the Si QD/SiO2 system was considered as a quantum well with a barrier height of ~ 2.65 eV,77 and (ii) The probability of resonant tunneling through the potential barrier defined by adjacent trap sites was considered to be equal to the non-radiative decay rate extracted from experiments.

The probability of tunneling was obtained by multiplication of the frequency of attempts (𝛼𝑎 = 𝜈/𝑑 where υ is the electron velocity and d is the quantum dot diameter) and the transmission coefficient calculated by the formula:78

𝑇 ≈ 16𝑄

𝑉0exp (−2𝜅𝑥) (4.6)

where E and V0 are the energy of excited electrons and the potential barrier of the trap site respectively and κ and x denote the wavenumber and the barrier width or the distance of the trap site with respect to the silicon quantum dot. Calculations using a trap site with a distance of ~ 1.5 nm with respect to Si QD‒1 results in a non-radiative decay channel with the transition rate of ~ 30 kHz at room temperature. The energy diagram of the Si QD including the adjacent trap site with a distance of ~ 1.5 nm is depicted in figure 4.15. Due to the homogenous linewidth broadening effect,12 the alignment of band states with trap sites becomes more probable at high temperatures

Figure 4.15 Energy diagram of a single Si QD with a diameter of 3 nm and surrounded by a thick SiO2 passivation. The depth of the conduction band was taken from literature.77

46

and thus, resonance tunneling will increase. Some effective phonon energy modes are increasingly populated at high temperatures resulting in the line width broadening and thus, higher possibility of such effect. Oxygen vacancies in the Si/SiO2 surface/interface have been reported as trap sites neutralized by the tunneling of carriers from adjacent silicon.79 Within the thick oxide matrix around single Si QDs under study no corresponding empty states are available for trapped carriers to recombine. Therefore the alternative process is non-radiative Auger recombination since the QD becomes ionized by charge trapping. Depending on the distance of trap sites the transition rate is determined. Thus, we purpose an explanation for the non-radiative channel resulting from tunneling of carriers to trap sites in the surrounding oxide. The nanocrystal is then left with a remaining charge resulting in Auger recombination during successive excitations.

4.1.5 High-excitation regime: biexciton creation versus Auger process?

According to the population rate equations (sec. 2.6.4), the PL intensity of excitons rises linearly by the excitation power, while the PL intensity from biexciton has a quadratic dependency on the excitation.16 In Si NCs, however, at strong excitations the Auger process might suppress the biexciton radiative recombination.16,80,81 Single

Figure 4.16 Normalized PL decay of a silicon quantum dot in a semi-logarithmic scale taken under low and high-excitation regimes (red and black data points respectively). A zoomed view of the initial 0.5 µs of the decay is shown in the inset. The error bars represent the standard deviation of the measured data.

47

dot time-resolved PL decay measurements were performed at various excitations on single Si/SiO2 QDs as a tool to probe the PL transient of biexcitons. In the high excitations PL decay curve, the slow power-independent exciton lifetime is distinguishable from the fast initial transient which is attributed to biexcitons.82 Figure 4.16 shows normalized PL decays of a single Si QD at RT under low and high-excitation power densities (20 and 60 W/cm2, respectively). The inset presents a zoom view of the first 0.5 µs PL decay. The slow exciton slow decay component for both low and high pumping were fit by a mono-exponential function (black dashed line in figure 4.16) with a lifetime of τ1=5.8±0.2 µs and τ2=0.11±0.04 µs for the fast component emerging at high pumping.

The internal quantum efficiency of the exciton and the biexciton process were estimated to be of ~ 9% and 0.4%, respectively at RT. Details on the calculation procedure can be found in paper VIII appended to this thesis. At lower temperatures (10K) the IQE of the biexciton is calculated to be 10-20 times lower than that of excitons. If the Auger recombination process efficiency is very low a second peak should appear in the emission spectra, which was not observed for single silicon QDs. Furthermore the PL intensity of single dots saturates in the high pumping regime. Hence, it is concluded that biexcitons are suppressed at high excitations by the Auger process.

4.2 Ligand-passivated silicon nanocrystals

Optical properties of silicon nanocrystals are strongly dependent on the surface passivation and preparation conditions.83,84 For instance, it has been shown that the PL increases significantly by molecular hydrogen passivation of silicon nanocrystals at 510°C.85 Thus, in the second part of the current project, we focus on photoluminescence properties of colloidal, ligand-passivated silicon nanocrystals prepared by annealing of dried hydrogen silsesquioxane (HSQ) powder at 1100 °C (section 3.1.2) and more specifically on spectrally-resolved PL decays of such nanocrystals.

48

4.2.1 General structural and optical characterization

Optical properties of ligand-passivated silicon nanocrystals, such as PL emission, absorption spectra, PL decays and quantum yields were initially studied.

Among fourteen different samples, two with the highest and lowest luminescence peak positions and corresponding decay rates (sample A and F, respectively) and six with intermediate optical properties (samples B‒D) were selected for detailed studies. Each sample was labeled with a specific color in plots for clarity. The specification of the samples can be found in paper V appended to this thesis. The six selected ligand-passivated silicon nanocrystals emit in the range of ~ 1.2‒2.2 eV at RT, under UV excitation. Sample A and F which have highest and lowest PL peak positions exhibit different corresponding absorption onset as well. Both measured PL absorption and emission spectra are typical for Si NC systems (figure 4.17a).4

Bright-field TEM imaging of sample A and F and the corresponding size distributions are shown in figure 4.17b and 4.17c, respectively. As it was expected the sample with smaller size distribution (sample A) had higher emission energy and vice versa. PL decays of ensemble of Si NCs with various ligand passivation were of stretched exponential character, 𝐼 = 𝐼0𝑒𝑥𝑝�−(𝑡/𝜏)𝛽�, where τ and β are lifetime and dispersion factor respectively, in agreement to previous reports for ensemble of Si NCs.76

Figure 4.17 PL emission spectra of silicon nanocrystals passivated with different ligand molecules and prepared under various conditions. Relative PL absorption of sample A and F is shown in the same plot. (b) Bright-field TEM images of Si NCs drop casted onto amorphous SiN membranes and (c) the related size distribution histograms.

