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Characterisation of Photovoltaic Solar Cells and
identification of Hot Carrier Phenomenon
(Caractérisation de Cellules Photovoltaïques et
Identification de Phénomènes de Porteurs Chauds)
Research Project Report
2nd March – 28th August 2009
By ZULFIQAR ALI UMRANI
At IRDEP (ENSCP-EDF-CNRS)
Under the direction of
J. F. Guillemoles and A. Le Bris
Submitted to INSTN-CEA for the requirement of the degree of
Master M2: Matériaux pour les Structures de l’Energie (MSE)
Dedicated to
Baba Rasool Bux,
Aman Zarina &
Aman Sharifa
II
ACKNOWLEDGEMENTS
Firstly, I would like to thank Arthur Le Bris for all his help during my research project. He has
helped me in many things. From helping me with the experiments, teaching Python and Matlab,
letting me work on his simulations to buying the best sandwiches in Paris. This report would
not have been possible without Arthur.
Secondly I wish to thank Mr Jean François Guillemoles, my Director of research and mentor.
Mentor, because it was he who guided me to pursue this master way back in the winter of 2007.
And than welcomed me in his research group at EDF. He has always been understanding and
cheerful despite all the excuses he has had to hear from me. It is because of him that I adore this
subject and hope to do further research in it.
Also, I thank the group PV-THR at IRDEP for their valuable discussions and carrot cakes with
champagne. This includes Par Olsson, Christophe, Mael, François, Julien and others. Brave
people working under 50000 suns’ conditions.
A thanks goes out to the entire team of IRDEP for it is really like a big family. It is wonderful to
be among such friendly and motivated researchers. Always helpful and smiling are Daniel
Lincot, Zachary, Jean, Frederique, Gregory, Hanane, Jacqueline, Lydie, Pascal and all.
At the end I acknowledge the help of Phillipe Christol and his team at IES, Montpellier for
providing us the samples, without which I could not characterise anything. Also I thank
Svetlana Ivanovna and Patrick Aschehoug at ENSCP for letting me use their laboratory and
helping me with the equipment. Furthermore, I really appreciated the useful discussions with
Dr. Yasuhiko Takeda Toyota at Toyota Central R&D Labs, Japan.
III
TABLE OF CONTENTS
TITLE……………………………………………………………………….…………I
DEDICATION…………………………………………………………………………II
ACKNOWLEDGEMENT…………………………………………………………....III
ABSTRACT……………………………………………………………….…………..IV
TABLE OF CONTENT……………………………………………………………….V
CHAPTER 1 INTRODUCTION………………………………………………..…...01
1.1 MOTIVATION……………………………………………………..……..01
1.2 OBJECTIVE………………………………………………...………..…...02
1.3 OUTLINE…………………………………………………..…..…….……03
CHAPTER 2 THEORY………………………………………………………...…….04
2.1 INTRODUCTION…………………………………………………..…….04
2.2 CONVENTIONAL SOLAR CELL………………………………..……..04
2.2.1 Dark Conditions…………………………………………..……..05
2.2.2 Effect of Light………………………………………………...….06
2.3 OPTICAL PROCESS………………………………………...…...07
2.4 DETAILED BALANCE LIMIT………………………………………….08
2.4.1 Shockley and Queisser Limit……………………………...……08
2.5 EFFICIENCY LIMITATIONS……………………………….……...…..09
2.5.1 Thermalisation…………………………………………………..10
2.5.2 Hot-Carrier Efficiency…………………………………………..11
2.6 HOT-CARRIER SOLAR CELLS………………………………………..12
2.7 QUANTUM STRUCTURES………………………………………..……13
Chapter 3 METHODOLOGY………………………………………………………..14
3.1 INTRODUCTION………………………………………………...………14
IV
3.2 PHOTOLUMINESCENCE BASICS…………………………………....14
3.2.1 Hot Carrier Temperature…………………………………..…..16
3.3 EXPERIMENT…………………………………………………………....16
3.4 SOLAR CELL SAMPLES…………………………………………….....16
3.4.1 Quantum Well (QW) Solar Cells……………………………....17
3.4.2 GaAs pn Junction Solar Cell……………………………..…….18
3.5 EXPERIMENT SET-UP……………………………………………..…..18
