Study of quantum dots on solar energy applicationskth.diva-portal.org/smash/get/diva2:525075/FULLTEXT01.pdf · Chapter 1 Introduction 1.1 Green energy: semiconductor solar cells Energy

Study of quantum dots on solar

energy applications

Xiang-Jun Shang

Doctoral Thesis in Theoretical Chemistry and Biology

School of Biotechnology

Royal Institute of Technology

Stockholm, Sweden 2012

Study of quantum dots on solar energy applications

Thesis for Philosophy Doctor degree

Division of Theoretical Chemistry and Biology

School of Biotechnology

Royal Institute of Technology


c© Xiangjun Shang, 2012

pp i-xii, 1-60

ISBN 978-91-7501-352-7

ISSN 1654-2312

TRITA-BIO Report 2012:12

Printed by Universitetsservice US-AB


To my parents

Abstract

This thesis is devoted to experimental and theoretical study of p-i-n gallium

arsenide (GaAs) solar cells with self-assembled indium arsenide (InAs) quantum

dots (QDs) inserted. It gives detailed study in aspects: the QD growth and the de-

sign and fabrication of QD solar cells; the photovoltaic (PV) current-voltage (I-V)

measurement under solar simulator and the diode performance analysis; the pho-

toluminescence (PL) spectroscopy and the photocurrent (PC) spectroscopy; the

simulation of the device energy-band structure; and the discussion of the mech-

anisms of PC production from QDs, based on bias- and temperature-dependent

PC spectra.

The values of this work lie in three aspects. First, by comparing the solar

cell performance with QDs in the i-region and the n-region, we prove that for the

PC production from QDs, either the pure thermal activation or the intermediate

band (IB) cascade absorption proposed by Luque et al has lower efficiency than

the tunneling and the thermal activation-assisted tunneling, so, the IB-based QD

solar cells with QDs in the n-region make no sense to raise the PV efficiency

of a traditional single-junction solar cell to a level beyond the Shockley-Queisser

limit (31%). Second, the efficiency of the PC production from QDs (i.e. the QD

responsivity), characterized by the device PC spectra, is helpful to the design

of InAs QD-based near-infrared photodetectors. Third, the 20 nm-thick GaAs

spacers for QD layers are proper in thickness to form dislocation-free strain cou-

pling in adjacent QD layers and vertically aligned QDs, between which a strong

inter-QD-layer tunneling exists, leading to an effective PC production from QD

states, even the ground state, which has been reflected from the bias dependence

of each peak intensity in the PC spectra. A much broad-band PC production is

thus expected in closely stacked QDs for solar cell and photodetector applications.

Fourth, by analyzing the temperature-dependent PC spectra it is found that the

minority photohole thermal escape is dominant for PC production from QDs in

the n-region. The activation energy (Ea) characterizes the energy offset between a

QD hole-state and flat GaAs valence bandedge, providing a means to reconstruct

the QD energy level diagram.

Apart from the study of InAs QDs, in cooperation with co-authors, I also ex-

plore the time correlation of the light emission from two individual colloidal CdSe

QDs. The light emission from each colloidal QD is intermittent, i.e. so-called

‘QD blinking’, with time constant varying from 1 ms to 1000 s. We record the

blinking of a QD-pair sample by a 1000-frame movie in 50 ms/frame, extract the

evolution of the light intensity from each QD, and analyze the time correlation

vi

between the two QDs as their interval time τ varies. It is found that, for QD

distance of 1 µm or less, there is a bunched correlation at τ = 0, meaning that the

two QDs blink synchronously; otherwise, such correlation disappears gradually.

Although the time scale, 50 ms/frame, is too rough to conclude a strict simulta-

neous photon emission, the synchronous blinking still extends the understanding

of colloidal QD blinking that is related to the photocarrier tunneling from a QD

to the surface traps. This correlation, possibly caused by the stimulated emission

(∼ ps) between two QDs, is potential to generate coherent photon-pairs.

Preface

The work presented in the thesis was fulfilled at the Division of Theoretical Chem-

istry and Biology, School of Biotechnology, Royal Institute of Technology, Stock-

holm, Sweden and State Key Laboratory of Superlattices and Microstructures,

Institute of Semiconductors, Chinese Academy of Science, Beijing, China. The

Fourier transformed infrared spectroscopy of photocurrent was performed at Cen-

ter for Applied Mathematics and Physics, Halmstad University, Halmstad, Swe-

den. The photovoltaic efficiency measurement under a Xenon lamp solar sim-

ulator and the monochromator-based photocurrent spectroscopy in 300-1000 nm

were performed under the help from Department of Chemistry, School of Chemical

Science and Engineering, Royal Institute of Technology, Stockholm, Sweden.

List of papers included in the thesis

Paper 1. Effect of built-in electric field on photovoltaic effect of InAs quantum dots

in GaAs solar cells,

X.-J. Shang, J.-F. He, H.-L. Wang, M.-F. Li, Y. Zhu, Z.-C. Niu, and Y.

Fu,

Appl. Phys. A 2011, 103, 335.

Paper 2. Quantum-dot-induced optical transition enhancement in InAs quantum-dot-

embedded p-i-n GaAs solar cells,

X.-J. Shang, J.-F. He, M.-F. Li, F. Zhan, H.-Q. Ni, Z.-C. Niu, H. Pet-

tersson, and Y. Fu,

Appl. Phys. Lett. 2011, 99, 113514.

Paper 3. Photocarrier extraction from closely stacked InAs quantum dot layers em-

bedded in GaAs solar cells,

X.-J. Shang, J.-F. He, M.-F. Li, F. Zhan, H.-Q. Ni, Z.-C. Niu, H. Pet-

tersson, and Y. Fu,

In manuscript.

Paper 4. Observation of bunched blinkings from individual colloidal CdSe/CdS and

CdSe/ZnS quantum dots,

H.-Y. Qin, X.-J. Shang, Z.-J. Ning, T. Fu, Z.-C. Niu, H. Brismar, H.

Agren, and Y. Fu,

Submitted.

viii

Comments on my contributions to the papers included

As the first author, I have taken the major responsibilities, i.e., sample fabri-

cations, experimental measurements, and formulating Papers 1-3, corresponding

with the journals. As a co-author, I did the numerical analysis and writing of the

time correlation of QD-pair blinking, participated in the discussions and formula-

tion of paper 4.

Acknowledgments

I want to give my sincere gratitude to my supervisor Dr. Ying Fu. I am benefit a

lot from his continuous guidance on my study and assistance on my totally new life

in Sweden. His trust, encouragement and support help me to keep self-confidence

in front of each scientific problem and get out of valleys and difficulties on my

research road. His valuable suggestions often correct my naive ideas on science

and insight into the real interesting things of our research. I am thankful to him

for all these aspects.

I am grateful to my home supervisor, Prof. Zhichuan Niu, at Institute of

Semiconductors, Chinese Academy of Science. In his active research group I have

chance to study the molecular beam epitaxy of GaAs-based III-V compound semi-

conductors, especially self-assembled InAs QDs and QD-based optoelectronic de-

vices. I am also thankful to him because he gave me an opportunity to study

abroad in a beautiful, quiet, free and scientific environment.

Thank Prof. Hans Agren, head of Division of Theoretical Chemistry and

Biology, for building a friendly, free and scientific environment for study. Kindly

thanks to Prof. Yi Luo for his help in my study life here. Sincerely thanks to Dr.

Yaoquan Tu for friendly talking on the academic career. Thanks to Prof. Faris

Gel’mukhanov and Prof. Boris Minaev for setting good examples of true scientists

with continuous interest and assiduity on their work to young beginners in science

like me.

Thanks to Dr. Zhijun Ning, Dr. Qiong Zhang and Dr. Kai Fu for their kindly

help on my living in Stockholm. Thanks to my colleagues Zhihui Chen, Chunze

Yuan, Li Li, Dr. Xifeng Yang, Staffan Hellstrom, Guangjun Tian, Dr. Weijie

Hua, Dr. Qiang Fu, Dr. Xin Li, Xing Chen, Xiuneng Song, Yong Ma, Quan

Miao, Lili Lin, Yongfei Ji, Hongbao Li, Sai Duan, Lu Sun, Li Gao, Ying Wang, Ce

Song, Junfeng Li, Wei Hu, Yan Wang, Xiaoqiang Sun, Xinrui Cao, Lijun Liang,

Dr. Peng Cui and Dr. Liqin Xue, who have made my daily life in Sweden happy.

Thanks to Dr. Arul Murugan, Dr. Zilvinas Rinkevicius, Dr. Kestutis Aidas and

Bogdan Frecus for badminton exercise in weekend.

Sincerely thanks to Prof. Hakan Pettersson at Halmstad University for Fourier

transformed infrared spectroscopy of photocurrent and the valuable suggestions on

my manuscripts. Thanks to Dr. Haining Tian in Department of Chemistry, Royal

Institute of Technology for the help on the photovoltaic efficiency measurement

and the monochromator-based photocurrent spectroscopy.

x

I want to acknowledge the two-year financial support from the Chinese Schol-

arship Council.

Finally, I want to thank my parents for their selfless love, understanding and

support. As the thrifty holders of a peasant family, they sacrifice their material

and spiritual enjoyment to bring up two children, and allow their only son to

choose a path completely different from the surrounding peers.

Xiangjun Shang

2012-1-2, Stockholm

Contents

1 Introduction 1

1.1 Green energy: semiconductor solar cells . . . . . . . . . . . . . . . 1

1.2 Materials: Si or compound semiconductors? . . . . . . . . . . . . 3

1.3 High efficiency: by multi-junctions or nanostructures? . . . . . . . 4

1.4 Quantum dot solar cells . . . . . . . . . . . . . . . . . . . . . . . 5

2 Experimental techniques 8

2.1 Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Photoluminescence spectroscopy . . . . . . . . . . . . . . . . . . . 11

2.4 Photovoltaic I-V measurement . . . . . . . . . . . . . . . . . . . . 13

2.5 Photocurrent spectroscopies . . . . . . . . . . . . . . . . . . . . . 13

3 Self-assembled InAs quantum dots 17

3.1 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Photoluminescence spectrum . . . . . . . . . . . . . . . . . . . . . 21

3.4 Closely stacked QDs . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Quantum description of optical properties . . . . . . . . . . . . . 23

4 InAs QD-embedded solar cells 26

4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Photovoltaic I-V measurements . . . . . . . . . . . . . . . . . . . 31

4.4 Photocurrent spectra . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.5 Mechanisms of photocarrier escape from QDs . . . . . . . . . . . 37

xi

xii CONTENTS

5 Bunched correlation of two colloidal QD blinking 42

5.1 QD fluorescence imaging system . . . . . . . . . . . . . . . . . . . 43

5.2 Correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3 Statistical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.4 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6 Summary of the included papers 53

References 55

Chapter 1

Introduction

1.1 Green energy: semiconductor solar cells

Energy is the engine of economic development in a modern society. Fossil fuels

contribute more than 85% of the global energy consumption. As BP statistical

review reported [1], during 2010, the world consumes 4350.4 million tons of oil (i.e.

87382 thousand barrels daily), 3169.0 billion cubic meters of nature gas (or 2852.1

million tons of oil equivalent) and 3555.8 million tons of oil equivalent of coal,

meaning a total energy consumption of 4.7×1013 kWh. The shortage of these

fossil energies and the overdischarge of greenhouse gases have been global crises

in recent years. Governments and scientists in many countries have been making

efforts to find alternative energy, especially “green energy” that is friendly to the

environment. There are several kinds of green energy, including nuclear power,

hydroelectric power, wind power, geothermal power, tidal power, and solar cell.

Nuclear power and hydroelectric power are most effective to obtain considerable

and sustainable power supply. However, nuclear power is limited by sophisticated

technology and only widely used in a few developed countries until now; moreover,

it is quite dangerous if there are some operation faults that have been observed

during Fukushima nuclear disaster (2011). Hydroelectric power is limited by the

geography (i.e. a river) and the rainfall amount; it would influence the ecology and

the climate possibly. Compared to them, solar cell that utilizes solar light to create

electric energy is easier on technology, safer, without gas pollution, unlimited by

the geography (especially suitable for deserts) and with sufficient resource (the

solar energy is 925 W/m2 at Sea level (AM1), see the spectrum in Fig. 1.1, and

the earth cross-section area for the normal incident sunlight is 1.3 × 1014 m2),

showing potential on energy solution in future.

1

2 1 Introduction

Figure 1.1 Solar light spectrum [2].

electron

Front grid contactSolar light

oc Voc

Isc

I

V0

ηmax

electron

hole

donor ion

acceptor ion

+

–p-region

built-in

Vo

c Voc

Back contactn-region

built-in

field

EC

EF

EV

Figure 1.2 Structure, I-V curve and band diagram of p-n junction solar cell.

Solar cell is based on photovoltaic (PV) effect. Semiconductor p-n junction

solar cell is most popular. Its structure, band diagram and I-V curve under light

are shown in Fig. 1.2. In equilibrium, in the junction interface, free electrons

provided by donors in the n-region and free holes provided by acceptors in the p-

region will recombine each other (i.e. ‘depletion’), leaving donor ions and acceptor

ions form the ‘built-in’ electric field. The Fermi level is flat everywhere and there

is no voltage output. Under sunlight, excess electrons and holes generated by

photon absorption will be drifted by this field into opposite regions. If there is no

external connection (i.e. the open-circuit case), these excess carriers will accumu-

late, e.g. see the holes in the p-region in the band diagram, and give an additional

potential, the open-circuit voltage (Voc), that reduces the built-in field (see the

red band diagram), making an equilibrium of photocarrier drift and diffusion and

thus no photocurrent (PC) output. If there is an external connection or load,

these accumulated excess photocarriers will output to produce PC; meanwhile,

the output voltage is reduced. In the short-circuit case when the output voltage is

zero and the Fermi level (EF ) is forced to be flat everywhere (see the black band

diagram), the PC output reaches the maximum (Isc). Between the open-circuit

1.2 Materials: Si or compound semiconductors? 3

case and the short-circuit case, the output voltage and the corresponding output

PC give the I-V curve, along which there is a point corresponding to the maxi-

mum electric power output (i.e. the rectangular area in the I-V curve) and the

maximum PV efficiency (ηmax).

1.2 Materials: Si or compound semiconductors?

In principle, because solar spectrum has a broad distribution from 250 to 2500

nm (see Fig. 1.1), all kinds of semiconductors with bandgap between 0.35 and

3.5 eV, such as Ge (0.66 eV), Si (1.12), InAs (0.36), InP (1.35), GaAs (1.42),

GaP (2.26), GaN (3.44), AlAs (2.16), PbS (0.37), CdTe (1.49), CdSe (1.70), CdS

(2.42) and ZnO (3.35), can absorb above-bandgap photons for solar cell appli-

cation. The lower the bandgap is, the larger the solar light absorption and the

photocurrent are. However, as the bandgap reduces, the Voc also reduces; more-

over, the photocarrier relaxation to the band edge loses more energy. There is an

optimal bandgap for solar cell. Based on the detailed balance principle, Shockley

and Queisser deduced the banggap-related ideal ηmax of a single-junction solar cell,

i.e., Shockley-Queisser limit for real cells [3]. The highest value, 31 %, is obtained

at bandgap of 0.95 ∼ 1.6 eV [2,3]. Si, GaAs, InP and CdTe are good candidates.

Si is abundant on earth, cheap (even for Si crystal wafer), and mature on

technologies of growth, purification and microelectronic device fabrication. Com-

mercial solar cells are mostly made in Si. But, on optoelectronic properties, Si

is not as better as compound semiconductors like GaAs. Si has indirect bandgap

and thus lower absorption coefficient than direct-bandgap GaAs, so Si solar cells

must be much thicker (e.g. 100 µm) than GaAs solar cells (4 µm) in order to ab-

sorb sunlight completely. Moreover, the electron mobility of Si is much lower than

GaAs, resulting in a slower photoelectron drift and diffusion in Si solar cells. As

Solar Cell Efficiency Tables (Version 38) [4] reported, under one sun AM1.5G, the

highest ηmax of single-junction crystalline Si solar cells has reached 25.0±0.5 %;

while that of single-junction crystalline GaAs cell has reached 28.1±0.8 %. GaAs

has another advantage over Si: GaAs crystals can be nearly lattice-matched grown

on Ge substrates [5] and allow InGaP crystals then grown on it; this material serial

is proper for triple-junction solar cell fabrication whose highest ηmax has reached

32.0±1.5 % under one sun AM1.5G. While for Si, the lattice-matched growth of

other materials (e.g. GaP [6]) on it for multi-junction solar cell fabrication is unde-

sired. Of course, considering the expensive GaAs substrate and the growth cost,

high-efficiency GaAs-based solar cells are only potential on satellites.

