hot carrier solar cells

Hot Carrier Solar Cells

Modelling of Practical Efficiency and

Characterization of Absorber and

Energy Selective Contacts

Pasquale Aliberti

School of Photovoltaic and Renewable Energy Engineering

ARC Photovoltaics Centre of Excellence

The University of New South Wales

UNSW Sydney NSW 2052

Australia

A thesis submitted to The University of New South Wales

In fulfilment of the requirements for the degree of

Doctor of Philosophy

2011

PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES

Thesis/Dissertation Sheet Surname or Family name: Aliberti

First name: Pasquale

Other name/s:

Abbreviation for degree as given in the University calendar:

School: School of Photovoltaics and Renewable Energy Engineering

Faculty: Engineering

Title: Recent Progresses in Hot Carrier Solar Cells

Abstract 350 words maximum: (PLEASE TYPE)

The current increase in the demand for renewable energies has led to a fast growth of solar cells mass production over the past few years. Even though solar photovoltaic is currently the fastest growing renewable energy market, the cost per watt figure is still high compared to conventional energy sources. To decrease the cost per watt ratio of solar cells two basic approaches can be undertaken: the first one is to decrease the cost of the devices, using cheaper deposition techniques and materials; the other is to increase the efficiency of the cells, keeping the costs below an acceptable limit. The hot carrier solar cell is a promising third generation photovoltaic device which, consenting collection of highly energetic photogenerated carriers, allows efficiencies up to 60%. The efficiency gain is realized minimizing the losses due to poor conversion efficiency of photons with energy above the bandgap of the absorber. The two main building blocks of a hot carrier solar cell are: the absorber, were electrons and holes are photogenerated, and the energy selective contacts, which allow extraction of carriers to the external circuit in a narrow range of energies. In this thesis several theoretical and experimental aspects regarding the design and the realization of a hot carrier solar cell are discussed. Limiting efficiencies of the device have been calculated using a complex theoretical model. A maximum efficiency of 43% has been calculated considering a 1000 times concentrated radiation for a hot carrier solar cell with an Indium Nitride absorber. The velocity of carrier cooling in III-V compound semiconductors has been investigated using time resolved photoluminescence experiments. Hot carrier cooling transients of Gallium Arsenide, Indium Phosphide and Indium Nitride samples have been studied, confirming that hot phonon effect has a major role for hot carriers relaxation. In addition, the possibility of realizing energy selective contacts based on an all-Silicon structure is studied. Structures consisting of a single layer of Silicon quantum dots in a Silicon dioxide matrix have been deposited and characterized in order to investigate on their potential to be utilized as energy selective contacts for hot carrier solar cells.

Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). …………………………………………………………… Signature

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Originality statement

‘I hereby declare that this submission is my own work and to the best of my

knowledge it contains no materials previously published or written by another

person, nor material which to a substantial extent has been accepted for the

award of any other degree or diploma at UNSW or any other educational

institution, except where due acknowledgment is made in the thesis. Any

contribution made to research by others, with whom I have worked at UNSW or

elsewhere, is explicitly acknowledged in the thesis. I also declare that the

intellectual content of this thesis is the product of my own work, except to the

extent that assistance from others in the project’s design and conception or in

style, presentation and linguistic expression is acknowledged.’

Pasquale Aliberti

March 30, 2011

i

Copyright statement

‘I hereby grant the University of New South Wales or its agents the right to

archive and to make available my thesis or dissertation in whole or in part in

the University libraries in all forms of media, now or here after known, subject

to the provisions of the Copyright Act 1968. I retain all proprietary rights, such

as patent rights. I also retain the right to use in future works (such as articles or

books) all or part of this thesis or dissertation. I also authorise University

Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract

International (this is applicable to doctoral theses only). I have either used no

substantial portions of copyright material in my thesis or I have obtained

permission to use copyright material; where permission has not been granted I

have applied/will apply for a partial restriction of the digital copy of my thesis

or dissertation.’

Pasquale Aliberti

March 30, 2011

ii

Authenticity statement

‘I certify that the Library deposit digital copy is a direct equivalent of the

final officially approved version of my thesis. No emendation of content has

occurred and if there are any minor variations in formatting, they are the result

of the conversion to the digital format.’

Pasquale Aliberti

March 30, 2011

iii

iv

Abstract

The current increase in the demand for renewable energies has led to a fast

growth of solar cells mass production over the past few years. Even though

solar photovoltaic is currently the fastest growing renewable energy market, the

cost per watt figure of solar cells is still high compared to conventional energy

sources.

To decrease the cost per watt ratio of solar cells two basic approaches can be

undertaken: the first one is to decrease the cost of the devices, using cheaper

deposition techniques and materials; the other is to increase the efficiency of

the cells, keeping the costs below an acceptable limit.

The hot carrier solar cell is a promising third generation photovoltaic device

which, consenting collection of highly energetic photogenerated carriers,

allows energy conversion efficiencies up to 60%. The efficiency gain is

realized minimizing the losses due to poor conversion efficiency of photons

with energy above the bandgap of the absorber. This represents the main

energy loss mechanism in conventional solar cells, accounting for about 40

percent of the total losses. The two main building blocks of a hot carrier solar

cell are: the absorber, were electrons and holes are photogenerated, and the

energy selective contacts, which allow extraction of carriers to the external

circuit in a narrow range of energies.

In this thesis several theoretical and experimental aspects regarding the

design and the realization of a hot carrier solar cell are discussed in details.

Limiting efficiencies of the device have been calculated using a complex

theoretical model. A maximum efficiency of 43% has been calculated

v

considering a 1000 times concentrated radiation for a hot carrier solar cell with

an indium nitride absorber.

The velocity of carrier cooling in III-V compound semiconductors has been

investigated using time resolved photoluminescence experiments. Hot carrier

cooling transients of gallium arsenide, indium phosphide and indium nitride

samples have been studied, confirming that the hot phonon effect has a major

role for hot carriers relaxation and that the velocity of the cooling process is

strictly related to material quality.

In addition, the possibility of realizing energy selective contacts based on an

all-silicon structure is studied in details. Structures consisting of a single layer

of silicon quantum dots in a silicon dioxide matrix have been deposited and

characterized in order to investigate their potential to be utilized as selective

energy contacts for hot carrier solar cells.

vi

Alla mia famiglia.

Per essermi stati cosí vicino da tanto

lontano.

Sarete sempre il mio più grande

orgoglio.

vii

Acknowledgments

In the first place I would like to thank my supervisor Professor Gavin

Conibeer for allowing me to work on this challenging and exciting project. I

am grateful for his trust and for the autonomy that he gave me throughout the

entire degree. This allowed me to investigate aspects of the project that

interested me the most, keeping my curiosity always at high levels.

I am also grateful to Dr. Santosh Shrestha for supervising me during the

early stages of my experimental work, for his help with the daily laboratory

challenges and his scientific and moral support throughout the entire duration

of my studies. I would also like to thank my co-supervisor Professor Martin

Green for his precious advices and punctual guidance during crucial moments

of my research. It has been a great honour for me to be one of his students. A

special thank goes to Yu Feng who has been a brilliant student, always curious

and motivated. I appreciated his great help for the computation of numerical

results, presented in the second chapter of this thesis, and the theoretical

discussions on functional aspects of hot carrier solar cells. Precious have also

been discussions and advices of Dr. Dirk König, in particular for the

interpretation of carriers cooling transients, presented in chapter four, and the

relations with intervalley scattering. Thanks to Dr. Yasuhiko Takeda for the

scientific debates on efficiency limits of hot carrier cells and for his support

with the numerical calculations. I am grateful to Dr. Ivan Perez-Wurfl and Dr.

Chris Flynn for their help with processing and characterization, in particular

photolithography and optical measurements. Thanks also to Dr. Raphael Clady

for his great support and patience with our long sessions on the time resolved

viii

photoluminescence setup at Sydney University. Thanks to Murad Tayebjee and

Dr. Tim Schmidt for discussions of results of time resolved experiments.

Thanks to Dr. Shujuan Huang and Dr. Yidan Huang for their help with TEM

and to Dr. Bill Gong for the XPS measurements. Great thanks to Dr. Charlie

Kong, Katie Levick, Sean Lim and all the staff at the UNSW Mark Wainwright

analytical centre for their professional and continuous support. I’m also

thankful to the entire LDOT team of the SPREE for being so efficient in

keeping the laboratories in such an amazing working order, despite of the

enormous number of users that have been trying to break the unbreakable

during these four years.

Thanks to Mr. (soon Dr.) Bo Zhang for being my best desk neighborough

and mandarin teacher, and to Binesh for his revelations on scientific gambling.

I am deeply grateful to my friends, mates and colleagues Yong, Andy and

Rob for discovering the Asian half of my spirit, introducing me to karaoke and

Mahjong and for sharing with me the bright and dark moments of these years.

Making it to the end would have been a much harder job without them. I also

thank my mate and colleague Nino for dragging me to the best live gigs in

town. Thanks to Danny, Julie and the entire staff of the school for their friendly

and punctual help. I am also grateful to all my students of “applied

photovoltaics” and “introduction to electronic devices” for making my teaching

activity at UNSW such a rewarding experience.

I thank my Mum, my Dad and my Brother for being able to love and support

me despite of the 16143 kilometres that separate us. Thanks to my friends back

home Valentina, Michele, Ruben, Antonio and Donato for being so close and so

concerned about my safety in the Australian surf. I will be always grateful to

Maria Teresa for being so patient and helpful during these years. Without her

support it would have been hard to overcome some of the difficult times.

I finally thank the University of New South Wales for awarding me with

such a prestigious scholarship, which allowed me to enjoy this remarkable and

unforgettable time.

ix

‘Imagination is more

important than

knowledge.’

Albert Einstein

x

Contents

1 INTRODUCTION

1.1 Premise 1

1.2 Photovoltaic devices 4

1.3 Hot carrier solar cells 7

1.4 Aim and structure of this thesis 11

1.5 Bibliography 13

2 MODELLING EFFICIENCY LIMITS FOR HOT CARRIERS SOLAR CELLS

2.1 Introduction 16

2.2 Literature Review 19

2.2.1 Landsberg thermodynamic limit 19

2.2.2 Shockley-Queisser approach 21

2.2.3 Ross and Nozik approach for calculation of hot carrier

solar cell efficiency 22

2.2.4 Auger recombination-impact ionization model 24

2.2.5 Introduction of thermalisation time and absorber E-k

relation 26

2.3 Modelling efficiency limit for a hot carrier solar cell with an

indium nitride absorber 28

2.3.1 Model assumptions 28

2.3.2 Modelling of J-V characteristics 29

2.3.3 Carrier density calculation 32

2.3.4 Auger recombination and impact ionization coefficients

calculation 33

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2.3.5 Hot carrier solar cell efficiency calculation 35

2.3.6 Variation of conversion efficiency with carriers

extraction energy 36

2.3.7 Hot carrier solar cell operation analysis 37

2.3.8 Calculation of Auger recombination and impact

ionization rates 41

2.3.9 Thermalisation losses and efficiency versus

thermalisation time 42

2.3.10 Efficiency computation with indium nitride absorption

coefficient 44

2.4 Efficiency limit calculation with non ideal energy selective

contacts 47

2.4.1 Theoretical description of non-ideal energy selective

contacts 47

2.4.2 Results of calculation of efficiency limit with non-ideal

energy selective contacts 48

2.5 Summary 51

2.6 Bibliography 53

2.7 Publications 57

3 REALIZATION AND CHARACTERIZATION OF SINGLE LAYER SILICON

QUANTUM DOTS IN SILICON DIOXIDE STRUCTURES FOR ENERGY

SELECTIVE CONTACTS APPLICATIONS

3.1 Introduction 58

3.2 Literature review 60

3.3 Realization of single layer silicon quantum dots structure 64

3.3.1 Initial substrate preparation 64

3.3.2 Sputtering of the silicon rich oxide/silicon dioxide

structure 65

3.3.3 High temperature annealing 67

3.4 Investigation of optical and physical properties of silicon rich

oxides layers and nucleation of silicon nanoparticles 68

xii

3.4.1 Investigation of silicon rich oxide composition 69

3.4.2 Nucleation of silicon quantum dots in silicon rich oxide 74

3.5 Investigation of quantum dots nucleation and quantum

confinement in single layers of silicon quantum dots in silicon

dioxide 79

3.5.1 Quantum confinement effect in single layer quantum

dots structures 79

3.5.2 Study of nucleation process of single layer silicon

quantum dots in Nitrogen annealing atmosphere 84

3.5.3 Effects of forming gas annealing on single layer silicon

quantum dots structures 87

3.5.4 Oxidation of silicon quantum dots in Nitrogen annealing

environment 89

3.6 Summary 91

3.7 Bibliography 93

3.8 Publications 98

4 TIME RESOLVED PHOTOLUMINESCENCE EXPERIMENTS FOR

CHARACTERIZATION OF HOT CARRIER SOLAR CELL ABSORBERS

4.1 Introduction 100

4.2 Literature review 104

4.3 Probing ultrafast dynamic processes in semiconductors 110

4.3.1 Time resolved photoluminescence using up-conversion

technique 110

4.4 Comparison of hot carrier cooling gallium arsenide and

indium phosphide 114

4.4.1 Hot carriers cooling 115

4.4.2 Hot phonon effect in gallium arsenide and indium

phosphide 118

4.4.3 Inter-valley scattering of hot carriers in gallium arsenide

and indium phosphide 122

4.5 TRPL of hot carriers in indium nitride layers 124

xiii

4.5.1 Preliminary results on hot carriers cooling in wurtzite

indium nitride 124

4.6 Summary 129

4.7 Bibliography 131

4.8 Publications 137

5 DISCUSSION

5.1 Introduction 138

5.2 Correlation between important parameters of a hot carrier

solar cell 139

5.3 Considerations on energy selective contacts 142

5.3.1 Additional requirements for energy selective contacts

design 145

5.4 Considerations on absorber materials 147

5.4.1 Bulk semiconductors 147

5.4.2 Nanostructured semiconductors 149

5.5 Possible preliminary design of a hot carrier solar cell 150

5.6 Summary 152

5.7 Bibliography 153

6 CONCLUSIONS

Chapter 1

INTRODUCTION

Chapter 1: Introduction

1.1 Premise

Recent research studies have predicted that the world energy consumption

will increase by 49 percent (1.4 percent / year), from 145 trillion kilowatthours

in 2007, to 216 trillion kilowatthours in 2035 [1].

Figure 1.1.1 – World marketed energy consumption [1]. 1 kWh = 3.6 MJ.

The use of all energy sources is predicted to increase. The access to fossil

fuels, in particular liquid fuels and petroleum, will become more complicated

and expensive, thus the consumption of oil is predicted to grow at a very slow

rate. The growth in coal usage instead is determined by the fast developing rate

of China, which has an energy industry mostly based on coal fired power

plants.

A large increase in energy generation from renewable sources is expected to

meet the increment in energy demand in the next decades. Figure 1.1.2 shows

an increase in the projected renewable energy production from 3.46 trillion

kilowatthours in 2007 to 7.97 trillion kilowatthours in 2035. Currently

hydroelectric and wind energy represent the largest renewable sources,

accounting for 75 percent of renewable energy production [1]. A large growth

of wind and hydro is forecast for China and Canada, whereas other forms of

renewable energies are predicted to increase in other parts of the world.

1


Figure 1.1.2 – World electricity generation by fuel [1]. 1 kWh = 3.6 MJ.

In particular, between other renewables, solar energy is the fastest growing

energy industry. Solar photovoltaic energy demand has grown by an average 30

percent per annum over the past 20 years, thanks to the declining costs and

prices and to various governments funded innovative market incentives in

several key countries. This decrease in costs has been driven by economies of

manufacturing scale, manufacturing technology improvements, and the

increasing efficiency of solar cells [2].

In 2009, the photovoltaic solar industry generated $38.5 billion in revenues

globally, which includes the sale of solar modules and associated equipment,

and the installation of solar systems.

Figure 1.1.3 – Photovoltaics market size segmentation by application [2].

Despite the recent fast growth of the solar energy market, the cost / watt

figure of solar modules is still high compared to conventional energy sources

2


and other renewable energies, such as hydro and traditional biomass [4]. Figure

1.1.4 shows that wind, solar and geothermal energies were covering only 0.7

percent of total energy market share during 2008 [3, 4].

Figure 1.1.4 – Renewable energy share of global final energy consumption [4].

To allow an even wider spread of solar generated energy, photovoltaic

energy in particular, devices with higher efficiencies and lower production

costs have to be designed. The investigation of novel solar cells concepts,

which will allow higher efficiencies at lower prices, is the aim of current

research into “third generation photovoltaics”.

3


4

1.2 Photovoltaic devices

Photovoltaic (PV) devices convert radiant energy from the sun into electric

energy. Usually PV devices are referred as “solar cells”, and nowadays they

can be realized using different materials and configurations [3]. However, a

very large part of the solar cell market is based on crystalline silicon (c-Si)

solar cells [5]. These devices are designed as a large area p-n junction and their

structure is essentially a p-n diode. The first real silicon cell was realized

during 1950 and had a conversion efficiency of almost 6 percent [6].

Nowadays c-Si solar cells can reach laboratory efficiencies up to 25 percent

and large scale production efficiencies of up to 20 percent [7, 8].

Single junction solar cells can be realized using other materials such as

GaAs, InP, CdS, CuInSe2 and CdTe, in addition materials can be single

crystalline, multicrystalline or amorphous. In general solar cells based on

single crystal wafers, particularly silicon, are known as “first generation solar

cells”. These types of devices have relatively high production costs, due to the

high costs of the wafers.

The first approach that could be undertaken, to decrease the cost per watt

figure of solar cells, is to decrease the cost of the devices, using cheaper

deposition techniques and materials, as in thin film solar cells [5]. Thin film

solar cells do not involve the use of wafers. Devices are deposited on

inexpensive substrates, such as glass or polymers, starting from gas phase

precursors, like silane, in the case of silicon based cells. Thin film solar cells,

also known “second generation solar cells”, are not as expensive as first

generation solar cells, but in general are less efficient [9]. A very successful

example of a second generation solar cell is the CdTe cell manufactured by

First Solar, which is nowadays one of the major solar cell manufacturers in the

world [5].

Another approach that can be adopted to improve the cost per watt figure is

to increase the efficiency of the devices, keeping the costs below an acceptable

limit. In order to achieve better efficiencies solar cell losses have to be reduced

to a minimum, using techniques that are reasonably inexpensive.


5

The main sources of losses in conventional solar cells are due to inability of

collecting photons with energy below the bandgap, the very low conversion

efficiency of photons with energy above the bandgap (thermalisation losses),

the re-emission of photons by radiative recombination and losses related to

carrier recombination in different parts of the device [5, 10].

The interaction of these loss mechanisms gives rise to an intrinsic efficiency

limit for single junction solar cells. This limit is known as the Shockley-

Queisser limit and is around 28 percent for conventional c-Si solar cells [11],

for a 6000 K blackbody incoming radiation. The Shockley-Queisser limit is

very different from the thermodynamic limit for solar energy conversion, which

was first calculated by Landsberg to be above 90 percent [12]. Details on

efficiency limits will be discussed in the next chapter of this thesis.

The wide gap between the Landsberg limit and the single junction Shockley

Queisser limit indicates that there is a large amount of room for further

improvements of photovoltaic devices. Research in high efficiency

photovoltaics and “third generation photovoltaics” has the aim of engineering

solar cells with efficiencies higher than the Shockley Queisser limit, using

design solutions which are not bound to the single junction approach. Some of

these novel devices include tandem solar cells, quantum dot solar cells,

intermediate band solar cells, up-conversion and hot carrier solar cells (HCSC)

[13, 14]. These solar cell concepts are designed to minimize one or more of the

loss mechanisms mentioned in this section.

A third generation approach currently implemented in industry is based on

multiple junctions solar cells realised with III-V materials. These devices have

reached laboratory efficiencies of 41.1 percent [15, 16]. The main use of III-V

based multiple junction solar cells is, at present, limited to space applications

and solar farms for concentrated radiation due to the high costs of the materials

and realization process.


Figure 1.2.1 – Efficiency-cost trade-off for the three generations of solar cell technology,

wafers, thin films and advanced thin films (year 2003, U.S. dollars). Adapted from [17].

Figure 1.2.1 shows how the different categories of photovoltaic devices can

be located on an efficiency / costs chart. This graphic, published by Prof.

Martin Green during 2003, highlights the large room for improvement of solar

cells and the need of undertaking the challenge of implementing devices that

can overcome the Shockley Queisser limit, keeping realistic expenses below

first generation cells costs [17].

6


1.3 Hot carrier solar cells

The HCSC is a promising third generation photovoltaic device, first

theoretically investigated by Ross and Nozik during 1982 [18]. It has the aim

of achieving efficiencies well above the Shockley Queisser limit, converting

very efficiently photons with energies above the bandgap of the absorber

material.

Low wavelength photons, once absorbed, generate highly energetic electron-

hole (e-h) pairs; these are extracted before they are thermalised towards

respective band edges, losing their excess kinetic energy. The two basic

requirements necessary to accomplish extraction of high energy carriers are:

- The absorber material, which has to slow down the thermalisation of

carriers, by minimizing the carriers-phonons interactions.

- The energy selective contacts (ESCs), which have to allow extraction of

carriers only in a very narrow range of energies [18-20].

Figure 1.3.1 – Schematic diagram of a hot carrier solar cell [21].

Figure 1.3.1 shows a simplified schematic of a hot carrier solar cell. The

energy of electrons and holes above their respective band edges is carried as

kinetic energy. The interaction of carriers with phonons forces them to

thermalise towards band edges as shown in Figure 1.3.2. In general the energy

is lost by successive interactions with optical phonons.

7


Figure 1.3.2 – Schematic illustration of an electron-hole pair creation, following absorption

of a photon with energy 0. Energy relaxation follows via optical phonons emission ( ph).

Adapted from [22].

Once high energy photons are absorbed the energy is completely transferred

to the carriers. As the system advances towards equilibrium momentum and

energy relaxation occur via carrier-carrier scattering and carrier-optical phonon

scattering. Optical phonons decay into two or more multiple energy acoustic

phonons. The processes in which hot carriers in semiconductors are involved

after excitation are schematized in Figure 1.3.3 and time constants are

summarized in Table 1.3.1 [22].

Process Characteristic

time (s)

Carrier-carrier scattering 10-15 – 10-12

Intervalley scattering 10-14

Intravalley scattering ~ 10-13

Carrier-optical phonon thermalisation 10-12

Optical phonon-acoustic phonon interaction ~ 10-11

Carrier diffusion ~ 10-11

Auger recombination (carrier density 1020 cm-3) ~ 10-10

Radiative recombination 10-9

Lattice heat diffusion (1 m) ~ 10-8

Table 1.3.1 – Fundamental interaction processes in semiconductors [22].

If the interaction of optical and acoustic phonons is much slower than the

carrier to optical phonon interaction, large non-equilibrium optical phonon

populations can be generated, preventing energy relaxation of the hot carriers

(hot phonon re-absorption) [23, 24].

8


This characteristic can be found in some bulk and nanostructured materials.

Amongst bulk materials III-V and II-VI semiconductors systems appear to be

good candidates to implement hot carrier absorbers, due to their phononic

properties. In particular InN has also an optimum electronic bandgap to absorb

most of the solar spectrum, as will be discussed in the next chapter.

Although some bulk materials have shown slow carrier cooling, their hot

carriers thermalisation velocity appears to be still too fast for hot carrier

absorbers. The engineering of semiconductor nanostructures could allow even

fewer interactions between optical and acoustic phonons, and hence slower

thermalisation. In particular quantum dot superlattice systems can be designed

to have long phonon lifetimes [25].

Figure 1.3.3 – Diagram illustrating the energy flow in a photoexcited semiconductor [22].

Hot carriers can be converted efficiently only if extracted in a very narrow

range of energies. ESCs allow extraction of carriers in an optimal energy range.

Ideally this energy interval would be very narrow with a very high

conductivity. Carriers with energies above or below the extraction range need

to be reflected back into the absorber and re-normalize within the hot carriers

distribution.

The collection of carriers at the metal contact occurs with a small increase of

entropy, or is isoentropic for a discrete collection level [19].

9


Figure 1.3.4 – Simplified schematic of an electron energy selective contact.

Figure 1.3.4 shows a simplified schematic of an ideal electron ESC. The

selectivity and the conductivity of the device depend on the design and the

realization of the structure.

A possible method of implementing ESC structures is by using the resonant

tunnelling properties of a single layer of quantum dots in a dielectric matrix. Si

QDs in SiO2 matrix have shown theoretical and experimental evidence of being

suitable for selective energy extraction of carriers [19, 26]. However, obtaining

sufficient carrier extraction and energy selectivity using these structures is still

a challenging task, since it requires a very high uniformity of the Si QDs sizes

in the matrix [27, 28]. An investigation of properties of Si QDs in SiO2 is

presented in the third chapter of this thesis.

10


11

1.4 Aim and structure of this thesis

The main aim of this thesis is to investigate and study different aspects of

hot carrier solar cells. This is a novel third generation device that, despite its

structural simplicity, presents a series of unique scientific and technological

challenges.

In particular in this thesis several of the main aspects related to the

development of a hot carrier solar cell are addressed.

The thesis is divided into six main chapters. At the beginning of each

chapter a comprehensive review of the most important papers on the specific

topic is presented, at the end of every chapter a summary of the key results is

reported.