3.6 EXPERIMENT CONDITIONS……………………………………..…...19
3.6.1 Laser Power………………………………………………..……20
3.6.2 Absorbed Power……………………………………………..….21
3.7 CONCLUSION……………………………………………………..…….21
CHAPTER 4 RESULTS AND DISCUSSION………………………………..……..22
4.1 INTRODUCTION…………………………………………………..…….22
4.2 INTENSITY VS ENERGY PL SPECTRA………………………..…….22
4.3 TEMPERATURE DEPENDENCE………………………………………26
4.4 HOT CARRIER TEMPERATURE………………………………..……29
4.4.1 ABSORPTION CURVE…………………………………..……29
4.5 CARRIER COOLING BY LO PHONON…………………………..…..32
4.6 MEANING OF Q FACTOR………………………………………..……34
4.7 DISCUSSION………………………………………………………..……35
4.7.1 Hot carrier temperature…………………………………..……35
4.7.2 Carrier cooling……………………………………………..……36
4.7.3 The Q Factor………………………………………………..…...37
CHAPTER 5 CONCLUSION…………………………………………………..……39
5.1 FUTURE WORK ……………………………………………………..….40
V
CHAPTER 1
INTRODUCTION
1.1 MOTIVATION
Fossil Fuels cannot last forever. Furthermore, they have a detrimental effect on our
environment. For the progressive development of our society, we must seek cleaner
renewable sources of energy. Considering the abundance and equitable distribution of
solar energy, it can play a pivotal role in the future Energy Mix. Photovoltaic (PV) solar
cells provide a convenient method of converting solar energy into clean electrical energy.
However, there are two factors that hamper wider implementation of this clean form of
energy. One is the high cost associated with a conventional solar cell module. And other
is the efficiencies attained by such devices. The costs can be significantly decreased if we
are able to achieve higher efficiencies.
The 1st generation of PV devices consisted of Si wafer modules. Even at present they
dominate the market at around 90% of the market-share. These modules use a lot of
costly high purity Si material because of low absorption coefficient of Si. The efficiencies
are quite low at 10-15%. The 2nd generation tackles the problem of high costs due to
material requirements. Instead of wafers, the PV modules are made from thin films. The
more popular materials used are: CIGS and amorphous Si etc. These device modules have
efficiencies of around 5-10%.
This brings us to the 3rd generation PV solar cells. These devices seek to radically increase the
power efficiency by overcoming the Shockley-Queisser [Shockley(1961)] efficiency
1
limitation at 33%. This can approach the efficiency limitation defined by the upper
thermodynamic limit at 86% [Nozik(1982)]. Some of the potential concepts are multi-
junction cells, hot carrier cells, up-down converters, intermediate band cells and
thermophotovoltaic cells. Except for multi-junction cells, all other concepts are in the
theoretical research stage. [Green(2002)]
Among the above concepts, hot carrier solar cells provide a very attractive solution for higher
efficiencies. They promise the same efficiency (85%) as an infinite tandem cell without the
associated device complexity. Initially professed by Ross & Nozik in 1981,[Nozik(1982)]
research continues till date for the realisation of these devices. This in turn can permit
successful widespread utilisation of solar energy, beneficial to all and sundry.
1.1 OBJECTIVE
IRDEP (Institut de la Recherche et Développement de l’Energie Photovoltaïque) is a joint
project laboratory of EDF (Electricité de France), ENSCP (Ecole Nationale Supérieure de
Chimie de Paris) and CNRS (Centre national de la recherche scientifique) working on 2nd
generation Thin film devices and 3rd generation novel concepts. The PV-THR
(PhotoVoltaïque Très Haute Rendements) group at IRDEP is concerned with 3rd
generation photovoltaic devices Within PV-THR group, I am working on the hot carrier
solar cell research.