4 1 Introduction

Due to their optimal properties, compound semiconductors, especially III-V

ones, have been widely applied in optoelectronics such as light emitting diode

(LED), laser, photodetector and solar cell, and in microelectronics such as mi-

crowave and radio-frequency high-speed components in mobile devices [7], playing

a dominant role irreplaceable by the Si-based devices. Beyond these successes,

many potential ‘next steps’ have shown, for example, GaN-based blue and ultra-

violet LED, laser and photodetector [8], GaN power amplifier [9], III-Vs integration

on Si [10], and GaAs-based tera-Hertz devices [11]. Meanwhile, lots of novel nanos-

tructures fabricated on compound semiconductors, e.g. GaAs quantum rods [12]

and GaN nanowire [13], also show potentials for applications.

1.3 High efficiency: by multi-junctions or nanos-

tructures?

The Shockley-Queisser limit with highest value of 31 % forms an upper limit for

the practical single-junction solar cell. Now, the highest ηmax of single-junction

GaAs cell has reached 28.1±0.8 %, very close to this limit. To further increase

the PV efficiency, it must introduce new structures. One scheme is multi-junction

tandem solar cell. Several semiconductor p-n junctions in different bandgaps,

from the top wide-bandgap junction to the bottom narrow-bandgap junction, are

connected together with tunneling junctions, in order to absorb different-energy

photons in different junctions and fully utilize the generated photocarriers with lit-

tle energy loss during their relaxation into the bandedge. A multi-junction tandem

solar cell always works under concentrated solar light (e.g. 1000 suns). It produces

higher Voc. However, the Isc of each junction must be matched to avoid the bot-

tleneck of the maximum photocurrent output in some junctions, so the bandgap

and thickness of each junction must be proper. Moreover, limited by the lattice

match requirement for dislocation-free crystal growth, the material series of multi-

junctions is not free to choose. Now, the popular series is GaInP/Ga(In)As/Ge,

with the maximum PV efficiency beyond 40 % under 500 suns. Dilute nitride

is able to tune the InGaAs lattice constant and energy bandgap, making more

flexible on the material selection. The maximum ηmax of GaInP/GaAs/GaInNAs

triple-junction solar cells has reached 43.5 % under 400∼600 suns [14].

Apart from multi-junction tandem solar cells, in recent years, the popularly

studied nanostructures, such as quantum dots and quantum wells, provide new

ideas on improving the ηmax of a single-junction solar cell. The main idea is that

1.4 Quantum dot solar cells 5

except the above-bandgap photon absorption in the bulk host semiconductor, the

embedded nanostructures absorb and recycle sub-bandgap photons, which are

potential to raise the photocurrent as well as the PV efficiency. Another idea is

that these nanostructures are potential to well utilize the energy of ‘hot carrier’

before their relaxation into the low-energy bandedge [15]. This relaxation and its

energy loss are inevitable in bulk materials. Compared to multi-junction tandem

cells, nanostructure-embedded cells are more flexible on the material selection

and the structure design; they avoid the photocurrent match requirement and

the use of tunneling junctions. However, at present, there are still few solid

evidences demonstrating that nanostructures have improved the whole ηmax of a

single-junction cell, although sometimes there is a considerable increase of the

photocurrent Isc due to their additional absorption.

1.4 Quantum dot solar cells

As a kind of nanostructures, quantum dot is thought to have many desired qual-

ities: three dimensional quantum confinement, discrete energy levels, size and

energy-level tunability, long relaxation time due to phonon bottleneck effect [16],

and high-intensity light emission and absorption due to the confinement induced

high transition rate. Some scientists even proposed two conceptual mechanisms

in QDs that are helpful to raise the photocurrent. One is the multiple exciton

generation (MEG), meaning that a ‘hot’ electron generated in a high conduction-

band (CB) QD-level by absorbing a high-energy photon, will relax onto a low

CB QD-level, with the energy loss exciting additional electrons from valence-band

(VB) QD-levels to CB QD-levels. In other words, the absorption of a high-energy

photon creates more-than-one electron-hole pairs, similar to carrier impact ioniza-

tion and opposite to Auger relaxation. The MEG effect was reported in colloidal

QDs (e.g. colloidal CdSe QDs) [17] with high confinement barriers (i.e. the vacuum

levels), but not in epitaxial QDs like self-assembled InAs/GaAs QDs due to their

low barrier. The other mechanism is the intermediate band (IB) absorption [18]. It

means that the coupling of discrete levels in close-stacked epitaxial QDs forms one

or more IBs in the host semiconductor bandgap, enabling a cascade absorption of

sub-bandgap photons from the VB to the IBs, and from the IBs to the CB. Since

the IBs are electrically isolated from VB and CB, their introduction increases Isc

and keeps Voc unreduced.

This thesis mainly focuses on epitaxial QD-embedded p-n junction solar cells.

As for colloidal QDs-sensitized solar cells that are popularly studied recently,

6 1 Introduction

because their structure and principle (photocarrier selective extraction, similar to

dye-sensitized solar cells) are quite different, I do not want to detail them here.

In the study of p-n junction-based QD solar cells, the recent experimental

works usually compare the PV performance of single-junction solar cells with or

without QDs. Although sometimes there is a considerable increase of Isc, the re-

duced Voc is actually a common problem after embedding QDs, resulting in lower

PV efficiency. The reduced Voc is mostly attributed to strain induced disloca-

tions. The strain is always a drawback for epitaxial InAs QDs. A moderate strain

drives QD formation; while excessive strain induces dislocations. The disloca-

tions are serious for very closely stacked multiple QD layers, degrading both Voc

and Isc[19]. Introducing strain-compensated layers, e.g. GaInP, in QD-embedded

GaAs cells, is valid to reduce dislocations and PV degradation [19]. Meanwhile, the

strain-compensated layers with higher bandgaps also compensate the reduction of

bulk GaAs bandgap after embedding lower-bandgap InAs QDs. But, even for

far spaced dislocation-free InAs QDs, their embedded solar cells still have reduced

Voc. There must be some more essential reason. As for the photocurrent Isc, many

works expect the above-mentioned IB absorption would increase it. But, from PC

spectroscopy, we find that the PC from QDs is at least one order of magnitude

lower than the PC from the GaAs host. So, except the photocarrier generation in

QDs, the photocarrier extraction from QDs is even more important.

In this thesis, we design p-i-n GaAs solar cell and embed 20 nm spaced InAs

QD layers in its n-region and i-region and study their PV performance, with re-

spect to the non-QD control cell. The aim for QDs embedded in different regions

is to study their different mechanisms for photocarrier escape and check the roles

of the possible IB absorption the built-in electric field. Their different PV perfor-

mances help to understand the essential reason for the reduced Voc. The factors

of QDs and dislocations are distinguishingly shown in diode performance [20]. QDs

in the i-region enhance photocarrier radiative recombination and increase J0. It is

the essential reason for the commonly reduced Voc. While, dislocations caused by

strain in many QD layers induce Shockley-Read-Hall nonradiative recombination

(the ideality factor n close to 2) that also reduces Voc.

From the PC spectra we find that the above-GaAs-bandgap PC is enhanced

after embedding QDs in the i-region [21]. These QDs reflect the GaAs band wave-

functions, especially the valence band hole wavefunction, increasing wavefunction

overlap and interband absorption. From the bias- and temperature-dependent

sub-GaAs-bandgap PC spectra, we find that a strong built-in field is necessary

for effective photocarrier escape from QDs that is why QDs are mostly embedded

1.4 Quantum dot solar cells 7

in the i-region [19,22]. Inter-QD-layer tunneling under the field is effective between

closely stacked QDs. The IB absorption, if it exists, is very low in efficiency to

produce PC. The photocarrier escape from QDs in the n-region depends on the

minority hole thermal activation. It is poor in efficiency due to electron filling

induced potential variation.

The study of photocarrier escape from QDs is valuable for the design of

infrared photodetectors, e.g. p-i-n near-infrared photodiodes and n-i-n QD mid-

infrared photodetectors (QDIPs). Focal plane arrays of QDIP have been success-

fully produced for thermal imaging [23,24].

Chapter 2

Experimental techniques

The experimental work in this thesis covers the sample growth by molecular beam

epitaxy (MBE), morphology imaging by atomic force microscopy (AFM), photo-

luminescence (PL) spectroscopy, photovoltaic I-V measurement and photocurrent

spectroscopy, as detailed below.

2.1 Molecular Beam Epitaxy

Molecular Beam Epitaxy (MBE) is a method to grow crystals by the source

molecule epitaxy on the substrate in a high-vacuum and ultra-clean environment.

Most MBE systems use solid sources, e.g. our Vecco Gen II MBE. The schematic

of MBE system is shown in Fig. 2.1. There are three vacuum chambers, the

introducing chamber, the buffer chamber and the growth chamber, made from

stainless steel and separated by valves. The vacuum of the introducing chamber

(∼ 10−7 Torr) is maintained by the cascade pumping of a membrane pump and

a turbo molecular pump. The vacuum of the buffer chamber is kept by an ion

pump. The vacuum of the growth chamber is kept by a cryogenic pump and a

liquid nitrogen-cooled cryogenic panel inside the chamber. Sometimes, to start

the cryogenic pump operation, a prepump, i.e., a cascade turbo molecular pump

and membrane pump, is used. The cryogenic panel condenses impurities such

as H2O, N2, CO and CO2, making a high-vacuum and ultra-clean environment

around the heated substrate for sample growth. The background pressure of the

growth chamber in standby is 10−10 ∼ 10−9 Torr.

Substrates (e.g. GaAs) are fixed on substrate holders, located on the vehicle,

and transported inside the introduction chamber. In this chamber, the 180 ◦C bak-

ing is performed. Then, they are transferred into the buffer chamber to undergo

8

2.1 Molecular Beam Epitaxy 9

0

Sample moving poles

Orbit

Buffer chamber

Introducing chamber

Valve

0

Beam flux

gauge

180 C baking420 C degassing

Orbit

Vehicle

Growth

chamber

Valve

Baffle

Rheed gun

Rheed

screen

Substrate

gauge

Cryogenic

pump

chamberRotational

mechanics

Quadrupole

GaIn

AsSi

Reflection

spectrometer

Liquid nitrogen-cooled

cryogenic panel

Baffle

Heating

coil

Quadrupole

mass spectr.

spectrometercoil

Figure 2.1 Schematic of MBE system.

the 420 ◦C degassing one by one. When growing samples, a degassed substrate is

put into the growth chamber by the sample moving pole. Then, the substrate is

rotated to the growth position by the rotational mechanism and gradually heated

up to 650 ◦C for deoxygenating. The deoxygenation removes oxygen atoms from

oxides of Ga and As in the substrate surface, in an As-rich atmosphere that avoids

the As atom desorption. The baking, the degassing and the deoxygenating aim

the same, desorbing impurities from the substrate surface. After deoxygenating,

the substrate temperature is reduced to 600∼620 ◦C and a GaAs buffer layer in

thickness of 300 nm is grown, forming a flat and clean GaAs surface for sample

structure growth. After the sample growth has finished, the substrate will be re-

turned back to the buffer chamber and taken out from the introduction chamber

finally. The valves keep the vacuum of each chamber during these processes.

As for the sources, high-purity (99.9999%∼99.999999%) elementary sources

such as As, Ga, In, and Si (as dopant), are stored in separate effusion cells. These

cells are actually crucibles with the body heated up to about 1000 ◦C by a primary

filament and the mouth heated to even higher temperature by a tip filament (i.e.,

the ‘hot-lip’ mode [25]). Solid source inside each cell will evaporate as gaseous

atoms and effuse out. Only for the Al effusion cell, the tip filament is colder than

the body one (i.e., the ‘cold-lip’ mode), in order to avoid the Al spilling-caused cell

10 2 Experimental techniques

damage [25]. Moreover, the As cell has a two-zone crucible: the body contains solid

As source and the long tip cracks the evaporated As4 molecules into As2 ones. By

extensively controlling the base and tip temperatures with thermocouple probes

and electronic PID temperature-control modules, the effusion rate of source atoms

or molecules from each cell will be accurately controlled and tuned. By opening

or shuttering the baffle in front of each cell, different material or compositional

structures can be grown flexibly.

The effusion rate is measured by the beam flux gauge, i.e., a hot-filament

ionization gauge [26], after it is rotated to the growth position by the rotational me-

chanics. High-energy electrons, emitted from the filament cathode and speeded

up by a high positive grid voltage, will ionize the surrounding source atoms or

molecules, having them attracted to the collector in negative voltage and produc-

ing electric current that is proportional to the amount of source ions.

During the growth, the substrate is at 500∼650 ◦C, located at the growth

position in the center of the growth chamber. These gaseous atoms and molecules

deposited on it will migrate in the surface, react with each other, and eventually

form an epitaxial layer. The growth is a dynamic process, rather than a thermal

one. The crystalline substrate, acting as the template (or seed crystal), enables

the growth of lattice-matched crystalline materials on it. The epitaxy is a both

chemical and physical process. The deposited atoms and molecules firstly form

an amorphous material (chemical reaction); under the substrate temperature, the

amorphous material crystallizes into film (physical phase transition).

The epitaxial growth is in-situ monitored by Reflection High Energy Electron

Diffraction (RHEED). High-energy electrons, emitted from the high-voltage (14

kV) electron gun, inject on the sample surface and reflect. The reflecting electron

beam has diffraction due to the sample surface roughness in atomic monolayer

level. The diffraction pattern is recorded by the RHEED screen and displayed in

computer. A flat sample surface gives a multi-line pattern; while a rough surface

(e.g. quantum dots on it) gives a dotted pattern. The intensity of the RHEED

pattern is also oscillating during one crystalline monolayer growth, from which an

accurate monolayer epitaxy is available to control.

The rotational mechanics including several gears has two functions: one is

inverting the positions of the substrate and the beam flux gauge that enables

the transfer of a substrate to the growth position and the measurement of the

effusion rate; the other is axially rotating the substrate during the growth for

space-uniform epitaxy.

The quadrupole mass spectrometer [27] can detect gaseous impurities in the

2.2 Atomic Force Microscopy 11

growth chamber, such as H2O, CO, N2 and CO2, and oxides of As and Ga. The

reflection spectrometer uses halogen lamp, optical grating and photodetector for

in-situ measurement of sample’s reflection spectrum, which is useful to monitor the

layer thickness and optical mode during the growth of distributed Bragg reflectors.

Compared to Metal Organic Chemical Vapor Deposition (MOCVD) that

grows crystals fast by gas sources in low vacuum and suits the mass produce

of most optoelectronic devices like LED and VCSEL, MBE has its own features:

accurate control of monolayer growth, flexibility on energy band design and struc-

ture growth, high vacuum and relative low growth temperature, therefore, it is

suitable for the growth of superlattices [28], quantum cascade lasers [29] and high-

electron-mobility microwave devices.

2.2 Atomic Force Microscopy

The morphology of uncapped QDs, including their sheet density, shape and size,

is characterized by atomic force microscopy (AFM). AFM has a cantilever with a

sharp tip in µm-scale size and nm-scale curvature to scan the sample surface. For

the usually used contact mode, a van der Waals repulsive force exists between the

tip and the surface atoms it touches. The surface morphology of the sample will

vary this force, leading to a cantilever deflection that is determined by Hooke’s

law. A laser illuminates on the cantilever and reflects to a four-region detector to

show a light spot. The cantilever deflection is monitored by the shift of the spot

position, and transformed into morphological information of the sample surface.

In contact force operation, the spot shift is fed back to a piezoelectric element

behind the sample board that moves the sample slightly in vertical direction to

keep constant force and deflection. The displacement describes the local height

of the sample surface. Compared to another kind of scanning probe microscopy,

scanning tunneling microscopy, that is based on electron tunneling from atoms

on an electrically conductive sample to the probe tip and in 0.01∼0.1 nm spacial

resolutions, AFM is in lower (∼nm) spacial resolution, less limited on sample

conductivity and vacuum condition, and thus more widely used.

2.3 Photoluminescence spectroscopy

Photoluminescence (PL) is a phenomenon that a material absorbs high-energy

photons and generates photocarriers; these photocarriers relax into the low-energy


states, especially the ground state, of the material, and emit photons by the tran-

sition from these states. By spectroscopy of the luminescence, energy states of the

material are informed. For example, InAs QD samples, excited by a He-Ne laser

(λ =632.8 nm), give infrared luminescence due to the electron-hole recombination

on discrete QD states, whose spectrum with several peaks can characterize the

QD energy states.

The PL instrument is shown in Fig. 2.2. The power-tunable He-Ne laser beam

is incident from the central hole of the concave copper mirror onto the sample.

The luminescence emits from the sample, together with the reflected laser light.

It is reflected by the concave copper mirror and incident into the detector module

by the lens focus. The detection is based on the Fourier transform (FT) of the

incident light by a Michelson interferometer (for more detail, see Section 2.5). The

Ge detector is cooled by liquid nitrogen. The sample is located in a chamber at

room temperature.