In chapter two the calculation of the main efficiency limits for solar energy

conversion is presented and discussed in detail, together with preliminary

calculations of hot carrier solar cells efficiency limits. The main body of the

chapter is dedicated to the presentation of a novel hybrid model for efficiency

calculation. This model takes into account, at the same time, physical aspects

that have been treated separately in previous models. In addition, the

calculation has been performed for a specific semiconductor, InN, taking into

account all the specific electronic and optical properties, in order to obtain

efficiency limits close to real values.

In chapter three the possibility of realizing energy selective contacts using

silicon quantum dots in a silicon dioxide matrix is evaluated. The structural and

optical characterization of silicon rich oxide layers is presented at the

beginning of the chapter. The remaining part is dedicated to the analysis of the

properties of a single layer of silicon quantum dots in silicon dioxide. In

particular the possibility of controlling quantum confinement properties of this

structure is demonstrated and effects of different annealing conditions and

regimes are investigated.


12

Chapter four is dedicated to the investigation of hot carriers relaxation

velocities in III-V semiconductors. In particular a comparison of time resolved

photoluminescence data for GaAs and InP is presented, in order to investigate

the hot phonon effect and intervalley scattering phenomena. In the second part

of the chapter hot carrier transients are studied for wurtzite InN. This allows

comparison of experimental data with theoretical results obtained in chapter

two.

Chapter five is the last main chapter of the thesis and is dedicated to a

comprehensive discussion of results obtained in the other sections of the thesis.

The main aim of this chapter is to analyse and bring into a common picture the

different aspects of the hot carrier solar cell and present further challenges

related to the development of a prototype device. This discussion leads to an

outline of the current state of research on hot carrier solar cells and highlights

the different areas and directions where future research should be focused.

In chapter six the conclusion from this thesis are presented.


13

1.5 Bibliography

1. U.S. department of Energy, International energy outlook. Washinton

DC. 2010. p. 338.

2. Solarbuzz, Marketbuzz. www.solarbuzz.com. 2010.

3. Ginley, D., M.A. Green, and R. Collins, Solar energy conversion toward

1 terawatt. Mrs Bulletin, 2008. 33(4): p. 355-364.

4. Renewable Energy Policy Network for the 21st Century, Renewables

2010 global status report. 2010. p. 80.

5. Green, M.A., Crystalline and thin-film silicon solar cells: state of the

art and future potential. Solar Energy, 2003. 74(3): p. 181-192.

6. Chapin, D.M., C.S. Fuller, and G.L. Pearson, A new silicon p-n junction

photocell for converting solar radiation into electrical power. Journal of

Applied Physics, 1954. 25(5): p. 676-677.

7. Shi, Z., S. Wenham, and J. Ji. Mass production of the innovative pluto

solar cell technology. in 34th Ieee Photovoltaic Specialists Conference.

2009.

8. Zhao, J., A. Wang, and M.A. Green, High-efficiency PERL and PERT

silicon solar cells on FZ and MCZ substrates. Solar energy materials

and solar cells, 2001. 65(1-4): p. 429-435.

9. Green, M.A., Consolidation of thin-film photovoltaic technology: The

coming decade of opportunity. Progress in Photovoltaics, 2006. 14(5): p.

383-392.

10. Hirst, L.C. and N.J. Ekins-Daukes, Fundamental losses in solar cells.

Progress in Photovoltaics: Research and Applications, 2010.

11. Shockley, W. and H.J. Queisser, Detailed balance limit of efficiency of

p-n junction solar cells. Journal of Applied Physics, 1961. 32(3): p. 510-

519.

12. Landsberg, P.T. and G. Tonge, Thermodynamic energy conversion

efficiencies. Journal of Applied Physics, 1980. 51(7): p. R1-R20.

13. Conibeer, G., et al., Silicon nanostructures for third generation

photovoltaic solar cells. Thin Solid Films, 2006. 511: p. 654-662.

http://www.solarbuzz.com


14

14. Cuadra, L., A. Marti, and A. Luque, Present status of intermediate band

solar cell research. Thin Solid Films, 2004. 451: p. 593-599.

15. Dimroth, F., High-efficiency solar cells from III-V compound

semiconductors. Physica Status Solidi C - Current Topics in Solid State

Physics, 2006. 3(3): p. 373-379.

16. Guter, W., et al., Current-matched triple-junction solar cell reaching

41.1% conversion efficiency under concentrated sunlight. Applied

Physics Letters, 2009. 94(22): p. 223504.

17. Green, M.A., Third generation photovoltaics: advanced solar

conversion. 2003: Springer-Verlav.

18. Ross, R.T. and A.J. Nozik, Efficiency of hot carrier solar energy

converters. Journal of Applied Physics, 1982. 53(5): p. 3813-3818.

19. Conibeer, G., C.W. Jiang, D. König, S.K. Shrestha, T. Walsh, and M.A.

Green, Selective energy contacts for hot carrier solar cells. Thin Solid

Films, 2008. 516(20): p. 6968-6973.

20. Conibeer, G., D. König, M.A. Green, and J.-F. Guillemoles, Slowing of

carrier cooling in hot carrier solar cells. Thin Solid Films, 2008.

516(20): p. 6948-6953.

21. Shrestha, S.K., P. Aliberti, and G. Conibeer, Energy selective contacts

for hot carrier solar cells. Solar energy materials and solar cells, 2010.

94(9): p. 1546-1550.

22. Othonos, A., Probing ultrafast carrier and phonon dynamics in

semiconductors. Journal of Applied Physics, 1998. 83(4): p. 1789-1830.

23. Pötz, W. and P. Kocevar, Electronic power transfer in pulsed laser

excitation of polar semiconductors. Physical Review B, 1983. 28(12): p.

7040-7047.

24. van Driel, H.M., X.Q. Zhou, W.W. Ruhle, J. Kuhl, and K. Ploog,

Photoluminescence from hot carriers in low temperature grown GaAs.

Applied Physics Letters, 1992. 60(18): p. 2246-2248.

25. Patterson, R., M. Kirkengen, B. Puthen Veettil, D. Konig, M.A. Green,

and G. Conibeer, Phonon lifetimes in model quantum dot superlattice

systems with applications to the hot carrier solar cell. Solar energy

materials and solar cells. 94(11): p. 1931-1935.


15

26. Jiang, C.W., M.A. Green, E.C. Cho, and G. Conibeer, Resonant

tunneling through defects in an insulator: Modeling and solar cell

applications. Journal of Applied Physics, 2004. 96(9): p. 5006-5012.

27. Aliberti, P., Y. Feng, Y. Takeda, S.K. Shrestha, M.A. Green, and G.J.

Conibeer, Investigation of theoretical efficiency limit of hot carrier

solar cells with bulk InN absorber. Journal of Applied Physics, 2010.

108(9): p. 094507-10.

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Dimyati, and J. Mayer, Resonant and phonon-assisted tunneling

transport through silicon quantum dots embedded in SiO2. Applied


Chapter 2

MODELLING EFFICIENCY LIMITS

FOR HOT CARRIER SOLAR CELLS

Chapter 2: Modeling Efficiency Limits of Hot Carrier Solar Cells

16

2.1 Introduction

The calculation of limiting efficiencies for solar convertors has been a topic

of research interest since the high potential of solar cells, as a source of

renewable energy, was discovered in the late fifties. The first consistent

theoretical approach for an efficiency limit calculation was developed by

Shockley and Queisser and was published during 1961 [1]. Previous work on

maximum efficiency calculation was based on experimental results and simple

theoretical models, limiting the validity of results to very particular conditions

[2-4]. These limits have been successively defined by Shockley as “semi-

empirical”, since they were not supported by a solid theoretical framework.

The Shockley-Queisser limit is currently still used in the photovoltaic

industry as reference for first generation, wafer-based, solar cells and is

considered to be one of the most important contributions to the photovoltaic

field. The efficiency limit calculated by Shockley and Queisser is also known

as “detailed balance limit”, because it is based on the balance of absorbed and

emitted photons assuming a planar geometry and blackbody radiation.

Improvements to the Shockley-Queisser formulation can be obtained by

associating a chemical potential to photons emitted by electron-hole

recombination according to the theory developed by P. Würfel and also

described by Green [5, 6].

The aim of current research in photovoltaics, beyond improving the

efficiency of wafer-based solar cells, is to engineer devices that are not bound

to the single junction configuration and thus can aim for efficiencies higher

than the detailed balance limit. In principle the efficiency limit for solar cells is

the thermodynamic limit, which is represented by the Carnot efficiency.

The thermodynamic limit has been accurately calculated by Landsberg,

considering a temperature of 6000 K for the sun and 300 K for the solar cell

and taking into account losses due to re-emitted energy and increased entropy

in the absorber [7]. The efficiency limit calculated by Landsberg is 93.3% and

drops to 85.4%, considering entropy increase due to extraction of useful

electrical energy through contacts [8].


17

The large difference between the thermodynamic efficiency limit and the

detailed balance limit leaves a wide margin for research in third generation

photovoltaics to overcome the Shockley-Queisser limit. The hot carries solar

cell (HCSC) is one of the most promising third generation concepts which aim

to reach efficiency limits close to the thermodynamic limit. The calculation of

limiting efficiency for HCSC has been a topic of research since the concept

was first investigated by Ross and Nozik [9]. In their work Ross and Nozik

assumed that the number of carriers extracted from the device is equal to the

difference between the incoming and the re-emitted number of photons. This

approach, called particle conservation (PC model), leads to efficiencies of 65%

for non-concentrated solar radiation and 85% for full concentration, assuming

the sun to be a blackbody at 6000 K and no carrier thermalisation. Würfel

calculated these efficiency values using a different approach and considering

Auger recombination (AR) and impact ionization (II) as predominant

phenomena in determining carrier distributions (AR-II model) [10]. Very fast

AR-II rates tend to keep carriers always in equilibrium driving the quasi-Fermi

level difference towards zero. For this model calculated efficiencies were of

85% for a 0 eV bandgap semiconductor at full solar concentration and no

thermalisation with the lattice. During 2005 Würfel et al. re-visited the

approach used by Ross and Nozik proving that the PC model was valid only in

particular conditions and could lead to “non-physical” solutions in some cases,

confirming that the effects of AR and II are definitely not negligible [11]. Both

PC and II-AR models have been revisited by Takeda et al. and researchers at

the ARC Centre of Excellence for Photovoltaics and Renewable Energy

Engineering [12-15]. The first two reports from Takeda et al. improved the

theoretical frameworks developed by Ross and Nozik and Würfel, including in

the model thermalisation effects for hot carriers and using a parabolic bands

approximation to represent the E-k relations for the absorber. Results of these

calculations have shown lower efficiency limits compared to previous reports,

and proved that the value of maximum efficiency is strictly related to the

thermalisation time. Despite the improvements in the theoretical description,

Takeda et al. confirmed that either the PC model or the AR-II model are only

valid in particular conditions. To overcome this problem and calculate


18

efficiencies close to real values, a new theoretical framework that includes the

effect of particle and energy conservation plus AR-II mechanism has been

developed and is described in this chapter. Using this model a maximum

efficiency value of 43.6% has been calculated considering bulk InN as absorber

material and a 5760 K blackbody as incoming radiation source and using a

reasonable estimate for attainable thermalisation rate [12].


2.2 Literature Review

2.2.1 Landsberg thermodynamic limit

Landsberg et al. calculated the thermodynamic efficiency limit for sunlight

energy conversion using a rigorous mathematical formalism during 1980 [7].

The efficiency limit has been calculated by considering entropies associated

with the exchanged energy fluxes and applying the second law of

thermodynamics. There are no other applied restrictions to the model, which

improves the Carnot description, being still based on pure thermodynamic

principles.

Figure 2.2.1 - Schematic diagram of energy converter in Landsberg model [7].

Figure 2.2.1 shows the energy and entropy fluxes considered by Landsberg

for the model. and represent the energy and entropy fluxes respectively

coming from the external environment into the convertor, associated with the

sun radiation.

pE pS

sE and sS are instead the outgoing energy and entropy fluxes

from the device; they can be represented as one or more couples of fluxes

depending on the energy and entropy sinks they are directed to. Q is the rate of

heat transfer to the surroundings at a temperature T. The energy and entropy

rates of change into the convertor are respectively and . E S gS is the entropy

generation rate into the convertor due to internal processes and is assumed to

have its minimum value at zero.

gsp

sp

STSTQSTST

WEQEE (2.2.1)

19


Equations (2.2.1) balance energy and entropy fluxes. Defining effective

temperature fluxes an overall balanced equation can be written following from

(2.2.1).

gFs

sFp

pj

jFj STW

TTE

TTESTEpsjS

ET 11;,...),( (2.2.2)

Considering for example the steady-state condition with no sinks

( ) the balance equation 0ss SESE (2.2.2) yields to the Carnot

efficiency.

FppWg

Fpp T

TE

WSTTTEW 1;1 (2.2.3)

The equality holds for the ideal limiting case where . 0gS

In general if the emission into a sink is also taken into account equation

(2.2.2) yields to:

p

s

FsFpW E

ETT

TT 11 (2.2.4)

Considering the conversion of blackbody radiation of temperature TR by a

converter at ambient temperature T, which emits blackbody radiation itself we

have:

4

3344

31

341

43;

34;

34;

34;;

RRW

RFpFsRpspps

TT

TT

TTTTTSTSTETE

(2.2.5)

The right-end side of equation (2.2.5) represents the ratio of available

energy of blackbody radiation, defined as the maximum amount of work that

can be provided, to its internal energy. This corresponds to an efficiency of

93.3% and represents the ultimate conversion limit for solar energy.

It has been stated that the Landsberg efficiency limit is not even correct in

principle due to entropy generation during light absorption [16]. These theories

however are based on reciprocity between light absorption and emission.

20


2.2.2 Shockley-Queisser approach

In the detailed balance approach Shockley and Queisser described the photon

flux emitted from the solar cell, due to radiative recombination, using equation

(2.2.7) and assuming a flat geometry [6, 8]. This is an approximation of the

generalized Planck formula, equation (2.2.6). The approximation is valid in

non-degenerated conditions, since the Bose-Einstein distribution is

approximately equivalent to Boltzmann-Maxwell distribution. is the

difference between electro-chemical potentials of electrons and holes and TC is

the carrier temperature, which is assumed to be in common for electrons and

holes. TC = 300 K in the Shockley-Queisser derivation. 22 d

3 2 / 1CgE kTE

Fh c e

(2.2.6)

/ /22C CkT kT

3 2g

E EF e e d

h c (2.2.7)

FE represents the number of emitted particles (photons) per unit area per unit

time (neglecting stimulated emission). In conventional solar cells the splitting

of electro-chemical potentials for electrons and holes is equal to the electric

potential difference neglecting contact losses, thus = q V.

If = 0 V equation (2.2.7) represents the radiative recombination rate at

equilibrium, F0.

/22CkT

0 3 2gE

F e dh c

(2.2.8)

The current density through the cell is the difference of the incoming photon

flux and the radiative recombination, multiplied for the elementary charge. CqkTV

A eFFqJ /0

(2.2.9)

22 A d/3 2 1Sg

A kTEF

h c e (2.2.10)

FA represents the number of incoming photons per unit area per unit time,

which is approximated with the blackbody radiation spectrum. A is the solid

angle subtended by the sun and is equal to the concentration ratio divided by

the maximum possible concentration ratio. TS = 5760 K is the temperature of

the black-body [17]. Solving the system of equations (2.2.6) - (2.2.10) the J-V

characteristics of the device can be calculated. The value of maximum 21


achievable efficiency can be derived as a function of the semiconductor

bandgap EG.

Figure 2.2.2 – Efficiency for a blackbody solar cell at TC = 300 K, with sun at TS = 6000 K,

as a function of the absorber material electronic bandgap EG for different values of the

parameter f, curve (a) f = 1, curve (b) f = 10-3, curve (c) f = 10-6, curve (d) f = 10-9, curve (e)

f = 10-12. f is a function of the solid angle subtended by the sun [1].

The detailed balance approach can be improved associating a chemical

potential with the emitted photon flux due to electron-hole radiative

recombination as proposed by Würfel et al. in 1982 [6]. This approach has been

investigated by Green et al. in 2003 [5]. In this case the emitted photon flux

will be a function of and cannot be approximated with (2.2.8) any longer,

but by the complete expression as in (2.2.6). This implies that the emitted

photon flux is a function of the electric potential across the device and

complicates the model slightly. The results obtained using this approach are not

far from the ones calculated by Shockley and Queisser, but the method can be

applied in a wider range of cell operating conditions.

2.2.3 Ross and Nozik approach for calculation of hot carrier

solar cell efficiency

In their paper published in 1982 Ross and Nozik theorized the concept of

HCSC calculating limiting efficiency with an approach similar to the detailed

balance [9]. In this case the carrier system has a temperature, TC, much higher

than the external environment and the solar converter TRT. Carriers are

extracted through ESCs. 22


The approach is based on balancing the incoming and outgoing number of

particles in the device, giving particle conservation (PC). The processes taken

into account are photon absorption, radiative recombination and carrier

extraction. Emitted and absorbed particle fluxes can be represented as in

equations (2.2.6) and (2.2.10), and the extracted current density can be

calculated as in (2.2.11).

A EJ q F F (2.2.11)

The voltage across the device is a function of the splitting of quasi-Fermi

levels, , and TC. Assuming that e-h pairs are extracted at energy E, the

entropy increase for carrier extraction as a low entropy monochromatic flux in

the external circuit is:

/ CS E T (2.2.12)

Thus the electric potential across the device can be calculated as follows:

1 RT RTRT

C C

T Tq V E T S ET T

(2.2.13)

The highest achievable conversion efficiency of extraction process for

thermal energy into work is the Landsberg efficiency, as described in Section

2.2.1. This can only be reached in case of a reversible process and hence at

zero work. The maximum generated work for carriers transferred to the

external circuit is:

1 RT RTCarnot

C C

TW q V E ET T

T (2.2.14)

To calculate V the value of E is replaced by the average energy of

incoming photon flux and photo-generated carriers respectively.

/A EE E E J (2.2.15)

3

/3 2

21Sg

AA kTE

dEh c e

(2.2.16)

3

3 2 /

21Cg

E kTE

dEh c e

(2.2.17)

Values of TC, and J can be calculated for any V, thus J-V characteristics

and device efficiency can be obtained for the PC model.

23


3

/3 20

21S

AMPP MPP kT

dJ Vh c e

(2.2.18)

Figure 2.2.3 – Efficiency of an ideal hot carrier converter at 1 sun as a function of absorber

material electronic bandgap EG for different carrier temperatures TC [9].

In Figure 2.2.3 the curve at 300 K corresponds to the detailed balance limit.

Increasing the temperature of extracted carrier values of efficiency up to 65%,

for one sun, incoming radiation are predicted by the PC model for the HCSC.

2.2.4 Auger recombination-impact ionization model

The PC model is only valid in particular conditions. In fact AR and II have a

significant effect on the performances of the HCSC.

The high carrier temperatures imply high rates of AR/II possibly comparable

with the radiative recombination rate. When II and AR are taken into account

then particle number is no longer conserved. Würfel calculated the HCSC

efficiency limit using a model entirely based on AR/II, assuming infinitely

short lifetimes for these two processes [10]. AR and II are processes which

tend to maintain the equilibrium of electro-chemical potentials for electrons

and for holes. Having very high AR/II rates tends to reduce the splitting of

quasi-Fermi levels. For ultrafast AR/II the value of is considered to be

always zero. Therefore, the energy flux of extracted carriers can be expressed

as a function of carrier temperature.

24


3 3

/ /3 2 3 2

2 21 1S Cg g

Aextract A E kT kTE E

d dE E Eh c e h c e

(2.2.19)

The extracted current density is the extracted power divided by the

extraction energy level. 3 3

/3 2 3 2

2 21 1S Cg g

extract AkT kTE E

qE q dJE E h c e h c e /

d (2.2.20)

The voltage can be expressed as extracted carrier energy flux multiplying

Carnot efficiency.

1 RT

C

TqV ET

(2.2.21)

Given the properties of incoming radiation and the value of absorber

material bandgap, the output power from the solar convertor can be calculated

as a function of carrier temperature. Therefore, the efficiency of the device is

obtained as a function of absorber material bandgap, EG.

Figure 2.2.4 - Efficiency of a hot carrier converter as a function of absorber material

electronic bandgap EG for (a) maximum concentrated, (b) unconcentrated AM0 radiation [10].

For this model the efficiency has no dependence on the hot carrier extraction

energy level. A higher extraction level increases the extraction voltage and

reduces the current at the same time due to increasing AR rate which tends to

promote carriers to high energy levels. The energy is conserved for every AR/II

event, thus only thermal energy is involved in the model, leading to a constant

Carnot efficiency.

25


2.2.5 Introduction of thermalisation time and absorber E-k

relation

Both the Ross and Nozik (PC) and Würfel (AR/II) models take into account

the absorber of the HCSC only considering the electronic bandgap EG.

Absorber physical and electronic properties are not considered. This simplifies

the mathematical analysis making the models completely general but not

sufficiently accurate.

During 2008 and 2009 Takeda et al. investigated both PC and AR/II models,

improving both theoretical frameworks, including effects of carrier

thermalisation time constant, TH, and relations between carrier density, nC, and

quasi-Fermi potentials, , considering parabolic E-k dispersion relations [13,

14].

The analysis from Takeda et al. follows the approach used by Ross and

Nozik introducing equations to model the loss of energy due to thermalisation.

TH

RE

Sg

S

eF

kTEFF

dee

chEJ

RTg

kTE

kT

A

)3)(1(~11

23~2 32

(2.2.22)

Equations (2.2.22) represent the conservation of energy. The thermalisation

time, TH, is the average time that hot carriers spend in the absorber before

relaxing towards band edges. The retention time, RE, is the average time that

hot carriers spend in the absorber before being extracted into the ESCs. The

thermalisation time is assumed to be the same for electrons and holes at any

carrier temperature.

13/2

32

8 2 / 2 1e

Cg

C

kTeEC g

nd

mn E eh

A REF

d (2.2.23)

Equations (2.2.23) are two separate ways to calculate the carrier density.

Either by relating to the retention time or to the quasi-Fermi electron potential,

26


e. A parabolic approximation for both conduction and valence bands has been

assumed.

Results of this model show that the efficiency of the final device is a strong

function of the thermalisation time, Figure 2.2.5. This is confirmed also by

results presented in the next section of this chapter, where it has been

demonstrated that the carrier relaxation can be completely described with an

exponential energy decay process, which is a function of the thermalisation

velocity, as shown in equation (2.3.6), thus is not necessary to include the

retention time as a parameter in the model.

Figure 2.2.5 - Conversion efficiency and optimal bandgap versus carrier thermalisation time

for 1000 suns concentration [13].

It can be noted that for shorter thermalisation times the optimum bandgap

rises. This is because the shorter TH results in significant thermalisation and

hence need to stop carriers losing too much energy before extraction. This

offsets the advantage for current of having a narrower band gap.

27


28

2.3 Modelling efficiency limit for a hot carrier

solar cell with an indium nitride absorber

In this section results on the efficiency modelling of a HCSC with a bulk

InN absorber are presented. A hybrid model has been implemented, which

allows a quantitative combination of particle and energy balance and influence

of AR and II. The detailed band structure of bulk wurtzite InN has been

considered in the calculation of carrier densities. Real data for II-AR time

constants and realistic values of thermalisation rates have been used to

calculate carrier energies. The model includes both thermodynamic and kinetic

equations in order to calculate the realistic conversion efficiency limit for an

InN based HCSC.

The main reason for selecting InN as absorber material is the combination of

electronic and phononic properties. It has a small electronic band gap (0.7 eV)

for better light absorption, at the same time it has a very wide gap between

acoustic and optical branches in the phonon dispersion characteristic, allowing

slower thermalisation of hot carriers by suppression of optical to acoustic

phonon decay via the specific Klemens’ decay processes [18-20].

2.3.1 Model assumptions

The HCSC has been treated as a system which can interact with the external

environment through exchange of particles and energy fluxes. Hot electrons

and holes are extracted to the external circuit through ESCs, which in this

model have been considered to be ideal, such that they have infinite

conductivity and a very narrow allowed energy range for transmission.

Different realization techniques for ESCs are currently under investigation. A

promising approach, for instance, is using silicon quantum dots in a SiO2

matrix as a double barrier resonant tunneling structure [21-23]. For the

absorber hot Fermi distributions are assumed, for electrons and holes due to

fast carrier-carrier scattering rate. A common temperature value for hot

electrons and holes has also been assumed [24]. These assumptions have also


been considered in other reports [11, 20]. Other authors consider holes to be

always close to the lattice temperature, due to their high effective mass, with

only electrons being at a higher non-equilibrium temperatures [25].

2.3.2 Modelling of J-V characteristics

Figure 2.3.1 – (a) Simplified diagram of a HCSC with indication of major parameters used for

modelling. Eg (absorber electronic bandgap), μe (electrons chemical potential), μh (holes

chemical potential), μ (μe + μh + Eg), E (extraction energy of hot carriers). (b) Schematic

representation of energy and particle fluxes interactions used in the model (particle fluxes -

full arrows, energy fluxes - dotted arrows).

Figure 2.3.1 (a) shows a simplified diagram of a HCSC with important

parameters used for modelling. Figure 2.3.1 (b) shows the energy and particle

fluxes involved in the device operation. The particle flux coming from the sun

can be approximated with a blackbody radiation spectrum as shown in equation

(2.2.10). The particle flux due to radiative recombination is described as in

(2.2.6).

e h gE (2.3.1)

29

In equation (2.3.1) μe and μh represent quasi-Fermi energies of electrons and

holes measured from the conduction and valence band edges, respectively. μ


is the quasi-Fermi level separation, which includes the bandgap Eg, as shown in

(2.3.1).

Particle fluxes due to AR and II are calculated using coefficients derived for

bulk InN. Details of the derivation are reported in the next section.