Concerning the objectives of this internship, Firstly, it is to characterize the newly
fabricated PV cells including Quantum Well cell by Photoluminescence (PL) to get useful
physical parameters concerning their energy conversion behaviour. These samples are
fabricated in laboratory thus their optical properties are as yet not determined. It is my
task to carry out PL experiments to observe their behaviour under luminescence. Since
these samples do not have electrical contacts therefore we are limited to optical
characterisation.
Also we are interested in the hot carrier effects present in these devices; we would like to
observe the variation of hot carrier population in accordance with incident light. The
temperatures they achieve and the physical parameters predicting their efficiency.
2
Furthermore, the essential goal of this internship is the comprehension of the hot carrier
device concept and to get acquainted with the physics governing the functioning of these
devices. For the subject must also be treated in a broader aspect to observe the new
directions open to future research.
1.2 OUTLINE
The report is structured as follows:
Chapter 1 gives the introduction defining the context of the internship, including the
motivation for the research in the field of PV and in particular Hot Carrier Solar Cells.
The objectives of this internship are stated.
Chapter 2 presents the basic theory concerning the subject of PV and Hot carriers. It
explains the efficiency limitations on conventional solar cells and how hot carrier concept
can go beyond those limitations. Also quantum structures are briefly described as they
can play pivotal role in successful device implementation.
Chapter 3 provides background to the PL experiments and how PL can be used to
characterise solar cells and what useful information can be extracted. The samples used
for the experiments are described. The experimental set-up and conditions are given.
Chapter 4 treats the obtained results and their discussion. First, it presents the directly
observed data as observed from PL. Then the results derived from the observed data. Hot
carrier features are extracted. Their temperature, cooling mechanism and thermalisation
rates are approximated.
Chapter 5 is the conclusion. A review of stated objectives and what information could be
obtained by sample characterisation is given. Future direction of research is also
presented.
3
CHAPTER 2
THEORY
2.1 INTRODUCTION
This internship is concerned with the physics of solar cells. First of all, brief overview of
Photovoltaic solar cells is given, including semiconductor structures and the behaviour of
the system under illumination. Then the fundamental efficiency limitations of single
junction conventional PV cell are described. It is explained how the utilisation of Hot-
Carrier effect can result in significant efficiency gain. Afterward, the Hot-Carrier Solar
Cell (HCSC) module is described including the limitations on its practical application.
Finally, Quantum Structured solar cells, which can play a major role in the physical
implementation of HCSCs, are discussed.
2.2 CONVENTIONAL SOLAR CELL
The photovoltaic solar cell permits the direct conversion of incident solar radiation into
electricity. It generates electron-hole pairs by the process "excitation of charge carriers by
light". These Electrons and holes are collected after the carriers thermalise with the
lattice.