He-Ne lasermA

FT spectrometer

Michelson

interferometerConcave

copper

Mirror

Power-tunable electric power for laser

0

Lens

Sample

copper

mirror

Beamsplliter

0Liquid N2-cooled

Ge detector

Sample

Figure 2.2 Setup of PL spectroscopy.

There are some more advanced PL spectroscopies, such as excitation power-

varied PL, time-resolved PL, PL excitation (PLE) and selectively excited PL.

Excitation power-varied PL spectra are measured under varied exciting laser in-

tensity. It is benefit to characterize high-energy states due to their considerable

occupation under high-intensity excitation. Time-resolved PL uses a pulsed ex-

citing laser (e.g. a mode-locked Ti: sapphire laser in femtosecond-scale pulses)

and a pump-probe optical setup to measure the decayed PL intensity at a given

delay time, which is useful to define the lifetime of an energy state. PLE fixes the

detection energy by a monochromator instead of the FT spectrometer, and scans

the exciting photon energy by monochromizing a broad-spectrum light source,

e.g. a low-intensity tungsten lamp or a high-intensity continuous-wave Ti: sap-

2.4 Photovoltaic I-V measurement 13

phire laser. Selectively excited PL is the opposite, i.e., fixing the exciting photon

energy while scanning the detection energy by a monochromator. Both are helpful

to study the photocarrier relaxation on a low-energy state. On the other side, the

dependence of PL on temperature and bias voltage is also studied, extending the

understanding of photocarrier occupation, relaxation and escape from an energy

state.

2.4 Photovoltaic I-V measurement

For p-n junction solar cells, as said in Chapter 1, the maximum photovoltaic

(PV) efficiency is calculated by measuring the I-V relation under a solar light

simulator. The I-V relation is measured by a multimeter, e.g. a Keithley one, by

applying a scanning forward bias on the measured sample from 0 V to Voc when the

photocurrent becomes zero. The solar light simulator is a Xenon lamp with several

filters to get rid of several sharp emission peaks in Xenon spectrum. The lamp

power is properly tuned to 1 sun AM 1.5G (i.e., 100 mW/cm2) with a standard

Si cell calibration. The measurement is performed closely in a chamber to avoid

background light. The position of samples is fixed for an identical light intensity.

Along the resulted I-V relation, there is a point corresponding to the maximum

electric power output. The maximum PV efficiency is obtained by dividing the

maximum power by 100 mW/cm2. Sometimes, the concentrated PV efficiency is

measured. The light intensity of solar simulator is tuned to 10 ∼ 104 of the above

1 sun intensity; the sample temperature is well controlled by an additional air

condition; and the maximum efficiency is calculated after considering the increased

light power. Besides, the I-V relation in darkness is also useful to explore the diode

performance of these p-n junction solar cells.

2.5 Photocurrent spectroscopies

From the photovoltaic I-V measurement, we know the total photocurrent (PC)

of a solar cell. For QD solar cells, we want to study the contribution from QD

absorption; hence, the PC spectrum as function of photon energy is required. The

PC spectroscopy is performed by either monochromator or Fourier transform (FT)

infrared spectrometer.

The PC spectroscopy in 300∼1000 nm is performed under a Xenon lamp with

a monochromator. A beamsplitter is used to equally divide the monochromatic


light into two beams: the transmission one is incident on the sample; while the

reflection one is incident on a Si photodiode as reference. The sample is located

at a fixed position behind a hole for identical intensity and spot of light. As the

monochromatic light wavelength (λ) scans, the PC signals of both the sample

and the Si photodiode, Isample and ISi, are measured by a Keithley multimeter

simultaneously. The ISi(λ) is useful to eliminate the influence of the peakful Xenon

spectrum on Isample(λ), by considering Isample(λ)/ISi(λ). In other words, since the

external quantum efficiency (EQE) of the sample is obtained by EQEsample(λ) =

EQESi(λ) × Isample(λ)/ISi(λ) [30] and EQESi(λ) is almost saturated and constant

in 500∼900 nm, Isample(λ)/ISi(λ) becomes a good measure of EQEsample(λ) in this

wavelength region. The spectroscopy is in resolution of ∆λ = 5 nm/point, defined

by the automatic controlled monochromator.

The PC spectroscopy in the near-infrared region (i.e., QD contributions) is

measured in detail by a Bruker Vertex 80v FT infrared spectrometer equipped

with a quartz-halogen tungsten (QHT) lamp. The spectral range is 1200∼30000

cm−1 at most. The resolution is ∆k = 4 cm−1/point. FT infrared spectrometer is

often used for the absorption spectroscopy of materials. It can also characterize

PL spectrum as said before and PC spectrum, by modifying the setup accordingly.

The structure of FT spectrometer and the spectra of the QHT lamp and the CaF2

beamsplitter efficiency are presented in Fig. 2.3.

The QHT lamp emits light whose spot size is trimmed by the aperture (APT).

After being reflected by a concave mirror, the parallel light is incident into the

interferometer. The CaF2 UV/VIS/NIR beamsplitter (BMS) divides the incident

light into two parts: the reflection beam is then reflected back by the static planar

mirror and transmitted through the BMS; while the transmission beam is then

reflected back by the moving planar mirror and reflected by the BMS. Both beams

experience the same optical length in the BMS, leaving their optical length dif-

ference (∆L) only tuned by the moving mirror whose position is monitored by a

He-Ne laser inside. The two beams form an interferential light that is focusing

on the sample located in the dark chamber. For absorption spectroscopy, the

transmission light through the sample is collected by the installed detector (D1)

to produce PC signal; while for PC spectroscopy, the detector is unused and the

sample’s PC signal is directly acquired and amplified by an external current am-

plifier. Unlike monochromator, the spectral scan here is based on the ∆L-varied

interference and a Fourier transform of the resulted PC signal as a function of

2.5 Photocurrent spectroscopies 15

∆L. The principle is indicated as

PC(∆L) =

∫R(k)I(k) [1 + cos(2πk∆L)] dk

=

∫PC(k) [1 + cos(2πk∆L)] dk

(2.1)

Here, k is wave number [cm−1]; I(k) is light intensity [W]; PC(k) and PC(∆L)

are photocurrent [A]; R(k) = PC(k)/I(k) is responsivity [A/W] of the detector

or sample. Making Fourier transform on PC(∆L),

FTPC(∆L) =

∫PC(∆L)cos(2πk∆L)d∆L

=

∫ ∫PC(k′)× [1 + cos(2πk∆L)]dk′cos(2πk∆L)d∆L

=

∫PC(k′)×

∫[1 + cos(2πk′∆L)]cos(2πk∆L)d∆Ldk′

=

∫PC(k′)δ(k − k′)dk′ = PC(k)

(2.2)

The modified setup to measure PC spectrum is described in Fig. 2.4. The

sample is fixed in a cryostat. Its electrodes extend to the cryostat top plate. By

using a PCB connection, its PC signal is introduced to an external current ampli-

fier (Keithley 428), which amplifies the current signal and converts it into a voltage

signal, under tunable amplification gain and bias voltage. The voltage signal out-

puts to a multimeter (Keithley 2602) for voltage monitor; meanwhile, it feedbacks

through the serial-to-parallel converter to the FT spectrometer for Fourier trans-

form. The final data is sent to a computer for spectrum display. Sometimes,

to clarify the contributions from QDs, a GaAs filter is used at the incident light

aperture, only allowing the transmission of sub-GaAs-bandgap photons.

In the low-temperature PC spectroscopy, a liquid nitrogen-cooled cryostat

(Oxford OptistatDN ) and a temperature controller (Oxford ITC503 ) are needed.

On the top plate of the cryostat there is a 10-pin seal electrical port for temper-

ature control, behind which there is a thermometer and a heater. The electronic

communication between the multi-pin port and the temperature controller en-

ables an accurate control of the sample temperature from 77 K to 300 K. Before

cooling down the cryostat, gas evacuation and helium gas inflation are performed,

in order to avoid problems related to water vapor freeze. For room-temperature

PC spectroscopy, the temperature controller is not used and the cryostat is not

cooled.


Figure 2.3 FT spectrometer [31] and QHT lamp and BMS transmission spectra [32].

Serial->parallel

converter

Electronics (FT)

Computer

Multimeter

(V-monitor) FT spectrometer

+_

gainbias

IN

OUT

I->V amplifier cryostat

converter

GaAs filter

Temperature controllerelectric access for temperature control

Temperature setting I/O

sample

Figure 2.4 Setup for PC spectroscopy. Red arrows: the signal transport.

Chapter 3

Self-assembled InAs quantum

dots

Quite different from bulk materials, nanostructures show novel optical features,

such as wavelength-tunable emission and high emission intensity due to their nm-

scale size and quantum confinement. In recent two decades, epitaxial InAs QDs,

self-assembled on GaAs or InP substrates, have been extensively studied and

widely used in optoelectronic devices for infrared light emission and detection,

such as QD lasers and QD infrared photodetectors, because they are able to be

freely integrated into III-V bulk semiconductors. In this chapter, I will focus on

their growth, morphology imaging, quantum theory and photoluminescence (PL)

spectroscopy, in order to provide an overall knowledge of this kind of QDs.

3.1 Growth

The self-assembled growth of InAs QDs on GaAs (or InP) substrate is driven by

strain. InAs lattice constant (6.058 A) is larger than GaAs (5.653 A) and InP

(5.869 A), so the InAs epitaxy on GaAs (or InP) surface will accumulate strain.

There are two energies competing mutually during the dynamic growth process

and determining the growth mode, the strain energy that is proportional to the

volume of the strained material and the surface energy that is determined by the

surface area [33,34]. Fig. 3.1 schematizes the growth process. At first the strain

energy is zero while the surface energy is not. Indium and arsenic atoms are

effused on the substrate surface. They will migrate in the surface and bond each

other. The InAs deposition is dominated by two-dimensional (2D) film growth,

forming InGaAs wetting layer (WL) due to In-Ga intermixing. During the WL

17

18 3 Self-assembled InAs quantum dots

growth, the surface energy keeps constant while the strain energy accumulates as

the WL thickness increases. When the WL reaches a critical thickness, the strain

energy becomes dominant. Many nm-scale three-dimensional (3D) InAs islands

form suddenly. The strain is released by increasing the total surface area by these

3D islands. The growth is called Stranski-Krastanov (SK) growth, a mode of

crystal epitaxy [34]. Continuing the InAs epitaxy, these InAs islands will become

bigger and the strain will accumulate further. Finally, big clusters filled with

dislocations will form, reducing both the surface energy and the strain energy.

So, the InAs deposition amount must be proper. These islands become QDs after

cladding a GaAs barrier layer. Usually, an additional 5 nm In0.15Ga0.85As layer

is clad before cladding the GaAs layer. It flattens the surface strain, uniforms

the QD size and improves the QD optical properties by forming the Dot-in-Well

structure. Of course, the strain still exists in these QDs.

In As

InGaAs WL

InAs island InAs QD

GaAs

Strain

EnergyS-K growth mode

2D WL 3D island

Cluster and

dislocation

Surface

Strain

=> 2D growth

2D WL 3D island dislocation

InAs amount

Figure 3.1 InAs QDs growth in SK mode.

The InAs island nucleation is also related to the indium deposition, migra-

tion, evaporation and bonding on the substrate, and the indium segregation from

the WL after its content saturates [35]. It is affected by the growth temperature,

rate and interruption, the arsenic flux, and the surface lattice condition. In gen-

eral, high temperature enhances indium migration and evaporation; slow indium

effusion rate and interruption promote indium migration and island nucleation to

form big QDs; very high arsenic flux suppresses indium migration and forms big

clusters while very low arsenic flux affects indium adsorption; on a strain-relaxed

surface big QDs are formed with less strain; introducing little Sb elements on the

surface formes small QDs in an ultrahigh density ∼ 1000/µm2.

There are at least four examples to show the flexibility of the self-assemble

of InAs QDs on GaAs substrates. First, the normal QD growth is at 500 ◦C,

3.2 Morphology 19

0.1 ML/s in rate and 10 s interruption after each 1 s deposition, with the total

amount of 2.3 monolayer (ML). The formed QDs have density of 300/µm2 and

light emission around 1200 nm. Second, if increasing the growth temperature to

550 ◦C and effusing indium at a rate ∼ 0.005 ML/s with a total amount ∼ 1.9 ML,

critical for island formation, the formed InAs QDs will have a low density about

10/µm2 and show discrete emission lines due to single transitions in individual

QDs. Such QDs has been used to fabricate single photon sources [36]. Third, if

growing a thick metamorphic InGaAs buffer layer on GaAs substrate with the

indium composition increasing gradually, the InAs island nucleation on it will be

strain-relaxed, showing longer-wavelength emission and potentials for the 1.55 µm

telecom application [37,38]. Fourth, if growing closely stacked QD layers with GaAs

spacer ∼ 10 nm, the strain coupling between QD layers will lead to a vertical

aligned QD formation [39].

3.2 Morphology

AFM and PL spectrum are used to characterize the QD morphology and light

emission property and optimize the QD growth conditions. The test samples for

AFM and PL spectrum have three layers of InAs QDs with 5 nm In0.15Ga0.85As

capping layer and 50 nm GaAs spacer and an uncapped InAs island layer in the

end. The AFM image characterizes the surface morphology of the uncapped InAs

islands, such as shape, surface density and size distribution.

With different indium deposition amounts and growth interruptions, the nor-

mally grown QDs show AFM images in Fig. 3.2. The growth temperature is 500◦C. The arsenic partial pressure is 8.7× 10−7 Torr. QDs are lens-shaped, in small

height and large base diameter. Their density is ∼ 102/µm2. Their PL spectra

are shown in the left of Fig. 3.4. We find that the 2.3 ML indium amount and the

5 s interruption, i.e. sample (a), are optimal for QD light emission. The QD size

distribution in sample (a) is also analyzed in Fig. 3.2. The QD density is about

270/µm2. Most QDs are 7 ∼ 9 nm in height and 28 ∼ 32 nm in base diameter.

Sample (a) has no big clusters while the other samples have.

Fig. 3.3 gives the AFM image of QDs grown on a metamorphic In0.08Ga0.92As

buffer. The QDs are in a lower density about 120/µm2, mostly in height of 7 ∼ 10

nm and base diameter of 35 ∼ 50 nm, larger than the QDs in Fig. 3.2. Besides,

there are some 100 nm-sized big clusters.


2 3 4 5 6 7 8 9 10 110

20

40

60

80

QD height [nm]10 15 20 25 30 35 40 450

10

20

30

40

QD base diameter [nm]

QD total number

269 /µm2

Figure 3.2 AFM images of normal QDs grown with different indium amounts andinterruptions: (a) 2.3 ML, 5 s; (b) 2.4 ML, 5 s; (c) 2.3 ML, 3 s; (d) 2.4 ML, 3 s. Thegrowth temperature is 500 ◦C and the arsenic partial pressure is 8.7 × 10−7 Torr, forall. The QD size distribution of sample (a) is analyzed.

2 3 4 5 6 7 8 9 10 11 120

10

20

30

40

QD height [nm]

25 30 35 40 45 50 55 60 65 70 75 800

5

10

15

20

25

30

35

40

Metamorphic

InGaAs buffer

QD

Num

ber

QD base diameter [nm]

QD total number

126 /µm2

Figure 3.3 AFM of InAs QDs formed on a metamorphic InGaAs buffer layer.

3.3 Photoluminescence spectrum 21

3.3 Photoluminescence spectrum

PL spectrum was used to characterize the light emission property of QDs. Fig. 3.4

shows the PL spectra of the above mentioned QD test samples. In the left, the

four samples are the ones in Fig. 3.2. Their ground PL peaks are 1250 ∼ 1280

nm. A 5 s growth interruption after each 0.1 ML indium deposition is proper for

indium migration to form islands. The 2.4 ML QDs (L-b) have longer emission

wavelength than the 2.3 ML QDs (L-a).

800 1000 1200 1400 1600800 1000 1200 1400 1600

0

50

100

150

200

250

R-c

R-b

Wavelength [nm]

R-a

PL intensity [arb. uni.]

L-a 2.3ML, 5 s

L-b 2.4ML, 5 s

L-c 2.3ML, 3 s

L-d 2.4ML, 3 s

Figure 3.4 PL spectra of InAs QD samples. Left: normal QDs on GaAs in Fig. 3.2.Right: (R-a) 2.3 ML QDs on GaAs; (R-b) 2.8 ML QDs on metamorphic In0.08Ga0.92Asbuffer; (R-c) 2.9 ML QDs on metamorphic In0.15Ga0.85As buffer.