49

Figure 4.18 PL decay times (solid symbols) and dispersion factors β (empty symbols) versus emission energy extracted from stretched exponential fits to the experimental PL decay data, (b) stretched exponential decay of sample A and F in a semi-logarithmic scale.

The ensemble PL decay times were of ~ 45 to 90 µs with a dispersion factor of β ~ 0.8, which are consistent with previous results from Si NCs embedded in oxide.31 The measured PL decay data of sample A and F, as well as PL decay times and dispersion factors as a function of emission energy, extracted from the stretched exponential fit, are presented in figure 4.18.

A clear correlation between PL decay times and emission energies of Si NCs (NCs size) were observed. PL decay times of ligand-passivated Si NCs are much longer than that of single Si QDs (5‒45 µs). This suggests the presence of less non-radiative recombination channels in ligand-passivated Si NCs compared to Si NCs with thick oxide passivation, originating probably from the preparation conditions. Note that single Si QDs were prepared by oxidizing silicon nanowalls at 900°C, while ligand-passivated Si NCs were prepared by annealing of dried HSQ at 1100 °C through a chemical method.

In general the optical and structural characteristics of ligand-passivated Si NCs presented in the current section are typical for such material systems.86

4.2.2 Spectrally-resolved PL decays

Spectrally-resolved decays of Si NCs with different ligand passivation and preparation methods were studied for a broad range of detection energies (~ 1.4‒2.2 eV). PL decay data of sample A and F (empty symbols in pink and black

50

respectively), normalized to the corresponding measured total lifetimes (τ0m) at the detection energy (Edet) of 1.82 eV, as well as PL decay data for the whole ensemble (blue) are shown in figure 4.19. Stretched exponential fits related to each data set are plotted in solid lines in the same figure. PL lifetime values and dispersion factors at different Edet were extracted from the stretched exponential fit and were labeled as measured lifetime (τ0m) and measured dispersion factor (βm), respectively.

Corresponding βm values as a function of detection energies for sample A and F (filled triangles) are shown in the inset of figure 4.19 left and right, respectively. For comparison βm values reported for Si NCs implanted in SiO2

31 are shown in both inset figures.

The measured dispersion factors (βm) of ligand-passivated Si NCs (0.85‒1) are larger than the values reported for oxide-passivated ensemble of Si NCs (0.4‒0.75).

Figure 4.19 PL decays (open symbols) and stretched exponential fit (solid line) of sample A and F (left and right respectively), normalized to corresponding measured lifetime values (τ0m) at the detection energy of 1.82 eV and for the full ensemble of ligand-passivated Si NCs (blue). The inset shows corresponding βm values as function of detection energies (filled triangles) and the values reported by Linnros, et al.31 for silicon nanocrystals passivated by SiO2 (open triangles).

For both samples A and F, βm values deviate more from unity at larger detection energies. As it can be seen from figure 4.19, βm values of Si NCs implanted in SiO2

31 exhibit a similar variation. The homogenous PL emission linewidth of ligand-passivated Si NCs is relatively broad at room temperature (~200 meV).12 Therefore, the variation of βm from unity for larger Edet can be explained by considering a

51

contribution of the NCs with emission energies close to the detection energy to the measured signal, as well as influencing the decay parameters (τm and βm). For smaller NCs (larger detection energies) and therefore shorter lifetimes, the relative variation in contributed lifetime values from neighboring NCs is larger, resulting in a stronger dispersion (lower β), while for larger NCs (smaller detection energies) βm is only slightly affected by contributed lifetimes from adjacent color NCs due to smaller relative lifetime variations. The red line in the inset of figure 4.19 right is the simulation results. Hence, we conclude that the stretched exponential decay of ensembles of ligand-passivated Si NCs was converted to mono-exponential decays at various detection energies.

Figure 4.20 Total PL decay rates of two ligand-passivated silicon nanocrystals (solid triangles), sample A and F (in pink and black, respectively), obtained from spectrally-resolved PL decay measurements and subsequent mathematical corrections for the homogenous linewidth broadening effect. For comparison total and radiative PL decay rates of Si NC/SiO2 reported by Fujii, et al.87 were plotted in the same figure, as rectangular and circular open symbols, respectively.

Through a mathematical approach, the contribution of homogenous linewidth broadening effect into the measured decay signal was excluded and accordingly the intrinsic PL decay times (τ0i) for different detection energies were extracted. Thus a mathematical size selection method was applied to the measured data, without any physical size separation of the NCs. Therefore intrinsic PL lifetimes can be referred to as PL lifetimes of “size-selected NCs”. More details of evaluating the intrinsic decay times can be found in paper V appended to the thesis. Figure 4.20 presents total

52

recombination rates Γ0(ε)=1/τ0(ε) of two ligand-passivated Si NCs (sample A and F, pink and black triangles, respectively) at different detection energies obtained from spectrally-resolved PL decay measurements and subsequent mathematical evaluations taking into account the homogenous linewidth broadening effect. The measured PL decay rates (Γ0) exhibit a clear energy dependency for both samples A and F over a wide energy range in addition to a partial overlap in the range of ~ 1.6‒1.8 eV. Therefore it is concluded that the PL decay rates are dependent only on the NC size (quantum confinement effect),88 regardless of the impact of shape (assuming that NCs are spherical), passivation, etc. Moreover, the total PL decay rates of sample A and F coincide with the radiative rates reported for Si NCs passivated with SiO2suggesting that no non-radiative recombination channels were involved in the PL decays of ligand-passivated Si NCs.