4
Fig 2.1: The solar cell behaviour when illuminated showing the excitations
according to Photon Energy. [Böer(1996)]
2.2.1 Dark Conditions
Semiconductors are materials having energy band gap Eg between its completely filled
valence band and empty conduction band. For solar cells, the semiconductor materials are
chosen taking into consideration their bandgap, which must be matched to incident solar
radiation. Basically the material conducts as a pn-junction diode in the dark and generates
a photovoltage under light. [Smestad(2002)][Nelson(2006)]
For the equilibrium conditions, the density of electrons is given by electron distribution
function and density of states in a semiconductor:
Equation 2.1
Where dne is density of electrons with energy εe; being distributed over energy interval
dεe. De(εe) is the density of states and fe(εe) is the electron distribution function. The
electron distribution function satisfying the condition of Pauli’s exclusion principle, only
5
eeeeeee dfDdn εεεε )()()( =
energy dependent leading to the minimum of free energy is the Fermi distribution, given
by,
( )1
1
)(+
=−
KT
ee fe
e
f εε
ε Equation 2.2
)(KT
ce
fc
eNnε
ε −= Equation 2.3
2
3
2)
2(2
�
KTmN e
c
π= ; ne<<Nc Equation 2.4
*
*
ln4
3)(
2
1
e
hcvf m
mKT+−= εεε Equation 2.5
Here Ef is the Fermi energy being the characteristic occupied state energy. mh* and me*
are hole and electron effective masses respectively. Nc is effective density of states in
conduction band; ne is the density of electrons; εv, εc and εf are electron valence band
energy, conduction band energy and Fermi level energy respectively. [Wurfel(2005)]
2.2.2 Effect of Light
Consider a flux of photons incident on a solar cell having energy above the bandgap
E>Eg. The absorption of these photons excites the electrons from the conduction band
into the valence band. In the initial state, the energy distribution of the electrons is not
defined by the fermi-dirac distribution and reflects the broad energy spectrum of the
absorbed photons and the band structure. However, the electrons rapidly (10E-14 secs)
thermalise amongst themselves, and then with the lattice (10E-12 secs); until the dark
condition energy distribution is achieved (10E-9 secs in direct bandgap semiconductors
and 10E-6 – 10E-3 secs in indirect bandgap semiconductors)
6
Under the influence of light and consequent generation of electron-hole pairs, the electron
and hole densities are higher than at dark conditions. These higher carrier densities result
in quasi-Fermi distribution in which the quasi-Fermi level for the electrons is closer the
conduction band and the quasi-fermi level for hole is closer to the valence. The shift is
from the central position of the Fermi level in between the conduction and the valence
band and is called Fermi level splitting. the density of the electron in the conduction band
is defined as
)(KT
ce
FCC
eNnεε −−
= Equation 2.6
εFC is the Fermi energy for occupation of states in conduction band.
Fig. 2.2 : The semiconductor under illumination has band occupations defined by
the different Fermi levels. [Wurfel(2005)]
2.3 OPTICAL PROCESS
Considering a semiconductor illuminated by steady state light with energy equivalent to
the difference of energy between CB and VB; in which the system is at quasi thermal
equilibrium. A photon can be absorbed and promote an electron from VB to CB or and
electron can relax to VB from CB and generate an electron. The net absorption rate is
given as:
).(2 2
cvcvabs fffHr −=�π
Equation 2.7
7
Hcv is the optical matrix element, f is the probability if there is a photon in the mode and
fv,c the Fermi-Dirac Distribution for valence and conduction bands.
The net spontaneous emission rate is given as
)1.(2 2
vccvsp ffHr −==π
Equation 2.8
in steady state these rates balance each other and thus
1
1)(
−= ∆−
KT
µE
e
f Equation 2.9
[Nelson(2006)]
where ∆µ=Efc-Efv ; it is the chemical potential of radiation. This is assuming an optical
process which causes change in energy and momentum and that all excess energy goes
into the excited electron. This is because of the much smaller effective mass of the
electron.
2.4 DETAILED BALANCE LIMIT
The detailed balance limit establishes the basic physical limit on the efficiency of solar
cells. The cell not only absorbs solar radiation but also exchanges thermal radiation with
environment. The photon emission rate and photon absorption rate must be equal in order
that the steady state concentration of electrons is constant at open circuit voltage.
[Nelson(2006)]
2.4.1 Shockley and Queisser Limit
8
Shockley and Queisser[Shockley(1961)] calculated efficiency limits for conventional
solar cell by combining the black body radiation property with detailed balance. The
method only considers the system as an external two body system . This approach gives
the following current-voltage relation
)1)(,,(),,(..
−∞−∞= KT
qV
CGCSGso eTENqAfTENqAfI
Equation 2.10
Where q is the electron charge, A is the cell area, fs and fc are geometrical factors (related
to solid angles of absorption and emission of radiation), Ts is the sun’s temperature, Tc is
the cell operating temperature and EG is the material bandgap. N is the ideality factor for a
system approximated as a black body In Shockley and Queisser’s analysis, for EG = 1.3
eV, Ts = 6000K and Tc =300K, the peak efficiency is around 31%.