The right of Fig. 3.4 compares the PL spectra of InAs QDs formed on meta-

morphic InGaAs buffer and directly on GaAs. R-a is the best sample in Fig. 3.2,

i.e. L-a in the left of Fig. 3.4, with 2.3 ML InAs on GaAs. Its ground PL peak is

at 1270 nm and the 1st-excited peak is at 1180 nm, spaced by 75 meV. R-b is the

sample in Fig. 3.3, with 2.8 ML InAs QDs grown on a metamorphic In0.08Ga0.92As

buffer, capped by 5 nm In0.25Ga0.75As and spaced by 50 nm In0.08Ga0.92As. The

growth temperature is 510 ◦C. Its ground peak is at 1370 nm and the 1st-excited

peak is at 1290 nm, spaced by 56 meV. R-c is another QD sample, with 2.9 ML

InAs deposition, formed on a metamorphic InxGa1−xAs buffer (x step graded from

0.02 to 0.18 and then set back to 0.15), capped by 3.5 nm-thick In0.33Ga0.67As and

spaced by 50 nm-thick In0.15Ga0.85As. The QD growth temperature is 510 ◦C. Its

ground peak is at 1440 nm and its 1st-excited peak is at 1370 nm, spaced by 44

meV. The high indium composition in the metamorphic InGaAs buffer relaxes the

strain and realizes longer-wavelength emission in QDs. The reduced PL peak sep-

aration is related to the strain relaxation and the reduced barrier for QDs. From


R-a to R-c, the PL intensity also decreases since lots of dislocations have been

introduced in the metamorphic buffer and the QDs growth on it is not optimal.

3.4 Closely stacked QDs

Based on the optimal QD growth conditions, in this thesis, the InAs QDs in QD

solar cells were deposited at 500 ◦C, in rate of 0.1 ML/s and interrupted 10 s after

each 0.1 ML, in arsenic partial pressure of 8.7 × 10−7 Torr, on a rotating GaAs

substrate. The total InAs deposition amount is 2.3 ML. InAs starts to island after

1.8 ML; the rest 0.5 ML makes these islands growing bigger. These InAs islands

are directly clad by 20 nm-thick GaAs layer in a rate of 1 ML/s, instead of the 5

nm InGaAs capping layer and the 50 nm GaAs spacer. After the 20 nm GaAs,

the next QD layer would be grown. Five such QD layers were grown as a QD

matrix.

As seen in the cross-sectional transmission electron microscopy [33,39], verti-

cally aligned QDs have formed in closely stacked QD layers, due to the inter-QD-

layer strain coupling. The thicknesses of the GaAs spacer is critical for such QD

alignment [33,40–42]. We use closely stacked QDs for QD solar cells, because these

closely spaced and aligned QDs could allow an interlayer state coupling [43,44] and

form intermediate bands (IBs), for free carrier transport and cascaded absorption

of sub-bandgap photons [45].

0.9 1.0 1.1 1.2 1.3800 1000 1200 1400 1600

0

50

100

150

200

Sample A

Energy [eV]

Sample B(b) Coupled

QDs

PL intensity [arb. uni.]

Wavelength [nm]

(a) Uncoupled

QDs

Figure 3.5 PL spectra of coupled QDs used for solar cells.

Fig. 3.5 shows the PL spectra of closely stacked QDs in our QD solar cells.

There is a broad profile including many closely spaced peaks. These peaks come

from the energy state coupling and the QD size distribution. Compared to the

best uncoupled QD sample mentioned above, the PL intensity of coupled QDs is

much reduced because of the strain induced dislocations.

3.5 Quantum description of optical properties 23

3.5 Quantum description of optical properties

The essence of the novel optoelectronic properties in nanostructures is the quantum

confinement in their nm-scale size. Carriers (e.g. electrons) are confined in a

region comparable to their de Broglie wavelength, and the carrier wave property

therefore becomes considerable. Quantum wells (QWs) confine carriers in one

dimension, leaving the other two dimensions (2D) free for carrier motion (e.g.

2D electron gas); quantum wires (QWires) confine carriers in 2D, allowing carrier

free motion along the wire. Quantum dots (QDs), or namely, nanocrystals, confine

carriers in three dimensions (3D), providing all-space discrete energy states and δ

function-like density of states. The energy of these confined states is tunable by

changing the QD size. The smaller the QD is, the higher the confinement and the

state energy are, as demonstrated in the multi-color visible light emission from

colloidal II-VI QDs with the same material [46]. Here, I will introduce some basic

concepts to describe QDs.

The carrier wave property in a QD can be depicted by the 3D steady-state

Schrodinger equation

[−~2

2m0

∇( ∇

me(r)

)+ V (r)− En

]Ψ(r) = 0, V (r) =

EGaAs, r ∈ GaAs

EInAs, r ∈ QD(3.1)

where V (r) is the electric potential; En and Ψ(r) are the QD state energy and

wavefunction; me is the carrier effective mass; EGaAs (EInAs) are conduction band

(CB) edge for electron and valence band (VB) edge for hole in GaAs barrier (InAs

QD). The QD band diagram is shown Fig. 3.6. Both CB electron and VB hole are

confined in QDs. The solutions of this equation are the bound states s, p and so on,

with even or odd parities. This equation is the same as the Schrodinger equation

to describe electronic states in an atom, so QDs are also called “artificial atoms”.

For spherical colloidal QDs, V (r) has spherical symmetry, so this equation can be

analytically solved by setting the wavefunctions as Ψ(r) = Rnl(r)Ylm(θ, ϕ). The

radial component Rnl has quantum numbers (n, l) and the spherical harmonic

function Ylm(θ, ϕ) has quantum numbers (l, m), analog to atomic states. For

lens-shaped QDs, there is only axial symmetry, the QD states can be numerically

rather than analytically solved. The 3D confinement can be separated into the

confinements in the normal direction and the lateral plane. Since the QD height

is 7 ∼ 9 nm and base diameter is 28 ∼ 32 nm, the normal confinement is so large

that only one confined state is allowed. Bayer [47] thus proposed that the lateral


confinement is responsible for the discrete QD states in separation of 50 ∼ 100

meV. Their wavefunctions also show parity features in the lateral plane, such as s,

p and so on. The s-state can accommodate two carriers with opposite spins; the

p-state can accommodate four carriers with either different spatial distributions

or opposite spins; while the d-state can accommodate six carriers. The confined

carriers tend to relax and distribute on low-energy states, e.g. the ground s-state.

Since the QD material is still periodic crystal and in each QD (∼ 103 nm3)

there are ∼ 104 atoms, the potential V (r) and the wavefunction Ψ(r) must be able

to describe the lattice periodicity, i.e., the periodic nuclear potential on the lattice

with distance (i.e. lattice constant) of 0.56∼0.6 nm. So, similar to bulk crystals,

the Bloch theorem is still valid for QDs, i.e., Ψ(r) = ϕ(r)u(r), where ϕ(r) is the

slowly-varied envelope around QD and the Bloch function u(r) is periodic, i.e.,

u(r + r) = u(r), where r is a lattice vector.CB

Intraband

p-state

WL state

)()()( rurrrvr ϕψ =

Interband

transition

Intraband

transition

s-state

QD

)(rvϕ

)(rur

p-state

s-state

QD

Lattice constantNucleus

VB

WL state

Figure 3.6 Schematics of QD band diagram, wavefunction and transition.

There are two kinds of optical transition between QD states, one is the in-

terband transition, the other is the intraband transition, as seen in Fig. 3.6. The

transition rate Ti→f from an initial state i to a final state f depends on the tran-

sition matrix element, as the Fermi golden rule Ti→f ∝ (2π/~) |<Ψf |E · r|Ψi >|2,where the assumption of electrical dipole E ·r transition is used. Using the Bloch

wavefunction, the transition matrix element is expressed as

< ϕecuc|E · r|ϕh

vuv >=< ϕec|ϕh

v >< uc|E · r|uv >, (interband)

< ϕec1uc|E · r|ϕe

c2uc >=< ϕec1|E · r|ϕe

c2 >< uc|uc >, (intraband)(3.2)

where ϕec1,2 are CB electron states and ϕh

v is VB hole state; uc and uv are CB

and VB Bloch functions. For the interband transition, the rapidly varied Bloch

functions uc and uv give a constant dipole moment while the overlap of the slowly

3.5 Quantum description of optical properties 25

varied envelops ϕec and ϕh

v determines the size of the matrix element. The maxi-

mum overlap is obtained between the same states (e.g. s-state) for electron and

hole. This transition describes the interband absorption of near-infrared photons

in QDs. For the intraband transition between two CB electron states, since the

two states have the same rapidly varied Bloch function, the matrix element is

determined by the dipole moment of the envelope functions, <ϕec1|E · r|ϕe

c2 >. It

requires opposite parities of the wavefunction envelops (e.g. s-state and p-state).

Moreover, the external electric field must be parallel to the confined dimension

that shows opposite parities. It is why in QW infrared photodetectors only the

electric field component in the normal direction is effective to create the intraband

transition by absorbing mid-infrared photons.

The optical transition also satisfies the angular momentum selection rule.

For example, s-state has two degenerations, | ± 1/2〉 for electron, | ± 3/2〉 for

heavy holes; the transition only occurs between |1/2〉 and |− 3/2〉 (emit left-hand

circularly polarized light), or between |−1/2〉 and |3/2〉 (emit right-hand circularly

polarized light). The exciton state in a single InAs QD thus has two configurations

for polarized light emission, based on which the polarization-entangled photon-pair

emission has been realized [48].

The optical transition is also sensitive on electric field. Under an electric

field, the wavefunctions of CB electron and VB hole in a QD separate, reducing

their overlap (transition rate) and transition energy. It is so called quantum Stark

effect. Fig. 3.7 shows the bias-dependent PL spectra of our QD solar cell sample

A, with QDs in the built-in field region. The lowest QD transition (QD6*) is most

reduced as the electric field enhances.

0.9 1.0 1.1 1.40 1.45 -1.0 -0.8 -0.6 -0.4 -0.2 0.0

Photo

lum

inescence [arb

. units]

Photon energy [eV]

(a)0 ~-1 V (-0.1 V/step)

(b)

Bias [V]

QD4

QD5

QD6

QD6*

Relative PL

intensity

Figure 3.7 Bias-dependent QD PL spectra, vertically shifted by ×10 for clarity.

Chapter 4

InAs QD-embedded solar cells

In this chapter, I will describe the design, fabrication and photovoltaic (PV) ef-

ficiency measurement of our InAs QD solar cells. The QD performance on pho-

tocurrent (PC) production is analyzed from the bias- and temperature-dependent

PC spectra. The reduced Voc of both QD solar cells is because of: 1) the Shockley-

Read-Hall (SRH) recombination in QDs and dislocations; 2) the reduced photo-

carrier lifetime when QDs are embedded in the depletion region. The interlayer

tunneling in closely stacked QD layers helps the PC production from QDs in the

depletion region.

4.1 Design

p-n junction solar cells are based on the light absorption in semiconductors and

the photocarrier transport and extraction under the built-in electric field before

recombination. The light absorption satisfies the Beer law ln(It/I0) = −αL where

α is absorption coefficient; I0 is the initial light intensity; It is the light intensity

in depth of L. The photocarrier generation is thus exponentially dependent on

the depth. The α is dependent on wavelength. For GaAs, it is 2 × 103 cm−1 at

870 nm (i.e. the GaAs bandedge), 3 × 104 cm−1 at 600 nm and even higher for

shorter wavelengths. Most ultraviolet photons are absorbed in the front surface

and recombine before drift. Solar cell design mainly focuses on visible and near-

infrared photons absorbed in ∼ µm depth. The built-in electric field, determined

by the Poisson equation ∇2ψ = ∇·E = −(e/ε)(p−n+N+D−N−

A ), distributes in a

width of W (i.e. ‘depletion region’), with the total potential Vbi and the maximal

26

4.1 Design 27

field Em expressed by

Vbi =kBT

qln(

NAND

n2i

),W =

√2e

ε(Vbi − V )(

NA + ND

NAND

), Em =2(Vbi − V )

W(4.1)

where NA and ND are acceptor and donor densities; ψ and E are electric potential

and field; n2i (=n0p0) is equilibrium carrier product; V is bias voltage; ε is dielectric

constant; kBT is 25.8 meV at 300 K.

The function of a p-n diode can be described by the drift-diffusion model [49,50]

in Eqs. 4.2. n and p represent electron and hole; µn,p are carrier mobilities; Dn,p

(=µn,pkBT/e) are diffusion coefficients; Jn and Jp are current density. There

are two kinds of currents: the drift current (e.g. enµnE) proportional to the

electric field and the diffusion current (e.g. eDn∇n) related to the carrier density

gradient. In the steady state, the local carrier generation G and recombination U

keep conservation with their output in form of current. U depends on the extra

carriers, np− n0p0. For electrons (i.e. the minority carriers) in the p region (np),

U ≈ (np − np0)/τn, where τn is their lifetime; Dn∇2np ≈ (np − np0)/τn gives an

effective diffusion length before recombination, Ln =√

Dnτn. It is similar for the

minority holes in the n region (pn), i.e. Lp =√

Dpτp.

Jn = enµnE + eDn∇n, ∇ · Jn/(−e) = G−R

Jp = epµpE − eDp∇p, ∇ · Jp/e = G−R (4.2)

Fig. 4.1 shows the principle of a p-n junction solar cell. In darkness (G = 0), in

zero bias (flat Fermi level), the carrier diffusion, e.g. electrons from the n region to

the p region, keep equilibrium with the carrier drift in opposite directions. Under

a forward bias V , the built-in potential becomes lower; the diffusion is enhanced

while the drift is reduced, contributing to a total current Jtotal,

Jtotal = Jn + Jp = J0(eqV/kBT − 1)

J0 = e(np0

√Dn

τn

+ pn0

√Dp

τp

) (4.3)

Under light, there are extra minority photocarriers in both p and n regions, Gτn

and Gτp. They will diffuse to the depletion region and drift to the other sides.

Their diffusion lengths Ln and Lp, plus the width of the depletion region W ,

are the total area for effective photocarrier extraction, producing a photocurrent

JL ∼ qG(Lp + W + Ln). The total current is J = J0(eqV/kBT − 1)− JL. For direct

band semiconductors like GaAs, the dominant recombination in the depletion

28 4 InAs QD-embedded solar cells

region leads to a total current J = J0(eqV/nkBT − 1)− JL where the ideality factor

n > 1.

EC

EF V

free electron diffusion

free hole

Photocarrier

drift Photocarrier

diffusion

EV W

Depletion

region

npn0 p0

free hole

diffusion

pn0 p0

W

p =n 2/nnp0=ni

2/p0

Lp

Ln

ln(n),

ln(p)

p =n 2/nnp0=ni

2/p0

Lp

Ln

Gτp

Gτn

pn0=ni2/n0

Jtotal

pn0=ni2/n0

Jp Jn

0

Jp Jn

JL

0

In darkness

Under light

In darkness

Figure 4.1 Band structure, carrier and current densities in darkness or light.

The lifetime τ and the mobility µ of the minority carriers are two essential

parameters to determine the performance of a p-n junction. µ is degraded by

dopant ion scattering; τ is inversely dependent on the majority carrier density.

Low doping levels will keep high mobility and long lifetime. Since µp is much

lower than µn, most single junction solar cells use a thin n layer as the top emitter

for hole diffusion and a thick p layer as the base for electron diffusion. The emitter

is relatively heavily doped to keep a strong built-in field. In my solar cells, as seen

in Fig. 4.2, low doped p-i-n structure is applied: the p region in 2×1017 cm−3; the

n region in 2× 1016 cm−3; the i region intrinsic. The µn and µp are 5000 and 300

cm2/(Vs) respectively; estimating τ ∼ ns, the diffusion lengths Ln and Lp will be

3.6 and 0.9 µm. But, limited by the n+ GaAs substrate, our solar cells use p-GaAs

as the emitter and n-GaAs as the base. The three layers are in thickness of 500

nm (p region), 140 nm (i region) and 1860 nm (n region). The built-in field is ∼

4.1 Design 29

45000 V/cm in the i region; the depletion region is in width of 400 nm, extending

into the n region by 220 nm and the p region by 40 nm.

Outside the p-i-n structure, there is a 500 nm-thick n+ : 1×1018 cm−3-doped

GaAs layer and p+ Al0.85Ga0.15As layer as the top window and n+ Al0.2Ga0.8As

layer as the back-surface field. The AlGaAs layers, both in thickness of 100 nm,

promote the electron extraction from the back electrode and the hole extraction

from the top electrode while prevent the opposite carrier extraction, and thus

reduce the surface recombination. In the top, a 20 nm p+ GaAs doped at 2×1018

cm−3 is used as the top electrode.