4.3 Internal and external quantum efficiency of silicon quantum dots

As it was already explained in chapter 2 (4.2.2), the QY of Si NCs is defined as the number of emitted photons over the number of absorbed photons, and thus includes all possible non-radiative recombination processes inside the ensemble. In general, non-radiative processes in silicon nanocrystal systems can be classified into three different categories, based on their transition time scale with respect to exciton decay rate:

(i) fast non-radiative transitions (ii) non-radiative transitions with similar rate as that of excitons radiative

decay rates (iii) slow non-radiative transitions

Dark nanocrystals contribute to the absorption but release their excess energy

thermally. They typically originate from dangling bonds, defects, and etc.24,65 and their characteristics time are of nanoseconds (or even faster) and thus belong to the first category. Auger recombination is an example of such fast non-radiative processes (~ ns).89

Resonant tunneling of excited carriers into the trap sites, adjacent to Si NCs, can be the origin of non-radiative transitions related to category (ii), with the decay rates similar to the radiative recombination rate (~µs), as was discussed in subsection (4.1.4.2). The details of such trap sites can be found in paper IV appended to the

53

thesis. Finally blinking (characteristics time of seconds to even hours)15 are considered as slow non-radiative decay channels for trap sites further away from the NC. The quantum yield (QY) or the external quantum efficiency (EQE) of silicon nanocrystals with various ligand passivation molecules was measured. Absolute QY values of Si NCs versus their emission peak position (varying between ~ 30‒70%) are shown in figure 4.21a. These QY values were independently checked at University of Amsterdam and at Hamamatsu Company and similar results were obtained. The QY values appear to be high compared to the other studies.90,91 Note that QYs obtained for ligand-passivated Si NCs measured here are independent of the excitation wavelength, which directly follows from the Kasha–Vavilov rule,92 as it is shown in figure 4.21b. In contrast to the total PL decay efficiency is influenced by the parameters such as passivation or preparation method rather than only nanocrystal size.

Figure 4.21 (a) Absolute PL quantum yields of Si NCs with various ligand molecules and preparation conditions as a function of their emission energies. (b) Absolute PL quantum yields of Si NCs at indicated excitation photon energies. Low absorption of samples and the system response calibration result in the uncertainty of the QYs shown as error bars.

The QY data alone is not sufficient to times there is no obvious correlation between QYs and nanocrystal sizes extracted from the quantum confinement theory.88 This suggests that the total luminescence understand the recombination mechanism of Si NCs. Hence, through spectrally-resolved PL decay measurements the IQE of ligand-passivated Si NCs were studied.

54

Figure 4.22 Schematic of various possible non-radiative decay channels in size-selected Si NCs ensembles and their impact on the corresponding PL decay curves, size-selected Si NCs containing (a) all types of non-radiative recombination channels, (b) type (ii) non-radiative decay channels. The star-like symbols represents the defect sites adjacent to NCs with microsecond decay rates. Black circles illustrate dark nanocrystals.

According to the spectrally-resolved PL decay results presented in section 4.2.2, the stretched exponential PL decay characters of ensembles of ligand-passivated Si NCs changed to mono-exponential decays when measured at different detection energies.

The mentioned mono-exponential PL decay of size-selected Si NCs suggests that no non-radiative decay transitions with microsecond decay rate similar to radiative rates (non-radiative decay transitions of type ii) are present in the system. This is because non-radiative process would influence each nanocrystal differently depending on the traps, defects, etc. yielding different total recombination rates and thus a stretched exponential decay even at fixed detection energies. The impact of

55

different non-radiative decay processes on the shape of the PL decay curve is demonstrated schematically in figure 4.22.

According to figure 2.22a the presence of competitive non-radiative decay channels of type (ii) in size-selected Si NC systems results in a dispersion of the total decay rates and therefore a stretched exponential decay character.

Figure 4.23 Schematic of a single Si NC containing various non-radiative transitions and the corresponding mono-exponential decay. The star-like symbol is a non-radiative decay center close to the Si NC.

Considering the discussion above, as well as the coincidence of the measured total PL decay rate of size-selected, ligand-passivated Si NCs with the radiative decay rates reported by Fujii, et. al.87 for Si NCs/SiO2 the IQE is concluded to be 100% (the case of figure 4.22b).

In single Si QDs, passivated by a thick oxide shell however, the measured IQE is much lower at room temperature (~ 9%). A schematic of a single Si QD with non-radiative decay channel of type (ii) is shown in figure 4.23 with the corresponding PL decay curve of mono-exponential character. Due to the existence of various non-radiative decay channels (according to the PL intermittency of single Si QDs the non-radiative channels of type (i) and type (iii) present as well) the QY is below one. The low internal QE to our knowledge, and as discussed in section 4.1.4, is due to the resonant tunneling of the excited carriers through a potential barrier formed by an oxide adjacent to the NC trap sites consisting trap sites (figure 4.15). Thus, for ligand-passivated NCs in the liquid such trap sites may be absent.

56

57

Chapter 5 Conclusions

In this thesis the carrier dynamics of single silicon quantum dots with thick oxide passivation as well as ligand-passivated silicon nanocrystals have been studied through various PL spectroscopy techniques, such as single-dot PL imaging and spectroscopy, time-resolved PL imaging and single photon counting, and spectrally-resolved ensemble PL decay measurements. The obtained results provide a deeper understanding of the physics behind the absorption and recombination mechanisms which consequently led to obtaining quantum efficiency values of silicon nanocrystal systems.

The conclusions drawn from this study can be listed as follows:

Single dot photoluminescence decay character: • The PL of single Si QDs decay mono-exponentially with a quite long decay

range (~µs) and strong dot-to-dot lifetime variation. • PL lifetimes of single Si QDs with the same size (i. e. PL emission energy)

vary significantly from dot to dot. • The origin of the stretched exponential decay of an ensemble of Si NCs can

be attributed to a distribution of the individual Si QD PL lifetimes due to differences in size, shape and passivation.

•

Carrier dynamics of the luminescence in single silicon quantum dots: • PL decay rates of single Si QDs below 70 K follow the singlet-triplet

model. Accordingly the extracted splitting energy of single Si QDs is Δ ≈ 6‒12 meV.

• Simulation confirms that the singlet and triplet spectral peaks are not resolvable in the PL emission spectra of single Si QDs.