The detailed balance approach is based on the following assumptions:
- All photons of energy greater than Eg, are absorbed to create one electron-hole
pair. All photons with energy less than Eg are not absorbed.
- The electrons and holes populations relax to form separate, distributions in quasi
thermal equilibrium with the lattice at temperature Tc and with quasi Fermi levels
separated by ∆µ.
- Each electron is extracted with chemical potential energy ∆µ such that qV=∆µ.
Meaning that carriers have infinite mobility.
- The only loss process is spontaneous emission which is required by detailed
balance. [Nelson(2006)]
2.5 EFFICIENCY LIMITATIONS
9
Thinking beyond the single p-n junction device, and by using the black-body model for
sun and the cell, the simplest thermodynamic upper limit on solar energy conversion is
the Carnot efficiency [Green(2003)]. The sun’s temperature is assumed to be at 6000K
and the ambient at 300K, the maximum efficiency value is 95%. If we consider the
Landsberg’s limit, energy and entropy re-emitted by the absorber are added and the
corresponding efficiency becomes 93.3%. Further, taking into the account of the
unavoidable entropy production during the absorption and emission of light by the black-
body , the maximum efficiency is 85.4% at an effective converter temperature of 2544K.
These thermodynamic limits are much higher than the current single p-n junction cell
conversion efficiency. Therefore there is great room for improvements in efficiency if we
think beyond the conventional p-n model. [Jiang(2005)]
2.5.1 Thermalisation
One of the major loss processes for standard cells are due to the rapid thermalisation of
the photoexcited carriers with the lattice. If this thermalisation can be avoided, much
higher efficiency would be possible. Theoretically, these carriers could still thermalize by
collisions with one another to stabilise in a distribution described by a temperature much
higher than the lattice temperature. [Nozik(1982)]
Consider a photovoltaic system immediately after being excited by a pulsed laser. The
photogenerated carrier population is superimposed upon equilibrium concentration. For
mono- chromatic laser light, these carriers are excited from and to specific regions of
energy-momentum space, giving sharply peaked ‘coherent’ distributions. The peak in the
valence band will generally lie closer to the band edge than that in the conduction band,
due to the generally higher valence band effective mass. This means that more of the
surplus photon energy is absorbed in the conduction band than in the valence band.
10
Fig. 2.3: Fig. 6.2: Time evolution of electron and hole distributions in a
semiconductor subject to a short, high intensity, monochromatic pulse of light from a
laser: (1) Thermal equilibrium before pulse (2) coherent stage straight after pulse (3)
carrier scattering (4) thermalisation of hot carriers (5) carrier cooling; (6) lattice
thermalised carriers (7) recombination of carriers (8) return to thermal equilibrium.
[Green(2003)]
The laser excitation terminates and the carriers begin their long process back towards
equilibrium. Initially, carrier-carrier collisions come into effect and act to more uniformly
distribute the excess energy amongst the carriers. The carriers evolve towards a Fermi-
Dirac distribution in energy, as in thermal equilibrium, but one characterised by a much
higher temperature than that at thermal equilibrium. During this carrier collision stage,
there is no energy lost; energy is more equitably shared between the photoexcited and
original carriers. The effective temperature of the carriers will depend upon the total
energy shared amongst them. Electrons and holes could initially reach distributions
characterised by different temperatures, depending upon the amount of electron-hole
scattering taking place [Othonos(1998)] [Green(2003)]
2.5.2 Hot-Carrier Efficiency
Ross and Nozik published the first analysis on hot carrier cell conversion efficiency
limits[Nozik(1982)]. With the hot carrier cell approach, the theoretical limit can reach the
11
same limit as the infinite tandem approach with an efficiency of 86.8% for direct sunlight
and 68.2% for global sunlight.