, , , ,IA abs II e h C abs AR e h CF d R T d R T (2.3.2)

FIA is the particle flux associated with AR and II events. This is directly

related to total AR-II rates (RAR, RII) and to the absorber thickness dabs. The

current density in steady state can be calculated by balancing incoming and

outgoing particle and energy fluxes.

A E IAJ e F F F (2.3.3)

The calculation of current density as a function of carrier temperature and

quasi-Fermi levels, according to (2.3.3), is completely general and allows

computation of extracted current for a given extraction voltage across the

device.

AR and II rates depend on the quasi-Fermi level separation. A net AR rate is

obtained for positive μ and a net II rate for negative μ.

The flux of energy due to incoming solar illumination ( A) is considered

together with the energy flux emitted by the cell due to emission of photons

( E) and the flux due to carrier thermalisation process ( TH). 3

/3 2

21Sg

AA kTE

dEh c e

(2.3.4)

3

3 2 /

21Cg

E kTE

dEh c e

(2.3.5)

' , ' , ' , ' ,e e C e e RT h h C h h RTTH e abs h abs

TH TH

T T TE n d n d

T (2.3.6)

The energy flux due to electrons and holes thermalisation losses is shown in

equation (2.3.6). TRT is room temperature (300 K), TH is the characteristic

thermalisation lifetime for hot carriers, ne and nh are the electron and hole

densities respectively, 'e and 'h are the average energy values for electron and

hole populations. The net thermalisation loss is a function of the carrier

temperature and quasi-Fermi potentials.

30


The average energy decays during thermalisation towards ’e (μe, TRT) and

’h (μh, TRT), which are close to the thermal energy value 3kTRT. The energy

reference levels are the corresponding band edges.

0

0

,'

,

e e e Ce

e e e C

D f T d

D f T d (2.3.7)

0

0

,'

,

h h h Ch

h h h C

D f T d

D f T d (2.3.8)

In equations (2.3.7) and (2.3.8) De( ) and Dh( ) represent the electron and

hole densities of states whilst fe and fh are the electron and hole occupancy

probabilities. The sub-picosecond carrier to carrier scattering rate justifies the

assumption of hot populations distributed according to Fermi-Dirac statistics

and hence fe and fh will depend exponentially on TC, Ee and Eh respectively.

Thus TH represents an exponential decay of hot carrier energy. However, the

consideration of non-equilibrium AR and II coefficients can modify

occupancies as discussed below. The product of the extracted current and the

extraction energy represents the “extracted energy flux” and can be calculated

balancing the three energy fluxes as in equation (2.3.9).

THEA EEEqEJ (2.3.9)

Here J is the extracted current as in (2.3.3) whilst E represents the

extraction energy of hot carriers from the absorber as shown in Figure 2.3.1.

This value is fixed and depends on the properties of the ESCs [22]. Even

assuming ideal ESCs, and hence isoentropic carrier transfer, the voltage of

carriers in the external circuit, V, must be lower than E/e. This is described

by a Carnot type relation between the voltage across the device and the

extraction energy [9].

1 1 RT RT

C C

T TV Ee T T

(2.3.10)

31


32

2.3.3 Carrier density calculation

To be able to calculate the J-V characteristic of the HCSC using the

equations described above, a relation between carrier density, electron and hole

quasi-Fermi levels and carrier temperatures for bulk wurtzite InN is necessary.

The carrier density can be calculated from the electron and hole densities of

states, which can be obtained from the dispersion relation.

E-k relations for high purity wurtzite InN have been calculated by Fritch et

al. using an empirical pseudopotential method [19]. Results of the calculations

illustrate that, in the energy range of interest for solar cells, wurtzite InN shows

two separated bands at the point plus a satellite band at the M-L symmetry

point, along the crystal direction for the conduction band. For the valence

band the calculation confirms two main bands with a point of degeneration at

, which can be identified as heavy and light hole bands, in addition a

separated split-off band is considered.

A multivalley approximation for the bulk InN band structure which takes

into account the three lowest conduction band minima ( 1, 3 and M-L) and

three hole valleys for the valence band has been used for calculations. The non-

parabolicity of InN main conduction band has also been considered. Parameters

for effective masses in satellite bands and non-parabolicity coefficients are

reported in Table 2.3.1 [19, 26].

Conduction Band Valence Band

1 3 M-L 1 (HH) 2 (LH) 3 (SO)

Effective mass m/m0 0.04 0.25 1 2.827 0.235 0.479

Non-parabolicity factor 1.43 0 0 0 0 0

Intervalley Energy Separation (eV) 0 1.77 2.71 0 0 0.25

Number of equivalent valleys 1 1 6 1 1 1

Table 2.3.1 - Model parameters for bulk indium nitride conduction and valence bands. Values

have been extracted from Fritch et al. [19].


2.3.4 Auger recombination and impact ionization coefficients

calculation

The influence of AR-II on the efficiency of the HCSC has been taken into

account amending the expression for the total current from the cell, as shown in

equation (2.3.3). Such a modelling approach allows consideration of II-AR

effects for all operating regimes of the HCSC. AR-II rates have been calculated

considering the three most probable processes for bulk InN, CCCH, CHHS,

CHHL, as reported by Dutta et al. [27], and neglecting high k-vector

mechanisms [28-30]. The phonon-assisted and trap-assisted AR-II processes

have been neglected because of the InN narrow electronic bandgap. The band

structure used for the II-AR rate computation is the same as for carrier density

calculations. The momentum conservation arises from the assumption of the

states as being the product of a plane wave and a Bloch function [27]. The

CCCH AR process involves three conduction band electrons and one hole. A

conduction band electron recombines with a hole, giving energy to a second

conduction band electron and raising it to a higher energy level. CCCH was

first investigated by Beattie et al [31]. 4

03 2

32 c CHCCCH

g

e mR Ih E

(2.3.11)

A simplification of the rate expression was formulated by Dutta et al. [27]

and is used in equation (2.3.11) with a technique developed by Sugimura [32].

The integral I can be evaluated according to (2.3.12). Definitions for functions

F and G can be found in [27], Z1 and Z2 are calculated as in (2.3.13).

1

2 21 2 1 2 1 2 1 2 00

, , 1 cA ZI dZ dZ F Z Z G Z Z Z Z J f 2' (2.3.12)

021 1 2 2' ; ' ;

1 2c

v

Z k Z km

' mk (2.3.13)

The CHHS AR process involves one electron, two heavy holes and a split-

off band hole. A conduction band electron recombines with a hole in the HH

band giving energy to another hole which can then move from the HH band to

the SH band. The rate for this process has also been investigated by Beattie et

33


al. and has been used in (2.3.14) with the same approach as for equations

(2.3.11) to (2.3.13).

1 1

40

3 2

12 2

1 2 1 1 10 1

32

1' ,1 2 / 1 2 /

c CH SHCHHS

g

cA Z

e mRh E

Z ZdZ dZ dtJ Lf Z F Z Z2

(2.3.14)

2 2 2 0 01 2 1

82 2 21 ; 12

c cS g S S ;

s

m mJ a Z Z E ah m

(2.3.15)

2 21 2 0

1 1 12 22 2 21

41; 124

cg

S S

h j mL A Z Za a hh j

E (2.3.16)

The function F is the same as in equation (2.3.12), SH and CH are due to the

modulating part of Bloch functions in the conduction band and have been

calculated numerically, ms is the effective mass of holes in the split-off band

for a particular value of energy E* [27].

* 0

0

22

v cg

v c s

m mE Em m m

(2.3.17)

The CHHL process is similar to CHHS but involves a hole from the HL band

instead of the SH band. Hence calculation of the AR rates for the two processes

is very similar. The AR rate for CHHL can be written as in equation (2.3.18).

2 1

4 1 2 201 2 2 1 1 2 13 2 0 1

32 ' 'c CH LHCHHL cA Z

g

e m2, 'R dZ dZ dtJ Lf k Z Z F k k

h E (2.3.18)

Expressions for Z1 and Z2 are as in (2.3.13) and formulae for computing

quantities in equation (2.3.18) are reported in (2.3.19) and (2.3.20). The value

of ml is the effective mass of holes in the split-off band for a particular energy

E**.

2 2 2 0 02 2 1

82 2 21 ; 1 ;2

c cL g L L

l

m mJ a Z Z E ah mL (2.3.19)

2 02 1 1 2

41 12

cg

L L

mA Z Za a

Eh

(2.3.20)

** 0

0

22

v cg

v c l

m mE Em m m

(2.3.21)

The overall AR rate can be calculated by adding the AR rates of different

processes. 34


AR CCCH CHHS CHHLR R R R (2.3.22)

II can be considered as the inverse process of AR. Highly energetic carriers

impact with carriers bound in the lattice, ionizing them and creating new

electron-hole pairs. The total II rate is the summation of II rates for different

mechanisms and is calculated from the total AR rate [27].

Bk TII ARR R e (2.3.23)

Thus for = 0 the II and AR rates are the same and cancel out, such that

particle number is conserved and both electron and hole populations can be

described by the same Fermi-temperature. If is positive the II rate is less

than that for AR. This is the case when carrier extraction is not immediate and

there is a build-up of generated carriers such as to create a positive chemical

potential, . There is therefore pressure to reduce the particle number and AR

processes dominate. On the other hand, if is negative then the II rate is

greater than that for AR, implying a faster carrier extraction compared to

generation. This will in turn suppress emission and drive the particle number to

increase through II.

2.3.5 Hot carrier solar cell efficiency calculation

As every flux mentioned in the previous sections is a function of and TC,

these two parameters can be calculated, together with current density J, solving

numerically equations (2.3.3), (2.3.9) and (2.3.10). The solar cell efficiencies

have been calculated as the ratio of extracted power at the MPP of operation

and the total power in the incoming spectrum, Pin. Pin is the sum of all the

photon energies, multiplied by their individual intensities, IA.

in

J VP

(2.3.24)

0in AP I d (2.3.25)

35


36

2.3.6 Variation of conversion efficiency with carriers

extraction energy

The system of equations reported in the previous sections can be solved

using numerical methods and assuming particular constraints for the operation

of the solar cell. The current density J can be calculated for a given voltage V

across the device terminals, fixing the absorber thickness and thermalisation

velocities. Results presented in this section have been calculated for no

concentration ( A = 6.8 × 10-5), the maximum concentration ratio ( A = 1) and

a concentration ratio of 1000 suns ( A = 0.068), the last of which appears to be

the upper limit for practical achievable concentration in solar cells [33]. An

absorber thickness dabs = 50 nm has been used, unless otherwise noted. A

thermalisation constant th = 100 ps has been adopted, as a reasonable

compromise between values recently reported in the literature [34-37]. In fact

the thermalisation velocity of hot carriers in InN is still under debate and

depends strongly on the quality of the films and deposition technique [34, 35].

Including the value of th in the kinetic equation (2.3.6) will certainly lead to an

efficiency limit lower than the thermodynamic limit discussed in previous

sections. The gap between the realistic efficiency limit and the thermodynamic

limit could be reduced if the carrier cooling velocity could be further reduced.

Figure 2.3.2 shows the dependence of the calculated efficiency on the

extraction energy E. For 1000 suns the efficiency curve reaches a peak value

of 0.436 for hot carrier extraction energy of 1.44 eV. Maximum efficiencies of

0.52 and 0.225 have been calculated respectively for full concentration and

non-concentrated spectra. For the maximum concentration case the dependence

on extraction energy is very flat. This is because, at these very high

illumination levels, thermalisation only plays a minor role compared to energy

flux associated with carrier generation. For the 1 sun and 1000 suns cases,

there is a broad optimum in extraction energy (at 1.47 eV and 1.45 eV

respectively) between not having it too low in order to maintain voltage, whilst

not having it too high such as to reduce current. This current limiting effect is

most marked when the extraction energy is higher than 1.62 eV, which is close

to the average energy of the incoming photon population. At the MPP, in order


to provide carriers to fill the gap denuded at the extraction energy, carriers are

forced to undergo AR. For these extraction energies the AR rate is larger than

the II rate, with a positive quasi-Fermi gap and a very low carrier temperature.

Figure 2.3.2 - HCSC efficiency as a function of carrier extraction energy level.

Thermalisation time is 100 ps, lattice temperature is 300 K. Absorber thickness is 50 nm.

2.3.7 Hot carrier solar cell operation analysis

In this section relations between main HCSC parameters and extraction

voltage are discussed, all the results presented here and in following sections

have been calculated considering a concentration ratio of 1000 suns, if not

otherwise stated. Figure 2.3.3 (a) shows J-V characteristics for the HCSC for

four different extraction energies. The value of VOC increases when the

extraction energy is increased according to equation (2.3.10). Under open

circuit conditions, as the carrier temperature TC is very high (1000 K), the VOC

is directly related to E. The short circuit current decreases monotonically as a

function of extraction energy due to the increase of AR events, which are

necessary to raise the carrier energies to the extraction level and hence drive

down μ.

37


38

Figure 2.3.3 - (a) J-V relations, (b) carriers temperature, (c) carriers densities, (d) quasi-

Fermi potentials separation, versus extraction voltage for different extraction energies.

The low voltage part of the relationships, Figure 2.3.3 (a) (dashed lines), has

been calculated considering unlimited II and AR rates. In fact, according to the

model, carrier temperatures at very low extraction voltages tend to be

extremely high, as shown in Figure 2.3.3 (b). Such high temperatures, and

hence high occupancy of high energy states, can enlarge II rates in order to

decrease carrier energies to the extraction level. In this regime the theoretical II

and AR rates, calculated as explained in the previous sections, are not exact,

since other multiple carrier generation mechanisms can be involved, preventing

further increase of carrier temperature. This allows TC to remain in a physically

acceptable range, and thus addresses the objection to the PC model discussed

by Würfel [11].

The value of 3000 K for carrier temperature has been used as the threshold

between current values calculated with the hybrid model presented here (TC <

3000 K) and values computed using the unlimited II/AR rates (TC > 3000 K)

[36]. This particular temperature value allows matching the two currents,


39

calculated with the two models, since the high II rate drives μ to very low

values, reducing carrier density and making thermalisation losses negligible.

Thus, the hybrid model at low voltages becomes similar to the II-AR model

[10, 38].

For an extraction energy of 1.6 eV the J-V curve of Figure 2.3.3 (a) shows

two possible stable steady states of operation at voltages close to the maximum

power point (MPP), which correspond to two possible solutions of the model.

For this particular value of E (bi-stable region) the device can work both in

AR regime and II regime, due to the interaction of AR and II processes with

carrier thermalisation. For the first solution (dotted line) the quasi-Fermi level

separation is positive, hence the AR rate is higher than the II rate, increasing

the average energy of the carrier distribution as shown in Figure 2.3.3 (d).

Although a fast thermalisation rate will offset this average energy increase. For

the second solution (continuous line) the quasi-Fermi level separation is

negative, hence the net II rate decreases the average carrier energy. This

decrease in energy appears similar to the carrier thermalisation process, but in

reality competes with it, as II also involves an increase in carrier number,

unlike thermalisation.

Figure 2.3.3 (b) shows that for higher extraction energy, the temperature of

carriers is low, 500 K for E = 1.8 eV at MPP. In this case the extraction

energy is higher than the average energy of absorbed photons and hence J

should be decreased, due to very significant AR (equation (2.3.3)), so that the

energy conservation represented by equation (2.3.9) stands. Although a net AR

rate is always present to increase the energy of carriers once, the role of even a

moderate thermalisation rate is enhanced in this regime and the carrier

temperature is reduced at all extraction voltages. II becomes negligible and

efficiency is basically related to the limitation of the AR rate, which depends

on the material dispersion relation. On the other hand for E < 1.62 eV the

MPP is in II regime. Here the carrier temperatures increase with extraction

energy and high values of temperature are observed at low extraction voltage

due to high II rate. Instead temperature drops with increasing voltage, reaching

acceptable values around MPP.


40

The quasi-Fermi level gap μ changes from large negative values, at low

voltages, to very small positive values, at open circuit conditions as shown in

Figure 2.3.3 (d). At low voltages radiative recombination is suppressed and

most of the photogenerated carriers are extracted from the device as current.

For such extraction voltages multiple electron-hole pair generation due to II is

dominant and AR is negligible. The high extraction current also keeps the

carrier density in the absorber low (1011 - 1012 cm-3), although extra carriers are

generated by II. With increasing voltage towards the VMPP, μ increases

towards small negative values, as shown in Figure 2.3.3 (c), contributing to the

increase in thermalisation losses. Higher carrier densities are reported when

voltage is increased because of the decrease in extraction current and despite

the increase in the emission due to the lower II rate, which also makes

thermalisation significant. At MPP carrier density values of 1016 cm-3 are

shown in Figure 2.3.3 (c) with carriers temperature below 1000 K for all

extraction energies considered, these being feasible values for an InN absorber

[35]. A very high carrier temperature has been found at low voltages for

extraction energies E < 1.62 eV, Figure 2.3.3 (b), with values reaching above

3000 K when approaching short circuit. In these conditions additional II

mechanisms will occur limiting the carrier temperature and the quasi-Fermi

level gap from reaching extremely high values, which are unphysical, as

explained in the previous section. This process acts as a self limiting

mechanism for carrier temperature, which is intrinsic in the nature of the

device and highlights the influence of II for cell operation [19]. After reaching

a minimum around the MPP, due to increased emission and thermalisation, the

carrier temperature increases again with voltage due to rapid increase of AR.

The fast increase of carrier temperature at low voltages is not observed at

higher extraction energies. For E = 1.8 eV the carrier temperature carries on

decreasing monotonically as the voltage approaches short circuit, reaching

values lower than the lattice temperature, TC < TRT. This condition, which

appears unphysical, is due to the fact that the extraction energy is too high

compared to the average energy distribution of incoming photons. As

previously discussed a very high AR rate is necessary to increase the average

carrier energy for extraction, suppressing temperature below TRT.


The absorber carrier density, Figure 2.3.3 (c), has a very strong influence on

cell performances, being strictly related to thermalisation losses, equation

(2.3.6). At open circuit, which is the starting operating condition of the solar

cell, a relatively high carrier density is calculated (nC 1017 cm-3) due to low

extraction. In this case the value of nC is mainly related to the incoming

particles flux, radiative emission and AR. On decreasing the extraction voltage,

the carrier density deceases to about 1016 cm-3 at VMPP. A further decrease of

the voltage causes an additional reduction of nC related to the temporary large

increase of carrier extraction rate. The carrier density drop is only partially

compensated by the increase of II rate, but this is only a second order effect.

On the other hand only a very moderate decrease of nC is observed for

extraction energy of 1.8 eV, which indicates a relatively faster stabilization of

nC in response to voltage variation.

2.3.8 Calculation of Auger recombination and impact

ionization rates

Total rates for AR and II as function of voltage have been calculated using

equation (2.3.23) and results are plotted in Figure 2.3.4 (a,b). AR and II

lifetimes are calculated dividing the carrier density by the rate [14].

;CAR II

AR II

n CnR R

(2.3.26)

Under open circuit conditions the lifetime for AR is shorter than the lifetime

for II. AR lifetime is slightly higher than the carrier thermalisation constant

(100 ps). This implies that the average energy increase due to AR is negligible

compared to thermalisation losses, hence the average kinetic energy of new

photogenerated carriers is dissipated by thermalisation. On decreasing the

voltage towards VMPP an increase in AR and II lifetimes is observed, together

with decreasing of thermalisation losses, Figure 2.3.5 (a). For further decrease

of the voltage AR and II rates show opposite trends due to the inversion of the

quasi-Fermi energy gap. In terms of device operation this means that AR is

negligible at low voltages and II plays the dominant role in determining the

carrier distribution properties ( E < 1.62 eV) and allows the temperature to be 41


contained whilst increasing the number of carriers available for extraction. For

extraction energy of 1.8 eV no inversion of μ is observed and the carrier

temperature drops monotonically towards the lattice temperature in the low

voltage regime.

Figure 2.3.4 - AR and II lifetimes versus extraction voltage for different extraction energies.

2.3.9 Thermalisation losses and efficiency versus

thermalisation time

Most of the conclusions reached by analysing AR and II rates match quite

well with results shown in Figure 2.3.5 (a), where the energy losses due to hot

carrier thermalisation are reported in units of eV per unit area per unit time.

42


Figure 2.3.5 - (a) Thermalisation losses versus extraction voltage for different extraction

energies. Thermalisation constant is 100 ps. (b) Calculated efficiency limit versus

thermalisation constant.

The quasi-exponential increase of thermalisation losses with extraction

voltage, given a constant TH, is mainly due to the increase in carrier density.

These results confirm that, even considering AR and II in the calculation, the

value of TH has still a major influence on the final device efficiency. Figure

2.3.5 (b) shows calculated efficiency as a function of the TH for different

extraction energies. For very fast thermalisation ( TH = 10-14 s) an efficiency of

22.3% is calculated. This value does not depend on E and is very close to the

Shockley-Queisser efficiency limit for bulk InN when AR is taken into account.

Increasing the value of TH, a splitting of the efficiency curves for different E

has been found. This is due to the complex interaction between carrier

43


thermalisation and the influence of AR and II. A monotonic fast increase of

efficiency is shown for all extraction energies when TH is between 0.1 ps and 1

μs. For TH = 10-10 s, which is the value used for all the calculations presented

in the previous sections, four different values of efficiency can be identified

along the black vertical line in Figure 2.3.5 (b). In this particular case TH is

closer to the AR and II lifetimes at the MPP. These are respectively AR = 4.5 ×

10-9 s and II = 3.21 × 10-7 s for E = 1.6 eV and V = 0.72 V. This implies that

AR/II processes begin to have enough time to supply carriers for extraction

before complete thermalisation. A further increase of TH leads to a significant

increase of efficiency until it reaches saturation at TH = 1 ms, = 73%. In this

region does not depend on E, indicating that the II-AR model can be applied

with a high accuracy. This result determines for the first time the region of

validity of the II-AR model, which was demonstrated to be valid only in

particular conditions by Takeda et al [14]. In general this region is

characterized by AR,II << TH, which implies that the carrier energy distribution

can be affected by AR and II before thermalisation, hence the extraction energy

does not play a major role when thermalisation processes are reasonably slow.

2.3.10 Efficiency computation with indium nitride

absorption coefficient

The results of the calculations shown in the previous sections of this report

assume ideal absorption properties, which imply that every incoming photon

with energy above the bandgap is absorbed and generates an electron-hole pair.

In this section, results of efficiency computation and J-V characteristics are

reported based on the actual bulk InN absorption coefficient. Real absorption

properties have also been used to modify the ingoing and outgoing particle

fluxes, FA and FE, according to the generalized Kirchhoff law for thermal

photon currents emitted by a non-black emitter [6]. 2

/3 2

2'1Sg

AA kTE

dF ah c e

(2.3.27) 2

3 2 /

2'1Cg

E kTE

dF ah c e

(2.3.28)

In equations (2.3.27) and (2.3.28) ( ) represents absorptivity as a function

of the energy for bulk wurtzite InN. Data for InN absorption coefficient can 44


be found in the literature and are plotted in Figure 2.3.6 together with the PL

signal and the approximation used in the calculation [39]. The value of

absorptivity can be calculated from the absorption coefficient according to

equation (2.3.29), where dabs is the InN layer thickness.

1 absda e (2.3.29)

In Figure 2.3.7 (a,b) the efficiencies of the HCSC for different thicknesses

of the absorber layer are shown. For all the extraction energies the efficiency

increases in the first region of the plot, dabs < 1000 nm, and decreases for a

thicker absorber. These opposing trends are due to the influence on efficiency

of the competitive interaction between thermalisation and absorption. On

increasing dabs a larger quantity of light is absorbed, thus more photo-generated

carriers are available for extraction, which results in an efficiency increase. At

the same time there is a net increase of losses due to hot carrier thermalisation,

as evidenced in equation (2.3.6). In reality, on increasing dabs there is also a net

decrease in carrier density, which would lead to smaller thermalisation losses,

but this is a second order effect. Instead, when thermalisation losses begin to

play a major role, the efficiency starts to drop. Such behaviour is more or less

pronounced depending on E. Figure 2.3.7 (b) shows that at higher extraction

energies the efficiency peak occurs at lower absorber thickness and in addition

the slope of the curve is more pronounced. This confirms that high

thermalisation losses cause a drop in the average carriers energy making

extraction more difficult and so requiring a higher AR rate for larger extraction

levels.

Figure 2.3.6 - Bulk InN absorption coefficient from [39] (dashed line) and approximation

used for calculation (solid line), (inset) InN photoluminescence signal.

45


The value of maximum efficiency is considerably lower when real

absorption properties are taken into account, Figure 2.3.7 (c), compared to the

case of ideal absorption, 0.436 and 0.322 respectively. This implies that to gain

both the increased absorption and reduced thermalisation a light trapping

technique has to be implemented on a thin absorber. Using an effective light

trapping scheme the effective light path in the absorber can be enlarged,

increasing absorption without changing physical thickness and allowing

thermalisation losses to remain moderate. Different techniques to implement

light multiple passes are currently implemented in conventional and thin film

solar cells and could potentially be transferred to HCSCs [40].

46

Figure 2.3.7 - (a) Efficiency limit versus extraction energy for different absorber thicknesses.

(b) Efficiency limits versus absorber thickness for different extraction energies. (c) J-V

relations for different absorber thicknesses. Thermalisation constant is 100 ps.


2.4 Efficiency limit calculation with non ideal

energy selective contacts

Results presented in Section 2.3 of this chapter are calculated assuming ideal

ESCs for the HCSC as explained in Section 2.3.1. This implies that the

extraction energy level for ESCs is discrete and there are no resistive losses in

the ESCs, thus there is no entropy increase during carrier extraction. In reality

there is an entropy increase during the carrier extraction process which limits

its efficiency to values lower than Carnot efficiency.