• A model of resonant tunneling of the excited carriers to the adjacent trap sites in single Si QDs explains the well-known thermal quenching of the PL intensity.

58

Photoluminescence absorption: • The absolute values of the optical absorption cross-section of single Si

QDs with a thick oxide passivation are in the range of ~ 7×10-15 ‒1.46×10-

14 cm2 at the excitation energy of 3.06 eV. • The Si QDs with thick oxide passivation under study have higher

absorption cross-sections (~ by a factor of 10) compared to reported values for ensembles of silicon nanocrystals for the excitation energy of 3.06 eV. This is due to the elongated, nanorod-like structural geometry of these types of single Si QDs and the effect of the near-field strength of the excitation field.

Quantum efficiency: • The PL internal quantum efficiency of single Si QDs is ~ 10% at room

temperature, for oxide-passivated NCs. • The absolute quantum yield of ligand-passivated silicon nanocrystals

measured in an integrating sphere is relatively high (~30‒70%), which manifests the absence of the defect sites induced by oxide matrix in Si NCs with oxide passivation.

• The stretched exponential PL decay of ensembles of ligand-passivated silicon nanocrystals with dispersion factor of β=0.8 changes to single exponential decays (β=1.0) for spectrally selected energies. Furthermore, the total PL decay rates coincide with radiative rates reported for Si NCs/SiO2. Therefore, the internal quantum efficiency of ligand-passivated Si NCs is concluded to be close to 100%. The difference to the quantum yield measurements can then be attributed to dark NCs or to the off-periods of blinking NCs.

• In spectrally-resolved PL decay measurements the homogeneous linewidth broadening influences on the obtained PL decay time τ and dispersion factor β values and therefore should be accounted for. This can be done through a mathematical approach proposed in this thesis.

• PL Lifetimes of the oxide-passivated Si QDs (5‒45 µs) are much shorter than for ligand-passivated Si NCs (40‒90 µs). This suggests the presence of less non-radiative recombination channels in ligand-passivated Si NCs compared to Si NCs with thick oxide passivation, originating probably from the preparation conditions and oxide matrix.

59

High-excitation regime: • No extra PL peak related to the creation of biexcitons at strong excitations

was observed for single Si QDs. • The Auger recombination rate in single silicon QDs is about tens-hundreds

of nanoseconds at room temperature. • The efficiency of the biexciton emission is very low at low temperatures

(10-20 times lower than excitons). • The PL intensity of single Si QDs saturate at high excitations suggesting

that the Auger recombination is the dominant process.

Emission intermittency/blinking (switching between on and off state): • In blinking the on- and off-times of single Si QDs follow a mono-

exponential distribution in contrast to the results reported for other material system (e. g. CdSe NCs).

• The average blinking frequencies increase linearly by pumping, suggesting that the blinking is through a one-photon absorption and trapping mechanism.

60

61

Appendix A: System detectivity and QE estimation

In order to express the PL intensity in absolute units (photons/s) and thus estimate the ratio between absorbed and emitted photons by a single nanocrystals (external quantum efficiency), it is essential to determine the energy loss of the optical pathway to obtain the system detectivity. For this aim, the transmissivity of each optical component in the setup as well as the sample emissivity were estimated. The emissivity is the total number of the photons emitted by nanocrystal per unit area per unit time and represents how efficient the nanocrystal emits light. In figure A.1 a schematic of the optical apparatus and corresponding Transmissivity is shown.

The transmittance of typical filters and mirrors were found in specification sheets prepared by the corresponding companies, while a Newport-model 1918-C power meter was used to measure the efficient transmittance of the cryostat and the spectrometer.

The power meter was placed before and after the cryostat glass, taking into account the angle of the incoming photons with respect to the cryostat glass (~ 45°) in the dark field configuration and the angle of the emitted photons of silicon nanocrystals under UV excitation (perpendicular). The transmittance of the cryostat glass was measured to be of ~ 80.5% and ~ 97% for the dark field excitation and the perpendicular photon emission to the glass surface, respectively.

62

Figure A.1 Schematic of the PL setup and the optical pathway. The enlarged image shows how the transmittance of the cryostat is determined. The value of efficient percentage of the measured/estimated transmitted light is written next to each component as well.

Taking all the transmission coefficients into account as well as the estimated sample emissivity to the upper hemisphere, the detectivity of the system is estimated to be ~ 1%. Using the obtained detectivity value, it is then possible to calculate the QE of a single silicon quantum dot.

As discussed in section 2.4.6 for weak excitation regime below saturation the QE can be calculated as:

𝑄𝐸 =𝐼

𝑛 ∙ Φ ∙ 𝐷

63

Figure A.2 The ratio of the total power emitted to the upper and lower hemisphere as a function of substrate refractive index.93 The top right frame shows our sample consisting of the silicon quantum dot embedded in SiO2 which is considered as a semiconductor substrate with a refractive index of ~3.5.

where σ, Φ, D and I are absorption cross-section, excitation flux and system detectivity, and the number of emitted photon from the Si NC, respectively.

In order to extract the intensity of the emitted photons from a typical PL image the mean value of the signal inside a 4×4 px2 area at the dot position was subtracted from the mean value of the signal obtained of the area around the dot as the background. A simple schematic of the area defined to extract the intensity and the background signal is shown in figure A.3. Then the extracted value was divided by the total acquisition time. This is proportional to the number of the detected photons per second. The unit of the extracted intensity signal is counts/px/s which is proportional to the number of emitted photons detected by the EMCCD camera per unit area and per unit time. Thus the conversion of the incident photons camera counts must be obtained. This is accomplished by using the camera specification sheet and based on the parameters used for performing the measurements. The diagram of count conversion is shown in figure A.4, which is taken from the Andor company website. Quantum efficiency of the EMCCD camera is around 98% at 700 nm. The EM gain, pre-amp and bias offset of 20, 5.2x and 100 counts/s were considered. The excitation flux is calculated by dividing the laser power density to the laser energy. The laser power density was measured at the position of the sample.