2.6 HOT-CARRIER SOLAR CELLS
In Ross and Nozik’s analysis of the hot carrier solar cell, carriers are extracted at a
specific energy in the conduction band and returned to the valence band at another
specific energy [Nozik(1982)]. Carriers in the conduction band and the valence band are
assumed to have one equilibrium temperature TH. The electron and hole distributions are
described by the quasi-Fermi energies µc and µv with the difference given by ∆µH. With
the particle and energy balance equations, the final power output can be calculated as a
function of bandgap, TH, and ∆µH.[Wurfel(1996)]
Fig. 2.4 : The schematic of Hot carrier solar cell showing the absorber and the
energy selective contacts. [Stanford(2008)]
Hot carrier cells consist of an absorber designed to reduce the carrier cooling and an
energy selective contact to collect carriers through a narrow energy range. The successful
utilisation of the excess kinetic energy in hot carrier cells requires to extract hot carriers
by selective contacts and to reduce their cooling rate in the absorber. [Stanford(2008)]
12
2.7 QUANTUM STRUCTURES
The nanostructures can help in two fundamental design issues concerning Hot carrier
solar cells. first is the collection of hot carriers before they cool to the lattice temperature
and second is the energy selective contacts that allow only narrow range of electrons to
reach the contacts, thus by stopping cooling by contacts the hot electron population can
remain hot. [Connibeer(2006)]
The relaxation dynamics of photogenerated carriers can be influenced by quantization
effects in the semiconductor (i.e., in semiconductor quantum wells, quantum wires, QDs,
superlattices, and nanostructures). The change comes into effect when the carriers in the
semiconductor are conveyed by potential barriers to regions of space that are smaller than
or comparable to their deBroglie wavelength or to the Bohr radius of excitons in the
semiconductor bulk. Thus the hot carrier cooling rates may be reduced. [Nozik(2002)]
[Green(2002)]
Possible reasons for these reduced cooling rates in QS are: narrower conservation rules in
the carrier-phonon interaction that couples carriers to fewer vibrational modes; carrier
localization that prevents carrier cooling by out diffusion from the hot phonon region, a
mechanism very effective on short time scales. Both lead to efficient reheating of carriers
by emitted optical phonons (equivalent to renormalization of the free carrier calorific
capacity). [Guillemoles(2005)]
One possible implementation for energy selective contacts is to use resonant tunnelling
devices, such as resonant tunnelling through defects or quantum dots in an insulator
matrix. Quantum dots provide the opportunity to control the energy of carrier states by
adjusting the confinement in three dimensions. They would permit hot carriers of
particular energy to be collected at contacts thus maintaining the hot carrier population at
higher-than-lattice temperature.[Connibeer(2008)]
13
Chapter 3
METHODOLOGY
3.1 INTRODUCTION
Series of Photoluminescence (PL) experiments were carried out on different solar cell
samples developed at Institut d'Electronique du Sud (IES), Université Montpellier 2,
including Quantum Well (QW) solar cells. These experiments were carried out at Ecole
Nationale Superieure de Chimie Paris (ENSCP) laboratory.
In this chapter, we will give an introduction to PL characterisation method. Then we shall
describe the significance of PL method for extracting Hot-carrier effects. Afterwards the
experimental conditions are presented including a description of the samples used. This is
followed by the method employed to determine the incident laser power.
3.2 PHOTOLUMINESCENCE BASICS
PL serves as an important tool for material characterisation. From the PL response of the
samples; basic Intensity – Energy/Wavelength data, we can calculate further sample
characteristics. Such as, variation in the spectral response with respect to the varying
temperature and Laser intensity; Hot-carrier temperature, absorption and Hot-carrier
thermalisation.
14
Basically, PL is the spontaneous emission of light when a sample is optically excited.
When above bandgap energy light is incident on the sample, incident photons are
absorbed and electronic higher energy transitions occur. Then these excited electrons
relax and return to their ground states.