In this section results of efficiency limits calculated taking into account non-

ideal energy selective contacts will be presented. In particular ESCs with a

finite energy transmission window ( E) have been considered, taking into

account contact resistance and entropy generation effects. Figure 2.4.1 shows

carriers transmission probability for ideal and non-ideal ESCs as a function of

energy.

Figure 2.4.1 - Carriers transmission probability versus energy for (a) ideal ESC, (b) non-ideal

ESC.

2.4.1 Theoretical description of non-ideal energy selective

contacts

The flux of current travelling through the ESCs towards the cold metal

electrodes can be described using the following relation.

, ,, , , , 3min 0 0

( ) ( )z

C e h rt e h

y ze h e h T T V y z

y z

dk dkeJ T f f d dd d

(2.4.1)

47


The current density in this case is proportional to the occupation probability

at the two sides of the ESC. Figure 2.4.2 shows the simplified InN E-k

dispersion relation used for current calculation.

Figure 2.4.2 – Simplified diagram of InN E-k dispersion relation used for current density

calculation [41].

Equation (2.4.1) has been derived assuming no correlation of energy of

electrons in three different directions as shown in (2.4.2). This assumption is

acceptable if there is a parabolic dispersion relation at the minimum energy

point along the three different directions. In addition for this calculation ESCs

with a finite transmission energy window and a transmission probability equal

to 1, as in Figure 2.4.1 (x = 1) are considered.

zkykxkkzyx zyxzyx ; (2.4.2)

Based on the energy and carrier conservation, and TC at steady state are

calculated using equations similar to (2.3.3) and (2.3.9) as shown in (2.4.3).

0;0e

EEEEeJFFF J

THEAIAEA (2.4.3)

Parameters in (2.4.3) are the same as reported in Section 2.3.2.

2.4.2 Results of calculation of efficiency limit with non-ideal

energy selective contacts

In this section we report on results of calculation of limiting efficiency of

HCSC with an InN absorber using non-ideal ESCs modelled as described in the

previous section. Illumination conditions and physical parameters of the

absorber are same as in Section 2.3, apart from the fact that the ESCs

transmission energy window is not discrete but has a width E.

48


Figure 2.4.3 – (a) HCSC efficiency as a function of extraction width of ESCs for different

extraction energies E. (b) HCSC efficiency as a function of extraction energy E for

different ESCs energy width. Thermalisation time is 100 ps, lattice temperature is 300 K.

Absorber layer thickness is 50 nm.

The maximum efficiency has been found for a E between 1.15 eV and 1.2

eV with a transmission energy window E of 0.02 eV. The value of limiting

efficiency was 39.6% compared to 43.6% calculated in the previous section

using ideal ESCs. The drop of efficiency is mostly due to the decrease of open

circuit voltage related to the lower extraction level, equation (2.3.10). This is

partially compensated by an increase in extracted current due to increased II

rate.

49

Figure 2.4.3 (a) shows calculated efficiency as a function of E for several

values of extraction energy. In all the curves two different trends can be

identified. If the value of E is too close to zero, the efficiency is very low due

to low carriers extraction, thus a very small value of short circuit current. The

conductivity of the contact in this case is indefinitely large. Enlarging E the


50

number or carriers available for extraction increases, improving JSC and so the

efficiency. In general the efficiency peak has been found for values of E from

0.02 eV to 0.1 eV depending on the extraction energy E. For the

configurations which show higher efficiencies, E < 1.35 eV, the optimum

value of E goes from 0.02 eV to 0.05 eV. This result shows that the

transmission energy range has to be very small and confirms once again the

high selectivity requirements of ESCs for HCSC [22]. Recently Le Bris et al.

calculated efficiencies beyond the Shockley-Queisser limit using high pass

ESCs instead of band pass ESCs, but they used a simplified model considering

only PC conditions at full concentration [42]. In Figure 2.4.3 (b) the value of

maximum efficiency as a function of E is reported for different values of E.

It can be observed that for small transmission energy window the extraction

energy which allows maximum efficiency is lower compared to the one

calculated using ideal ESCs. This effect is related to the higher occupancy at

lower energies, which increases the value of JSC for contacts with a small

transmission window.

It has to be mentioned that a simpler configuration could be potentially used

for ESCs. This consists of a potential barrier at the contact with a height that

coincides with the peak of Boltzman distribution of the carriers at a specific

temperature. However, it has been found that such configuration introduces

additional losses limiting the excitation of low energy carrier to higher states,

thus further reducing the efficiency. This is also partially supported by results

in Figure 2.4.3, which shows a marked decrease in efficiency when the

transmission energy width of the contacts exceeds a certain threshold.


51

2.5 Summary

The calculation of efficiency limits for solar converters has been the topic of

research since the very first discovery of photovoltaic effect. Different

theoretical models have been proposed to calculate thermodynamics maximum

conversion efficiency limits of semiconductor based solar converters. The most

important theoretical works are reviewed in the first section of this chapter,

where the famous Shockley-Queisser limit is also derived. The gap between the

detailed-balance approach and the thermodynamic conversion limits justifies

recent research efforts in calculation of efficiency limits for third generation

devices.

The calculation of limiting efficiency of HCSC has been attempted since the

concept was first developed by Ross and Nozik. Several models have been

proposed over the last few years. Many of them improved significantly the

original theoretical framework, although including many assumptions and not

taking into account very important physical phenomena for semiconductors

such as AR and II. Also no significant effort was invested in specifying

properties of the material to achieve efficiency limits close to a real device.

To improve HCSC theoretical characterization, in this chapter, achievable

efficiencies for HCSC have been calculated using bulk wurtzite InN as

absorber layer. A hybrid model, which takes into account both particle balance

and energy balance, has been implemented and adopted for calculations. The

model also considers influence of real AR and II rates on cell performances for

the first time. In addition actual thermalisation losses are included. AR-II rates

have been calculated including the most important three-carrier interaction

mechanisms which can occur in InN, at energies of interest for solar

applications.

The real InN dispersion relation has been reconstructed using actual

effective masses for different bands and non-parabolicity coefficients. The

limiting efficiency as a function of carrier extraction energy has been studied

for a fixed absorber thickness and thermalisation constant. A maximum

efficiency of 0.436 has been found for 1000 suns solar concentration and


52

energy extraction level of 1.44 eV, assuming a thermalisation constant of 100

ps. An efficiency of 0.52 was found for full solar concentration. Current-

voltage relationships have been calculated for different extraction energies. In

addition the influence of thermalisation constant on maximum efficiency has

been investigated, showing a very close correlation between hot carriers

cooling velocity and HCSC performances. The influence of real InN absorption

properties has also been studied, proving that a light trapping scheme is

important to achieve sensible efficiency improvements in HCSCs.

In the last section of the chapter the influence of having non-ideal ESCs on

the HCSC performances is studied. It has been found that to maintain high

efficiency, 39.6%, the width of the contacts has to be about 20 meV. This result

narrows the range of material systems and fabrication techniques available to

realize suitable ESCs.

In summary, when a real material is considered for performances calculation

of HCSC, values of efficiency limits can be considerably different as compared

to ideal absorbers and ESCs. This implies that the gain in efficiency which can

be achieved using bulk materials as absorbers in HCSCs is limited, due to

phononic properties. The thermalisation constant used (100 ps) is thought to be

a good approximation, but could be different for specific high quality

materials, as it depends on the exact suppression of phonon decay mechanisms

in the sample. Nevertheless, the fact that an efficiency of 0.436 can be obtained

with a bulk absorber encourages investigators to perform additional research on

phononic properties of different materials. In particular, engineering the

phononic bandgap of nanostructured semiconductors can allow slowing down

carrier cooling further in order to achieve more significant efficiency gains.


53

2.6 Bibliography

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p-n junction solar cells. Journal of Applied Physics, 1961. 32(3): p. 510-

519.

2. Lannoo, M., C. Delerue, and G. Allan, Theory of radiative and

nonradiative transitions for semiconductor nanocrystals. Journal of

Luminescence, 1996. 70(1-6): p. 170-184.

3. Loferski, J.J., Theoretical considerations governing the choice of the

optimum semiconductor for photovoltaic solar energy conversion.

Journal of Applied Physics, 1956. 27(7): p. 777-784.

4. Pfann, W.G. and W. Vanroosbroeck, Radioactive and photoelectric p-n

junction sources. Journal of Applied Physics, 1954. 25(11): p. 1422-

1434.



6. Wurfel, P., The chemical potential of radiation. Journal of Physics C-

Solid State Physics, 1982. 15(18): p. 3967-3985.

7. Landsberg, P.T. and G. Tonge, Thermodynamic energy conversion

efficiencies. Journal of Applied Physics, 1980. 51(7): p. R1-R20.

8. Plank, M., The theory of heat radiation. 1959, New York: Dover.

9. Ross, R.T. and A.J. Nozik, Efficiency of hot carrier solar energy

converters. Journal of Applied Physics, 1982. 53(5): p. 3813-3818.

10. Wurfel, P., Solar Energy conversion with hot electrons from impact

ionisation. Solar energy materials and solar cells, 1997. 46: p. 43-52.

11. Wurfel, P., A.S. Brown, T.E. Humphrey, and M.A. Green, Particle

conservation in the hot-carrier solar cell. Progress in Photovoltaics,

2005. 13(4): p. 277-285.




108(9): p. 094507-10.


54

13. Takeda, Y., T. Ito, T. Motohiro, D. König, S.K. Shrestha, and G.

Conibeer, Hot carrier solar cells operating under practical conditions.


14. Takeda, Y., T. Ito, R. Suzuki, T. Motohiro, S.K. Shrestha, and G.

Conibeer, Impact ionization and Auger recombination at high carrier

temperature. Solar energy materials and solar cells, 2009. 93(6-7): p.

797-802.

15. Takeda, Y. and T. Motohiro, Requisites to realize high conversion

efficiency of solar cells utilizing carrier multiplication. Solar energy

materials and solar cells, 2010. 94(8): p. 1399-1405.

16. Devos, A. and H. Pauwels, Comment on a thermodynamical paradox

presented by P. Wurfel. Journal of Physics C-Solid State Physics, 1983.

16(36): p. 6897-6909.

17. Wurfel, P., Physics of Solar Cells. 2005, Weinheim: Wiley - VCH.

18. Davydov, V.Y., V.V. Emtsev, I.N. Goncharuk, A.N. Smirnov, V.D.

Petrikov, V.V. Mamutin, V.A. Vekshin, S.V. Ivanov, M.B. Smirnov, and

T. Inushima, Experimental and theoretical studies of phonons in

hexagonal InN. Applied Physics Letters, 1999. 75(21): p. 3297-3299.

19. Fritsch, D., H. Schmidt, and M. Grundmann, Band dispersion relations

of zinc-blende and wurtzite InN. Physical Review B, 2004. 69(16): p.

165204.

20. Luque, A. and A. Marti, Electron-phonon energy transfer in hot-carrier

solar cells. Solar energy materials and solar cells, 2010. 94(2): p. 287-

296.

21. Aliberti, P., S.K. Shrestha, R. Teuscher, B. Zhang, M.A. Green, and G.J.

Conibeer, Study of silicon quantum dots in a SiO2 matrix for energy

selective contacts applications. Solar energy materials and solar cells,

2010. 94(11): p. 1936-1941.



Films, 2008. 516(20): p. 6968-6973.


55



94(9): p. 1546-1550.



25. Shah, J., C. Lin, R.F. Leheny, and A.E. Digiovanni, Pump wavelenght

dependence of hot-electron temperature in GaAs. Solid State

Communications, 1976. 18(4): p. 487-489.

26. Fu, S.P. and Y.F. Chen, Effective mass of InN epilayers. Applied Physics

Letters, 2004. 85(9): p. 1523-1525.

27. Dutta, N.K. and R.J. Nelson, The case for Auger recombination in In1-

xGaxAsyP1-y. Journal of Applied Physics, 1982. 53(1): p. 74-92.

28. Cao, J.C. and X.L. Lei, Investigation of impact ionization using the

balance-equation approach for multivalley nonparabolic

semiconductors. Solid-State Electronics, 1998. 42(3): p. 419-423.

29. Lyon, S.A., Spectroscopy of hot carriers in semiconductors. Journal of

Luminescence, 1986. 35(3): p. 121-154.

30. Wilson, S.P., S. Brandt, A.R. Beattie, and R.A. Abram, Use of realistic

band structure in impact ionization calculations for wide bandgap

semiconductors: thresholds and anti-thresholds in indium phosphide.

Semiconductor Science and Technology, 1993. 8(8): p. 1546-1556.

31. Beattie, A.R. and P.T. Landsberg, Auger effects in semiconductors.

Proceedings of the Royal Society of London Series a-Mathematical and

Physical Sciences, 1959. 249(1256): p. 16-29.

32. Sugimura, A., Band-to-band Auger effect in GaSb and InAs lasers.


33. Yamaguchi, M. and A. Luque, High efficiency and high concentration in

photovoltaics. Electron Devices, IEEE Transactions on, 1999. 46(10): p.

2139-2144.

34. Chen, F., A.N. Cartwright, H. Lu, and W.J. Schaff, Ultrafast carrier

dynamics in InN epilayers. Journal of Crystal Growth, 2004. 269(1): p.

10-14.


56

35. Jang, D.J., G.T. Lin, C.L. Wu, C.L. Hsiao, L.W. Tu, and M.E. Lee,

Energy relaxation of InN thin films. Applied Physics Letters, 2007.

91(9): p. 092108.

36. Wen, Y.C., C.Y. Chen, C.H. Shen, S. Gwo, and C.K. Sun, Ultrafast

carrier thermalization in InN. Applied Physics Letters, 2006. 89(23): p.

232114.

37. Yang, M.D., Y.P. Chen, G.W. Shu, J.L. Shen, S.C. Hung, G.C. Chi, T.Y.

Lin, Y.C. Lee, C.T. Chen, and C.H. Ko, Hot carrier photoluminescence

in InN epilayers. Applied Physics a-Materials Science & Processing,

2008. 90(1): p. 123-127.

38. Spirkl, W. and H. Ries, Luminescence and efficiency of an ideal

photovoltaic cell with charge carrier multiplication. Physical Review B,

1995. 52(15): p. 11319-11325.

39. Wu, J., W. Walukiewicz, K.M. Yu, J.W. Ager, E.E. Haller, H. Lu, W.J.

Schaff, Y. Saito, and Y. Nanishi, Unusual properties of the fundamental

band gap of InN. Applied Physics Letters, 2002. 80(21): p. 3967-3969.

40. Wenham, S.R. and M.A. Green, Silicon solar cells. Progress in

Photovoltaics, 1996. 4(1): p. 3-33.

41. Jenkins, D., Properties of group III nitrides. EMIS Data Reviews, ed. J.

Edgar. 1994.

42. Le Bris, A. and J.F. Guillemoles, Hot carrier solar cells: Achievable

efficiency accounting for heat losses in the absorber and through

contacts. Applied Physics Letters, 2010. 97(11): p. 113506.


57

2.7 Publications P. Aliberti, Y. Feng, Y. Takeda, S.K. Shrestha, M.A. Green, G.J. Conibeer,

“Investigation of theoretical efficiency limit of hot carrier solar cells with bulk

InN absorber”, Journal of applied physics, Volume: 108, Pages: 094507(10),

2010.

P. Aliberti, Y. Feng, R.Clady, M.J.Y. Tayebjee, T.W. Schmidt, S.K.

Shrestha, M.A. Green, G.J. Conibeer, “On efficiency of hot carriers solar cells

with a indium nitride absorber layer”, Oral Presentation, Proceedings of

European photovoltaic conference, Valencia, Spain, 6-10 September 2010.

Y. Takeda, T. Motohiro, D. König, P. Aliberti, Y. Feng, S. Shrestha, G.J.

Conibeer, “Practical factors lowering conversion efficiency of hot carrier solar

cells”, Applied physics express, Volume: 3, Pages: 104301(3), 2010.

G. Conibeer, R. Patterson, P. Aliberti, L. Huang, J.-F. Guillemoles, D.

König, S. Shrestha, R. Clady, M. Tayebjee, T. Schmidt and M.A. Green, “Hot

Carrier Solar Cell Absorbers”, Proceedings of 24th European Photovoltaic

Solar Energy Conference, Hamburg, Germany, 21-25 September 2009.

Chapter 3

REALIZATION AND CHARACTERIZATION OF SINGLE

LAYER SILICON QUANTUM DOTS IN SILICON

DIOXIDE STRUCTURES FOR ENERGY SELECTIVE

CONTACTS APPLICATIONS

Chapter 3: Silicon Quantum Dots in SiO2 for Energy Selective Contacts Applications

58

3.1 Introduction

Energy selective contacts (ESCs) are a crucial element for the operation of

hot carrier solar cells (HCSCs). The presence of two membranes which can

selectively filter carriers to external circuit was first considered by P. Würfel

[1]. Theoretical and experimental work has been developed, particularly at the

University of New South Wales, in order to understand requirements for ESCs

and investigate suitable material systems and structures for realization and

integration with absorber layers [2-4].

As discussed in Chapter 2 the main role of ESCs is to allow carriers to be

transmitted from the absorber to the “cold” metal electrodes only within a

certain range of energies. Carriers which have different energies are reflected

back into the absorber where they can re-normalize within the hot carriers

distribution [5]. Ideally a discrete transmission level would give the best

efficiency, but in reality if the transmissions energy window is very narrow,

carriers extraction is insufficient to achieve reasonable currents. However, to

achieve high efficiencies very thin transmission windows are mandatory.

A clear indication of energy selectivity is the negative differential resistance

(NDR) behaviour in the current-voltage characteristics of the device. NDR has

been observed in III-V structures used in resonant tunnelling diodes

applications. Quantum wells (QWs) structures realized with a thin layer of

GaAs between two AlGaAs barriers show optimal resonant tunnelling

properties [6].

In this chapter the possibility of realizing ESCs structures using quantum

confined nanostructures based on Si-SiO2 system is investigated. In particular

properties of a single layer of Si quantum dots (QDs) in SiO2 will be studied

[4, 7]. ESCs devices based on Si nanostructures have two main advantages.

First, the relatively simple realization process, given that UNSW has a well

developed Si technology and experience with Si-SiO2 material system. Second,

the real possibility of integration with a nanostructured absorber based on the

same Si-SiO2 superlattices [8, 9]. In addition, QDs allow better hot carrier

selectivity compared to QWs due to confinement properties in three dimensions

[3].


59

A great research effort on Si nanoparticles in SiO2 has been observed since

the discovery of emission of visible light in nanocrystals and porous materials

[10, 11]. Results relevant to this work are reviewed and summarized in Section

3.2. Many of these studies have been performed in order to explain physical

mechanisms which cause light emission from nanoparticles, although they are

still subject of scientific debate [12-15].

In this study single layer Si QDs in SiO2 structures have been realized using

RF magnetron co-sputtering technique and thermal annealing of SiO2/SRO

(silicon rich oxide)/SiO2 structures. Details of processing and typical

deposition parameters are presented in Section 3.3. During the high

temperature annealing the excess Si in the SRO layer (SiOx, X < 2) segregates

to form Si nanoparticles. Physical, optical and structural properties of SRO

layers have been investigated extensively and results are presented in Section

3.4. Results of investigation on single layer Si QDs in SiO2 are also presented.

Quantum confined properties of these structures are discussed in Section 3.5

together with the study of nucleation process in annealing atmosphere. In

addition, in Section 3.5.3, effects of forming gas (FG) annealing on the PL

properties of single layer QDs structures are discussed in order to clarify on

light emission mechanisms and role of interface defects and dangling bonds.


3.2 Literature review

Structures containing Si nanocrystals in SiO2 matrix are interest of research

since 1993, when visible PL was first discovered by Kanemitsu et al. [11]. In

this paper the authors proposed a theoretical model to explain the emission

process. In this model excitons are confined on a spherical shell, an interfacial

layer between the c-Si core and the a-SiO2 surface layer is considered. Data

show a constant PL peak at 1.65 eV independent of the size of the crystalline Si

core, in contrast to evidences reported in subsequent research work.

In 1994 Wang et al. developed a new method for calculation of the

electronic structure of Si QDs with more than 1000 atoms. The model allowed

calculation of eigenstates within a desired “energy window” with a linear-in-N

scaling instead of the N3, making the entire computation feasible [16]. Results

of this work are shown in Figure 3.2.1. These results are still considered as a

reference for the emission energy of Si QDs in SiO2.

Figure 3.2.1 – HOMO (highest occupied molecular orbital) – LUMO (lowest occupied

molecular orbital) band gap vs effective size for three prototype quantum dots shapes. The

symbols , + and stand for spheres, rectangular boxes and cubic boxes, respectively [16].

The experimental approach used to realize devices described in this chapter

was first implemented by M.Zacharias et al. [15, 17]. In this work structures

were deposited in a multilayer SRO/SiO2 configuration using reactive

evaporation of SiO powders in oxygen atmosphere. Evidence of Si QDs

confined between SiO2 barriers were observed by a comprehensive TEM study

of the multilayered structure. The blue-shift of the PL energy with the

decreasing size of the QDs was also demonstrated. 60


During the same period several other reports on the investigation of different

aspects of self nucleation of Si QDs in thick SRO layer were published. Iacona

et al. reported nucleation of Si QDs in SRO layers prepared by PECVD [18]. A

red shift of the PL energy was observed with increase in Si concentration in the

SRO films as well as with increasing the annealing temperature. Using these

results the authors proposed two different models for QDs nucleation in a

dielectric matrix. The investigation of nanoparticles sizes in this work was

realized using TEM images. These were taken at a relatively low magnification

and lead to nanoparticles sizes from 0.7 nm to 2.1 nm. However, these results

do not seem very reliable, as conventional TEM is not an appropriate technique

for Si QDs sizes investigation due to poor contrast between Si and SiO2.

A comprehensive study of the correlation between average size and density

and PL of Si QDs in SiO2 was published at the end of 2001 Garrido et al. [19].

In this paper an effective method for imaging Si nanocrystal in SiO2 matrices

was applied to a series of samples. Images were taken using a high resolution

TEM in conjunction with conventional TEM in dark field conditions. SRO

layers of roughly 800 nm were realized implanting Si in thermally grown SiO2

layers. Si excess in the films was changed by varying the implantation dose.

Efficient HR-TEM images were taken on samples with Si excess from 10% to

30%. No consistent data were presented for lower excess due to low contrast.

Cross correlation of TEM images and PL data allow to infer on the nucleation

process of the QDs.

Figure 3.2.2 - Simulated size distributions superimposed on the TEM stack histograms. (a)

SRO 10% Si excess annealed 1100 °C for 8 hrs, (b) SRO 20% Si excess annealed at 1100 °C

for 16 hrs [19].

61


62

Figure 3.2.2 shows the simulated size for Si QDs superimposed with

histograms obtained with TEM. The uncertainty in size in the TEM

measurements is due to proximity effects. In this work is also concluded that

the nucleation process of the nanoparticles occurs during the first minutes of

annealing and the remaining evolution is a conservative asymptotic Ostwald

ripening process. However results obtained from PL measurements on films

realized by ion implantation have to be carefully evaluated, since it has been

claimed that there is always a strong contribution to the PL signal from

interface (Si-SiO2) defects [39]. Shimizu-Iwayama et al. published a report in

2001 analysing PL of Si implanted thermal oxide films [20]. They found that,

despite a red-shift of the PL with an increasing Si excess, the peak energy

returned to its original (as-deposited) position (1.6 eV) after re-annealing the

film. This was attributed to cluster-cluster interaction or to the roughness of the

interfaces.

A fast increase in the number of papers has been observed during 2007,

when several reports on both optical [21-25] and electrical [26-28]

characterization of Si QDs in SiO2 were published. Majority of this work was

based on thick SRO layers but not on superlattice structures. The debate

regarding the nature of the bandgap of Si QDs is still open together with the

discussion on the mismatch between theoretical and experimental luminescence

wavelengths.

Meier et al. used time resolved PL (TRPL) to evaluate the dependence of the

oscillator strength from the nanoparticles size [22]. Applying a theoretical

model to absorption and PL data, they claim an indirect bandgap for Si QDs in

SiO2. It is relevant to highlight that this conclusion is reached assuming a

direct bandgap, similar to c-Si, for single nanoparticles. Sias et al. have

demonstrated, using forming gas annealing experiments, that the emission peak

at 780 nm, sometimes present in the PL signal, has its origin in radiative

interfacial states [24]. Effects of a pre rapid thermal annealing step on this PL

peak are reported by Iwayama et al. [21]. A very interesting report on QDs

nucleation was given by Yu et al. [25]. Here the nanocrystals nucleation

mechanism is examined using a combination of quantum mechanical and Monte

Carlo (MC) simulations. A major outcome of this work is that the formation of


Si nanoparticles is primarily controlled by oxygen diffusion rather than excess

Si diffusion and agglomeration, as stated in previous reports.

Figure 3.2.3 - Series of snapshots from KMC simulations of phase separation in Si

suboxide with the initial Si supersaturation of (a) 10%, (b) 20%, (c) 30% at 1100 C. Only Si

atoms are displayed, box is a cube with 8.1 nm side [25].

Figure 3.2.3 shows snapshots from MC simulation of the annealing process

for three SRO samples with different Si excess. It is very interesting to note

how, in low Si excess films, clusters nucleate with high size uniformity.

Whereas for higher silicon excess, despite bigger clusters are obtained for the

same annealing time, the uniformity seems to be poorer. In particular QDs can

grow above the critical radius for quantum confinement. Such large

nanoparticles do not contribute to the PL emission. In general during the

formation of these large clusters smaller QDs are also formed. These are quite

stable and do contribute to the high energy PL emission. The experimental

proof of this theory will be presented and further analysed in Section 3.4.