Al0.85Ga0.15As 100nm (Be:1E18)

GaAs 20nm (Be: 1E18)

Au-alloy electrode

GaAs 140nm (undoping) GaAs 80nm (undoping)

light

GaAs 0.5µm (Be:2E17)

GaAs 1.86µm (Si: 2E16)

GaAs 140nm (undoping)

GaAs 360nm (Si: 2E16)


GaAs 140nm (undoping) GaAs 80nm (undoping)

5××××InAs QD (undoped) spaced by GaAs 20nm

Top 2 layers are undoped, GaAs 1.86µm (Si: 2E16)

GaAs 0.5µm (Si:1E18)

Al0.2Ga0.8As 100nm (Si:1E18)

GaAs 488nm (Si: 2E16)GaAs 1.78µm (Si: 2E16)

5××××InAs QD 2.3ML (undoped) spaced by GaAs 20nm (doped)

Top 2 layers are undoped,

i.e. 80+20××××2=140nm

Al0.2Ga0.8As 100nm (Si:1E18)

GaAs buffer 300nm (Si:1E18)

GaAs substrate (Si:1.6E18)


BC

A

Figure 4.2 Solar cell structures with or without QDs embedded. Taken from Paper1. Reprinted with permission of Springer.

To study the QD performance on PV conversion and the built-in field role on

PC production from QDs, we use five 20 nm-GaAs spaced InAs QD layers as a QD

matrix (mentioned in Chapter 3) and design three samples: sample A with one

QD matrix in the built-in field; sample B with three separated QD matrices in the

n region, away from the built-in field; sample C has no QD as the control sample,

as shown in Fig. 4.2. Each region is well designed to keep the same thickness

between samples. For example, in sample A, the top two QD layers (QD height

∼ 8 nm) are spaced by 20 nm undoped GaAs, so the total thickness of the i

region is 80 + (20 + 8) × 2 ≈ 140 nm; in sample B, the 360 nm n-GaAs keeps

QD layers away from the built-in field and the total thickness of the n region is


360 + 488× 2 + 100 + (20 + 8)× 15 ≈ 1860 nm. Sample B is also used to study

the QD intermediate band (IB) absorption where IBs must be flat and partially

filled [51].

Samples’ one dimensional (1D) band structures are presented in Fig. 4.3. In

sample A, QDs are empty of free carriers because the built-in field avoids carrier

occupation in QDs. In sample B, electrons from the surrounding n-GaAs host fill

in QDs, inducing a potential variation around each QD matrix. The QD states

are not completely filled. The band structures are still valid under solar light (100

mW/cm2, 3.6× 1017 photons/(s cm2)), since the photocarrier density Gτ ∼ 1012

cm−3 is much less than the free carrier density (e.g. 2× 1016 cm−3).

-2

-1

0

1

2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-2

-1

0

1

2

-2

-1

0

1

2

(a) sample A

VB

CB

5 InAs QD layers

n+-AlGaAs

p+-AlGaAs

Fermi level

z axis [µm]

(c) sample C

Electron energy [eV]

(b) sample B

Figure 4.3 1D energy band structures. Each QD layer is equivalent to 0.7 nmInAs quantum well, with δ function-like densities of states featuring the 3D discrete-ness of QD levels. The 1D Schrodinger equation and Poisson equation are solvedself-consistently [52,53]. Taken from Paper 1. Reprinted with permission ofSpringer.

4.2 Fabrication

The three samples were grown on n+ GaAs substrates by solid-source MBE. Before

growing the solar cell structures, a 300 nm n+ GaAs was grown as buffer. Except

the growth of QD matrices at 500 ◦C, the other structures were grown at 600

4.3 Photovoltaic I-V measurements 31

◦C. The QD growth has been mentioned in Chapter 3. The donor dopant is Si

and the acceptor dopant is Be. After the sample growth, the top contact was

fabricated by evaporating Au and Cr and metalizing them into alloy. The circular

window is optical lithographed and etched for the light incidence. Its diameter,

defined by the lithography pattern, is 2 mm for sample B and C and 6 mm for A.

Then, the samples were thinned down from the back side to 130 µm to fabricate

the AuGeNi-alloy back contact. Both Ohmic contacts tunnel the corresponding

carriers from the semiconductor to the contacts, as seen in Fig. 4.4(a). The back

electrode was mounted with indium on an Al-alloy heat sink. The heat sink has

an insulated base for the top electrode bonding with gold wires and extension with

metal wires. The device is schematized in Fig. 4.4(b). There is no antireflection

coating layers or the top grid electrode in our samples.

Ф = 5.1 eVФ = 4.8

vacuum (a)

Ф = 5.1 eVФ = 4.8

(4.5~5.1)χ = 4.07

Eg = 1.42CB

VB

ψBn=1.03

ψBp= 0.69

AuGeNi

n-contact

CrAu

p-contactn+ GaAs

substraten- GaAs p GaAs

VB

Sample (b)

Gold wire bonding

Al-alloy heat sink

(back contact)

Indium

mounting Metal wire

Sample

Circular light

window

(b)

mounting Metal wire

(top contact)

Figure 4.4 (a) Band structure of Ohmic contacts; (b) device schematic.

4.3 Photovoltaic I-V measurements

The results of photovoltaic (PV) I-V measurements are shown in Fig. 4.5. First

of all, the efficiencies (ηmax) of all three samples, 3∼5 %, are much lower than

the record of single junction GaAs solar cells (28 %). It is due to the un-optimal

designs, such as no top grid electrode, no antireflection coating layer, no effective

surface passivation, defects in material and the structure limit (i.e., p-GaAs as the


0.0 0.2 0.4 0.6 0.80.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.80

2

4

6

8

10

12

14

Current [m

A]

External bias [V]

D

A: D=0.6 cm

C: D=0.2 cm

B: D=0.2 cm

Current density [mA/cm

2]

A: η=4.3%FF=0.63

B: η=3.1%FF=0.69

C: η=5.3%FF=0.67

Figure 4.5 PV measurements under Xenon-lamp solar simulator whose intensity hasbeen adjusted to 100 mW/cm2. D: diameter of the light window. Taken from Paper1. Reprinted with permission of Springer.

top emitter and n-GaAs as the base). We do not care these low efficiencies since

our interest is to study QD role in PV conversion.

Compared to the control sample C (Voc = 0.74 V, Jsc = 10.1 mA/cm2 and ηmax

= 5.3 %), QD samples A and B behave differently. The Voc of sample A reduces

to 0.50 V while its Jsc increases to 13.5 mA/cm2; the Voc and Jsc of sample B

reduce to 0.62 V and 7.4 mA/cm2. The ηmax of sample B is the lowest.

The decrease of Voc is common for most QD solar cells [19,22,51,54,55] and at-

tributed to dislocations in multiple closely stacked QD layers [19,51]. Our sample

A has 5 layers of QDs while sample B has 15 layers. If the dislocations are the

reason, more dislocations and larger decrease of Voc will be expected in sample B.

But, the reduced Voc of sample B is still larger than that of sample A. So, apart

from dislocations, there are more essential reasons for the degradation of Voc.

The 1/3 increase of Jsc in QD sample A is interesting here. The increase of Jsc

in QD solar cells has been reported before [55,56] and attributed to the improved

additional sub-bandgap absorption in QDs. While, some others [19,54] reported

degraded Jsc as well as Voc in QD solar cells. On the theoretical aspect, both

multiple exciton generation effect and intermediate band effect are expected to

enhance Jsc. These conflicting results confuse the understanding of QD roles on

PC production.

A drawback here is that the comparison cannot avoid the factor of disloca-

tions. The strain-induced InAs QD growth is flexible. If the growth is not optimal,

many dislocations will be introduced; then, both Jsc and Voc will degrade, for ex-

ample, QD solar cells with 10 nm-GaAs spaced multiple QD layers [19,51]. If the

4.3 Photovoltaic I-V measurements 33

GaAs spacer is proper in thickness (20∼50 nm) and the QD layer number is few

(e.g. 5), there will be not so many dislocations.

Apart from dislocations, the comparison of Jsc makes sense only when the

solar cell structure especially the depletion region keeps the same. However, most

previous works just embedded multiple QD layers in a p-i-n structure and did not

keep the same width of each region. For example, Martı et al [51] put 10, 20 and 50

layers of QDs with 10 nm GaAs spacers in the i region respectively; Zhou et al [54]

embedded the same 5 layers of QDs in the p, i and n regions respectively, without

considering the width increase in the region and its influence on the other regions;

Sablon et al [56] applied a Si:δ-doping layer with different doping levels in each 50

nm-thick GaAs spacer of the 20 layers of QDs, without considering the built-in

field change by these Si dopant ions. My samples here keep the same width of each

region. The comparison between them will indicate the QD performance. In next

section, I will present the photocurrent spectra and determine which wavelength

of light absorption is responsible for the enhanced Jsc.

Let us return to the reduced Voc. It can be analyzed in the viewpoint of

the p-n diode performance. The diode performance is extracted from the PV I-V

curves by plotting Jsc − J ∼ V , as shown in Fig. 4.6. In the semi-log plot, the

linear region near Voc will give the J0 and the ideality factor n, characterizing the

drastic reduce of photocurrent near Voc.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.01

0.1

1

10

100

J0 (estimated in the line-fitted region):

A: 6.60; B: 0.353; C: 0.572 [µΑ/cm2]

nC = 3.02

nB = 2.34

Sample A

Sample B

Sample C

Current density [mA/cm2]

Voltage [V]

J = J0(eqV/nkT

-1)

nA = 2.53

Figure 4.6 Diode performances of three solar cells. Taken from Paper 1.Reprinted with permission of Springer.

The ideality factor n is 3.02 for sample C, 2.53 for A and 2.34 for B. The

reduced n of QD samples A and B is because of a dominant SRH recombination,

induced by QDs and/or dislocations. The n is near 2 when this recombination is


dominant. Sample C has no QDs and few dislocations; the direct recombination

is dominant, giving a high n.

The main difference lies in J0. It is 6.60 µA/cm2 for sample A, 0.353 µA/cm2

for B and 0.572 µA/cm2 for C. The one-order of magnitude increase of J0 in sample

A, according to Eq. 4.3, is due to a large decrease of photocarrier lifetime. The

QD confinement increases the chance that electrons and holes meet and recombine

with each other, enhancing the recombination current in the depletion region. The

slightly reduced J0 in sample B is due to the potential variations around QDs (see

Fig. 4.3). QDs with electron filling, served as Coulomb scattering centers, will

reduce the carrier mobility in the n region, as well as J0 and Jsc. The same scale

of J0 in samples B and C indicates the similar depletion region and the same scale

of photocarrier lifetime.

The Voc can be deduced when J = 0, i.e.,

Voc =nkBT

qln(

Jsc

J0

+ 1) (4.4)

The Jsc of all samples are in the same scale, so the reduced Voc of sample A

is related to the large increase of J0, i.e. the reduced photocarrier lifetime. In

sample B, both J0 and Jsc are reduced and their ratio Jsc/J0 is little changed, so

the reduced Voc of sample B is because its n is most reduced, related to the most

enhanced SRH recombination.

4.4 Photocurrent spectra

The photocurrent (PC) spectra are presented here, from which we can find the

contribution in different wavelengths and the reason for the increased Jsc. The

300∼1000 nm PC spectra are measured by a monochromator and a Si reference

photodiode under a Xenon lamp, as shown in Fig. 4.7. The sub-GaAs-bandgap

PC spectra are measured by a Fourier Transform (FT) spectrometer, as presented

in Fig. 4.9.

In Fig. 4.7, the PCs of samples (Isample(λ)) and the reference Si diode (ISi(λ))

are recorded at the same time. The illumination area of samples is fixed to

be the same by an aperture with the area of 0.32 cm2. The relative intensity

Isample(λ)/ISi(λ) spectra, as shown in the inset, reflect the external quantum ef-

ficiency (EQE) of samples, EQEsample(λ), since the EQE of the Si diode is little

changed in 500∼900 nm [1]. For sample A, the >900 nm spectrum is clearly

observed, due to QD absorption.

4.4 Photocurrent spectra 35

300 400 500 600 700 800 900 1000

0

1

2

3

4

5

400 500 600 700 800 900 10000

1

2

3

4

5

Photocurrent [10-5 A]

Wavelength [nm]

A

BC

Si

Relative intensity A C

B

Figure 4.7 300 ∼ 1000 nm PC spectra. Inset: relative intensity Isample(λ)/ISi(λ).Taken from Paper 2. Reprinted with permission of American Institute ofPhysics.

The PC spectral integrations in the dominant 300∼1000 nm region agree with

the 1/3 raise (decrease) of Jsc in sample A (sample B) compared to sample C in the

PV measurement, so the Isample(λ) of each sample can be compared directly. In

sample B, the lowest Isample(λ) is because the potential variation around each QD

matrix reduces the carrier mobility in the n region. Besides, the most dislocations

and SRH recombination are also the reasons.

In sample A, the enhanced above-GaAs-bandgap PC spectrum is responsible

for the increased Jsc. There are several possible reasons for it. One is the multiple

exciton generation (MEG) in QDs. Since sample A has a 80 nm-thick undoped

GaAs layer above the QD matrix, the photoelectrons in the p region will drift

through this layer and accelerate without dopant ion scattering; when they reach

QDs, these electrons with high kinetic energy will impact ionize electron-hole pairs

and produce more photocarriers. But, the built-in field in our samples cannot

increase the photoelectron kinetic energy to twice the QD ground-state transition

energy (∼1 eV) that is believed to be the threshold for the MEG [57].

We think the above-bandgap photon absorption is enhanced after embed-

ding QDs. In the depletion region, most photocarriers move at the drift velocity.

QDs will reflect electron and hole wavefunctions and increase their overlap and

transition (i.e. absorption) rate.

We make a simulation in Fig. 4.8. In the depletion region in width of W ,

the five QD layers are modeled as five 1D quantum wells with thickness of 0.7

nm; the electron and hole wavefunctions are modeled as 1D free particles, e±ikz,

incident into the QD matrix from opposite directions [58]. The k characterizes


0

1

2

0

1

2

VB

CB

QD QD QD QD QD

transmission

amplitude of CB electron

incidencereflection

reflection

transmission

amplitude of VB hole

incidence

Figure 4.8 Wavefunctions of CB electron and VB hole in the depletion region withQDs embedded (solid) and without QDs (dotted). ~ω = 1.593 eV is chosen to showa complete reflection of the hole wavefunction. Taken from Paper 2. Reprintedwith permission of American Institute of Physics.

the drift velocity. QDs will reflect and transmit the carrier wavefunctions, giving

components re±ikz and te±ikz. The hole wavefunction is reflected serious due to

its large effective mass. It is completely reflected when the transition energy is

1.593 eV. If there is no QD, the wavefunction overlap is

WC = 〈eikez|e−ikhz〉 =

∫

W

ei(−ke−kh)zdz (4.5)

If there are QDs, assuming a complete hole reflection and a complete electron

transmission, the wavefunction overlap is

WA = 〈eikez|e−ikhz + eikhz〉 =

∫

W

ei(−ke−kh)zdz +

∫

W

ei(−ke+kh)zdz (4.6)

Since the optical absorption in GaAs is mainly direct transition, i.e., ke = kh, the

WC oscillates while the second term of WA gives a large contribution to PC.

This enhancement is too large as compared with the experiments, since the 1D

quantum wells exaggerate the wavefunction reflection in 3D QDs; not all-energy

holes are completely reflected. Besides, the direct absorption in GaAs creates

electron and hole moving in the same direction and one of them will re-orientate

under the built-in field in ∼10 ps (~k/eE), contributing to the PC as well.

The FT-based PC spectra are shown in Fig. 4.9. Compared to sample C,

both QD samples A and B show sub-GaAs-bandgap spectral features, including a

clear wetting-layer peak near 920 nm and QD features extended in 950∼1300 nm.

To clarify the sub-bandgap PC spectra, Fig. 4.9(b) uses a GaAs-filter to filter the

4.5 Mechanisms of photocarrier escape from QDs 37

incident QHT light. There are multiple QD peaks, due to the size distribution

and/or the energy state coupling in closely spaced QD layers.

The sub-bandgap PC spectrum of sample B is about 30 times lower than that

of sample A, even for the wetting-layer peak. It indicates that the photocarrier

extraction from QDs in the depletion region is effective while that from QDs in

the n region is weak. The QDs in the n region are partially filled with electrons,

so the QD interband absorption is suppressed. Besides, the potential variation

around each QD matrix reduces the carrier mobilities (see the spectra backgrounds

nB < nC) and increases the thermal activation energy for the minority photohole

extraction from QDs. In addition, if the intermediate band absorption exists in the

partially filled and coupled QDs, its PC production via the minority photocarrier

diffusion (Lp ∼ 0.9µm) is still quite lower in efficiency than the built-in field

extraction and drift.