In the case of radiative relaxation, the emitted light is called PL. These radiativily emitted
photons are collected by a spectrometer to give information about the sample. Parameters
(temperature & incident intensity) are varied to observe the change in the collected PL
intensity and hence extract useful properties. [Gfroerer(2000)]
Extraction of these physical properties requires the comprehension of the observed
phenomenon. Here we have for example the PL spectra of V812 sample at 30K.
Fig. 3.1: PL spectra of GaInSb quantum well sample at 1321 W/cm2 intensity. The
lattice temperature at 30K.
15
3.2.1 Hot Carrier Temperature
The density of states (DOS) function and Fermi-Dirac distribution are the two limiting
functions that define the shape of the PL spectra curve. The DOS establishes the limit of
the minimum energy emission at the bottom of the conduction band (CB) to the valence
band (VB). Which (CB& VB) move according to the change in sample temperature and
causes a shift in the minimum energy limit. Higher energy emissions are governed by the
Fermi-Dirac distribution. Continuous external flux of incident photons establishes quasi-
equilibrium for each CB and VB resulting in quasi-Fermi-Dirac distributions. This in
turn, sets up an upper limit for the allowed electron occupation levels in the CB and also
limits the high energy emissions. The quasi-Fermi-Dirac distribution is carrier
temperature dependent. Therefore, the width of the sample spectra becomes broader or
narrower as excitation power is increased or decreased, respectively. As such, from the
slope of the higher energy emissions, we can extract the hot carrier temperature.
[Phillips(2004)]
3.3 EXPERIMENT
It is our object to carry out PL on the given solar cell samples while varying two
parameters, i.e. Intensity of incident Laser and Temperature of the given sample. The
intensity was varied with a filter and Temperature was varied with regulator-resistor of
the Cryostat.
3.4 SOLAR CELL SAMPLES
Following is a brief detail of the given solar cell samples:
16
3.4.1 Quantum Well (QW) Solar Cells
AlSb (20 nm)
substrat GaSb (n)
buffer GaSb n = 1.1016/cm3 ; e = 200 nm
GaSb p = 1.1016/cm3 ; e = 100 nm
5 MQW GaInSb (10nm) / GaSb( 20nm)
AlSb (20 nm)
couche contact GaSb p = 1.1016/cm3 ; e = 10 nm
V-812
Fig. 3.2: Diagram of the layered quantum well V812 sample with barrier cladding
of AlSb (20 nm)
substrat GaSb (n)
buffer GaSb n = 1.1016/cm3 ; e = 200 nm
couche contact GaSb p = 1.1016/cm3 ; e = 100 nm
5 MQW GaInSb (10nm) / GaSb( 20nm)
V-809
Fig. 3.3: Diagram of the layered quantum well V812 sample without barrier
cladding
17
Name Active Zone Thickness WavelengthV-812 5Multi QW Ga0.8In0.2Sb/GaSb
Bordered by 2 layers of AlSb (20 nm)
Wells 10 nm
Barriers 20 nm
D= 5*10 = 50 nm
λ = 1.9 µm
at 300 K
V-809 5 Multi QW Ga0.8In0.2Sb/GaSb Wells 10 nm
Barriers 20 nm
D= 5*10 = 50 nm
λ = 1.9 µm
at 300 K
Table 3.1: Description of the quantum well samples.
3.4.2 GaAs pn Junction Solar Cell
Name Active Layer GaAs Window LayerThickness Doping Thickness Doping Alnm cm-3 nm cm-3 %
O - 1 1000 1E+19 1500 1E+17 57
Table 3.2: Description of the GaAs sample.