Recently it has been demonstrated that electronic structures based on silicon

QDs can be realized using colloidal dispersion techniques. This approach is

very promising for the development of silicon based organic light emitting

devices and innovative types of solar cells [29, 30]. Ordered arrays of QDs

grown by colloidal dispersion techniques are also very attractive for realization

of HCSCs absorbers and ESCs. 63


64

3.3 Realisation of single layer silicon quantum

dots structure

The single layer Si QDs in SiO2 structure has been realized depositing a

SRO layer and a SiO2 layer, on Si crystalline wafers and quartz substrates, by

RF magnetron co-sputtering. A thin thermal oxide layer was grown on Si wafer

before sputtering, using dry oxidation. The structure was then annealed at

temperature up to 1100 °C to allow nanoparticles formation. Structures

deposited on quartz were used for optical characterization. Aluminium layers

were deposited (by evaporation) on structures deposited on wafers, both on

back and front surfaces, for electrical measurements.

3.3.1 Initial substrate preparation

Quartz and highly doped Si wafer (0.1 – 1.0 /cm) have been used as

substrates. They were chemically cleaned before thin film deposition using

RCA1 and RCA2 process for 5 minutes [31]. Subsequently Si wafer was

immersed in a Hydrofluoric acid (HF) / H2O – 1:10 solution for about 30 s in

order to remove Si native oxide.

After HF cleaning the Si substrates were loaded into a high temperature

furnace (800 °C) in order to grow a thin layer of thermal SiO2 [31]. The

oxidation occurred in dry conditions with a continuous O2 flux into the furnace

tube. For oxidation intervals of twelve minutes, ellipsometry measurements

reported thickness of thermal oxide to be 3 nm ± 10%. The growth of the oxide

could not be modelled using the classic Deal-Grove model (linear-parabolic),

since this model is only accurate for films thicker than 30 nm. More

complicated theories can be used for modelling in this particular case [32].


3.3.2 Sputtering of the silicon rich oxide/silicon dioxide

structure

Substrates were loaded into sputtering chamber for deposition. Samples

presented in this thesis have been prepared using two different sputtering

systems, which will be referred to as single target and multi-target sputtering

system.

Single target system is a home built single target conventional RF (13.56

MHz) magnetron sputtering apparatus, with manual controls. Ar and O2 were

used as processing gases. Gas flows to the chamber can be controlled by

electronic mass flow controllers. The chamber configuration is shown in Figure

3.3.1.

Figure 3.3.1 - Schematic diagram of sputtering chamber for system 1.

For this system both SRO and SiO2 layers were sputtered from a combined

target consisting of a 4-inch-diameter quartz disc partially covered with a

moderately doped silicon mask, as shown in Figure 3.3.2. The SRO layers were

deposited by sputtering with high purity Argon (99.95%), with a chamber

pressure of 0.1 Pa and RF power density of 0.25 W/cm2, on an electrode area of

105 cm2. SiO2 layers were deposited by reactive sputtering in a mixed Argon-

Oxygen atmosphere using the same RF conditions. The chamber pressure, in

this case, was 0.2 Pa. The RF power source is tuned to the chamber impedance

using a manual matching network with an inductor and two tuneable capacitors.

No substrate heating was used during depositions. The stoichiometry of SRO

film can be varied changing the area coverage of the Si mask.

65


Figure 3.3.2 - Schematic configuration of sputtering target for system 1.

The multi-target sputtering system is an automated multi-target RF

sputtering machine (AJA ATC-2200). The system has five different guns which

can be operated at the same time, using three 4 inches targets and two 2 inches

targets. A schematic representation of the sputtering chamber is shown in

Figure 3.3.3.

Figure 3.3.3 - Schematic diagram of sputtering chamber for system 2. Source

http://www.ajaint.com/systems_atc.htm.

With the multi-target system the SiO2 layers have been deposited sputtering

from a single quartz target, whereas SRO layers have deposited co-sputtering

of an intrinsic Si target and a quartz target. The stoichiometry of the deposited

SRO film can be controlled tuning the ratio of the RF power on the i-Si and

SiO2 guns [33]. Typical chamber pressure during deposition for this system was

1.5 mT. Typically no substrate heating was used. In general the power used for

66

http://www.ajaint.com/systems_atc.htm


the SiO2 gun was kept constant to values around 120 W and whereas it was

varied between 70 W to 150 W for the Si gun.

3.3.3 High temperature annealing

The as-deposited samples have been chemically cleaned and loaded on

quartz boats. Two different boats were used for samples grown on Si substrates

and quartz substrates. Boats were loaded into a horizontal surface in an

ultrapure N2 atmosphere. Samples were annealed for different time intervals in

order to study nucleation properties, as will be explained in next section, and

different temperatures. In general all samples were annealed for specific time

intervals, no cumulative annealings were performed. The formation of Si QDs

during annealing can be represented by the following indicative reaction [15].

SixSiOxSiOx 21

2 2 (3.3.1)

This reaction is an overall description of a series of chemical reactions that

form Si radicals and eventually crystalline Si (c-Si) [18]. The relation between

the silicon excess in the SRO film (SiOx where x < 2) and the amount of c-Si in

form of Si QDs in the final structure is depicted. This has been experimentally

verified by Conibeer et al. [3]. The formation of QDs in the structure has been

confirmed and studied using cross sectional transmission electron microscopy

(TEM) [34]. Figure 3.3.4 shows a schematic representation of the single layer

Si QDs structure after deposition and after high temperature furnace annealing.

Figure 3.3.4 - Schematic representation of the single layer Si QDs structure after

deposition and after high temperature furnace annealing.

67


68

3.4 Investigation of optical and physical

properties of silicon rich oxides layers and

nucleation of silicon nanoparticles

A crucial step to control the confinement of Si QDs in single layer structures

is to investigate physical and optical properties of SRO layers. More

specifically, it is very important to quantify the amount of excess silicon

present in the SRO film and, for a given Si excess, try to understand how the

nucleation process evolves during annealing.

If the density of Si QDs exceeds a certain limit, bigger dots can merge

together during the coalescence phase of the nucleation process, affecting the

confinement properties of the structure. On the other hand, if the amount of Si

in the film is too low, nucleation of QDs could become difficult, and particles

could not be able to reach their critical radius [25].

Annealing relatively thick SRO films with different compositions at

different temperatures allows investigating nucleation dynamics of

nanoparticles in the film. This permits to infer on the average size that

nanoparticles would reach without being confined by dielectric layers, thus

provides information on the final morphology of the single Si QDs layer

between two SiO2 barriers, which will be investigated in the next section.

In this section, results of investigation on properties of SRO layers will be

presented. The stoichiometry of the films has been studied using two

independent methods: Rutherford back scattering spectroscopy (RBS) and

numerical fitting of UV-VIS-NIR spectrum. The nucleation process has also

been studied using PL and XRD and Raman spectroscopy techniques. SRO

samples with different Si excess have been annealed at different temperatures,

ranging from 850 °C to 1150 °C. Only results of samples annealed at 1100 °C

will be presented here.


3.4.1 Investigation of silicon rich oxide composition

The chemical reaction (3.3.1) shows that the amount of c-Si in the form of

nanoparticles in the single layer QD structure is directly related to the Si

excess in the former SRO layer. Understanding how sputtering parameters are

related to stoichiometry of SRO films is thus essential. Different techniques

can be used to investigate film stoichiometry albeit with different level of

accuracy [35].

In a RBS measurement a thin film is bombarded with high energy ions and

scattered ions are measured allowing quantification of elements that compose

the material. RBS measurements were performed on as-deposited SRO layers

using a 2 MeV He++ ion beam delivered by a 1.7 MeV tandem accelerator at the

Australian National University in Canberra.

Figure 3.4.1 - (a) Energy spectrum from RBS analysis of a SRO layer. The inset shows

high energy section of the spectrum. Fits to determine (b) oxygen and (c) silicon

concentration of the film are shown [34].

69


Figure 3.4.1 (a) shows an energy spectrum from RBS analysis of a SRO film

grown on a silicon substrate. The figure shows detected events as a function of

measured energy of scattered projectile. For a given incident energy and

scattering angle, the energy of the scattered projectile depends on the mass of

the target ion. This allows identification of different elements in a target. Also

for a given target atom, the energy of the projectile scattered of deep inside the

film is smaller than that scattered of the surface of the sample, due to the

energy loss by the projectile in the sample before and after the collision.

The events associated with ion scattered from a particular chemical element

in the target are indicated. Here, the events with higher energies are from Si

and with lower energies are from O, as labelled in the diagram. The scattering

yield, Yi, for each element in the film is obtained by integrating respective

region of the energy spectrum. The integration of the oxygen yield YO was

obtained by subtracting the oxygen peak from the background counts, which

was determined by a second order polynomial fit. An example of this fit is

shown Figure 3.4.1 (b). The determination of silicon yield YSi is complicated as

it is present in both the film and the substrate. In this case Si yield has been

obtained by fitting the spectra with a combination of the linear and the error

function. This is shown in Figure 3.4.1 (c). It is evident from Figure 3.4.1 (b)

and (c) that the quality of fits is excellent. The average oxygen-to-silicon

atomic ratio, O-Si, of each film has been calculated using the following

relation: 1

O Si

O Si

Y YOSi d d

(3.4.1)

Where d O and d Si are the mean differential scattering cross sections for

oxygen and silicon, respectively. An O-Si ratio of 0.95 (± 0.05) was determined

for the particular film shown in the figure [36].

The UV-VIS-NIR spectrum of as-deposited samples has been measured with

Cary500 spectrophotometer. Transmission and reflection spectra can be

modelled with an effective medium approximation as a combination of SiO2

and Si. Since the deposition occurs at room temperature, this layer can be

modelled with a random bonding model (RBM) as simple mixture of Si and

SiO2 that contains all the intermediate oxidation states. In this case the

70


71

composition of the film is not strongly determined by chemistry but is related

to the flux of O and Si atoms on the substrate surface during deposition [37,

38]. SRO reflection and transmission data have been fitted using Wolfram

Wvase32 software. Figure 3.4.2 (a) and (b) show fitted and measured spectra

for reflection and transmission of three chosen SRO samples with different Si

excess. Figure 3.4.2 (c) shows a schematic of the used Wvase model and

parameters of the Effective Medium Approximation (EMA) layer applied to

model the as-deposited SRO.

The EMA layer is constituted by a mixture of two materials, SiO2 and a-Si.

The fitting procedure only fits one parameter, the amount of a-Si in the film.

The film thickness, red circle in the figure, has been accurately calculated

using XRR and height profile measurements. XRR was performed with a

Philips X’Pert pro system equipped with a PixCEL detector. Film height

profiling was performed with Sloan Dek Tak II profilometer. Data from XRR

and Dek Tak matched very well, confirming the accurate evaluation of film

thickness. Samples for Dek Tak were prepared using a photolithography step

and selective chemical etching by buffered etch oxide. This allowed creating

optimized stepped patterns on the film.

Samples thickness has been re-measured after annealing of specimens at

different temperatures, up to 1150 °C and for different annealing durations, up

to four hours. It is very interesting to note that, for all the samples analysed

here, no shrinking of the films has been observed. This is an indication that,

despite the deposition process occurs at room temperature, the films grow quite

compact during the sputtering process.


Figure 3.4.2 – Wvase fittings of (a) reflection and (b) transmission spectra of SRO layers

with different Si excess. Red lines are measured data and black lines are fittings. (c) Wvase32

model and EMA details.

72


Figure 3.4.3 – (a) XRR spectra for selected SRO layers with different Si excess, (b)

thickness fitting procedure, (c) Structure for height profile measurement, (d) example of

height profile measurement.

73


Figure 3.4.4 shows the SRO growth rates and the calculated Si-O atomic

ratios versus the power ratio used on SiO2 and i-Si targets during deposition.

The figure shows results obtained by RBS measurements and Wvase fittings.

Data are in good agreement for low Si contents, whereas for high Si excess

more discrepancy can be observed. For high Si concentration, in fact, the

extraction of the composition by RBS becomes slightly less accurate, since the

Si content in the film is harder to separate from substrate signal.

Figure 3.4.4 - Si to Oxygen calculated atomic ratio (blue line RBS, black Wvase32) and

Growth Rate versus SiO2/Si power ratio on targets during sputtering process (system 2).

3.4.2 Nucleation of silicon quantum dots in silicon rich oxide

Structures analysed in the previous section have been annealed at 1100 °C in

order to investigate nucleation of Si nanoparticles.

The formation of Si nanoparticles has been confirmed by XRD, Raman

scattering and TEM. Figure 3.4.5 shows XRD spectra of SRO layers with

different compositions. Measurements have been performed with same system

used for XRR using a proportional detector. The penetration depth of the

incident x-ray beam is larger than the sample thickness, so cristallinity

information is averaged over the entire film.

74


Figure 3.4.5 – XRD spectra of SRO samples with different composition. (a) as-deposited,

(b) annealed.

TEM has confirmed that for a Si-O ratio close to 1 the average size of the Si

QDs can be controlled tuning the thickness of the SRO layer between SiO2

barriers. Cross-sectional high resolution TEM (HRTEM) has been performed

with a Philips CM 200 apparatus. Specimens for cross section images have

been prepared with focused ion beam (FIB) technique using a FEI NOVA 2

double beam machine.

75


Figure 3.4.6 – HR-TEM images of SRO layers with different Si excess (a) 0.92 (b) 1.17

(c) 1.42.

76


77

Figure 3.4.7 (a) shows the energy peak and intensity of the PL signal as a

function of Si-O atomic ratio. For a low Si excess higher emission energy can

be observed. This is due to the small size of the Si QDs, thus higher quantum

confinement of recombining carriers [19]. Increasing the Si concentration in

the as-deposited SRO film the average size of the Si QDs in the annealed film

increases considerably but the number of Si QDs decreases at the same time.

This causes a red-shift of the PL signal due to lower confinement and a

decrease in signal intensity, related to the smaller number of nanoparticles in

the film [25].

It is interesting to note that when the Si excess is above a certain threshold

(Si-O = 0.9), the PL signal starts to blue-shift again, whereas the PL intensity

maintains the same decreasing trend. The blue-shift is due to advanced

nucleation of several Si QDs which, due to the large amount of Si, can grow in

large nanocrystals or clusters. Large clusters do not induce any quantum

confinement effect and do not contribute to PL. The remaining part of the

excess Si segregates in smaller QDs, which do have optical confinement,

contributing to the high energy PL signal [25]. The presence of larger Si QDs is

also established by TEM, XRD and absorption spectra. In fact in Figure 3.4.7

(b) a clear continuous red-shift of absorption edge can be observed when Si

excess is increased. This confirms that absorption is only related to amount of

crystallized Si and not to size of nanoparticles.


Figure 3.4.7 – (a) PL peak energy and intensity versus Si – O atomic ratio for different

SRO layers, (b) Tauc plot of absorption coefficient for SRO layer with different Si excess.

78


79

3.5 Investigation of quantum dots nucleation

and quantum confinement in single layers of

silicon quantum dots in silicon dioxide

A series of samples with different SRO between two SiO2 layers has been

deposited in order to investigate on quantum confinement properties using PL.

SRO thickness was varied in the range 1.4 nm – 6 nm. The thickness of the

SiO2 barriers was maintained constant to 6 nm for most of the structures except

for devices with SRO layer thickness smaller than 2.5 nm, for which a 30 nm

capping oxide layer was used, in order to prevent oxidation during annealing.

Following deposition samples were annealed at 1100 °C in N2 atmosphere,

for time intervals between few minutes and 6 hours in order to probe the whole

nanoparticles evolution process, from nucleation to pure growth and ripening

stage [25].

After the high temperature annealing in N2, some samples have been

annealed in FG (Ar + 4.1% H2). The temperature of the furnace was ramped

from 1100 °C to 600 °C maintaining the N2 atmosphere. At 600 °C the

annealing atmosphere was changed to FG and temperature was kept constant

for 30 minutes to allow saturation of defects by FG. Successively temperature

was ramped down to 400 °C and kept stable for one hour to allow freezing of

saturated defects [19].

3.5.1 Quantum confinement effect in single layer quantum

dots structures

TEM investigation confirmed that for a Si-O ratio of ~ 0.9, the average size

of the Si QDs can be controlled tuning the thickness of the SRO layer between

SiO2 barriers. For lower Si excess the average diameter of the Si QDs is

generally smaller that the SRO thickness, whereas for higher excess Si can

nucleate in larger clusters [25].


Figure 3.5.1 - Cross section TEM of an annealed SiO2/SRO 5-bilayer structure. (Top inset)

As-deposited structure. (Bottom inset) High magnification image of a single Si QD.

Figure 3.5.1 shows HR-TEM images of a SiO2/SRO 5-bilayers structure. In

this case the thickness of each SiO2 and SRO layer was 6 nm and 5 nm,

respectively. The layer structure is clearly visible in the top inset. Importantly,

Si QDs of approximately 5 nm in between the two SiO2 layers are evident in

the diagram, and better highlighted in the bottom inset. A 5 bi-layers structure

has been chosen for TEM investigation because of damage caused by focused

ion beam during sample preparation on the single layer Si QDs structure. The

FIB sample preparation, in fact, involves deposition of a thick platinum layer

with ion beam before the milling process; during this step specimens

experience high pressure and major compression damages. To obtain an image

of a single layer structure a special sample has been prepared with a thicker top

oxide. The platinum coating has been deposited using electron beam instead

than ion beam, this results in much less pressure on the film and a more gentle

deposition, although makes the FIB procedure more delicate and complicated.

A low magnification image of this sample is shown in Figure 3.5.2.

80


Figure 3.5.2 - TEM image of a single layer Si QDs in SiO2.Si-O atomic ratio is 0.93.

Platinum coating was deposited using electron beam.

Figure 3.5.3 (a) shows the normalized PL signal for single layer Si QDs

structures with QDs diameter from 6 nm to 1.4 nm. All samples were deposited

on quartz substrates and annealed at 1100 °C for 2 hours. It is evident that all

the samples show strong PL signals. No other data on PL from single-layer

Si/SiO2 have been found in the current literature.

81


Figure 3.5.3 - (a) Normalized PL peak for samples with Si QDs from 1.4 nm to 6 nm; (b)

quadratic fitting of the PL peak and normalized FWHM as a function of Si QDs diameter; (c)

comparison of PL peak energy as a function of Si QDs diameter for different authors.

The broad PL peaks suggest a distribution of QDs sizes around a mean

diameter, which suggests the presence of a dispersed confined energy level in

the structure. This gives in a deterioration of the energy selectivity properties 82


83

of the ESC structure which results in a decrease of efficiency of the final

HCSC device.

It has been demonstrated that, assuming the size distribution of the single

layer QDs to be Gaussian, the conductivity and the selectivity of these

structures is dramatically affected [39].

Improving SiO2 layers and interface quality allows obtaining a more uniform

distribution of Si QDs sizes, thus a sharper PL signal and better energy

selectivity. In fact, if the SiO2 layer does not have a perfect stoichiometry, for

example if it has a Si excess, Si QDs can grow larger than the SRO thickness,

enlarging the QDs size distribution. A good indicator of the PL peak broadness

is the normalized full width half maximum value (FWHM). This figure recently

has been related to the geometrical standard deviation of the nanoparticles sizes

in the oxide matrix [22]. In Figure 3.5.3 (b) the normalized FWHM as a

function of the Si QDs diameter is shown. The increase in the FWHM with a

decrease in the nanoparticles size, is a clear indication of a longer

coalescencelike process for smaller QDs [25].

The evident peak energy shift of the PL signal shown in Figure 3.5.3,

demonstrates that the average size of the Si QDs varies according to the

thickness of the SRO layer. In Figure 3.5.3 (b), we have plotted the PL peak

energy from different samples as a function of average QD diameter (SRO

thicknesses) (black squares). For comparison data from other authors are shown

in Figure 3.5.3 (c). A rapid and non linear blue-shift of the PL peak with the

decrease of the diameter of the Si QDs can be observed. The black curve is the

quadratic fit to our experimental data. Although the fit follows the

experimental data quite well, this is only in partial agreement with theoretical

ab-initio calculations by Wang et al. [16]. The discrepancy between theoretical

and experimental values is higher for small diameter QDs. Different theories

have been proposed in order to explain the physical mechanism which causes

this mismatch, but results are still controversial and a debate is still open. The

main reason for the divergence is the recombination via free exciton states and

the contribution to the PL signal of defects present at the Si-SiO2 interface.

These defects can introduce allowed energy states within the forbidden gap of

the material, preventing an effective opening of the bandgap as discussed in


84

[16]. This hypothesis is also supported by the data on porous silicon from Von

Behren et al. [40]. In their report measurements were performed in an oxygen

free environment with samples encapsulated in Ar. The energy of the measured

PL peak agrees in a good approximation with theoretical modelling predictions

by Wang. No PL signal has been observed for our as-deposited samples, in

agreement with results from other reports where chemical vapour deposition

(CVD) techniques were used for the growth [18]. Instead, a high energy PL

signal for as-deposited samples has been observed by other authors that

adopted ion implantation to introduce Si into the SiO2 as mentioned in the

previous section of this chapter [21].

3.5.2 Study of nucleation process of single layer silicon

quantum dots in Nitrogen annealing atmosphere

Figure 3.5.4 (a) shows the evolution of the PL peak intensity against the

annealing time in minutes for single layer Si QDs structures. The effective time

of annealing at 1100 °C is given. Furnace ramping up and down periods (to and

from 600 C), which are typically 30 minutes and 60 minutes, respectively, are

not taken into account. Annealing intervals from few minutes to 6 hours have

been investigated in order to probe the whole silicon nanoparticles evolution

process, from nucleation to pure growth and ripening stage [25]. No cumulative

annealing has been performed. A stable PL signal is observed for all samples

after exposition to 1100 °C for few seconds, demonstrating that the nucleation

step of the coalescencelike phase is completed during the very early stage of

the annealing for QDs larger than 2 nm in diameter. No consistent PL signal

has been observed for the samples with Si QDs of 1.8 nm diameter or less for

annealing intervals shorter than 2 hours. This is in agreement with the

suggestion that longer annealing periods are required for very small QDs [25].

For all the samples, two main phases of the growth process can be identified

in Figure 3.5.4 (a). During the first phase, which extends from few minutes to

about 150 minutes, an increase in the intensity of the PL can be observed, in

agreement with data shown in other reports [19, 21, 24]. This increase can be

attributed to the annealing of non radiative defects in the matrix during the


85

Ostwald ripening phase of the Si QDs [19, 41]. The ripening process is much

slower than the very quick coalescencelike crystallization phase, thus the

evolution of the PL signal can be observed for approximately 150 minutes of

annealing duration, depending on the thickness of the SRO layer. During this

phase the oxygen atoms diffuse through oxygen empty states in the matrix

annealing a fraction of the non-radiative defects present at the interface with

the Si QDs. The highest PL intensities, for most of the samples, were found for

annealing intervals of 150 minutes.

A second phase of the growth (annealing intervals longer than 200 minutes),

which shows a drop in the PL signal intensity, can be observed in Figure 3.5.4

(a). This is due to the partial oxidation of the Si QDs, caused by residual

oxygen content in the annealing atmosphere. A further effect of the oxidation is

the shift of the PL peak towards higher energies with annealing time, Figure

3.5.4 (c). This process reduces the average size of the QDs modifying the

confined levels as reported in the next section.

Figure 3.5.4 (b) shows the evolution of the normalized FWHM versus the

annealing time for structures with Si QDs of different sizes. Also in this case,

as for the intensity, two different regimes of the growth process can be

identified. The increase of the FWHM observed during the first annealing

period is attributed to the annealing of non-radiative defects at interfaces of

small QDs. These can shadow the PL of the smaller particles making the size

distribution of the dots to appear more uniform, as proposed by Sias [24].


Figure 3.5.4 - PL (a) intensity, (b) signal normalized FWHM, (c) peak position, as a

function of the annealing duration for samples with different Si QDs diameter (lines are not

fittings but guides for the eyes).

During the second phase of the growth, a decrease of the FWHM is observed

for most of the samples. This is attributed to the Ostwald ripening process of

small nanoparticles. During the ripening, in fact, oxygen atoms diffusion

causes the shrinkage, and eventually the disappearance, of critically small Si

QDs, making the size distribution more uniform [25]. Elongated Ostwald

ripening phase for very small nanoparticles have also been discussed by Yu et

al. [25], in agreement with data shown in Figure 3.5.4 (c), where the

86


87

normalized FWHM for the sample with 2.4 nm QDs increases over the whole

range of investigated annealing intervals.

3.5.3 Effects of forming gas annealing on single layer silicon

quantum dots structures

If the PL mechanism was mostly related to interface defects at the Si-SiO2

boundary, as discussed in [18, 42], a consistent shift of PL peak energy with

annealing duration would have been expected, due to rearranging of defects

during the ripening phase. In addition, it has to be noted that no PL signal has

been detected on as-deposited single layer Si QDs samples, which should have

a higher defect concentration compared to annealed specimens. Some authors

have found a strong, high energy, PL signal when measuring thick layers of

SRO [23, 24]. This PL can be clearly attributed to defects caused by ion-

implantation. In fact, the high energy peak disappears completely after high

temperature annealing.

To further investigate on the role of defects, a FG post-annealing process has

been performed on all samples investigated in the previous section.


Figure 3.5.5 - (a) Improvements in percentage of the PL signal after FG post-annealing of

single layer Si QDs in SiO2 annealed in N2 for different periods. (b) PL signals before and

after FG annealing for two structures with different QDs size, samples have been annealed in

N2 for 5 minutes.