64

Figure A.3 Schematic of the area defined to extract the PL intensity signal of a single silicon quantum dot.

In temperature dependent intensity studies, in order to extract the intensity of a single dot from a PL decay image taken under high-excitation, first the ratio between the fast and slow transient of the same dot were obtained from the corresponding PL decay curve under the same excitation condition. Then this ratio was taken into account in extracting the intensity signal of the PL image. The extracted value thus is ascribed to the exciton. This saturation occurred when at low temperatures the saturation level dropped due to the longer decay times, and all the measured data therefore needs to be treated according to the above saturation model (see section 2.4.6).

Figure A.4 Count Converter diagram from website: http://www.andor.com/learning-academy/count-convert-quantifying-data-in-electrons-and-photons.

65

REFERENCES

(1) Lehmann, V.; Gösele, U. Porous Silicon Formation: A Quantum Wire Effect. Appl. Phys. Lett. 1991, 58, 856.

(2) Canham, L. T. Silicon Quantum Wire Array Fabrication by Electrochemical and Chemical Dissolution of Wafers. Appl. Phys. Lett. 1990, 57, 1046.

(3) Hybertsen, M. S. Absorption and Emission of Light in Nanoscale Silicon Structures. Phys. Rev. Lett. 1994, 72, 1514–1517.

(4) Kovalev, D.; Heckler, H.; Polisski, G.; Koch, F. Optical Properties of Si Nanocrystals. Phys. status solidi 1999, 215, 871–932.

(5) Cullis, A. G.; Canham, L. T.; Calcott, P. D. J. The Structural and Luminescence Properties of Porous Silicon. J. Appl. Phys. 1997, 82, 909–965.

(6) Low, S. P.; Voelcker, N. H.; Canham, L. T.; Williams, K. a. The Biocompatibility of Porous Silicon in Tissues of the Eye. Biomaterials 2009, 30, 2873–2880.

(7) Nishimura, H.; Ritchie, K.; Kasai, R. S.; Goto, M.; Morone, N.; Sugimura, H.; Tanaka, K.; Sase, I.; Yoshimura, A.; Nakano, Y.; et al. Biocompatible Fluorescent Silicon Nanocrystals for Single-Molecule Tracking and Fluorescence Imaging. J. Cell Biol. 2013, 202, 967–983.

(8) Bruhn, B. Fabrication and Characterization of Single Luminescing Quantum Dots from 1D Silicon Nanostructures; 2012.

(9) Cohen, M. L.; Bergstresser, T. K. Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-Blende Structures. Phys. Rev. 1966, 141, 789–796.

(10) Fujii, M.; Kovalev, D.; Diener, J.; Koch, F.; Takeoka, S.; Hayashi, S. Breakdown of the K-Conservation Rule in Si1-x Gex Alloy Nanocrystals: Resonant Photoluminescence Study. J. Appl. Phys. 2000, 88, 5772.

(11) Pelant, I.; Valenta, J. Luminescence Spectroscopy of Semiconductors; Oxford University Press, 2012.

(12) Sychugov, I.; Fucikova, A.; Pevere, F.; Yang, Z.; Veinot, J. G. C.; Linnros, J. Ultranarrow Luminescence Linewidth of Silicon Nanocrystals and Influence

66

of Matrix. ACS Photonics 2014, 1, 998–1005.

(13) Chelikowsky, J.; Cohen, M. Electronic Structure of Silicon. Phys. Rev. B 1974, 10, 5095–5107.

(14) De Mello, J. C.; Wittmann, H. F.; Friend, R. H. An Improved Experimental Determination of External Photoluminescence Quantum Efficiency. Adv. Mater. 1997, 9, 230–232.

(15) Sychugov, I.; Juhasz, R.; Linnros, J.; Valenta, J. Luminescence Blinking of a Si Quantum Dot in a SiO2 Shell. Phys. Rev. B 2005, 71, 115331–115335.

(16) Kovalev, D.; Diener, J.; Heckler, H.; Polisski, G.; Künzner, N.; Koch, F. Optical Absorption Cross-Sections of Si Nanocrystals. Phys. Rev. B 2000, 61, 4485–4487.

(17) Priolo, F.; Franzò, G.; Pacifici, D.; Vinciguerra, V.; Iacona, F.; Irrera, A. Role of the Energy Transfer in the Optical Properties of Undoped and Er-Doped Interacting Si Nanocrystals. J. Appl. Phys. 2001, 89, 264.

(18) Efros, A.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D.; Bawendi, M. Band-Edge Exciton in Quantum Dots of Semiconductors with a Degenerate Valence Band: Dark and Bright Exciton States. Phys. Rev. B 1996, 54, 4843–4856.

(19) Calcott, P. D. J.; Nash, K. J.; Canham, L. T.; Kane, M. J.; Brumhead, D. Identification of Radiative Transitions in Highly Porous Silicon. J. Phys. Condens. Matter 1993, 5, L91–L98.

(20) Uhlir, A. Electrolytic Shaping of Germanium and Silicon. Bell Syst. Tech. J. 1956, 35, 333–347.

(21) Sykora, M.; Mangolini, L.; Schaller, R.; Kortshagen, U.; Jurbergs, D.; Klimov, V. Size-Dependent Intrinsic Radiative Decay Rates of Silicon Nanocrystals at Large Confinement Energies. Phys. Rev. Lett. 2008, 100, 067401.

(22) Miller, J. B.; Van Sickle, A. R.; Anthony, R. J.; Kroll, D. M.; Kortshagen, U. R.; Hobbie, E. K. Ensemble Brightening and Enhanced Quantum Yield in Size-Purified Silicon Nanocrystals. ACS Nano 2012, 6, 7389–7396.

(23) Mastronardi, M. L.; Maier-Flaig, F.; Faulkner, D.; Henderson, E. J.; Kübel,

67

C.; Lemmer, U.; Ozin, G. A. Size-Dependent Absolute Quantum Yields for Size-Separated Colloidally-Stable Silicon Nanocrystals. Nano Lett. 2012, 12, 337–342.