900 1000 1100 1200 1300

0.00

0.05

0.10

0.15

0.30

0.35

0.40

0.45

400 600 800 1000 120010

-5

10-4

10-3

10-2

10-1

100

WL

Wavelength [nm]

Photocurrent intensity [arb unit]

1

(b)

AB(x30)

4

6

5

3

7

2

A

B

C

(a) WL

nA

nC

nB

Figure 4.9 PC spectra measured by a FT infrared spectrometer under a quartz halo-gen tungsten lamp (a) and GaAs-filtered light (b). Taken from Paper 2. Reprintedwith permission of American Institute of Physics.

4.5 Mechanisms of photocarrier escape from QDs

The photocarrier extraction from QDs is essential for QD applications in pho-

todiodes, photodetectors and solar cells. Two mechanisms have been proposed,

tunneling and thermal activation [59,60]. In our QD sample A, the strong built-in

field enables photocarrier tunneling out from QDs to GaAs. The thermal activa-

tion is also enhanced due to the reduced barrier height under the field, i.e. the

Poole-Frenkel effect [61]. In our QD sample B, the photocarrier extraction only


relies on thermal activation. By analyzing their bias- and temperature-dependent

PC spectra, I find that sample A has an inter-QD-layer tunneling and sample B

is dominated by the hole thermal escape.

I first position the energy of each PC peak, by combining with the Gaussian-

line fitted PL spectra in Fig. 4.10. There are seven QD peaks and two wetting-layer

(WL) peaks (dashed Lorentzian lines). These densely (50 meV) packed QD peaks,

unlike the usual ∼70 meV separation for uncoupled QDs [59,60], are caused by the

QD size distribution and the energy state coupling between adjacent QD layers.

The non-uniform QD height, discrete by a step of atomic monolayer (ML), will

give a stepwise change of the QD state energy. It is profound on small QDs when

the QD height is as low as 3 nm [62,63]. The QD1 to QD3 in our samples may

be from the non-uniform small QDs. This size distribution in large QDs only

induces a continuous modification of QD state energy, corresponding to the QD4

to QD6 in our samples. QD6* in sample A, separated from QD6 by 36 meV in

PL spectrum and 43 meV in PC spectrum, is possible due to a coupling between

the QD6 exciton and the LO phonon [64]. The two WL peaks, separated by ∼20

meV, are from the non-uniform wetting layer thickness [65].

0.9 1.0 1.1 1.2 1.3 1.4

0.9 1.0 1.1 1.2 1.3

0.9 1.0 1.1 1.2 1.3

WL1

WL2

QD1QD2

QD3QD4

QD5QD6

PC

(a) Sample A

QD6*

no-filter

WL1

WL2

QD1QD2

QD3

QD4QD5PC

(b) Sample B

Photon energy [eV]

QD6

filter

QD2

QD3

QD4

QD5PL

QD6

QD4

QD5

QD6PL

QD6*

Figure 4.10 Room temperature PC and PL spectra. Each peak position is marked.


The bias-dependent PC spectra of QD samples A and B and the bias depen-

dence of each peak are presented in Fig. 4.11. As the reverse bias increases, the

PC intensity enhances. WL1 becomes increasingly important as compared with

WL2, because it is closer to the GaAs bandedge. A ∼2 meV red-shift of WL2

is observed in sample A when the bias scans from 0.5 V to -1.0 V due to the

quantum Stark effect [66]. QD peaks show no shift when the bias changes.

For sample A, as the external bias changes from 0.5 to -1 V, the PCs from QDs

and WLs first increase rapidly, then increase slowly and finally become saturated,

similar to the behavior at the GaAs bandedge. It implies that the photocarrier

extraction from WLs and QDs is effective. For sample B, the PC contributions

from WLs and QDs are linearly dependent on the external bias from 0.2 V to

-0.4 V, due to the extension of the built-in field and the change of the minority

hole diffusion. The linear bias dependence is very different from that at the GaAs

bandedge, implying that the photocarrier extraction from WLs and QDs in sample

B is very poor.

In detail, the bias dependence of each PC peak shows fine features. For sample

A, the bias dependences of GaAs, WL1, WL2, QD1 to QD3 are similar while QD4

to QD6 and QD6* show stronger bias dependence. The lower the energy is, the

stronger the bias dependence is, indicating a tunneling mechanism for photocarrier

escape from QDs [67,68]. For uncoupled QDs, e.g. single QD layer or multiple QD

layers with GaAs spacers thicker than 40 nm, the photocarrier tunneling escape

from deep QD levels is believed to be exponentially dependent on the external

bias [68]; however, the deep QD peaks here such as QD6 show bias dependence in

similar trend with the PC from GaAs, suggesting a significant interlayer tunneling

between the 20 nm GaAs spaced QD layers. Closely stacked QD layers will form

vertically aligned QDs and vertical state coupling. Photocarriers in deep QD

states in one QD layer can tunnel into adjacent QD layers and finally escape, as

schematized in Fig. 4.12. For sample B, all QD peaks show an identical linear

bias dependence, weaker than the linear bias dependence of WL peaks, because

the photocarrier thermal activation from WL is larger than that from QD states

and photocarriers cannot escape from QDs via inter-QD-layer tunneling.

Then, I measured the temperature-dependent PC spectra of sample B, which

are presented in Fig. 4.13(a). Below 200 K, there is no PC spectrum (see the 200 K

grey line). From 250 K to 295 K, the PC intensity increases. The position of each

QD peak is almost unchanged; while WL peaks are red-shifted. WL2 is shifted by

20 meV and WL1 is shifted from the filter region of the room-temperature GaAs

filter to 1.368 eV at 295 K.


0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.9 1.0 1.1 1.2 1.3 1.40.00

0.02

0.04

0.06

0.08

0.10

0.01

0.02

0.03

0.04

0.12

0.16

0.20

1.0

1.2

1.4

1.6

1.8

2.0

-0.8 -0.4 0.0 0.4

1.0

1.2

1.4

1.6

y-shift:

0.0002 / line

QD1

QD2

QD3

QD4

QD5

QD6

(a) Sample A

Room temperature,

104 V/A

Photocurrent

QD6*

-1.0, -0.8, -0.6, -0.4, -0.2,

0.0, 0.2, 0.4, 0.5V

-0.4, -0.2, 0.0, 0.2V

y-shift:

0.003 / line

WL1

WL2

QD1

QD2QD3

QD4QD5

QD6

Photon energy [eV]

(b) Sample B

Room temperature,

107 V/A

y-shift:

0.0015 / line

WL2WL1

Relative PC intensity

GaAs

WL1

WL2

QD1

QD2

QD3

QD4

QD5

QD6

QD6*

(c) sample A

(d) sample B

WL1

WL2

QD1

QD2

QD3

QD4

Bias [V]

Figure 4.11 Bias-dependent PC spectra at room temperature. (a) Sample A underQHT light. External current amplifier gain of 104 V/A, from -1.0 V to 0.5 V with 0V in red and 0.5 V in blue for clarity. The QD range (0.9∼1.3 eV) is shown in theleft, vertically shifted by 0.0002/line; the WL and GaAs bandedge range (1.3∼1.44 eV)is shown in the right, in a large vertical scale and vertically shifted by 0.0015/line.(b) Sample B under GaAs-filtered QHT light. Gain 107 V/A, from -0.4 V to 0.2 V,vertically shifted by 0.003/line. (c) and (d) compare the relative bias dependence ofeach peak, with the intensity accumulated in its width and scaled to the intensity at0.5 V for A and 0.2 V for B.

thermal activation

interlayer tunneling

QD-stateWL-state

WL-state

QD-state

(a) thermal activation

tunneling

tunneling

thermal activation

(b)

VB

QD state

QD state

QD state

QD state

CB

Figure 4.12 Interlayer tunneling from closely stacked QDs (a) compared to the ordi-nary tunneling from far spaced QDs (b).


The temperature dependence of each peak intensity, as shown in Fig. 4.13(b),

is exponentially dependent on 1/kBT , indicating the thermal activation e−Ea/kBT

(Ea: activation energy). The deduced Ea of each peak is larger than 210 meV,

even for WL2, much larger than the result of a single layer of QDs in the depletion

region [60]. The large Ea suggests that the thermal activation from QDs is dom-

inated by the minority photoholes, because the potential variation around each

QD matrix increases the barrier for photohole escape from QDs. Therefore, the

Ea characterizes the offset between the QD hole-state and the flat GaAs valence

bandedge. Based on Ea and the energy (Eph) of each PC peak, the QD matrix’s

energy-level diagram is reconstructed, as seen in Fig. 4.13(c).

1.0 1.1 1.2 1.3 1.4

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1/3001/290

1/2801/270

1/2601/250

1/240

10-4

10-3

10-2

10-1

1.0 1.1 1.2 1.3

0.0

0.4

0.8

1.2

1.6

2.0

1200 1300 1400 1500

0.0

0.2

0.4

1.0

1.2

1.4

1.6

295 K

290 K

285 K

280 K

275 K

260 K

250 K

200 K

Photo

current

Photon energy [eV]

WL2

(a) (b)

236.5

236.5

253.7

QD1-3

QD5, 296.7

QD4, 275.2

QD6, 322.5

1/T [K -1]

WL2

Ea=210.7 meV

QD4

QD5

x 100

QD6

Ea

Eph

QD6

QD6

WL2 (c)

Energ

y [eV]

Position [nm]

WL2QD1-QD3

Figure 4.13 (a) Temperature-dependent PC spectra of sample B (unbiased), with QDcontributions zoomed in the inset; (b) Temperature dependence and activation energyEa of each peak; (c) Reconstructed energy level diagram of the QD matrix.

The photohole extraction also dominates the PC production from QDs in the

depletion region [59,60]. That is why in closely stacked QDs when the temperature

varies from 300 K to 20 K the PC spectral intensity shows negligible temperature

dependence; while in uncoupled QDs the PC intensity of each QD peak, especially

the ground QD peak, is very sensitive on the temperature [59].

Chapter 5

Bunched correlation of two

colloidal QD blinking

In this chapter I study another subject, colloidal QD blinking. Colloidal QDs

(e.g. CdSe QDs) have big potentials on applications of photon emission such as

bioimaging [69] and LED [70], and light absorption such as QD solar cells with QDs

replacing the dye molecules in dye-sensitized solar cells [71]. For light emission,

a colloidal QD has an intrinsic drawback: its emission is intermittent and often

switches between the on and off states. The fluorescence blinking is related to

the surface traps, i.e., dangling bonds in the QD surface. Under light excitation,

electron-hole pairs are created in a QD. They will relax to the ground QD states

and recombine radiatively to emit photons (i.e. the on state). Sometimes, a pho-

tocarrier will escape from QD and occupy the surface state. The left photocarrier

in the QD, as a charge, will suppresses the bright exciton formation if there is

another electron-hole pair excited subsequently. Now, electrons and holes will

recombine non-radiatively (i.e. the off state) until the trapped carrier returns to

the QD. Fig. 5.1 gives an example of the light intensity evolution of colloidal QD

blinking. The blinking seems random. But, the previous studies have shown some

law. By introducing a threshold above which the intensity is defined to be 1 (the

on state) while below which the intensity is defined to be 0 (the off state), the

statistical probability distribution of the on/off state shows an inverse power law

on the on/off time [72,73]. This law is valid for the time from 1 ms to several 100

s, implying a multi-time constant process. From Fig. 5.1 we also find that the

multi-shell QD light intensity is higher and more steady than the single-shell QD

light intensity, because the multi-shell is thick for photocarrier escape and blinking

occurring. In this chapter, I found that the light intensity from two individual

42

5.1 QD fluorescence imaging system 43

blinkingfull QDs with distance less than 1 µm tend to have a time correlation, i.e.

bunched photon emission, due to their mutually stimulated emission.

0

500

1000

1500

2000

0 100 200 300 400 500 600 700 800 900 10000

2500

5000

7500

10000

12500

Light inensity [counts/frame]

CdSe/ZnS core/shell water-soluble QD

CdSe/CdS/Zn0.5Cd

0.5S/ZnS core/multi-shell oil-soluble QD

Time frames [50 ms/frame]

Figure 5.1 Colloidal QD blinking, 1000 frames, 50 ms/frame. Top: a single-shell QD;Bottom: a multi-shell QD.

5.1 QD fluorescence imaging system

The colloidal CdSe QD solution is diluted into a concentration less than 10−9

mol/L and deposited on a clean glass. The samples are dried in air and imaged

under a microscope under a mercury lamp (λ = 436nm) excitation. The imaging

system includes a 100× oil-immersed objective (NA=1.45) and a camera. The

camera can record 128×128 pixel movies in 50 ms per frame and 64×64 pixel

movies in 5 ms per frame. The camera scene covers single, double or several

QDs, and records their blinking for a long time (1000 frames). A typical blinking

movie is shown in Fig. 5.2. Each QD has a light spot whose maximal intensity is

extracted as the QD blinking intensity, I(t), as a function of the time frame.

5.2 Correlation analysis

The time correlation function of two QD blinking is defined to be

gAB(τ) =<IA(t)IB(t + τ)>t

<IA(t)>t · <IB(t + τ)>t

(5.1)

where < . . . >t is the average on the time; τ is the delay between the two QD

signals. The unit of τ is a frame, i.e. 50 ms. The following correlation analysis

is valid in this time resolution. If the two QD blinking affect each other and tend

to emit photons synchronously (or bunched), the correlation function will give a

44 5 Bunched correlation of two colloidal QD blinking

0.72

Figure 5.2 A frame of CdSe QD blinking movie that includes 1000 frames in 50ms/frame. QDs A and B are 0.72 µm distant. Their light spot diameters are 7 pixelsat most.

peak at τ = 0. If their blinking affect each other and emit photons mutually

exclusively (antibunched), gAB(τ) will give a dip at τ = 0. If their blinking have

no correlation, gAB(τ) will be flat around τ = 0. The time correlation function is

often used to decide if there is a single photon emission [74,75,80] or a two-photon

emission [76,77] or a two-photon absorption [78], with the delay time smaller than

the emission time (∼ ns) and absorption time (∼ ps) and to characterize the

shape of an ultra-short (∼ fs) light pulse with an optically nonlinear crystal [79].

In principle, photon emission is a trigger process in time resolution smaller than

the emission lifetime. Here, we use correlation analysis to study the QD blinking

emission since it is a multi-time constant process and its dominant time constant

is possible comparable with 50 ms. For most multi-shell QDs with steady light

emission and few blinking observed (see Fig. 5.1), in order to record the real-time

blinking emission, the frame time must be much reduced. Furthermore, if the

above correlation is caused by the blinking itself, the steady emission with few

blinking will give no correlation.

In fact, our statistical correlation analysis is performed on 1000 frames rather

than infinite time; each frame records the total light intensity in 50 ms rather

than a real-time photon-number counting in resolution smaller than the intrinsic

photon emission lifetime (∼ ns), so gAB(τ) has a random fluctuation. In a large τ

range (e.g. ±200 frames = ±10 s), the fluctuation is serious, providing no valuable

information. We also deny the existence of a long-time correlation between two

QD blinking. In a local region around τ = 0 (e.g. ±5 frames = ±0.25 s), the fluc-

tuation is small. We use a scheme to compare gAB(0) and the surrounding gAB(τ)

5.2 Correlation analysis 45

and decide if there is a correlation: analyzing the average g and the standard

derivation σ of the surrounding 10 points of gAB(τ) where τ=±1, ±2, ±3, ±4 and

±5); if gAB(0) > g + σ, we believe gAB(0) is a peak (bunching); if gAB(0) < g−σ,

gAB(0) is a dip (anti-bunching); if gAB(0) is in the g±σ range, we believe it is flat

(no correlation). The decision will be more reliable if the tolerance range increases

to ±2σ, i.e., the bunched correlation must satisfy gAB(0) > g + 2σ.

Another problem is that for closely (e.g. 0.5 µm) spaced two QDs, their light

spots overlap and affect the independent acquiring of light intensity from each

QD. In this case, the above correlation will contain some contribution from the

autocorrelation of each QD that is defined to be

gA(τ) =< IA(t)IA(t + τ) >t

< IA(t) >t · < IA(t + τ) >t

(5.2)

For example, if the recorded IA(t) = a(t)IA(t)+b(t)IB(t) where IA(t) and IB(t) are

the real light intensity from each QD and a(t) and b(t) are contribution factors in

[0, 1], gAB(τ) will have a term from < IB(t)IB(t + τ) >t, i.e. gB(τ). The autocor-

relation function is symmetric with τ and has a peak at τ = 0 (see Fig. 5.3), even

for the background signal in the movie. It cannot conclude a bunched correlation.