Figure 3.5.5 (a) shows the relative improvement due to FG of PL intensity

for samples with different N2 annealing duration versus Si QDs diameter. A

significant enhancement of the PL intensity is observed when QD size is larger

than 4 nm, whereas a moderate enhancement is observed for QD size smaller

than 4 nm.

This PL enhancement is due to annealing of non-radiative defects at the Si-

SiO2 interface. It has already been shown that these defects can shade the

luminescence of Si QDs and that FG annealing is an efficient method to anneal

defects at interfaces [24, 43, 44]. The PL enhancement is more pronounced for

bigger Si QDs since the passivated area is considerably larger. Figure 3.5.5 (a)

also shows that the PL enhancement is strongly related to the duration of the

former annealing in N2 atmosphere. For samples annealed in N2 for few hours a

less significant improvement of PL with FG has been observed. Samples 88


89

annealed for 90 minutes instead show enhancements from 15 % to 120 %

depending on the Si QDs size. This indicates that the passivation of non-

radiative defects occurs both during N2 and during FG annealing. Passivation in

N2 is due to rearrangement of interfaces during Ostwald ripening phase and

takes place on a long time scale until it reaches saturation, as shown in Figure

3.5.5 (c). The saturation regime occurs after different intervals depending on

the Si QDs size [19]. Passivation in FG atmosphere, instead, is related to

annealing of dangling bonds which create non-radiative defects at interfaces.

Figure 3.5.5 (b) shows the PL spectra for two single layer Si QDs in SiO2

structures before and after FG annealing, one with 6 nm Si QDs and another

with 3.6 nm Si QDs. Apart from the intensity increase, for the structure with

larger QDs, it is relevant to notice that no significant variation of the peak

energy or appreciable difference in the spectral shape can be observed for both

samples. On this point discordant results have been reported by other authors

and the experimental evidence seems to be controversial [19, 21, 23, 24, 41].

The fact that the PL emission energy remains unmodified, for structures

analysed in this paper, is a clear indication that the PL cannot be attributed to

defects. Thus it appears that the PL is certainty related to quantum confinement

effect of Si QDs. The discrepancy between data presented here and calculations

reported in [16] can be attributed exclusively to the polar nature of the Si-O

bond, which increases exciton trapping at Si-SiO2 interface, or direct

recombination through interface Si=O centers [13]. This is confirmed by

observations performed on porous silicon, where Si=O centres are more likely

to develop after exposure to oxygen [40].

3.5.4 Oxidation of silicon quantum dots in Nitrogen

annealing environment

In order to confirm if oxidation of Si QDs during the annealing occurs, two

similar samples (A, B) with SiO2 / SRO / SiO2 structure have been annealed

together at 1100 C for different intervals. For both samples, the bottom SiO2

and SRO layers were deposited at the same time and had thicknesses of 4 nm


90

and 5 nm, respectively. The only difference between A and B was the thickness

of the top SiO2 layer, 6 nm for sample A and 30 nm for sample B.

Figure 3.5.6 (a) shows that no shift in the PL peak energy has been observed

for sample B up to 7 hours of annealing. For longer annealing periods a slight

shift towards higher energies is observed. For sample A instead a pronounced

shift of the PL energy, especially after 7 hours of annealing is shown. The

increase in PL energy can be attributed to decrease in average size of Si QDs,

resulting from partial oxidation during the annealing. This is further evidenced

by decrease in PL intensity with annealing duration, Figure 3.5.6 (b). The

decrease of PL intensity for sample A is much faster than for sample B since

sample A has a thin capping layer; hence the oxidation process occurs at a

faster rate. In fact, no distinct PL signals can be measured for sample A after

14 hours of annealing, suggesting complete oxidation of Si QDs in this sample,

whereas a clear PL signal is still measurable for sample B, confirming the very

slow oxidation rate.

Figure 3.5.6 - PL: (a) peak energy, (b) intensity versus annealing duration for two single

layer QDs samples with different SiO2 capping layer.


91

3.6 Summary

In this chapter theoretical and experimental aspects of realization of all-Si

ESCs for hot carrier solar cells are discussed. The possibility of realization of

energy selective contacts using Si QDs in a SiO2 matrix is presented together

with a review of the most important reposts on Si nanoparticles in SiO2 matrix

published during the last few years.

SiO2 and SRO films were deposited using RF magnetron sputtering and high

temperature furnace annealing.

The stoichiometry of the films as a function of the sputtering parameters has

been studied using RBS and fitting of the UV-VIS-NIR spectra with Wvase32

software. The self nucleation of Si QDs in SRO films has also been studied. PL

and absorption results confirm that the morphology of the nanoparticles in the

annealed film is strictly related to the former Si excess values. The formation

of Si QDs was confirmed by HRTEM and XRD measurements. It was found

that a Si-O atomic ratio of ~0.9 allows obtaining good size distribution and

density of Si QDs.

Double barrier structures, consisting of single layer of Si QDs in SiO2, have

been realized changing the thicknesses of SRO layers. It was demonstrated that

the average size of the QDs can be accurately controlled. A strong PL signal

from all of the structures consisting of Si QDs of different sizes has been

observed. The position of the PL peak energy is directly related to the diameter

of the Si QDs. Decreasing the diameter of the QDs a shift of the PL peak

towards higher energies has been observed. A mismatch between the

experimental emission energy of the investigated structures and data obtained

using theoretical calculations is reported. The discrepancy is attributed to the

fact that the PL signal is influenced by the presence of defects at Si-SiO2

interface and to the polar nature of the Si to O bond.

The evolution of the PL signal during the annealing process has also been

studied. It was found that the crystallization of the Si QDs occurs during the

very early stage of the annealing. Further evolution of the physical and optical

properties of the devices is strictly related to an Ostwald ripening process and

partial oxidation of the QDs in the annealing atmosphere.


92

An enhancement of the PL signal has been observed for most structures after

FG annealing. The enhancement was higher for samples with larger QDs size.

FG investigation confirmed that defects at Si-SiO2 interface play an active role

in the PL process but only creating non-radiative recombination centres and not

generating any additional radiative path for confined excitons. Moreover no

significant energy peak shift of the PL signal has been observed after FG

annealing, confirming that the main mechanism underlying the luminescence

for sputtered single Si QDs layer in SiO2 is optical quantum confinement. A

discrepancy between calculated emission energies and measured PL peak

energy in these structures is mainly due to the polar nature of the Si-O bond

and direct recombination through interface Si=O centers which create deep

levels into the confined energy gap.


93

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24. Sias, U.S., M. Behar, H. Boudinov, and E.C. Moreira, Optical and

structural properties of Si nanocrystals produced by Si hot implantation.

Journal of applied physics, 2007. 102(043513): p. 043513-9.

25. Yu, D.C., S.H. Lee, and G.S. Hwang, On the origin of Si nanocrystal

formation in a Si suboxide matrix. Journal of Applied Physics, 2007.

102(8): p. 084309-6.





27. Chakraborty, G., S. Chattopadhyay, C.K. Sarkar, and C. Pramanik,

Tunneling current at the interface of silicon and silicon dioxide partly

embedded with silicon nanocrystals in metal oxide semiconductor

structures. Journal of Applied Physics, 2007. 101(2): p. 024315-6.

28. Koyanagi, E. and T. Uchino, Evolution process of luminescent Si

nanostructures in annealed SiOX thin films probed by photoconductivity

measurements. Applied Physics Letters, 2007. 91(4): p. 041910-3.


96

29. Beard, M.C., K.P. Knutsen, P. Yu, J.M. Luther, Q. Song, W.K. Metzger,

R.J. Ellingson, and A.J. Nozik, Multiple Exciton Generation in Colloidal

Silicon Nanocrystals. Nano Letters, 2007. 7(8): p. 2506-2512.

30. Puzzo, D.P., E.J. Henderson, M.G. Helander, Z. Wang, G.A. Ozin, and

Z. Lu, Visible Colloidal Nanocrystal Silicon Light-Emitting Diode. Nano

Letters, 2011. 11(4): p. 1585-1590.

31. Plummer, J.D., M.D. Deal, and P.B. Griffin, Silicon VLSI technology:

fundamentals, practice and modeling. Prentice Hall electronics and

VLSI series. 2000: Upper Saddle River, NJ: Prentice Hall.

32. Glaze, W.H. and J.W. Kang, Advanced oxidation processes. Description

of a kinetic model for the oxidation of hazardous materials in aqueous

media with ozone and hydrogen peroxide in a semibatch reactor.

Industrial & Engineering Chemistry Research, 1989. 28(11): p. 1573-

1580.

33. Hao, X.J., A. Podhorodecki, Y.S. Shen, G. Zatryb, J. Misiewicz, and

M.A. Green, Effects of Si-rich oxide layer stoichiometry on the

structural and optical properties of Si QD/SiO2 multilayer films.

Nanotechnology, 2009. 20(48): p. 485703.




2010. 94(11): p. 1936-1941.

35. Feldman, L.C. and J.W. Mayer, Fundamentals of surface thin film

analysis 1986: Prentice Hall. 39-66.



94(9): p. 1546-1550.

37. F.Iacona, G.F., C.Spinella, Correlation between luminescence and

structural properties of Si nanocrystals. Journal of applied physics,

1999. 87(3): p. 9.

38. Philipp, H.R., Optical and bonding model for non-crystalline SiOX and

SiOXNY materials. Journal of Non-Crystalline Solids, 1972. 8-10: p. 627-

632.


97

39. Aliberti, P., B.P. Veettil, R. Li, S.K. Shrestha, B. Zhang, A. Hsieh, M.A.

Green, and G. Conibeeer, Investigation of single layers of Silicon

quantum dots in SiO2 matrix for energy selective contacts in hot carriers

solar cells, in AuSES Conference. 2010: Canberra - Australia.

40. Behren, J.V., M. Wolkin-Vakrat, J. Jorne, and P.M. Fauchet, Correlation

of photoluminescence and bandgap energies with nanocrystal sizes in

porous silicon. Journal of Porous Materials, 2000. 7(1-3): p. 81-84.

41. Fernandez, B.G., M. Lopez, C. Garcia, A. Perez-Rodriguez, J.R.

Morante, C. Bonafos, M. Carrada, and A. Claverie, Influence of average

size and interface passivation on the spectral emission of Si

nanocrystals embedded in SiO2. Journal of Applied Physics, 2002.

91(2): p. 798-807.

42. Shimizu-Iwayama, T., N. Kurumado, D.E. Hole, and P.D. Townsend,

Optical properties of silicon nanoclusters fabricated by ion

implantation. Journal of Applied Physics, 1998. 83(11): p. 6018-6022.

43. Lannoo, M., C. Delerue, and G. Allan, Theory of radiative and

nonradiative transitions for semiconductor nanocrystals. Journal of

Luminescence, 1996. 70(1-6): p. 170-184.

44. Lopez, M., B. Garrido, C. Garcia, P. Pellegrino, A. Perez-Rodriguez,

J.R. Morante, C. Bonafos, M. Carrada, and A. Claverie, Elucidation of

the surface passivation role on the photoluminescence emission yield of

silicon nanocrystals embedded in SiO2. Applied Physics Letters, 2002.

80(9): p. 1637-1639.


98

3.8 Publications

P. Aliberti, S.K. Shrestha, R. Li, M.A. Green, G.J. Conibeer, “Single layer of

silicon quantum dots in silicon oxide matrix: Investigation of forming gas

hydrogenation on photoluminescence properties and study of the composition

of silicon rich oxide layers”, Journal of crystal growth, Article Volume: 327,

Issue: 1, Pages: 84-88, 2011.

P. Aliberti, S.K. Shrestha, R. Teuscher, B. Zhang, M.A. Green, G.J.

Conibeer, “Study of silicon Quantum Dots in a SiO2 Matrix for Energy

Selective Contacts Applications”, Solar energy materials and solar cells, Article

Volume: 94, Issue: 11, Pages: 1936-1941, 2010.

P. Aliberti, S.K. Shrestha, B. Zhang, M.A. Green, G.J. Conibeer,

“Investigation of optical properties of single layer silicon quantum dots in a

SiO2 matrix”, Proceeding of AuSES conference, Canberra, Australia, 1-3

December 2010.

P. Aliberti, B.P. Veettil, R. Li, S.K. Shrestha, R. Teuscher, B. Zhang, A.

Hsieh, M.A. Green, G.J. Conibeer, “Study of silicon Quantum Dots in a SiO2

Matrix for Energy Selective Contacts Applications”, Proceedings of E-MRS

Spring Meeting Symposium B, Strasbourg, France, 8-12 June 2009.

S. K. Shrestha, P. Aliberti, G.J. Conibeer, “Energy selective contacts for hot

carriers solar cells”, Solar Energy Materials and Solar Cells, Volume: 94,

Issue: 9, Pages: 1546-1550, 2010.

S. K. Shrestha, P. Aliberti, G.J. Conibeer, “Energy selective contacts for hot

carriers solar cells”, Proceedings of PV SEC18, Kollata, India, 19-23 January,

2009.


99

G. Conibeer, M. Green, E-C. Cho, D. König, Y-H.Cho, T. Fangsuwannarak,

G. Scardera, E. Pink, Y. Huang, T. Puzzer, S. Huang, D. Song, C.Flynn, S.

Park, X. Hao, I. Perez-Wurfel, Y.So, P. Aliberti, “Third Generation

Photovoltaics at the University of New South Wales”, Proceeding NANOMAT,

Ankara, Turkey, 2008.

S. K. Shrestha, P. Aliberti, G.J. Conibeer, “Investigation of energy selective

contacts for hot carrier solar cells”, Proceedings of 3rd International Solar

Energy Society Conference, Sydney, Australia, 2008.

Chapter 4

TIME RESOLVED PHOTOLUMINESCENCE

EXPERIMENTS

FOR CHARACTERIZATION OF

HOT CARRIER SOLAR CELL ABSORBERS

Chapter 4: TRPL Experiments for Characterization of Hot Carriers Solar Cells Absorbers

100

4.1 Introduction

As discussed in chapter 2, a result in common for the various different

reports on modelling of HCSC efficiency is that the performance is strictly

related to the thermalisation velocity of hot carriers into the absorber layer [1].

Relaxation of hot carriers in semiconductors is an ultrafast phenomenon. In

conventional semiconductors high energy photoexcited carriers relax to energy

band edges in a few hundreds of femtoseconds. Thermalisation of highly

energetic carriers in bulk and nanostructured materials has been the object of

scientific research in recent years for different purposes [2-7].

After high energy photoexcitation, a non-thermal carrier distribution is

generated in the semiconductor. The carrier population equilibrates to a “hot

Fermi distribution” on a femtosecond time scale [8, 9]. The hot electron (hole)

gas formed can be characterized by a temperature Te (Th) which is greater that

the lattice temperature, TL. The interaction of carriers with the lattice results in

an energy exchange so that the temperature Te decays towards TL, this process

will be referred as hot carrier thermalisation [9]. The thermalisation of hot

carriers represents the major loss mechanism of conventional single junction

solar cells [10].

The energy loss of photoexcited electron-hole pairs (excitons) is mostly due

to interaction of carriers with optical phonons, energy is then transferred by

phonon scattering to acoustic phonon and thus lost into lattice heat [10].

Scattering between highly energetic carriers and optical phonon can create a

non-equilibrium “hot phonon” population. It has been observed that, in some

particular conditions, hot phonons decay at a slower rate, thus they can

potentially re-heat the hot carrier population, slowing down carrier cooling [2,

11].

The main optical-acoustic phonon scattering mechanism is the decay of an

optical phonon into two acoustic phonons of half energy and opposite

momenta. This mechanism was first investigated by Klemens [12]. If this

process could be suppressed, using particular materials or nanostructured

absorbers for example, the phonon population would in theory stay “hot”, thus

minimizing energy transfer from the hot carriers to the lattice. This is generally


referred as “hot phonon effect” and it has already been observed in bulk

materials under high illumination regimes [13]. Indications of slow hot carrier

cooling and hot phonon effect have been reported for quantum wells systems.

Promising theoretical results have also been obtained for quantum dots

superlattice structures [14, 15]. To minimize operation of the Klemens

mechanism a wide bandgap between optical and acoustic phonon modes is

necessary. This gap has been observed in several III-V compounds with a large

difference in their anion to cation masses, such as InN, GaN, InP [11].

Figure 4.1.1 - Schematic illustration of Klemens relaxation process of optical phonons,

adapted from [16].

In these types of polar materials hot electron energy is dissipated

predominantly through Fröhlich electron-phonon scattering. These have a long

range Coulomb effect which results in a strong predominance of zone centre

optical phonons [16]. Thus, in general, the generated optical phonons are zone-

center longitudinal optical (LO) phonons. If the zone centre optical phonon

energy is twice, or more, as large the maximum acoustic phonon energy (i.e. a

large phonon gap) then these phonons are too high in energy for conventional

Klemens decay. However, it has been shown that LO phonons can decay into a

transverse optical (TO) phonon and then a longitudinal acoustic (LA) phonon.

This three phonons decay process is referred as Ridley decay, and its

lifetime can be compared to Klemens decay in certain cases [17]. The

likelihood of Ridley decay should be limited in most cases due to constraints

101


related to phonon momentum conservation and if the optical phonon dispersion

is narrow.

Figure 4.1.2 - Schematic representation of Ridley decay mechanism in hexagonal InN.

Phonon energy as a function of momentum has been calculated by Davydov [18]. The phonon

interactions must conserve energy and momentum.

Another mechanism that can affect the carrier relaxation velocity is the

inter-valley scattering (IVS) of highly energetic carriers. Carriers in high

energy side bands can interact with phonon and be scattered into the main

valley. Also this process, generally limited to electrons in bulk direct

semiconductors, requires phonons with a particular momentum, thus it can

prevent carriers from thermalisation from side bands to the valley. It has

been theoretically and experimentally proven that inter-valley scattering rates

can be increased by a few orders of magnitude in the presence of hot electrons

and high carrier density due to Gunn effect [19, 20].

102


Figure 4.1.3 - Schematic representation of intra-valley and inter-valley scattering

mechanisms in GaAs, adapted from [16].

It is clear now that the measurement of hot carrier relaxation velocities is a

crucial step to identify possible candidate materials for HCSCs absorbers.

The first section of this chapter is dedicated to a general discussion of

ultrafast methods for probing hot carrier relaxation; in addition a review of the

most important published papers on this topic is presented (Sections 4.2 and

4.3).

The second part of the chapter is dedicated to the presentation and

discussion of results obtained by time resolved PL (TRPL) experiments. TRPL

has been used to compare relaxation of carriers in bulk GaAs and InP.

Although similar experiments have been performed in the past, results

presented here confirm and expand data available in the literature. The

advanced measurement technique, in fact, allows investigation of PL at any

wavelength, giving a clear picture of the spectra and allowing for more precise

fittings of carrier temperatures. In addition, having previous data available for

comparison, allows confirmation of the reliability of the complex measurement

apparatus.

In the last part of the chapter measurements of hot carrier relaxation velocity

of wurtzite InN layers are presented and discussed. This allows study of actual

hot phonon effect in InN and how the hot carrier cooling velocity relates to

material quality.

103


4.2 Literature review

The first evidence of radiative recombination of hot carriers has been

reported by Shah et al. during 1969. The authors observed PL on epitaxial

layers of doped GaAs excited with a continuous laser beam at different

wavelengths [9]. These experiments showed for the first time that electrons and

holes in the semiconductor thermalise amongst themselves and the hot carriers

system can be represented with an effective temperature (TE). This implies a

Maxwellian distribution for the carriers and their temperature increases with

increasing excitation energy. In this early work it was concluded that one of the

most probable mechanisms for carriers to lose energy is interaction with the

lattice via polar optical scattering. This was in contrast with earlier theories

which claimed energy loss was due to collisions with cold holes. Shah et al.

continued to focusing research activity on investigation of interaction of hot

carriers with semiconductor lattices, with particular attention to GaAs. During

1970 they confirmed the formation of a hot phonon population due to hot

carriers in GaAs using Raman scattering experiments [21]. The first detailed

study of hot carrier relaxation in GaAs was published by Shah [22]. In this

work bulk GaAs samples were excited using different laser energies and

several relaxation mechanisms were taken into account.

Figure 4.2.1 - Schematic representation of various relaxation processes of photoexcited

electrons. 1 and 3 correspond to emission of optical phonons with different wave vector, 2

corresponds to collision of energetic electron with electron gas (impact ionization) [22].

104


In this work a parabolic E-k relation for both conduction and valence bands

is assumed, with a hole effective mass much larger than the electron effective

mass. The excess energy for electrons and holes can be written as in (4.2.1).

egPh

h

egPe

EEhEm

mEhE

)(

1)(1

(4.2.1)

Using theory from relaxation of highly energetic carriers, excited using an

electric field, energy decay rates for electrons-phonons interactions and

electron-electron interaction can be calculated. Comparing these rates a critical

value of carrier density nC* can be found [22].

21

121

14

02

0* sinhsinh1))((8

oq

o

oq

oC h

Nh

hNe

KheEn (4.2.2)

Below this critical carrier density value electrons will relax by emitting

successive optical phonons. This is the typical case in III-V semiconductors

which are the main focus of this chapter. The equivalent temperature of

electrons is found balancing power flow into the electron gas against the power

flow out of the gas.

Although this paper demonstrates the possibility of calculating equivalent

hot carrier population temperatures, it does not give any information about

carrier dynamics. The development of ultrafast lasers, during the eighties,

allowed investigation of ultrafast dynamics. Shah and his co-workers published

a series of papers which investigated interaction of carriers-optical phonons,

carrier-carrier and inter-valley scattering interactions, in GaAs and GaAs

nanostructures, on a picosecond and femtosecond time scale [23-30]. During

1988 a paper on the PL from GaAs was published where PL was measured

using an up-conversion technique, with a picosecond resolution [29]. However,

the non-availability of optical parametric amplifiers (OPAs) limited the range

of available wavelengths that could be investigated. Experiments on hot carrier

interactions in GaAs and InP were performed by Elsaesser et al. following the

work from Shah. Elsaesser established that photoexcited electrons and holes in

GaAs and InP are redistributed over a wide energy range within the first 100 fs

after excitation [8].

105


The influence of intervalley scattering on the hot carrier cooling in GaAs

and InP was first investigated by Zhou et al. during 1990 [31]. In this work

IVS was used to explain the long measured hot carriers relaxation time of

GaAs. Clear evidence of the hot phonon effect, was then reported by Langot et

al. using time resolved absorption saturation techniques [32].

Figure 4.2.2 - Measured transient differential transmission T/T in GaAs at 295 K for a

probe wavelength of 810 nm (full line), 780 nm (dotted line), 835 nm (dashed line) [32].

Figure 4.2.2 shows the normalized transmission changes for identical pump

and probe wavelengths, E = P. In this study electrons have been found to be

hotter than the lattice for times as long as 8 ps in GaAs. The first evidence of

the dependence of electrons cooling time on excitation energy has also been

reported in this paper, although not studied in detail.

In the following sections of this chapter a study of both IVS and hot phonon

effect for GaAs and InP is presented. TRPL has been used to measure hot

carrier transients. The availability of OPAs permitted to probe PL signals over

a wide range of wavelengths with high resolution, allowing accurate hot carrier

temperature calculations.

In the last part of the chapter results of preliminary experiments on wurtzite

InN are presented. The investigation of hot carriers cooling in InN is very

interesting since InN seems to be the most suitable material, amongst III-V

semiconductors, for implementing HCSC absorbers. The reasons for this are

discussed in chapter 2 and briefly mentioned here.

One of the main advantages of InN is the wide bandgap between optical and

acoustic phonon branches in its phononic dispersion. This gap could prevent

cooling mechanisms discussed in the previous section, allowing for hot phonon 106


effect, thus slow carrier cooling. InN phononic dispersions were first

investigated by Davydov et al. and are presented in Figure 4.1.2 [18]. At the

stage of Davydov’s calculations, wurtzite InN was still showing an electronic

bandgap of 1.9 eV due to the poor quality of the material. Davydov et al. were

able to grow high quality InN using metalorganic molecular beam epitaxy

(MOMBE), demonstrating the narrow bandgap (0.7 eV) [33].

Figure 4.2.3 – (a) Absorption edge of MOMBE grown InN. (b) PL spectrum, the inset

shows: 1-PL, 2-optical absorption, 3-PLE [33].

Figure 4.2.3 shows the measured absorption coefficient and PL of an InN

thick layer grown on a sapphire substrate <0001>. Measurements confirmed an

absorption and emission edge at around 0.7 eV.

A detailed study of the InN electronic E-k was published by Fritch et al.

during 2004. This work was crucial in clarifying the carriers electronic

transitions in InN [34]. After 2002 several papers reporting on growth of high

quality InN and measurements of absorption edge at 0.7 eV have been

published [35-38]. The first relevant work on ultrafast time resolved

spectroscopy of hot carriers in InN was published by Chen et al. [39]. In this

paper differential optical transmission measurements were used to probe carrier

recombination dynamics and hot carrier relaxation process. According to the

authors, the transmission transients indicate slow relaxation decay times

ranging from 300 to 400 ps, depending on the probing energy [40]. A much

faster relaxation velocity of hot carriers in InN has been observed Wen et al.,

that also used transient transmission measurements as an investigation method

[6]. The authors used two different exponential functions to fit the

107


experimental data, representing the cooling process and the carrier

recombination with two different time constants. Carriers cooling time from

1.44 ps to 4.4 ps were reported as results from the fittings depending on the

photoexcited carrier density. The interdependence of the cooling velocity and

the carrier density was observed here for the first time, and was related to the

screening of electron-LO phonon interactions by dense electron plasma [41].