(24) Zacharias, M.; Hiller, D.; Hartel, A.; Gutsch, S. Defect Engineering of Si Nanocrystal Interfaces. Phys. status solidi 2012, 209, 2449–2454.

(25) Hiller, D.; Jivanescu, M.; Stesmans, A.; Zacharias, M. P[sub b(0)] Centers at the Si-nanocrystal/SiO[sub 2] Interface as the Dominant Photoluminescence Quenching Defect. J. Appl. Phys. 2010, 107, 084309.

(26) Godefroo, S.; Hayne, M.; Jivanescu, M.; Stesmans, A.; Zacharias, M.; Lebedev, O. I.; Van Tendeloo, G.; Moshchalkov, V. V. Classification and Control of the Origin of Photoluminescence from Si Nanocrystals. Nat. Nanotechnol. 2008, 3, 174–178.

(27) Timmerman, D.; Izeddin, I.; Gregorkiewicz, T. Saturation of Luminescence from Si Nanocrystals Embedded in SiO2. Phys. status solidi 2010, 207, 183–187.

(28) Moerner, W. E.; Fromm, D. P. Methods of Single-Molecule Fluorescence Spectroscopy and Microscopy. Rev. Sci. Instrum. 2003, 74, 3597.

(29) Bsiesy, a.; Vial, J. C.; Gaspard, F.; Herino, R.; Ligeon, M.; Muller, F.; Romestain, R.; Wasiela, A.; Halimaoui, A.; Bomchil, G. Photoluminescence of High Porosity and of Electrochemically Oxidized Porous Silicon Layers. Surf. Sci. 1991, 254, 195–200.

(30) Xie, Y. H.; Wilson, W. L.; Ross, F. M.; Mucha, J. a.; Fitzgerald, E. a.; Macaulay, J. M.; Harris, T. D. Luminescence and Structural Study of Porous Silicon Films. J. Appl. Phys. 1992, 71, 2403.

(31) Linnros, J.; Lalic, N.; Galeckas, A.; Grivickas, V. Analysis of the Stretched Exponential Photoluminescence Decay from Nanometer-Sized Silicon Crystals in SiO2. J. Appl. Phys. 1999, 86, 6128.

(32) Mihalcescu, I.; Vial, J. C.; Romestain, R. Carrier Localization in Porous Silicon Investigated by Time-Resolved Luminescence Analysis. J. Appl. Phys. 1996, 80, 2404.

(33) Pavesi, L. Influence of Dispersive Exciton Motion on the Recombination Dynamics in Porous Silicon. J. Appl. Phys. 1996, 80, 216.

68

(34) Martin, E.; Delerue, C.; Allan, G.; Lannoo, M. Theory of Excitonic Exchange Splitting and Optical Stokes Shift in Silicon Nanocrystallites: Application to Porous Silicon. Phys. Rev. B 1994, 50, 18258–18267.

(35) Skryshevsky, V. A.; Laugier, A.; Strikha, V. I.; Vikulov, V. A. Evaluation of Quantum Efficiency of Porous Silicon Photoluminescence. Mater. Sci. Eng. B 1996, 40, 54–57.

(36) Walters, R. J.; Kalkman, J.; Polman, A.; Atwater, H. A.; de Dood, M. J. A. Photoluminescence Quantum Efficiency of Dense Silicon Nanocrystal Ensembles in SiO2. Phys. Rev. B 2006, 73, 132302.

(37) Kalkman, J.; Gersen, H.; Kuipers, L.; Polman, A. Excitation of Surface Plasmons at a SiO2∕Ag Interface by Silicon Quantum Dots: Experiment and Theory. Phys. Rev. B 2006, 73, 075317.

(38) Park, N.-M.; Kim, T.-S.; Park, S.-J. Bandgap Engineering of Amorphous Silicon Quantum Dots for Light-Emitting Diodes. Appl. Phys. Lett. 2001, 78, 2575.

(39) Pi, X. D.; Liptak, R. W.; Deneen Nowak, J.; Wells, N. P.; Carter, C. B.; Campbell, S. A.; Kortshagen, U. Air-Stable Full-Visible-Spectrum Emission from Silicon Nanocrystals Synthesized by an All-Gas-Phase Plasma Approach. Nanotechnology 2008, 19, 245603.

(40) Belomoin, G.; Therrien, J.; Nayfeh, M. Oxide and Hydrogen Capped Ultrasmall Blue Luminescent Si Nanoparticles. Appl. Phys. Lett. 2000, 77, 779.

(41) Zou, J.; Sanelle, P.; Pettigrew, K. A.; Kauzlarich, S. M. Size and Spectroscopy of Silicon Nanoparticles Prepared via Reduction of SiCl4. J. Clust. Sci. 2006, 17, 565–578.

(42) Shimizu-Iwayama, T.; Nakao, S.; Saitoh, K.; Itoh, N. Photoluminescence from Nanoparticles of Silicon Embedded in an Amorphous Silicon Dioxide Matrix. J. Phys. Condens. Matter 1994, 6, L601–L606.

(43) Kanzawa, Y.; Kageyama, T.; Takeoka, S.; Fujii, M.; Hayashi, S.; Yamamoto, K. Size-Dependent near-Infrared Photoluminescence Spectra of Si Nanocrystals Embedded in SiO2 Matrices. Solid State Commun. 1997, 102, 533–537.

69

(44) Zacharias, M.; Heitmann, J.; Scholz, R.; Kahler, U.; Schmidt, M.; Bläsing, J. Size-Controlled Highly Luminescent Silicon Nanocrystals: A SiO/SiO2 Superlattice Approach. Appl. Phys. Lett. 2002, 80, 661.

(45) Abderrafi, K.; García Calzada, R.; Gongalsky, M. B.; Suárez, I.; Abarques, R.; Chirvony, V. S.; Timoshenko, V. Y.; Ibáñez, R.; Martínez-Pastor, J. P. Silicon Nanocrystals Produced by Nanosecond Laser Ablation in an Organic Liquid. J. Phys. Chem. C 2011, 115, 5147–5151.