-20 0 20 40 60 80 100

1.0

1.1

1.2

1.3

0 200 400 600 800 1000

100

200

300

400

500

600

700

800

0 200 400 600 800 1000

100

120

140

-20 0 20 40 60 80 100

1.000

1.002

1.004

Oil, multi-shell (steady-state)

Water, single-shell (trigger-like)

Autocorrelation g

A(τ)

Light intensity [counts/frame] Trigger-like (QD-A blinking in S32)

Time [x50ms]

Background signal

Background singal

Delay τ [x 50ms]

Figure 5.3 Light intensity and autocorrelation of a trigger-like QD blinking (water-soluble single-shell QD-A in S32) and the background, compared with the oil-solublemulti-shell QD in Fig. 5.1.

The third problem is that the recorded movie includes a noise caused by the


dark counting in the camera CCD, I(t) = I(t) + N(t). The background noise

N(t) is random on both time and position. If the real QD light intensity is as

low as N(t), the noise will give a considerable influence on gA(τ) and a random

local-region fluctuation on gAB(τ). In this case, gAB(τ) cannot reflect clearly the

real correlation information of two QDs.

A proper QD blinking sample for correlation analysis must have many obvious

blinking events, i.e., the recorded light intensity must be high trigger-like rather

than steady state-like. Fig. 5.3 shows a trigger-like QD blinking. Its short-time

autocorrelation, i.e., gA(1) is much lower than gA(0), is compared with the auto-

correlation of a steady state-like QD blinking that gradually decays from τ = 0.

The background signal and its autocorrelation are also presented, showing ‘white

noise’ features.

5.3 Statistical result

We made and measured 43 samples of dilute water-soluble CdSe/ZnS single-shell

QDs. Their blinking intensity is shown in Fig. 5.4. The samples grouped together

are actually the same sample measured several times. The other once-measured

samples are also listed together as the QD distance increases from 0.52 to 2.11

µm. Their correlation analysis is presented in Fig. 5.5 and 5.6. In Fig. 5.7,

we compare gAB(0) and the surrounding gAB(τ) values by the above-mentioned

scheme and determine which has bunched correlation. Fig. 5.8 makes a statistics

on the correlated samples as a function of QD distance. We find that for closely

spaced two QDs in distance of 0.7∼ 1.1 µm, gAB(0) is a peak, indicating a bunched

correlation; as the QD distance increases, this phenomenon disappears gradually;

for QDs distant from each other by 0.52 ∼ 0.55 µm, the two QD light spots

overlap obviously, although there is a gAB(0) peak, it cannot conclude a bunched

correlation. I will discuss them in detail below.

For QD distance between 1.33 and 5.78 µm, all the nine samples (N5, N6, N9,

N10, N12, N14, N15, S10 and S15) have no gAB(0) peak definitely. Their gAB(τ)

fluctuate randomly; the same sample measured in different times shows different

profiles, e.g. N5 and N6, N10 and N12, N14 and N15. When the QD distance

is between 1.23 and 1.29 µm, in the six samples (S2, S6, S9, S22, S23 and S24),

there are only two samples, S2 (1.23 µm) and S6 (1.24), satisfying gAB(0) > g+σ,

and only S2 satisfying gAB(0) > g + 2σ.

5.3 Statistical result 47

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 10000

300

600

900

1200

1500

0 200 400 600 800 10000

500

1000

1500

0

500

1000

1500

2000

0

200

400

600

800

1000

0 200 400 600 800 10000

500

1000

1500

0 200 400 600 800 10000

500

1000

1500

2000

0

500

1000

1500

2000

2500

0

300

600

900

1200

1500

0

300

600

900

1200

0 200 400 600 800 10000

100

200

300

400

500

0

200

400

600

0 200 400 600 800 10000

200

400

600

800

1000

0

100

200

300

400

500

0 200 400 600 800 10000

100

200

300

400

500

0 200 400 600 800 10000

100

200

300

0

300

600

900

1200

0

200

400

600

0

200

400

600

0

100

200

300

400

500

0

100

200

300

400

500

0

200

400

600

0 200 400 600 800 10000

100

200

300

400

0

200

400

600

800

0 200 400 600 800 10000

200

400

600

800

0

200

400

600

800

0

200

400

600

0 200 400 600 800 10000

200

400

600

0

200

400

600

800

1000

0

200

400

600

800

1000

0

200

400

600

800

1000

0

200

400

600

800

0 200 400 600 800 10000

200

400

600

800

0

200

400

600

800

0

200

400

600

0 200 400 600 800 10000

200

400

600

800

0

200

400

600

800

0 200 400 600 800 10000

100

200

300

400

500

0

200

400

600

800

0

200

400

600

800

0

200

400

600

800

0

200

400

600

800

0

200

400

600

0 200 400 600 800 10000

200

400

600

N5 ~ N6 Light intensity I(t)

N5 (5.76)

N6 (5.73)

N15 (1.39)

N14 ~ N15N14 (1.33)

N10, N12

N10 (3.98)

N12 (3.98)

N9 (2.11)

N16 (1.09)

Rest: N9, N13, N16, S1,

S2, S5, S8, S11, S15N13 (0.52)

S3 ~ S4

S3 (0.77)

S4 (0.84)

S6 ~ S7

S6 (1.24)

S7 (1.14)

S9 ~ S10

S9 (1.29)

S10 (1.36)

Background of N13

S8 (0.55)

S1 (0.78)

S5 (0.96)

S2 (1.23)

S19 ~ S21

S19 (0.52)

S20 (0.52)

S21 (0.52)

S12 ~ S13S12 (1.14)

S13 (1.14)

S16 ~ S18

S16 (1.16)

S17 (1.16)

Time t [x 50ms]

S18 (1.16)

S22 ~ S24S22 (1.23)

S23 (1.24)

S11 (0.78)

S15 (1.45)

S24 (1.23)

S25 ~ S27

S25 (0.80)

S26 (0.94)

S27 (0.94)

S28 ~ S29

S28 (0.72)

S29 (0.72)

S30 ~ S35S30 (0.82)

S31 (0.82)

S32 (0.72)

S33 (0.72)

S34 (0.72)

S35 (0.72)

Figure 5.4 Two QD blinking intensity as function of time. Samples as a group arethe same sample measured several times. Sample name is, e.g. S5, followed with theQD distance [µm].


-20 -10 0 10 200.96

0.98

1.00

1.02

1.04

-20 -10 0 10 20

0.99

1.00

1.01

1.02-20 -10 0 10 20

1.00

1.01

1.02

1.03

1.04

-20 -10 0 10 20

0.96

0.98

1.00

-20 -10 0 10 20

1.00

1.02

1.04

-20 -10 0 10 20

1.04

1.06

1.08

-20 -10 0 10 20

0.98

1.00

1.02

-20 -10 0 10 200.995

1.000

1.005

-20 -10 0 10 20

1.00

1.02

1.04

-20 -10 0 10 200.97

0.98

0.99

1.00

-20 -10 0 10 200.992

0.996

1.000

-20 -10 0 10 20

1.000

1.004

-20 -10 0 10 201.06

1.08

1.10

1.12

-20 -10 0 10 20

1.00

1.05

1.10

1.15

1.20

-20 -10 0 10 201.00

1.01

1.02

1.03

1.04

-20 -10 0 10 20

1.03

1.04

1.05

1.06

-20 -10 0 10 20

1.00

1.02

-20 -10 0 10 20

0.98

1.00

1.02

1.04

-20 -10 0 10 200.9996

1.0000

1.0004

-20 -10 0 10 20

1.03

1.04

-20 -10 0 10 200.99

1.00

-20 -10 0 10 20

1.01

1.02

1.03

N5 (5.76)

Corr

ela

tion g

AB

(τ)

N6 (5.73)

N10 (3.98)

N12 (3.98)

N14 (1.33)

N15 (1.39)

S3 (0.77)

S4 (0.84)

S6 (1.24)

S7 (1.14)

S9 (1.29)

Delay τ [ X 50ms]

S10 (1.36)

N13 (0.52)

S8 (0.55)

S1 (0.78)

S11 (0.78)

S5 (0.96)

N16 (1.09)

Background cross-correlation

S2 (1.23)

S15 (1.45)

N9 (2.11)

Figure 5.5 Correlation functions of samples (the left two columns in Fig. 5.4).


-20 -10 0 10 200.99

1.00

1.01

1.02

-20 -10 0 10 201.00

1.01

-20 -10 0 10 20

1.02

1.04

1.06

-20 -10 0 10 200.99

1.00

-20 -10 0 10 201.00

1.01

-20 -10 0 10 20

1.00

1.01

-20 -10 0 10 201.01

1.02

1.03

1.04

-20 -10 0 10 201.00

1.01

-20 -10 0 10 20

0.94

0.96

0.98

1.00

-20 -10 0 10 200.98

0.99

1.00

-20 -10 0 10 20

1.00

1.01

1.02

-20 -10 0 10 20

1.03

1.04

1.05

-20 -10 0 10 20

1.00

1.01

1.02

-20 -10 0 10 20

0.99

1.00

1.01

-20 -10 0 10 200.99

1.00

1.01

-20 -10 0 10 200.98

0.99

1.00

1.01

-20 -10 0 10 20

1.00

1.01

1.02

-20 -10 0 10 20

0.98

1.00

1.02

-20 -10 0 10 20

1.00

1.01

1.02

-20 -10 0 10 200.98

1.00

1.02

-20 -10 0 10 20

0.99

1.00

1.01

1.02

-20 -10 0 10 20

1.00

1.01

1.02

S12 (1.14)

Correlation g

AB(τ)

S13 (1.14)

S16 (1.16)

S17 (1.16)

S18 (1.16)

S19 (0.52)

S20 (0.52)

S21 (0.52)

S22 (1.23)

S23 (1.24)

S24 (1.23)

S25 (0.80)

S26 (0.94)

S27 (0.94)

S28 (0.72)

S29 (0.72)

S30 (0.82)

S31 (0.82)

S32 (0.72)

S33 (0.72)

S34 (0.72)

S35 (0.72)

Delay τ [ X 50ms]

Figure 5.6 Correlation functions of samples (the right two columns in Fig. 5.4).


When the QD distance is in 1.14 ∼ 1.16 µm, all the six samples (S7, S12,

S13, S16, S17 and S18) satisfy the requirement gAB(0) > g +σ and only S7 (1.14)

and S17 (1.16) do not satisfy gAB(0) > g + 2σ. S12, S13, S17 and S18 actually

have a bright QD and a dark QD. The dark QD often stays in the dark state

and has very few blinking triggers that are well resolved in the time line, so the

correlation function is less influenced by the fluctuation mentioned above. The

underline physics here is that the equivalent photon emission lifetime of the dark

QD (i.e., blinking time) is longer than the frame time 50 ms, so the camera CCD

can count the emitted photons in real time, leading to a good correlation analysis

and a clear peak at τ = 0 if there is correlation.

0.98

1.00

1.02

1.12

1.13

Noise

S21 (0.52)

S20 (0.52)

N13 (0.52)

S19 (0.52)

S11 (0.78)

S1 (0.78)

S8 (0.55)

S35 (0.72)

S34 (0.72)

S33 (0.72)

S32 (0.72)

S29 (0.72)

S28 (0.72)

S3 (0.77)

S25 (0.80)

S31 (0.82)

S30 (0.82)

S4 (0.84)

S27 (0.94)

S26 (0.94)

S5 (0.96)

N16 (1.09)

S13 (1.14)

S12 (1.14)

S7 (1.14)

S18 (1.16)

S17 (1.16)

S16 (1.16)

S24 (1.23)

S23 (1.24)

S22 (1.23)

S2 (1.23)

S6 (1.24)

S9 (1.29)

S10 (1.36)

N14 (1.33)

N15 (1.39)

S15 (1.45)

N12 (3.98)

N9 (2.11)

N6 (5.73)

N10 (3.98)

g(2)(0)/<g

(2)(τ≠0)>

1+σ/<g(2)(τ≠0)> 1-σ/<g(2)(τ≠0)>

Samples

N5 (5.76)

Figure 5.7 Correlation decision. The background noise has no correlation.

0

1

2

3

4

5

6

7

8

9

10

5.73-5.78

3.98

2.11

1.33-1.45

Distance [µm]

1.23-1.29

1.14-1.16

0.94-1.09

0.80-0.84

0.72-0.78

0.52-0.55

Number of QD pairs

Distance between paired QDs

QD pairs studied

with bunching, g(0) > <g(τ≠0)>+σ with bunching, g(0) > <g(τ≠0)>+2σ

Figure 5.8 Statistics on QD distance.


When the QD distance is between 0.72 and 1.09 µm, all the 17 samples show

the gAB(0) peak under the requirement gAB(0) > g + σ. Only 4 samples, S5, S29,

S31 and S32, cannot satisfy gAB(0) > g + 2σ. In S32 there is a side peak around

τ = 2 and 3; in S31 the gAB(0) peak is not clear. By comparing the different

measurements of the same sample (S30 to S35, 0.72 ∼ 0.82), we conclude that

the gAB(0) peak always exists although sometimes the background fluctuation is

serious. The same samples (S25, S26 and S27, 0.80 ∼ 0.94) and (S3 and S4, 0.77

∼ 0.84) show the gAB(0) peak definitely. The same sample S28 and S29 sometimes

shows a clear gAB(0) peak (S28) while sometimes not (S29). In all, for QD distance

of 0.7 ∼ 1.1 µm, most samples show a clear gAB(0) peak in most cases.

When the QD distance is between 0.52 and 0.55 µm, the QD light spots over-

lap obviously, e.g. N13 and S8 (see their images in Fig. 5.5). The two QD signals

are not independent; the autocorrelation gA(0) peak of each QD will contribute

to the cross-correlation gAB(0) peak. For N13, the QD light intensity is high and

steady state-like, i.e., most photons are emitted without correlation, so its gAB(0)

peak is small. S8 has trigger-like blinking from each QD and thus a huge gAB(0)

peak. Compared to N13 and S8, the same sample S19, S20 and S21 (0.52) has

lower light intensity and smaller overlap. Their gAB(0) peaks are similar to the

cases of 0.72 ∼ 1.09 µm.

0 200 400 600 800 10000

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000 100000

200

400

600

800

1000

-20 -15 -10 -5 0 5 10 15 20

0.99

1.00

1.01

1.02

1.03

Blinking intensity

Time frame [50 ms/frame] QD-A

QD-B

Time frame [5 ms/frame]

A

B

gAB(τ)

movie in 5 ms/frame

Time delay [x50 ms]

movie in 50 ms/frame

Figure 5.9 Steady-state QD blinking in 50 ms/frame or 5 ms/frame and their cross-correlation. QD distance is 0.61 µm.

Later, we tried closely spaced CdSe/CdZnS/ZnS multi-shell QDs. These QDs

have high and steady state-like light intensity. We extended the frame number


to 10000 and reduced the frame time to 5 ms. But, the blinking intensity is still

steady state-like, as shown in Fig. 5.9. There is no correlation between two QDs in

distance of 0.61 µm. We think the multi-shell QD light emission is continuous and

independent because of its thick and high-energy shells for photocarrier tunneling

out to the surface traps. There is seldom blinking and no correlation.

5.4 Explanation

The correlation between two closely-spaced single-shell colloidal QDs lies in the

trigger-like blinking itself. The light emission in one QD will stimulate the light

emission from the other QD if their distance is small. The former QD will be dark

if there is a carrier trapped in its surface state; until the trapped carrier returns

to it the QD cannot emit light to stimulate the light emission from the other QD.

The latter QD has more traps and often stays in the off state. Without the former

QD light stimulation, it tends to keep dark. The time correlation of their light

emission reflects their mutually stimulated emission. The stimulation rate is very

fast, typically ∼ ps−1. It is potential to generate coherent photon-pairs from the

blinking of the two QDs.

The Fourier transform of the autocorrelation function gives the power spec-

trum of each QD blinking (i.e., Wiener-Kintchine theorem). It satisfies the 1/f law

that is well known in random telegraph process, reflecting the random tunneling

and trapping process. The trigger-like QD blinking has a rapid reduce from gA(0)

to gA(1) and a thin gA(τ) profile. It indicates that the dominant time constant

for blinking is ∼ 50 ms and there are many triggers of light emission in the 1000

frames. For a dark QD, the difference of gA(0) and gA(1) is very small, close to

that of the background noise, implying that there is seldom trigger of light emis-

sion; for a steady-state QD blinking, the gradually reduced gA(τ) profile implies

that the dominant time constant for blinking is much larger than 50 ms, i.e., the

light emission is more continuous.

Chapter 6

Summary of the included papers

In Paper I, I studied the photovoltaic performance of InAs quantum dots (QDs)

in p-i-n GaAs cells. I find that the QDs in the depletion region will increase the

diode J0 and reduce the carrier lifetime. The sample with many layers of QDs in

the n-region, away from the built-in electric field, gives an open-circuit voltage Voc

higher than the sample with QDs in the depletion region. It indicates that the

reduced Voc in most QD solar cells has a more intrinsic reason except the strain-

induced dislocations. By analyzing the diode performance, we find that both QD

samples have enhanced SRH recombination due to dislocations and QDs; while

the QDs in the n-region do not reduce the carrier lifetime but reduce the electron

mobility due to the electron filling induced potential variation around QDs. The

photocurrent is also enhanced in the sample with QDs in the depletion region and

reduced in the sample with QDs in the n-region.