Time constants similar to the ones reported by Wen et al. are observed by

Ascázubi et al., that used time resolved reflectivity measurements [42].

Figure 4.2.4 - Normalized transient transmission change as a function of time delay, for

different photoexcited carrier concentrations. Carrier concentration goes from 5 × 1018 at a to

1.7 × 1016 at a’ [6].

Although results from transient absorption experiments give an idea of the

velocity of carrier relaxation, they do not allow relation of the entire hot carrier

energy distribution to the time domain. TRPL, instead, allows probing the

entire luminescent spectrum as a function of time, permitting to measurement

of the energy distribution of electrons and holes. If the photo-emitted spectrum

is known, the hot carrier temperature can be calculated using fitting techniques,

as will be discussed in the next sections.

Results from PL and TRPL experiments on InN have been presented in

recent reports, together with an interesting quantitative study of electron-

phonon and phonon-phonon interaction using ultrafast Raman spectroscopy [7,

43, 44].

Tsen et al. measured the electron-phonon and phonon-phonon interaction

using ultrafast Raman spectroscopy [43]. They observed electron-LO phonon

scattering rates of 5.1 × 1013 s-1 and lifetimes of A1(LO) and E1(LO) in the

108


range between 2.2 ps and 0.25 ps depending on photoexcited carrier density.

The reasons behind the relation between phonon lifetimes and carrier density

are currently not clear and more investigation is needed. However, the electron-

LO phonon scattering rate is much larger compared to values predicted by

theory. This is attributed to the extremely polar nature of InN which strongly

increases the Fröhlich interaction matrix element and is observed also in other

III-V semiconductors. The long LO phonon lifetimes have been recently

confirmed by Jang et al. using TRPL experiments [44]. TRPL allows

observation of a consistent hot phonon effect at carrier densities above 1018 cm-

3, as evidenced by the elongated relaxation transients in Figure 4.2.5.

Figure 4.2.5 – TRPL transients of wurtzite InN at several probe energies [44].

109


110

4.3 Probing ultrafast dynamic processes in

semiconductors

Over the last thirty years remarkable improvements in ultrafast carrier

spectroscopy have been achieved. The interest was driven both by fundamental

physics research and the need for faster and better performing microelectronic

devices. The study of the relaxation of excited non-equilibrium carriers in

semiconductors is nowadays a popular topic of research. This is also a crucial

matter to identify potential good absorber materials for HCSCs.

With the devolvement of femtosecond lasers and optical parametric

amplifiers it is possible to excite carriers in an extremely short time interval

and successfully probe the material optical properties, such as transmission or

reflection or PL, using a similar laser pulse, often at different wavelength.

Nowadays this is a common type of experiment to investigate ultrafast

processes in semiconductors. The most commonly used techniques are: pump

and probe, optical Kerr gate, up conversion gate and streak camera.

In this chapter the attention will be focused on pump and probe techniques,

in particular on TRPL.

4.3.1 Time resolved photoluminescence using up-conversion

technique

PL is a well known and widely used technique to investigate semiconductor

properties. PL has been presented in chapter 3 for investigation of single layer

QDs properties. In this chapter TRPL has been used to study hot carriers

relaxation transients in III-V semiconductors. TRPL has been used in pump-

probe configuration. In this setup an extremely short laser pulse is separated

into two different pulses the “pump” and the “probe” and an optical delay T is

placed between them. The pump pulse excites the sample generating a PL

signal. A probe pulse, which is referred to as “gate” pulse in this configuration,


is used to relate the PL signal to the time domain. TRPL experiments were first

used by Shah et al. [26]. Figure 4.3.1 shows the schematic of a TRPL setup.

Figure 4.3.1 – Schematic of a conventional TRPL measurement system, adapted from [26].

The PL signal is collected by an optical system and focused, together with

the gate pulse on a non-linear crystal; the two signals have to overlap spatially

[45]. The frequency sum of the PL signal and gate pulse is generated and phase

matched by the non-linear crystal. The PL wavelengths summed with the gate

frequency can then be focused and detected by a photomultiplier tube (PMT).

Varying the time delay between the pump pulse and the gate the time evolution

of every single wavelength of the PL can be monitored.

Figure 4.3.2 - PL up-conversion process with non-linear optical crystal at a given delay

time T.

Experiments presented in this chapter have been performed using a TRPL

setup at the School of chemistry at The University of Sydney. The laser source

was a Ti:sapphire mode-locked oscillator-regenerative amplifier system (Clark

MXR, CPA series). This delivers a 1 kHz train of ~ 150 fs, 1.5 mJ, and 780 nm

pulses. The laser source is split into two equal beams which in parallel pump

two OPAs, Light Conversion TOPAS-C. Both pump and gate laser beams lines

are equipped with optical delay stages to allow precise control of the T value. 111


112

In general the delay stage on the pump line is kept at a fixed position whereas

the stage on the gate line is electronically controlled by a software interface, to

allow measurements of signal transients with a ps resolution.

The visible-OPA produces signal and idler beams that are tunable from 1020

nm, to 1640 nm, and 1470 nm, to 2600 nm respectively. Two successive non

linear crystals (LBO) allow for second and fourth harmonic generation of the

amplified signal and idler, as well as sum frequency mixing with the remaining

portion of the pump pulse (780 nm). This system configuration provides 150 fs

pulses with tunable wavelength over a range from 256 nm (4.84 eV) to 2.6 m

(0.48 eV). The deep-UV-OPA uses a similar optical arrangement to produce an

independently tunable beam over a wavelength range from 187 nm (6.6 eV) to

2.6 m (0.48 eV) and is used to generate the pump pulse. The pump beam is

focused by a 1000 mm focal length lens and the beam profile, considered to be

gaussian, is measured to be 600 m in diameter (FWHM). The

photoluminescence signal from the sample is collected and focused on a 1 mm

beta barium borate (BBO) crystal, the visible-OPA beam, acting as a gate, is

directed and focused on the same spot on the BBO. The up-converted signal is

detected through filters and a double monochromator to eliminate background

light. The signal is then detected with a low noise Bi-PMT. The group velocity

mismatch between the pump and the luminescence wavelength is always less

than 50 fs/mm in BBO and the pulse duration is 150 fs, yielding an overall

temporal resolution of around 200 fs. The carrier concentration of the excited

samples has been determined considering the number of excited carriers (one

excited electron per incoming photon) in a volume limited by the beam spot

size and a depth 1/ ( ) (where ( ) is the absorption coefficient at excitation

wavelength ) in the material.


Figure 4.3.3 – Simplified schematics of the time resolved photoluminescence system at the

femtosecond laboratory, University of Sydney, Faculty of Chemical Sciences.

113


114

4.4 Comparison of hot carrier cooling gallium

arsenide and indium phosphide

Hot carrier relaxation in bulk GaAs and InP has been investigated by TRPL.

One of the aims of this work is to establish the role of the hot phonon effect in

carrier cooling for InP. The two semiconductors have similar electronic band

gaps (EG_GaAs = 1.43 eV, EG_InP = 1.35 eV), but quite different phononic band

gaps. In particular InP has a wider phononic bandgap, hence is expected to

show a slower carrier cooling.

Several excitation wavelengths have been used to investigate the effects of

satellite valley scattering on the relaxation. For an initial carrier concentration

of 8 × 1019 cm-3, a very broad emission spectrum which extends from the band

gap energy to energies above the pump has been measured both for GaAs and

InP, demonstrating the extremely fast interactions of carriers at very early

times (~ 100 fs) after the laser excitation. Full PL spectra have been simulated

and fitted with experimental data to extract the hot carrier temperature Te as a

function of time for both GaAs and InP. The difference between the GaAs and

InP PL decay rates depends on the excitation wavelength, proving the role

played by the X and L valleys in GaAs and the influence of IVS on the cooling

process. The temperature evolution is also related to the excitation wavelength.

Thermalisation of hot carriers in InP is always slower than in GaAs when

excitation energy below the satellite valleys thresholds is used, providing

evidence of a hot phonon effect in bulk InP.

In order to investigate and differentiate the influence of the hot phonon

effect and IVS on the hot carrier cooling rate, the evolution of the PL signal

has been studied for different pump wavelengths. Three different excitation

energies have been used to excite carriers in the different conduction band

valleys of the two materials. A schematic representation of the band structures

is depicted in Figure 4.4.1. E1 = 1.7 eV, which is below the IVS threshold for

GaAs and InP, E2 = 1.88 eV, which is below the L valley for InP but above the

L valley for GaAs and E3 = 2.4 eV, which pumps electrons above the L and X

valley for both materials.


Figure 4.4.1 - Schematic representation of GaAs (dot) and InP (dash) electronic band

structure. The different pump energies used for investigation are shown [46].

4.4.1 Hot carriers cooling

Figure 4.4.2 shows the evolution of the PL spectrum of GaAs and InP, for a

1.7 eV (730 nm) pump pulse, at a carrier density of 8.5 × 1019 cm-3. This value

of carrier density in the absorber is chosen because in a required range for

HCSC operating at maximum power point under full concentration [47].

Considering an ultrafast carrier-carrier scattering rate (see chapter 2), a hot

Fermi distribution can be assumed for photoexcited carriers. This assumption is

supported by the initial very broad PL spectrum (few ps) observed both in

GaAs and InP, Figure 4.4.2 [8, 9]. The energy distribution of the spectra

narrows down and the peaks shift towards the band edge due to carrier cooling,

Figure 4.4.2 (e,f). Figure 4.4.2 (c,d) shows the normalized PL transients for

some particular energies. It is evident that highly energetic states empty much

faster than states closer to the band edges and that IVS has a role only at the

very early stage of the cooling process. The PL signal below the bandgap can

be attributed to blurring of the bandgap energy states at high photoexcitation

regimes [48].

115


Figure 4.4.2 -3D evolution of PL spectra versus time (1.70 eV pump) for (a) GaAs and (b)

InP. The carrier concentration is 8.5 × 1019 cm-3. Transient PL spectra for different

wavelengths in (c) GaAs and (d) InP. Insets show the band edge PL emission. PL spectra for

different delay time in (e) GaAs and (f) InP.

Figure 4.4.3 shows the PL signal time constant, fitted using a simple

exponential function, versus the emission wavelength. Using a 730 nm (1.7 eV)

pump, no significant interaction of hot carriers with side valleys has been

observed. The L valley for GaAs, in fact, has a threshold of 725 nm (1.71 eV).

116


Figure 4.4.3 - Fitted PL signal decay constant as a function of wavelength for different

pump wavelengths, (a) 730 nm, (b) 660 nm, (c) 515 nm. Carrier concentration is always 8.5 ×

1019 cm-3, signals have been fitted using a single exponential [46].

117


4.4.2 Hot phonon effect in gallium arsenide and indium

phosphide

Figure 4.4.4 shows the phonon dispersion relations for GaAs and InP [49,

50]. The energy of the zone centre LTO phonon for InP is 10 THz and the

maximum LA phonon energy, at the zone edge, is 4.8 THz and 4.4 THz, for the

X and L directions respectively. These LA energies are smaller than half of the

LTO phonon energy; hence they are not sufficient for the decay of the LTO

phonon by Klemens mechanism. This suggests that Klemens mechanism would

be partially suppressed. However, the minimum energy of optical phonons is at

8.7 THz at the point in the X direction. This is less than twice the energy of

the maximum LA phonon, so in this case Klemens decay of the optical phonon

would be allowed.

Figure 4.4.4 - Calculated phonon dispersion relations for (a) GaAs and (b) InP [46].

118


119

The zone centre LTO phonon is however able to undergo Ridley decay by

emission of a LO phonon, at 8.7 THz to the point, and simultaneously a 1.3

THz TA phonon, to the point in the L direction. This balances both energy

and momentum and is an extra allowed transition to the more usual Ridley

decay to a TO and a LA phonon described in Section 4.1. The degeneracy of

LO and TO modes at zone center means that no specific translation is preferred

in the decay and either a TO or a LO phonon can be emitted, provided it is

matched by the appropriate LA or TA phonon of correct energy and

momentum. This zone center LTO degeneracy arises because of the cubic

zincblende structure of InP, which strictly gives zero dispersion at zone center,

and the relatively low polarity of the InP bond, which reduces the tendency for

splitting of LO and TO modes at zone center.

The effect on carrier cooling of the much larger phononic gap in InP, as

compared to GaAs, is clearly visible in Figure 4.4.5 and Figure 4.4.3, with

illumination at 730 nm. This is below the energy necessary for IVS, thus zone

centre valley interactions dominate in both InP and GaAs. The longer PL

lifetime for InP at all wavelengths, Figure 4.4.3(a), and the higher effective

carrier temperature at all times, Figure 4.4.5(a), clearly indicates slower carrier

cooling in InP. This suggests that the suppression of LTO decay by Klemens

mechanism enhances the hot phonon effect and slows down carrier relaxation.

For 8.7 THz optical phonons, at the point, the Klemens mechanism is allowed

and hence the decay would remain unrestricted. The important consideration in

the overall enhancement of the hot phonon effect is the distribution of optical

phonon momenta.


Figure 4.4.5 - Carriers temperature as a function of time after excitation with (a) 730 nm,

(b) 660 nm, (c) 515 nm pump pulses.

The distribution of momenta of the emitted optical phonons is strongly

peaked near zone center because the Fröhlich interaction in polar compound

semiconductors only allows emission of small wavevector phonons. In fact, the

long range electronic oscillations of oppositely charged atoms, set-up by the

phonon emission, create a strong coulombic repulsion of phonons with any

translational momentum [16]. The dependence of the phonon distribution on

wavenumber, q, varies as q-2. A further effect of the Fröhlich emission of low

wavenumber phonons occurs for higher energy electrons, in the region of the

120


121

conduction band, in which the assumption of parabolicity of the E-k

relationship is no longer valid. This non-parabolicity arises from hybridization

of s and p states and determines the band structure of higher bands [51]. As the

long range Coulomb effects determine emission of only low wavenumber

phonons, it is results very difficult for high energy electrons to emit a phonon

conserving both energy and momentum. This makes the emission of very low

energy acoustic phonons, close to zone center, the only available scattering

event. A large number of these events is required for the hot electron to lose a

significant amount of energy. The probability of emitting such a large number

of acoustic phonons is limited. The result is the creation of a large population

of optical phonons or, in other words, a hot phonon effect. This implies that the

gap between optical and acoustic phonon branches in InP is large enough to

prevent Klemens decay, enhance the hot phonon effect and produce the

observed slower carrier cooling.

However, as discussed above the alternative Ridley mechanism can still

occur for decay of low wavenumber LTO phonons. In InP this will be followed

by a rapid decay of LO phonons from the point via an off-zone centre

Klemens decay as discussed above. This is a two stages process, involving five

phonons and hence should have a lower probability compared to direct

Klemens decay of the LTO phonon.

Some result indicates that the overall rate of the Ridley/Klemens decay is

dominated by the slow Ridley part, which is a factor of ten times slower than

the Klemens part due primarily to the lower final DOS for the Ridley transition

[52]. This is only partially applicable in the InP case discussed here, as the

calibration of the phonon dispersions differs significantly, but it is indicative of

how Ridley decay can reduce the overall rate in a two-step decay process.

It can be concluded that the complex Ridley/Klemens decay required in InP

for decay of zone-center phonons as compared to the many routes allowed for

the rapid one step Klemens decay of optical phonons in GaAs, does explain the

observed slowed carrier cooling in the former by an enhancement of the hot

phonon effect. Nevertheless it is also valid to state that a wider phonon gap that

is sufficient to block both Klemens and Ridley decay, or to block the Klemens


decay of Ridley decayed phonons, should enhance the hot phonon effect further

and would be expected to slow carrier cooling to a greater extent.

4.4.3 Inter-valley scattering of hot carriers in gallium

arsenide and indium phosphide

Figure 4.4.5 (b) and (c) clearly show that with the inclusion of the L valley

of GaAs, the rate of cooling in the first 10 ps to 15 ps is significantly lower in

GaAs, suggesting an efficient IVS process in GaAs. This can be explained by

examining the electronic band structures of both semiconductors and the

Fröhlich interaction within the framework of Fermi’s Golden Rule [53]. For a

side valley (X, L) electron scattered into the valley, with momentum

conservation fulfilled by the emission of an off-center LO phonon, the

transition probability can be written as in (4.4.1):

,

2

, ,2 finfinih oscvLX (4.4.1)

The electron initial state (ini) is the L or X side valley, the electron final

state (fin) is given by an unoccupied valley state convoluted with the LO

phonon with an appropriate momentum to allow a X or L transition.

The oscillator strength of the transition (fosc), which describes the coupling

between initial and final state, is proportional to the Fröhlich interaction ( FRÖ)

[54].

For InP the Fröhlich interaction is larger than GaAs ( FRÖ_InP = 0.15 [55],

FRÖ_GaAs = 0.068 [56]) due to its more polar nature and lower LO phonon

frequency, yielding a higher oscillator strength for IVS [57].

The PL lifetime of GaAs is significantly shorter if no side valleys are

occupied despite its lower Fröhlich constant. This is a clear indication that the

wide phononic band gap of InP delays carrier cooling by slowing the decay of

optical phonons. When the pump energy exceeds the energy threshold for

transfer into satellite valleys, the PL lifetime of GaAs is equal or even exceeds

the values of InP, as evidenced Figure 4.4.3. This confirms the dominance of

FRÖ in the IVS process and appears to be plausible. Without Fröhlich

interaction, only a very small phononic coupling, between electrons in the side 122


123

valleys and unoccupied electronic states in the main valley exists, due to

electrons to acoustic phonon scattering. Acoustic phonons do not couple

readily to electrons due to their low electromagnetic moment. The higher LA

L intervalley deformation potential of GaAs does thereby contribute to IVS

only as a second order effect [58]. The respective electronic DOS appears to be

not as influential as FRÖ. This is due to the convolution product of the

electronic DOS of the side and main valleys, which only changes significantly

if both DOS are very small or large. In other words, the bottleneck of IVS is

given by the Fröhlich interaction. GaAs has thus a slower IVS mechanism and

can store hot electrons in the side valleys for a longer time as compared to InP.


124

4.5 Time resolved photoluminescence of hot

carriers in indium nitride layers

InN is a very good candidate, amongst others III-V semiconductors, to

implement a HCSC absorber. The reasons for this have been discussed in

Section 4.2. In summary, InN has a small electronic band gap (0.7 eV) for

better light absorption and, at the same time, it has a wide gap between

acoustic and optical branches in its phonon dispersion characteristic, allowing

slower thermalisation of hot carriers by hot phonon effect [18, 34]. Time

resolved experiments have reported hot carriers relaxation time longer than

theoretical calculations [39, 42, 59]. This prolonged hot carriers lifetime is

most probably due to hot phonon effect, thus minimization of the losses rate

via Fröhlich interaction under high photoexcitation [32, 60].

4.5.1 Preliminary results on hot carriers cooling in wurtzite

indium nitride

To investigate on the actual relaxation velocity of hot carriers in InN, TRPL

experiments have been performed on InN thick layers.

Samples have been deposited using plasma assisted molecular beam epitaxy,

by Dr. Y. Wen and Dr. C. Chen at the University of Taipei, on Sapphire

<0001> substrate using two GaN nucleation layers to optimize crystal

properties and minimize defects. Figure 4.5.1 shows the layered structure of the

examined sample and a SEM image of the sample surface. The measured

carrier concentration was around 1.5 × 1018 cm-3. Carrier mobilities were

measured to be around 2000 cm2/Vs.


Figure 4.5.1 - (a) InN sample layer structure. GaN nucleation layers are used to optimize

InN crystal structure. (b) SEM image of the investigated InN sample.

The samples have been excited using the pulsed laser described in the

previous sections, with an energy of 1.1 eV. The beam size was 0.8 mm and the

energy per pulse was 35 J. The gate wavelength used was 780 nm (1.59 eV),

which is the unmodified Ti:sapphire wavelength, thus the one with the highest

power. The up-converted wavelengths detected by the PMT were in the range

480 nm – 522 nm. Measurements have been performed at room temperature.

The collected raw data have been corrected for the cathode radiant

sensitivity of the PMT and pre fitted using weighted exponential functions, as

shown in Figure 4.5.2.

125


Figure 4.5.2 - 3D surfaces of collected and fitted TRPL data for bulk InN.

The figure is a three dimensional representation of PL as a function of time

for all the probed wavelengths. It can be observed that the PL sharply rises

when the carriers are photo-excited by the laser pulse. The fast decay of the PL

shows the thermalisation of carriers towards respective band edges. The decay

is faster for highly energetic carriers compared to carriers closer to the bandgap

as also observed for GaAs and InP. Thus the carrier population quickly

accumulates towards band edges during the thermalisation process. In InN the

thermalisation is most probably due to interaction of highly energetic electrons

and holes with LO phonons [6].

To investigate the velocity of the carrier cooling process, the effective

temperature of the carrier population has been calculated fitting the high

energy tail of the PL spectrum for every single time during the cooling

transient [44]. The PL has been fitted assuming that carriers assume a

Boltzmann-like distribution in a femtosecond time scale, as discussed at the

126


beginning of this chapter. Equation (4.5.1) shows the expression used to

calculate carrier temperature.

CB

G

TkEL exp)()( 2 (4.5.1)

L( ) represents the measured PL intensity at energy , ( ) is the measured

sample absorption coefficient, EG is the InN energy gap (0.7 eV), and kB is the

Boltzmann constant. TC is the fitted parameter and represents the hot carrier

temperature. Figure 4.5.3 shows the carrier temperature transient, which

follows quite well an exponential behaviour (dashed line – fit).

Figure 4.5.3 - Carrier relaxation curves for InN. The photoexcited carrier density is 1.5 ×

1019 cm-3. The blue dashed curve is a single exponential fitting.

The fitting of the calculated temperature data has been performed using a

single exponential as in equation (4.5.2).

KtCtTTH

exp)( (4.5.2)

Here TH represents the carriers thermalisation time constant, whereas C and

K are two constant parameters. The fitted value for TH is 7 ps. The relatively

long cooling constant can be attributed to hot phonon effect due to the long

lifetime of the A1(LO) phonon [7, 61], although this result is still controversial

[6]. This hot carrier relaxation velocity is still faster than the value previously

used in chapter 2 (100 ps) to evaluate limiting efficiency of a HCSC with an

InN absorber. However, it has been demonstrated that, for InN, the carrier

cooling velocity is strictly related to the quality of the material and slower

127


128

carrier cooling constants, compared to the ones calculated in this chapter, have

been reported in the literature [40].

It has to be highlighted that the growth of ultra high quality wurtzite InN

remains still a very complicated and expensive task, due to the involvement of

MBE growth technique [62].


129

4.6 Summary

In this chapter time resolved photoluminescence experiments have been

performed on several III-V bulk semiconductors in order to investigate the

factors that influence hot carrier cooling processes. The possibility of probing

hot carrier transients with picosecond accuracy allows study of the relations

between materials phononic dispersion curves and velocity of carrier cooling.

This is very useful to screen potential candidate materials for hot carrier solar

cells absorbers and, at the same time, is crucial for the designing of new

nanostructured absorbers based on superlattices.

In the first part of the chapter the topic of hot carriers relaxation in

semiconductors is introduced and several significant papers on the

investigation of ultrafast phenomena in semiconductors are presented and

discussed. In addition an introduction of ultrafast measurements and systems is

given; this includes a presentation of up-conversion time resolved

photoluminescence techniques.

In the second part of the chapter results on the influence of the hot phonon

effect and IVS on the hot carrier cooling rate in bulk GaAs and InP is

presented. Experiments have been performed using femtosecond luminescence

spectroscopy with different pump energies. Under high carrier concentration, a

longer hot carrier cooling transient has been observed in InP as compared to

GaAs, when electrons energy is not high enough to access satellite valleys,

proving the influence of the hot phonon effect on the carrier relaxation. A clear

indication that the wide phononic bandgap of InP slows carrier cooling, by

minimizing the decay of zone center optical phonons, has also been observed.

This is explained by the stronger Fröhlich interaction for InP as compared to

GaAs. It was found that the Fröhlich interaction is not the limiting factor for

electron cooling in the valley. Photoluminescence at wavelengths shorter

than the excitation of the ground valley has also been presented, demonstrating

that spectral broadening occurs during the early stage of the thermalisation

process. It has also been shown that intervalley scattering decreases the hot

carrier cooling rate into the main valley. The Fröhlich interaction appears to


130

dominate intervalley scattering, resulting in slowing of carrier cooling in GaAs

by storing hot electrons in side valleys.

The last part of the chapter is dedicated to the investigation of hot carrier

cooling in bulk wurtzite InN samples. Theoretically InN would be the best

candidate, amongst bulk III-V semiconductors, to realize a hot carrier solar cell

absorber. Time resolved photoluminescence experiments have demonstrated

that carriers can be excited above 2000 K in InN using laser pulses of 35 J at

1.1 eV. In the analysed sample, carrier temperature decays towards lattice

temperature with a time constant of around 7 ps, which demonstrates the

presence of hot phonon effect in InN. Although this value is reasonably high, it

is still below the minimum acceptable value for realizing an InN based hot

carriers solar cell absorber. Slower thermalisation constants can be obtained

improving the quality of the material, but this involves demanding deposition

techniques.


131

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59. Pacebutas, V., G. Aleksejenko, A. Krotkus, J.W. Ager, I.W.

Walukiewicz, H. Lu, and W.J. Schaff, Optical bleaching effect in InN

epitaxial layers. Applied Physics Letters, 2006. 88(19): p. 191109.

60. Sun, C.K., Y.L. Huang, S. Keller, U.K. Mishra, and S.P. DenBaars,

Ultrafast electron dynamics study of GaN. Physical Review B, 1999.