(46) Liu, H. I. Self-Limiting Oxidation of Si Nanowires. J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 1993, 11, 2532.

(47) Cui, H.; Wang, C. X.; Yang, G. W. Origin of Self-Limiting Oxidation of Si Nanowires. Nano Lett. 2008, 8, 2731–2737.

(48) Bruhn, B.; Valenta, J.; Linnros, J. Controlled Fabrication of Individual Silicon Quantum Rods Yielding High Intensity, Polarized Light Emission. Nanotechnology 2009, 20, 505301.

(49) Hessel, C. M.; Henderson, E. J.; Veinot, J. G. C. Hydrogen Silsesquioxane: A Molecular Precursor for Nanocrystalline Si−SiO 2 Composites and Freestanding Hydride-Surface-Terminated Silicon Nanoparticles. Chem. Mater. 2006, 18, 6139–6146.

(50) Rodríguez Núñez, J. R.; Kelly, J. a.; Henderson, E. J.; Veinot, J. G. C. Wavelength-Controlled Etching of Silicon Nanocrystals. Chem. Mater. 2012, 24, 346–352.

(51) Bruhn, B.; Valenta, J.; Sychugov, I.; Mitsuishi, K.; Linnros, J. Transition from Silicon Nanowires to Isolated Quantum Dots: Optical and Structural Evolution. Phys. Rev. B 2013, 87, 045404.

(52) Valenta, J.; Bruhn, B.; Linnros, J. Coexistence of 1D and Quasi-0D Photoluminescence from Single Silicon Nanowires. Nano Lett. 2011, 11, 3003–3009.

(53) Bruhn, B.; Valenta, J.; Sangghaleh, F.; Linnros, J. Blinking Statistics of Silicon Quantum Dots. Nano Lett. 2011, 11, 5574–5580.

(54) Wang, S.; Querner, C.; Emmons, T.; Drndic, M.; Crouch, C. H. Fluorescence Blinking Statistics from CdSe Core and Core/shell Nanorods. J. Phys. Chem. B 2006, 110, 23221–23227.

70

(55) Issac, A.; Krasselt, C.; Cichos, F.; von Borczyskowski, C. Influence of the Dielectric Environment on the Photoluminescence Intermittency of CdSe Quantum Dots. Chemphyschem 2012, 13, 3223–3230.

(56) Efros, A. L.; Rosen, M. Random Telegraph Signal in the Photoluminescence Intensity of a Single Quantum Dot. Phys. Rev. Lett. 1997, 78, 1110–1113.

(57) Rosen, S.; Schwartz, O.; Oron, D. Transient Fluorescence of the Off State in Blinking CdSe/CdS/ZnS Semiconductor Nanocrystals Is Not Governed by Auger Recombination. Phys. Rev. Lett. 2010, 104, 157404.

(58) Galland, C.; Ghosh, Y.; Steinbrück, A.; Sykora, M.; Hollingsworth, J. a; Klimov, V. I.; Htoon, H. Two Types of Luminescence Blinking Revealed by Spectroelectrochemistry of Single Quantum Dots. Nature 2011, 479, 203–207.

(59) Frantsuzov, P.; Kuno, M.; Jankó, B.; Marcus, R. A. Universal Emission Intermittency in Quantum Dots, Nanorods and Nanowires. Nat. Phys. 2008, 4, 519–522.

(60) Pavesi, L.; Dal Negro, L.; Mazzoleni, C.; Franzò, G.; Priolo, F. Optical Gain in Silicon Nanocrystals. Nature 2000, 408, 440–444.

(61) Bruhn, B.; Sangghaleh, F.; Linnros, J. Fabricating Single Silicon Quantum Rods for Repeatable Single Dot Photoluminescence Measurements. Phys. status solidi 2011, 208, 631–634.

(62) Guichard, A. R.; Kekatpure, R. D.; Brongersma, M. L.; Kamins, T. I. Temperature-Dependent Auger Recombination Dynamics in Luminescent Silicon Nanowires. Phys. Rev. B 2008, 78, 235422.

(63) Absorption and Scattering of Light by Small Particles; Bohren, C. F.; Huffman, D. R., Eds.; Wiley-VCH Verlag GmbH: Weinheim, Germany, 1998.

(64) Ricard, D.; Ghanassi, M.; Schanne-Klein, M. C. Dielectric Confinement and the Linear and Nonlinear Optical Properties of Semiconductor-Doped Glasses. Opt. Commun. 1994, 108, 311–318.

(65) Hartel, A. M.; Gutsch, S.; Hiller, D.; Zacharias, M. Intrinsic Nonradiative Recombination in Ensembles of Silicon Nanocrystals. Phys. Rev. B 2013, 87, 035428.

71

(66) Rinnert, H.; Jambois, O.; Vergnat, M. Photoluminescence Properties of Size-Controlled Silicon Nanocrystals at Low Temperatures. J. Appl. Phys. 2009, 106, 023501.

(67) Varshni, Y. P. Temperature Dependence of the Energy Gap in Semiconductors. Physica 1967, 34, 149–154.

(68) Heitmann, J.; Müller, F.; Yi, L.; Zacharias, M.; Kovalev, D.; Eichhorn, F. Excitons in Si Nanocrystals: Confinement and Migration Effects. Phys. Rev. B 2004, 69, 195309.

(69) Hartel, a. M.; Gutsch, S.; Hiller, D.; Zacharias, M. Fundamental Temperature-Dependent Properties of the Si Nanocrystal Bandgap. Phys. Rev. B 2012, 85, 165306.

(70) O’Donnell, K. P.; Chen, X. Temperature Dependence of Semiconductor Bandgaps. Appl. Phys. Lett. 1991, 58, 2924.

(71) Time-Resolved Light Scattering from Excitons; Stolz, H., Ed.; Springer Tracts in Modern Physics; Springer-Verlag: Berlin/Heidelberg, 1994; Vol. 130.