In Paper II, I further explore the photocurrent (PC) contribution in different

wavelength regions. The above-GaAs-bandgap absorption is dominant for the

enhanced PC of QD solar cell with QDs in the depletion region and the reduced

PC of QD solar cell with QDs in the n-region. The enhanced PC is understood

by the enhanced absorption due to the hole wavefunction reflection; while the

reduced PC is caused by the reduced carrier mobility due to the up-bent potential

variation around QDs. The sub-GaAs-bandgap PC spectra show the wetting

layer and QD contributions clearly. The contributions are considerable for QDs

in the depletion region since photocarriers can tunnel out via the built-in electric

field; the contributions for QDs in the n-region, away from the built-in field, are

much lower, since only the thermal activation works for photocarrier escape from

QDs. It demonstrates that although there are many QD layers and good photon

absorption as expected, the photocarrier extraction is more important for PC

53

54 6 Summary of the included papers

production. The cascade photon absorption via intermediate bands formed by

closely spaced QD layers, even if it exists, will have a problem on photocarrier

extraction through the depletion region.

In Paper III (in manuscript), I study the bias- and temperature-dependent

photocurrent spectra of the above QD samples. From the bias and temperature

dependence of each photocurrent peak that corresponds to QD state or wetting-

layer state absorption, I find different photocarrier escape mechanisms in the two

samples. The interlayer tunneling is responsible for the similar trend of bias

dependence in the sample with closely spaced QDs in the i-region; while the

minority hole thermal escape is responsible for the high activation energy in the

sample with QDs in the n-region, due to the up-bent potential variations around

QD matrix.

In Paper IV (submitted), I study the time correlation between two colloidal

QDs. CdSe/ZnS single-shell QDs have trigger-like blinking emission that can be

real-time recorded by the camera CCD in frame of 50 ms. If the two QD distance

is as small as 0.7∼1.1 µm, their blinking emission shows a clear correlation peak

at the zero delay, suggesting bunched emission. For CdSe/CdxZn1−xS/ZnS multi-

shell QDs, the light intensity is high and steady state-like, with no correlation.

It indicates that there are few blinking events and the light emission from each

QD is independent. We think the mutually stimulated light emission between

two closely spaced QDs is possible the reason for this bunched correlation. The

blinking of one QD affects its stimulation on the light emission from the other

QD, as a result, the two QDs show bunched blinking.

References

[1] BP statistical review of world energy 2011, www.bp.com/statisticalreview.

[2] http://en.wikipedia.org/wiki/File:Solar Spectrum.png.

[3] W. Shockley, and H. J. Queisser, J. Appl. Phys., 32, 510, 1961.

[4] M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, Prog.

Photovolt: Res. Appl., 19, 565, 2011.

[5] J.-F. He, Z.-C. Niu, X.-Y. Chang, H.-Q. Ni, Y. Zhu, M.-F. Li, and X.-J.

Shang, Chin. Phys. B, 20, 018102, 2011.

[6] S. R. Huang, X. Lu, A. Barnett, and R. L. Opila, ”GaP films grown on

Si by liquid phase epitaxy”, 34th IEEE Photovoltaic Specialists Conference

(PVSC), 241-243, 2009.

[7] K.-S. Lee, Y.-S. Kim, Y.-K. Hong, and Y.-H. Jeong, IEEE Electron Device

Lett., 28, 672, 2007.

[8] Y. Zhang, S.-C. Shen, H. J. Kim, S. Choi, J.-H. Ryou, R. D. Dupuis, and B.

Narayan, Appl. Phys. Lett., 94, 221109, 2009.

[9] http://www2.electronicproducts.com/Using GaN power amplifiers-article-

farr nitronex nov2007-html.aspx

[10] Yu. B. Bolkhovityanov, and O. P. Pchelyakov, The Open Nanoscience Jour-

nal, 3, 20, 2009.

[11] M. Feiginov, C. Sydlo, O. Cojocari, and P. Meissner, Appl. Phys. Lett., 99,

233506, 2011.

[12] M. DeJarld, J. C. Shin, W. Chern, D. Chanda, K. Balasundaram, J. A.

Rogers, and X. Li, Nano Lett., 11(12), 5259, 2011.

55

56 REFERENCES

[13] http://www.compoundsemiconductor.net/csc/news-

details.php?cat=news&id=19734300.

[14] M. Wiemer, V. Sabnis, H. Yuen, Proc. of SPIE, 8108, 810804, 2011.

[15] M. A. Green, G. Conibeer, D. Konig, S. Shrestha, S. Huang, P. Aliberti,

L. Treiber, R. Patterson, B. P. Veettil, A. Hsieh, Y. Feng, A. Luque, A.

Marti, P. G. Unares, E. Canovas, E. Antolln, D. F. Marron, C. Tablero, E.

Hernandez, J-F. Guillemoles, L. Huang, A. L. Bris, T. Schmidt, R. Cladl,

and M. Tayebjee, ”Hot carrier solar cells: Challenges and recent progress”,

35th IEEE Photovoltaic Specialists Conference (PVSC), 57-60, 2010.

[16] K. Ikeda, H. Sekiguchi, F. Minami, J. Yoshino, Y. Mitsumori, H. Amanai, S.

Nagao, and S. Sakaki, J. Lumin., 108, 237, 2004.

[17] A. J. Nozik, Physica E, 14, 115-120, 2002.

[18] A. Luque and A. Marti, Prog. Photovolt: Res. Appl., 9, 73, 2001.

[19] S. M. Hubbard, C. D. Cress, C. G. Bailey, R. P. Raffaelle, S. G. Bailey, and

D. M. Wilt, Appl. Phys. Lett., 92, 123512, 2008.

[20] X. J. Shang, J. F. He, H. L. Wang, M. F. Li, Y. Zhu, Z. C. Niu, and Y. Fu,

Appl. Phys. A, 103, 335, 2011.

[21] X.-J. Shang, J.-F. He, M.-F. Li, F. Zhan, H.-Q. Ni, Z.-C. Niu, H. Pettersson,

and Y. Fu, Appl. Phys. Lett. 99, 113514, 2011.

[22] D. Guimard, R. Morihara, D. Bordel, K. Tanabe, Appl. Phys. Lett., 96,

203507, 2010.

[23] S. Krishna, S. D. Gunapala, S. V. Bandara, C. Hill, and D. Z. Ting, Proc. of

the IEEE, 95, 1838, 2007.

[24] S. D. Gunapala, S. V. Bandara, C. J. Hill, D. Z. Ting, J. K. Liu, S. B. Rafol,

E. R. Blazejewski, J. M. Mumolo, S. A. Keo, S. Krishna, Y. C. Chang, and

C. A. Shott, Proc. of SPIE, 6206, 62060J, 2006.

[25] http://www.veeco.com/markets/materials-science/effusion-cells,-valved-

crackers,-and-gas-injectors.aspx.

[26] http://en.wikipedia.org/wiki/Hot-filament ionization gauge.

REFERENCES 57

[27] http://www.pfeiffer-vacuum.com/know-how/mass-spectrometers-and-

residual-gas-analysis/introduction-operating-principle/quadrupole-mass-

spectrometers-qms/technology.action?chapter=tec4.1.2.

[28] J. B. Rodriguez, P. Christol, L. Cerutti, F. Chevrier, A. Joullie, J. Crystal

Growth, 274, 6, 2005.

[29] C. Manza, Q. Yanga, K. Kohlera, M. Maiera, L. Kirstea, J. Wagnera, W.

Sendb, D. Gerthsen, J. Crystal Growth, 280, 75, 2005.

[30] C.-C. Chen, H.-W. Chung, C.-H. Chen, H.-P. Lu, C.-M. Lan, S.-F. Chen, L.

Luo, C.-S. Hung, and E. W.-G. Diau, J. Phys. Chem. C 112, 19151, 2008.

[31] http://www.laballiance.com.my/brochure/spectroscopy/FTIR/VERTEX80v Flyer EN.pdf

[32] http://www.brukeroptics.com/downloads.html, Guide for Infrared Spec-

troscopy.

[33] M. Sugawara (volume editor), R. K. Willardson and E. R. Weber, Semicon-

ductors and Semimetals Volume 60, Self-Assembled InGaAs/GaAs Quantum

Dots, Academic Press, New York, 1999.

[34] D. J. Eaglesham, and M. Cerullo, Phys. Rev. Lett., 64, 1943, 1990.

[35] J. M. Moison, C. Guille, F. Houzay, F. Barthe, and M. van Rompay, Phys.

Rev. B, 40, 6149, 1989.

[36] C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, Phys. Rev.

Lett., 86, 1502, 2001.

[37] J.-F. He, H.-L. Wang, X.-J. Shang, M.-F. Li, Y. Zhu, L.-J. Wang, Y. Yu,

H.-Q. Ni, Y.-Q. Xu, and Z.-C. Niu, J. Phys. D: Appl. Phys. 44, 335102, 2011.

[38] Z. Mi, P. Bhattacharya, and J. Yang, Appl. Phys. Lett., 89, 153109, 2006.

[39] J. S. Wang, S. H. Yu, Y. R. Lin, H. H. Lin, C. S. Yang, T. T. Chen, Y.

F. Chen, G. W. Shu, J. L. Shen, R. S. Hsiao, J. F. Chen, and J. Y. Chi,

Nanotechnology, 18, 015401, 2007.

[40] G. S. Solomon, J. A. Trezza, A. F. Marshall, and J. S. Harris, Phys. Rev.

Lett., 76, 952, 1996.

[41] A. Hospodkova, V. Krapek, K. Kuldova, J. Humlicek, E. Hulicius, J. Oswald,

J. Pangrac, and J. Zeman, Physica E, 36, 106, 2007.

58 REFERENCES

[42] Q. D. Zhuang, S. F. Yoon, H. X. Li, J.M. Li, Y. P. Zeng, M. Y. Kong, and

L. Y. Lin, Physica E, 11, 384, 2001.

[43] C. H. Chan, H. S. Chen, C. W. Kao, H. P. Hsu, and Y. S. Huang, Appl.

Phys. Lett., 89, 022114, 2006.

[44] S. Chakrabarti, N. Halder, S. Sengupta, S. Ghosh, T. D. Mishima, and C. R.

Stanley, Nanotechnology, 19, 505704, 2008.

[45] A. Marti, E. Antolin, C.R. Stanley, C.D. Farmer, N. Lopez, P. Diaz, E.

Canovas, P.G. Linares, A. Luque, Phys. Rev. Lett., 97, 247701, 2006.

[46] P. O. Anikeeva, J. E. Halpert, M. G. Bawendi, and V. Bulovic, Nano Lett.,

9, 2532, 2009.

[47] P. Michler, Single Quantum Dots Fundamentals, Applications, and New Con-

cepts, Springer, 2003.

[48] A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon,

Nature Photonics, 4, 302, 2010.

[49] S. M. Sze, Semiconductor Devices Physics and Technology, John Willey and

Sons, 1985.

[50] M. A. Green, Solar cells: Operating principles, Technology, and System Ap-

plications, Prentice-Hall, 1982.

[51] A. Marti, N. Lopez, E. Antolin, E. Canovas, A. Luque, C. R. Stanley, C. D.

Farmer, P. Diaz, Appl. Phys. Lett., 90, 233510, 2007.

[52] Y. Fu, M. Willander, J. Appl. Phys. 71, 3877, 1992.

[53] Y. Fu, M. Willander, J. Appl. Phys. 76, 4225, 1994.

[54] D. Zhou, P. E. Vullum, G. Sharma, S. F. Thomassen, R. Holmestad, T. W.

Reenaas, and B. O. Fimland, Appl. Phys. Lett., 96, 083108, 2010.

[55] T. Sugaya, Y. Kamikawa, S. Furue, T. Amano, M. Mori, and S. Niki, Solar

Energy Material & Solar cells, 95, 163, 2011.

[56] K. A. Sablon, J. W. Little, V. Mitin, A. Sergeev, N. Vagidov, and K. Rein-

hardt, Nano Lett., 11, 2311, 2011.

REFERENCES 59

[57] R. J. Ellingson, M. C. Beard, J. C. Johnson, P. Yu, O. I. Micic, A. J. Nozik,

A. Shabaev, and A. L. Efros, Nano Lett., 5, 865, 2005.

[58] Y. Fu, Superlattices Microstruct., 30, 69, 2001.

[59] E. S. Shatalina, S. A. Blokhin, A. M. Nadtochy, A. S. Payusov, A. V. Savelyev,

M. V. Maximov, A. E. Zhukov, N. N. Ledentsov, A. R. Kovsh, S. S. Mikhrin,

and V. M. Ustinov, Semiconductors, 44, 1308, 2010.

[60] W.-H. Chang, T. M. Hsu, C. C. Huang, S. L. Hsu, C. Y. Lai, N. T. Yeh, T.

E. Nee, and J.-I. Chyi, Phys. Rev. B, 62, 6959, 2000.

[61] J. L. Hartke, J. Appl. Phys., 39, 4871, 1968.

[62] S. Rodt, R. Seguin, A. Schliwa, F. Guffarth, K. Ptschke, U.W. Pohl, D.

Bimberg, J. Lumin., 122-123, 735, 2007.

[63] R. Heitz, F. Guffarth, K. Ptschke, A. Schliwa, and D. Bimberg, Phys. Rev.

B, 71, 045325, 2005.

[64] M. Gong, G. Chen, L. He, C.-F. Li, J.-S. Tang, F.-W. Sun, Z.-C. Niu, S-S

Huang, Y.-H. Xiong, H.-Q. Ni, and G.-C. Guo, epl, 90, 37004, 2010.

[65] V. Turck, F. Heinrichsdorff, M. Veit, R. Heitz, M. Grundmann, A. Krost,

and D. Bimberg, Appl. Surface Science, 123-124, 352, 1998.

[66] J.-H. Ser, Y.-H. Lee, J.-W. Kim, and J.-E. Oh, Jpn. J. Appl. Phys., 39, L518,

2000.

[67] G. Vincent, A. Chantre, and D. Bois, J. Appl. Phys. 50, 5484, 1979.

[68] Y. Fu, O. Engstrm, and Y. Luo, J. Appl. Phys. 96, 6477, 2004.

[69] I. L. Medintz, H. T. Uyeda, E. R. Goldman, and H. Mattoussi, Nat. Mater.,

4, 435. 2005.

[70] Q. Sun, Y. A. Wang, L. S. Li, D. Wang, T. Zhu, J. Xu, C. Yang, and Y. Li,

Nature Photonics, 1, 717, 2007.

[71] Z. Ning, H. Tian, H. Qin, Q. Zhang, H. Agren, L. Sun, and Y. Fu, J. Phys.

Chem. C, 110, 389, 2010.

[72] M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, J.

Chem. Phys., 112, 3117, 2000.

60 REFERENCES

[73] K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empedocles, W.

K. Woo, and M. G. Bawendi, Phys. Rev. A, 63, 205316, 2001.

[74] Z. Yuan, B. E. Kardynal, R. M. Stevenson, A. J. Shields, C. J. Lobo, K.

Cooper, N. S. Beattie, D. A. Ritchie, and M. Pepper, Science, 295, 102, 2002.

[75] V. Zwiller, H. Blom, P. Jonsson, N. Panev, S. Jeppesen, T. Tsegaye, E.

Goobar, M.-E. Pistol, L. Samuelson, G. Bjok, Appl. Phys. Lett., 78, 2476,

2001.

[76] A. J. Shields, R. M. Stevenson, R. M. Thompson, M. B. Ward, Z. Yuan, B.

E. Kardynal, P. See, I. Farrer, C. Lobo, K. Cooper, and D. A. Ritchie, phys.

stat. sol. (b), 238, 353, 2003.

[77] A. Dousse, J. Suffczynski, A. Beveratos, O. Krebs, A. Lemaıtre, I. Sagnes, J.

Bloch, P. Voisin, and P. Senellart, Nature, 466, 217, 2010.

[78] P. Aivaliotis, E. A. Zibik, L. R. Wilson, J. W. Cockburn, M. Hopkinson, and

N. Q. Vinh, Appl. Phys. Lett., 92, 023501, 2008.

[79] http://www.rp-photonics.com/autocorrelators.html

[80] H. Paul, Rev. Mod. Phys., 54, 1061, 1982.

Documents

Study of quantum dots on solar energy applicationskth.diva-portal.org/smash/get/diva2:525075/FULLTEXT01.pdf · Chapter 1 Introduction 1.1 Green energy: semiconductor solar cells Energy