59(21): p. 13535-13538.

61. Tsen, K.T., J.G. Kiang, D.K. Ferry, H. Lu, W.J. Schaff, H.W. Lin, and

S. Gwo, Direct measurements of the lifetimes of longitudinal optical

phonon modes and their dynamics in InN. Applied Physics Letters, 2007.

90(15): p. 152107-3.

62. Bhuiyan, A.G., A. Hashimoto, and A. Yamamoto, Indium nitride (InN):

A review on growth, characterization, and properties. Journal of



137

4.8 Publications

R. Clady, M.J.Y. Tayebjee, P. Aliberti, D. König, N. Ekins-Daukes, G.

Conibeeer, T.W. Schmidt, and M.A. Green, “Interplay between Hot phonon

effect and Intervalley scattering on the cooling rate of hot carriers in GaAs and

InP”, Progress in photovoltaics, 2011.

Chapter 5

DISCUSSION

Chapter 5: Discussion

138

5.1 Introduction

In the first four chapters of this thesis some of the main scientific and

technological aspects related to the development of a HCSC have been

analysed. Although different aspects of the HCSC design have been treated

separately, one of the clear outcomes of this thesis work is that physical and

electrical properties of absorber and ESCs are highly correlated. The

characteristics of ESCs determine requirements of the absorber material and

vice versa, thus the design of a HCSC has to be seen as a single task, where the

properties and structures of the different components have to be engineered

simultaneously.

This chapter has the aim of bringing the contents studied in the thesis into a

single broad picture, discussing the relations between the properties of ESCs

and absorber material together with technological issues related with the

fabrication of a HCSC device. In particular the first part of the chapter is

dedicated to the discussion of the main parameters that determine the final

device performances and how they are cross-linked with each other.

Subsequently the influence of extraction properties of ESCs on the device

performances is analysed. Two different techniques for realization of contacts

are discussed with some references to compatibility of deposition methods of

contacts and absorber. The second part of the chapter is dedicated to the

analysis of different III-V bulk materials and group IV nanostructures that can

potentially be used as absorbers for HCSC. In the last part of the chapter a

possible preliminary design for a prototype of a HCSC is presented with band

diagrams and potential device configuration.


139

5.2 Correlation between important

parameters of a hot carrier solar cell

In chapter 2 the efficiency limits of a HCSC have been studied in relation to

absorber physical, electrical and optical properties for ideal and non-ideal

ESCs. The modelling work demonstrated that the extraction energy level and

the ESCs selectivity are closely related to hot carrier energy distribution into

the absorber. Thus, the ESCs requirements are different according to E-k

dispersion and absorption properties of the absorber. In addition the energy

distribution of the hot carriers is correlated to their thermalisation velocity [1].

A very fast thermalisation rate implies high losses and that the carrier energy

distribution will have its peak closer to the conduction band of the absorber. A

slow thermalisation velocity allows carriers to stay hot for longer periods,

permitting extraction at higher energies, and thus with a smaller energy loss.

The hot carrier relaxation velocity depends on the absorber layer phononic

dispersion relations and carrier density [2]. The carrier density is directly

related to the equilibrium between absorption, emission and extraction of

carriers established at steady state device operation. Absorption and re-

emission of carriers are related to the electronic properties of the absorber, but

also depend on the hot carrier energy distribution or hot carrier effective

temperature [3].

In Figure 5.2.1 the main properties and processes involved in the energy

conversion are shown schematically with the aim of clarifying their first order

interactions.


Figure 5.2.1 – Block diagram of main mechanisms involved in the HCSC energy

conversion.

Results from theoretical modelling discussed in chapter 2 allow the

conclusion that the limiting efficiency of the device is directly proportional to

the carrier cooling constants. In other words, the slower the cooling of the hot

carriers the higher is the maximum achievable efficiency [1, 4].

Thus, as schematically reported in Figure 5.2.2, the design of a hot carrier

cell should start from choosing the material system that offers the best

properties in terms of carrier cooling and absorption of the solar spectrum.

Furthermore realization of a device with this material system has to be

technologically feasible at moderate costs. The technology has to allow design

and realization of ESCs, possibly using the same deposition methods. This

minimizes the chances of having carrier transport problems at interfaces

between absorber layer and ESCs. After the material system has been selected,

the carrier cooling velocity can be measured using techniques described in

chapter 4. Once thermalisation behaviour is known, the energy distribution of

hot carriers can be calculated for different extraction regimes using techniques

described in chapter 2. This assumes that the optical, electrical and phononic

properties of the absorber are known in detail. Using results of the theoretical

calculations the properties of the ESCs can be optimized [1]. The selected

140


structure should allow some flexibility in defining the energy extraction levels

and the selectivity of the contacts. The ESCs system analysed in chapter 3, for

instance, provides a high flexibility in choosing the extraction energy, but does

not offer a good possibility of modifying energy selectivity.

Figure 5.2.2 – Schematic steps sequence for the HCSC design.

141


142

5.3 Considerations on energy selective

contacts

In chapter 3 the possibility of realizing ESCs using Si QDs in a SiO2 matrix

has been studied. The opportunity of tuning the extraction energy in an

acceptable range has been demonstrated [5]. However, selectivity requirements

of the structures do not match required values. In particular the poor selectivity

observed in the I-V characteristic of the device is most probably due to the

non-uniformity of QDs sizes and positions in the dielectric matrix, besides the

high density of defects. Figure 5.3.1 (a) shows the electron transmission

probability through a Si QDs in SiO2 structure for different device total

thickness and constant QD size. The calculated transmission peak has a FWHM

that goes from 1 μeV, for the thickest structure, to 74 meV for the thinnest.

These values appear to be matching quite well with results of calculations in

chapter 2, where an optimal energy extraction window of 20 meV to 50 meV

has been reported. Unfortunately the poor uniformity of QDs sizes in the

structure and the distribution of QD positions around the centre of the device

generate a drop in the transmission probability of the entire device and thus the

ESCs conductivity [6-8]. This implies much higher FWHM values. It has been

demonstrated that a poor uniformity of the QDs sizes completely deteriorates

the energy selectivity properties of the entire structure, flattening out any

negative differential resistance peak in the current-voltage characteristics [7].

Despite the technological challenges in obtaining very uniform QD layers, the

Si/SiO2 system remains an interesting option for realization of ESCs due to

processing flexibility and the possibility of integration with group IV based

nanostructured absorbers.


Figure 5.3.1 – (a) Transmission coefficient of Si QDs in SiO2 structures for different

thickness of the dielectric matrix. (b) Transmission coefficient assuming normal distribution

of QDs position around the matrix center, adapted from [8]. (c) Transmission coefficient

assuming normal distribution of QD sizes, is the distribution standard deviation [6].

143


The possibility of realizing absorber materials using either bulk or

nanostructured III-V semiconductor systems has been demonstrated in chapter

2. ESCs for III-V based absorber could be realized using a QW structure in a

resonant tunneling diode (RTD) like configuration. RTD structures based on

III-V semiconductor structures have been intensively studied during the last

fifteen years for their importance in the nanoelectronics field and their

potential applications in very high speed devices and circuits. Nowadays III-V

based RTDs with good NDR properties can be fabricated using MBE [9-11].

Figure 5.3.2 – (a) Schematic diagram of AlN/GaN double barrier resonant tunneling diode

grown by rf-MBE on MOCVD-GaN template. (b) Theoretical calculation of first resonant

energy level of AlN/GaN double barrier structure as a function of GaN well width [10].

Figure 5.3.2 (a) shows a schematic of an AlN/GaN RTD realized on a

sapphire substrate. A MOCVD-GaN layer and a series of multiple AlN and

GaN interlayers are grown to minimize threading dislocations and flatten the

surface morphology of GaN layers [12]. Figure 5.3.2 (b) shows that the

resonant energy level can be varied changing the width of the GaN well,

satisfying the main requirements for ESCs discussed in the previous section.

However, this structure is not suitable for integration with an InN absorber

since the electronic bandgap of GaN is too wide (3.4 eV).

For integration with an InN based absorber a GaN/InN RTD should be

adopted. This structure can be grown in a configuration similar to the device

shown in Figure 5.3.2 and would also be optimum for the successive growth of

the InN absorber layer. In fact, GaN nucleation layers are currently used on a

144


sapphire substrate for the growth of bulk InN and InN nanostructures, since no

lattice matched substrates are available [13-16].

5.3.1 Additional requirements for energy selective contacts

design

The tunable resonant energy levels in a GaN/InN RTD are different in the

conduction and valence bands of the QWs due to the different effective masses

of electrons and holes.

22

22

2 mLvhE n

n (5.3.1)

Equation (5.3.1) is a simplified formula to calculate the energy of confined

levels in a finite potential quantum well. In (5.3.1) vn is a number that depends

on the width of the well and it comes from the numerical solution of the

Schrödinger equation. L represents the width of the quantum well and m is the

effective mass of the tunneling particle. The equation shows that for particles

with higher masses the confined energies are closer to the respective band

edge. This implies that for heavier particles a thinner QW is needed in order to

obtain similar confined energy levels.

Assuming that electrons and holes maintain the same effective mass as in the

absorber during the extraction process, the width of the electrons ESC QW can

be easily calculated. Hot electrons, in fact, are distributed along the main

valley, thus they all have a similar effective mass.

Holes in the valence band of the absorber are distributed on three different

bands: light holes (LH), heavy holes (HH) and split off (SH). These bands have

three different effective masses for holes. This implies that, to optimize

extraction of holes, the width of the ESC QW has to be calculated taking into

account the holes energy distribution in the absorber at steady state operation

of the device. It has to be highlighted that the HH band has a much higher

density of states and it hosts most of the hole population. As HH holes a higher

overall effective mass the confined energy levels in the holes ESC QW are

quenched on the valence band edge of the InN layer. This implies that the holes

145


146

ESC QW should be physically thinner than the electron ESC QW to achieve

high extraction energies.

The considerations reported in this section are valid for an InN absorber and

can be generalised to III-V absorbers and ESCs. However, they would have to

be reconsidered in case of other material systems, where the band structures

can be considerably different.

The QW structures discussed in this section allow energy selectivity of

extracted carriers by double barrier resonant tunnelling. However these

structures do not have any selectivity in terms of carrier type. In other words

they do not have a rectifying characteristic. In theory electrons could tunnel

through the confined energy level of the holes ESC and vice versa. To obtain

rectifying ESCs different approaches can be used, for example each ESC could

include a thin layer of a doped wide bandgap semiconductor that acts as an

electron or hole reflective membrane. This membrane layers should have a

wide phonon gap as well, to prevent thermalisation. A diagram of a possible

configuration of these membrane layers is shown in the last section of this

chapter.

The real losses due to the non rectifying behaviour of ESCs have not been

evaluated yet and are not included in the model presented in chapter 2.

However it is possible that these losses do not have a major influence on device

performances if asymmetric QWs are used as ESCs. In fact, as mentioned

earlier, the holes QW has to be much thinner than the electron QW, due to the

difference in effective masses. This would bring the confined energy level for

extraction of electrons at the holes contact to very high energies, preventing

extraction. Hence, as electrons extraction is only possible from one contact,

holes will only be extracted from the holes ESC as a consequence, allowing the

device to have the rectifying behaviour of a conventional solar cell, even

without rectifying membranes.


147

5.4 Considerations on absorber materials

The selection of an appropriate absorber material is the first step towards the

fabrication of a HCSC, as discussed in the Section 5.2. In general this selection

has to be done according to four criteria: good phononic and optical properties,

feasible technological processability, which allows realizing low defects and

good quality structures at a reasonable cost, abundance on earth, possibility of

integration with the ESCs system. For the HCSC design to be successful the

absorber material has to satisfy these four requirements at the same time.

5.4.1 Bulk semiconductors

The possibility of having an absorber layer based on bulk semiconductors is

very attractive. This would keep processing of the device reasonably simple

and it would minimize carrier transport related issues. Bulk materials, direct

bandgap materials in particular, also show good absorption properties and can

potentially be very well integrated with ESCs. The main drawback of using

bulk absorbers is that, in general, the carrier cooling is ultrafast, from hundreds

of femtoseconds to few picoseconds, at most. The reason for this is that many

bulk materials and compounds show either very small phononic gaps or no

phononic gaps. Bulk semiconductors with a large difference in their anion and

cation masses have wider bandgaps between highest acoustic phonon energy

and the lowest optical phonon energy. To prevent Klemens decay of optical

phonons this bandgap has to be larger than the maximum acoustic phonon

energy [2]. This property can be observed in some III-V materials such as: InN,

GaN, InP, BBi and AlSb. Similar properties have also been observed in II-VI

systems. II-VI compounds will not be discussed here because currently it is

very complicated to deposit high quality films with reasonable costs.


Figure 5.4.1 – Ratio of phononic bandgap energy values and electronic bandgap values for

some III-V binary compounds. Data on phononic bandgaps are adapted from [17]. BiB

electronic bandgap is extracted from [18].

Figure 5.4.1 shows phononic and electronic bandgaps for several III-V bulk

compounds. The InP phonon gap is just the below the necessary value to

prevent Klemens mechanism (dashed line). BBi, InN, GaN and AlSb have

phononic gaps which are large enough to prevent Klemens mechanism.

However GaN is clearly not suitable as an absorber due to its large electronic

bandgap. The maximum theoretical efficiency of a GaN based HCSC,

calculated using a simple PC model, is below the efficiency of current wafer

based solar cells. The same model predicts an efficiency of less than 50 percent

for an AlSb HCSC in full concentration conditions. Nevertheless it has been

demonstrated in chapter 2 that, when a calculation method more detailed than

PC is adopted, efficiency figures can drop more than 30 percent. This would

give an efficiency which is too low to justify the use of AlSb for solar cell

fabrication. BBi has a reasonably low electronic bandgap and a very wide

phononic gap. Furthermore, according to theoretical simulations, BBi is stable

in a zinc-blende form [18]. Unfortunately BBi has not been synthesized yet due

to the very large difference in atomic masses of B and Bi. Others III-V

compounds of potential interest are ScN, YN, LuN, CeN, GdN, but they are too

rare to be utilized for solar cells fabrication. Hence it appears that InN is the

best solution to attempt a first realization of a bulk HCSC absorber, since it has

suitable phononic and electronic properties. In addition currently there is an

148


149

established technology to deposit high quality InN layers using plasma assisted

MBE.

5.4.2 Nanostructured semiconductors

The main problem related with realization of absorbers using bulk III-V

materials is the fixed hot carrier cooling velocity and the rarity on the earth

crust of some materials, such as In. Nanostructured semiconductors permit

using the Bragg reflection of phonons at the interfaces of mini-Brillouin zones

in order to prevent phonon decay. This allows slower carrier cooling in III-V

superlattices and engineering phononic gaps in more abundant materials, such

as group IV elements.

The dependence of hot carrier cooling time on the structure dimensionality

has been initially investigated in bulk GaAs and GaAs/AlxGa1-xAs quantum

wells (QWs). It has been proven that for high photoexcited carrier density

regimes the hot carrier relaxation in QWs structures is much slower than in

bulk GaAs. This is due to the enlarged phononic bandgaps caused by the

decrease in structure dimensionality and, as a second order effect, by the

enhanced screening of the electron-LO phonon interaction in QWs in high

carrier density conditions [19]. In addition for GaAs QWs the exciton that

forms near the band edges has a large wave vector, thus does not tend to couple

to photons and undergo radiative decay [20]. Folding of acoustic phonon

branches can be obtained using QDs superlattices in III-V systems. This has

been theoretically and experimentally verified using time resolved Raman

scattering experiments and TRPL for InGaAs/GaAs and GaAlAs QDs

superlattices [21-24]. In theory also in group IV QDs superlattices the LA

phonon scattering rates are supposed to decrease with increasing quantization

energies [25, 26]. Scattering of conduction band electrons and large wave

vector phonons has been observed in colloidal Si QDs using time resolved

optical spectroscopy. These have been found to be responsible for slow decays

of photoinduced absorption bands (470 nm, 600 nm and 700 nm) with time

constants from 110 ps to 180 ps [27].


150

5.5 Possible preliminary design of a hot

carrier solar cell

Figure 5.5.1 (a) shows a simplified, unbiased, band diagram of a possible

implementation of HCSC. In particular here the solution based on the model

presented in chapter 2 is shown. The HCSC is constituted of a bulk InN

absorber and ESCs based on a GaN/InN QW system. The figure also shows the

carrier selective membranes for rectifying ESCs discussed in Section 5.3.1.

These membranes could be implemented using a doped high bandgap III-V

semiconductor, such as GaN, which has a wide phonon gap and can prevent

thermalisation. Holes and electrons are extracted to respective metal contacts

through GaN/InN/GaN QW structures which act as double barrier resonant

tunnelling devices. The figure shows that a different width of the QWs is

necessary to tune extraction energy level of holes and electrons due to their

difference in effective masses. Figure 5.5.1 (b) shows a detail of the GaN/InN

barrier with values of bandgap and energy steps for electrons and holes. Values

have been calculated respective to intrinsic Fermi level, taking into account the

effective density of states. The figure is in scale along the y axis but not along

the x axis. In fact an absorber layer with thickness between 50 nm and 100 nm

has to be used to optimize light absorption and thermalisation, whereas

thickness of QWs would be less than 10 nm for each ESC.

A possible realization of the structure shown in Figure 5.5.1 is presented in

Figure 5.5.2 with details of the different layers. The device can be grown on a

sapphire (Al2O3) <0001> substrate using plasma assisted MBE. GaN nucleation

layers have to be used to improve crystal quality and reduce defect density.

SiO2 can be adopted to insulate the structure from metal contacts. Two

successive photolithography steps have to be performed to contact the holes

ESC QW. SiO2 passivation and Ti/Al contacts can be realized using sputtering

or PECVD and evaporation techniques respectively.


Figure 5.5.1 – (a) Simplified band diagram of a possible implementation of an InN based

HCSC. (b) Detail of energy barriers at the InN/GaN interface.

Figure 5.5.2 – Possible layered structure of an InN based HCSC.

151


152

5.6 Summary

In this chapter the contents and the results presented in the first four

chapters of this thesis have been further analysed and discussed in the

framework a HCSC device design and realization. The different challenges

related to the integration of absorber layers and suitable energy selective

contacts are addressed.

In particular in the first part of the chapter the interactions between the main

physical parameters of a HCSC are analysed using a schematic approach. This

confirms the necessity of designing the entire HCSC at once, since interaction

of absorber and energy selective contacts are crucial for the device

functionality. In this section a possible sequence of design step for a HCSC is

also presented.

The second section of the chapter is dedicated to a series of considerations

on energy selective contacts, mainly inspired by results obtained in chapters 2

and 3. The requirements of energy selective contacts structures in terms of

energy selectivity and integration with the absorber are discussed together with

advantages and drawbacks of both III-V and Si QDs based structures. The

possibility of having rectifying energy selective contacts is also addressed.

The third section of the chapter is dedicated to a presentation of possible

materials that stimulated research interest as possible hot carrier solar cells

absorbers, with a particular focus on bulk III-V compounds. A careful

screening of these compounds shows that InN is the most reasonable solution to

realize a bulk III-V absorber. The possibility of using nanostructure based

absorbers is also briefly discussed.

The last part of the chapter is dedicated to the presentation of a possible

implementation a HCSC based on InN/GaN system. A simplified band diagram

schematic is reported together with a schematic representation of the final

device.


153

5.7 Bibliography




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Chapter 6

CONCLUSIONS

AND FUTURE WORK

Chapter 6: Conclusions and future work

156

In this thesis different aspects related to the designing and the realization of

a hot carrier solar cell converter have been investigated. This project

contributes to the research in “third generation photovoltaics” which has the

aim of engineering novel solar cell devices that can overcome the Shockley-

Queisser efficiency limit.

The work is divided in five main chapters.

The first chapter gives an overview of the current world energy consumption

and generation, focusing the attention on the role of renewable energies in the

near future energy market. In this chapter an introduction to photovoltaic

devices is given with details of different “generations” of solar cells. The status

of current research in third generation is depicted before introducing the

concept and operating principle of the hot carrier solar cell. The main

theoretical aspects related to the functionality of the hot carrier solar cell are

briefly described introducing the detailed discussion presented in the rest of the

thesis.

In the second chapter the calculation of real efficiency limits for a hot

carrier solar cell based on an indium nitride absorber is presented. A hybrid

model, which takes into account both particle balance and energy balance, has

been implemented. The model allows consideration of the influence of real AR

and II rates on cell performances, together with actual thermalisation losses.

The real InN dispersion relation has been reconstructed using actual effective

masses for different bands and non-parabolicity effects. A maximum efficiency

of 43.6 percent has been found for 1000 suns solar concentration. A close

relation between carrier thermalisation velocity and solar cell maximum

efficiency has also been found. In the last section of the chapter the influence

of non-ideal energy selective contacts on cell performances is discussed. It was

found that to maintain high efficiency (39.6 percent) the width of the contacts

has to be about 20 meV.


157

In chapter three theoretical and experimental aspects of all-silicon energy

selective contacts for hot carrier solar cells are investigated. Structures

consisting of a single layer of silicon quantum dots in a silicon dioxide matrix

have been realised using radio frequency magnetron co-sputtering and high

temperature annealing. Physical and optical properties of silicon rich oxide and

silicon dioxide layers have been studied in order to optimize the characteristics

of the single layer quantum dot structures. Photoluminescence and absorption

measurements confirmed that the morphology of the nanoparticles in the films

is related to the former silicon excess values. It was found that an atomic ratio

of silicon to Oxygen around 0.9 allows obtaining good size distribution and

density of the silicon quantum dots. It has also been demonstrated that the

average size of the quantum dots can be accurately controlled modifying the

thickness of the silicon rich oxide layers and that the position of the

photoluminescence peak is directly related to the diameter of the quantum dots.

In addition the evolution of the PL signal during the annealing process has been

studied. It was found that the crystallization of the silicon quantum dots occurs

during the very early stage of the annealing process. Further evolution of the

physical and optical properties of the samples is strictly related to an Ostwald

ripening process and partial oxidation of the quantum dots in the annealing

atmosphere. The optical properties of the structures after furnace forming gas

treatments confirmed that defects at Si-SiO2 interface have an active role in the

photoluminescence process. These defects can create non-radiative

recombination centres but they do not generate any additional radiative paths

for confined excitons. Since no significant energy peak shift was observed after

forming gas annealing, it was concluded that the main mechanism underlying

the luminescence of sputtered single silicon quantum dots in silicon dioxide is

optical quantum confinement.

In the fourth chapter time resolved photoluminescence experiments have

been performed on III-V bulk semiconductors in order to investigate the factors

that influence hot carrier cooling processes. The influence of the hot phonon

effect and intervalley electron scattering on the hot carrier cooling rates of bulk

gallium arsenide and indium phosphide have been studied. Under high carrier


158

concentrations, a longer hot carrier cooling transient was observed in indium

Phosphide compared to Gallium Arsenide when electron energy is not high

enough to access satellite valleys. This proved the influence of the hot phonon

effect on the carrier relaxation. It was also demonstrated that intervalley

scattering decreases the hot carrier cooling rate into the main valley. The

Fröhlich interaction appears to dominate intervalley scattering, resulting in

slowing of carrier cooling in GaAs by storing hot electrons in side valleys. The

second half of this chapter is dedicated to the investigation of hot carrier

cooling in bulk wurtzite indium nitride samples. Time resolved

photoluminescence experiments have demonstrated that carriers can be excited

above 2000 K in indium nitride using laser pulses of 35 J at 1.1 eV. The

carrier temperature decays towards the lattice temperature with a time constant

around 7 ps, which demonstrates the presence of a pronounced hot phonon

effect in indium nitride.

In chapter five a review and discussion of results presented in the other

chapters is presented within the framework of the design of a hot carrier solar

cell. The interactions between the main physical parameters of the cell are

analysed and discussed, confirming that the hot carrier solar cell has to be

designed as a whole device at once. In fact, the interaction of absorber and

energy selective contacts properties are crucial for the device functionality.

The requirements of energy selective contacts in terms of energy selectivity

and integration with the absorber are discussed in this chapter together with the

possibility of having rectifying contacts. The last section of the chapter is

dedicated to a screening of possible III-V compounds which can be used as

potential hot carrier solar cell absorbers and to the presentation of a possible

implementation a hot carrier solar cell device.

This thesis investigated some of the basic aspects related to the development

of a hot carrier solar cell. The aim of the work was to study solutions and

materials in order to achieve actual progress towards the fabrication of the

device. Results have been obtained for the calculation of maximum efficiencies

of hot carrier solar cells, for the realization of energy selective contacts and in


159

addition a potential structure for a hot carrier solar cell based on III-V

compounds has been presented. However, this thesis is still to be considered as

a preliminary step towards the realization of a hot carrier solar cell, since this

task still faces great scientific and technological challenges. Much room exists

for further investigation of nanostructured absorbers, both in III-V compounds

and group IV materials, in order to obtain slower hot carrier cooling

behaviours. The electrical properties of energy selective contacts based on III-

V quantum wells has to be studied in order to optimize extraction from

different absorbers. Additional investigation is also required to study carrier

transport mechanisms in both absorbers and energy selective contacts, with the

aim of clarifying whether it is possible to extract carriers very rapidly after

generation, in order to prevent thermalisation losses.

In conclusion this thesis presents recent progresses towards the development

of the hot carrier solar cell. Results provide a detailed picture of this device in

terms of potential achievable efficiencies, development of absorber materials

and energy selective contacts. Findings of this work have to be considered as a

preliminary insight for the development of the hot carrier solar cell. Further

research is needed in order to accomplish the successful realization of an actual

device.

hot carrier solar cells

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