(72) Dovrat, M.; Goshen, Y.; Jedrzejewski, J.; Balberg, I.; Sa’ar, A. Radiative versus Nonradiative Decay Processes in Silicon Nanocrystals Probed by Time-Resolved Photoluminescence Spectroscopy. Phys. Rev. B 2004, 69, 155311.

(73) Calcott, P. D. J.; Nash, K. J.; Canham, L. T.; Kane, M. J.; Brumhead, D. Spectroscopic Identification of the Luminescence Mechanism of Highly Porous Silicon. J. Lumin. 1993, 57, 257–269.

(74) Proot, J. P.; Delerue, C.; Allan, G. Electronic Structure and Optical Properties of Silicon Crystallites: Application to Porous Silicon. Appl. Phys. Lett. 1992, 61, 1948.

(75) Vial, J. C.; Bsiesy, A.; Gaspard, F.; Hérino, R.; Ligeon, M.; Muller, F.; Romestain, R.; Macfarlane, R. M. Mechanisms of Visible-Light Emission from Electro-Oxidized Porous Silicon. Phys. Rev. B 1992, 45, 14171–14176.

(76) Pavesi, L.; Ceschini, M. Stretched-Exponential Decay of the Luminescence in Porous Silicon. Phys. Rev. B 1993, 48, 17625–17628.

(77) Seguini, G.; Castro, C.; Schamm-Chardon, S.; BenAssayag, G.; Pellegrino,

72

P.; Perego, M. Scaling Size of the Interplay between Quantum Confinement and Surface Related Effects in Nanostructured Silicon. Appl. Phys. Lett. 2013, 103, 023103.

(78) Davies, J. H. The Physics of Low-Dimensional Semiconductors; Cambridge University Press: Cambridge, 1997.

(79) Schwank, J. R.; Shaneyfelt, M. R.; Fleetwood, D. M.; Felix, J. A.; Dodd, P. E.; Member, S.; Paillet, P.; Overview, A. Radiation Effects in MOS Oxides. 2008, 55, 1833–1853.

(80) Mihalcescu, I.; Vial, J. C.; Bsiesy, A.; Muller, F.; Romestain, R.; Martin, E.; Delerue, C.; Lannoo, M.; Allan, G. Saturation and Voltage Quenching of Porous-Silicon Luminescence and the Importance of the Auger Effect. Phys. Rev. B 1995, 51, 17605–17613.

(81) Delerue, C.; Lannoo, M.; Allan, G.; Martin, E.; Mihalcescu, I.; Vial, J. C.; Romestain, R.; Muller, F.; Bsiesy, A. Auger and Coulomb Charging Effects in Semiconductor Nanocrystallites. Phys. Rev. Lett. 1995, 75, 2228–2231.

(82) Bacher, G.; Weigand, R.; Seufert, J.; Kulakovskii, V. D.; Gippius, N. A.; Forchel, A.; Leonardi, K.; Hommel, D. Biexciton versus Exciton Lifetime in a Single Semiconductor Quantum Dot. Phys. Rev. Lett. 1999, 83, 4417–4420.

(83) Brongersma, M. L.; Polman, A.; Min, K. S.; Boer, E.; Tambo, T.; Atwater, H. a. Tuning the Emission Wavelength of Si Nanocrystals in SiO2 by Oxidation. Appl. Phys. Lett. 1998, 72, 2577.

(84) López, M.; Garrido, B.; Garcıa, C.; Pellegrino, P.; Pérez-Rodrıguez, a.; Morante, J. R.; Bonafos, C.; Carrada, M.; Claverie, a. Elucidation of the Surface Passivation Role on the Photoluminescence Emission Yield of Silicon Nanocrystals Embedded in SiO2. Appl. Phys. Lett. 2002, 80, 1637.

(85) Lockwood, R.; McFarlane, S.; Rodríguez Núñez, J. R.; Wang, X. Y.; Veinot, J. G. C.; Meldrum, A. Photoactivation of Silicon Quantum Dots. J. Lumin. 2011, 131, 1530–1535.

(86) Miller, J. B.; Van Sickle, A. R.; Anthony, R. J.; Kroll, D. M.; Kortshagen, U. R.; Hobbie, E. K. Ensemble Brightening and Enhanced Quantum Yield in Size-Purified Silicon Nanocrystals. ACS Nano 2012, 6, 7389–7396.

(87) Miura, S.; Nakamura, T.; Fujii, M.; Inui, M.; Hayashi, S. Size Dependence of

73

Photoluminescence Quantum Efficiency of Si Nanocrystals. Phys. Rev. B 2006, 73, 245333–245335.

(88) Takagahara, T.; Takeda, K. Theory of the Quantum Confinement Effect on Excitons in Quantum Dots of Indirect-Gap Materials. Phys. Rev. B 1992, 46, 15578–15581.

(89) Pevere, F.; Sychugov, I.; Sangghaleh, F.; Fucikova, A.; Linnros, J. Biexciton Emission as a Probe of Auger Recombination in Individual Silicon Nanocrystals. J. Phys. Chem. C 2015, 119, 7499–7505.

(90) Jurbergs, D.; Rogojina, E.; Mangolini, L.; Kortshagen, U. Silicon Nanocrystals with Ensemble Quantum Yields Exceeding 60%. Appl. Phys. Lett. 2006, 88, 233116–233118.

(91) Mangolini, L.; Kortshagen, U. Plasma-Assisted Synthesis of Silicon Nanocrystal Inks. Adv. Mater. 2007, 19, 2513–2519.

(92) Vavilov, S. I. Die Fluoreszenzausbeute von Farbstof Losungen Als Funktion Der Wellenlange Des Anregenden Lichtes. Z. Phys. 1927, 42, 311–318.

(93) Sychugov, I.; Omi, H.; Kobayashi, Y. On the Role of Substrate in Light-Harvesting Experiments. Opt. Lett. 2008, 33, 1807.