3.5 EXPERIMENT SET-UP
Basically, light is projected on the sample to generate excited photoelectrons. Laser was
used as the coherent incident light source (Laser argon Coherent Sabre 22 W, Laser
sapphire titane Coherent 899) . Infra-red Mirror was used to reflect the laser on the
sample at 45° degrees. Chopper is used to synchronize the Lock-in mechanism for
improved sensitivity. The Neutral Density filters can be adjusted to have desired incident
laser intensity. The focusing lens 1(focal length 10 cm) is first used to focus the laser on
the sample and then Lens 2,3(focal length 15 cm) are used to focus the emitted photons
on the monochrometer aperture.
The sample was placed inside the cryostat which was cooled by a Helium cycle. The IR
(PbS) detector was cooled by liquid nitrogen. The experimental setup is given below:
18
Fig. 3.4: Schematic of the PL experimental setup at ENSCP laboratory.
3.6 EXPERIMENT CONDITIONS
Following are the experimental conditions used for each sample:
- The incident laser wavelength was at 750 nm
- The temperature was varied from 10, 30, 50 to 300 K
- At each temperature, the incident laser power was varied from 100, 34.8, 10.7,
3.3, 1.1, 0.33, 0.1%
- The sensibility of the detecting chain (Lock-in amplifier) was adjusted for each
power intensity.
3.6.1 Laser Power
The Laser power incident on the sample was determined using FieldMaster instrument
and the surface area of the incident Laser beam was determined by Beamview software.
19
From the FieldMaster:Power incident = 520 mW ±5mW
From Beamview Beam surface area = 9.722 E –5 cm2
This is the half peak width of the Laser intensity photo. From which we calculate the
incident power at:
Incident Surface Power = 5.349 E 3 W/cm2
However this power is at normal to the sample and in the experiment the laser arrives at
45°, so the Incident surface power is multiplied by the factor 0.71. Thus,
Incident Surface Power = 3.798 E 3 W/cm2
Fig. 3.5 : Laser Intensity according to surface area deduced from the Beamview
photo. Plotting by Arthur Le Bris.
3.6.2 Absorbed Power
The system behaviour and the extracted hot carrier effects have been compared to the
absorbed power and not the incident laser power. This was made possible by Arthur Le
20
Bris’s simulation on the V812 layers. Each absorbant layer was considered by putting in
their real and imaginary absorption coefficients and their respective layer-thickness at
laser wavelength 750 nm from the database of [SOPRA]. The simulation calculates the
behaviour of incident light as it propagates through the material. Thus it calculates the
absorbed power between cladding layers at approximately 50%.
Fig. 3.6 : Absorption curve for GaInSb quantum well sample(V812) at 750 nm.
3.7 CONCLUSION
A brief introduction to Photoluminescence is given. Samples to be characterized are
described. Experimental setup and conditions are defined. Also the method to calculate
the laser power arriving on the sample is given.
21
CHAPTER 4
RESULTS AND DISCUSSION
4.1 INTRODUCTION
The results obtained from the Photoluminescence (PL) experiments are presented. Firstly,
we have PL spectra results obtained directly from the experiments. Than we have the
results derived from the basic spectra to characterize the solar cell samples. Also the Hot-
Carrier characteristics are extracted. The theoretical bandgap energies (Eg) as mentioned
for each sample have been determined from the Varshni formula. Finally, we discuss the
significance of the results and offer possible explanations.
4.2 INTENSITY VS ENERGY PL SPECTRA
i) V812 : 5QWs+ GaSb + cladding layer
In fig 4.1 we have Intensity(log scale) – Energy graph at different incident laser intensity
at 10K. The graph has been rescaled taking into consideration the selected sensitivity used
for each laser intensity. The position of curves is independent of incident laser intensity.
Whereas, the slope broadens after the sample-curve-maxima (peak) as the intensity
increases. The maximum of the curve is at 0.725 eV. The theoretical Bulk Eg (10 K ) =
0.617 eV.
22
Fig. 4.1: PL spectra of GaInSb QW sample V812 at 10K with varying intensity.
ii) V809 : 5QWs+ GaSb
In Fig 4.2, the sample peak is at 0.7 eV. This sample does not give sufficiently clear
results to be properly characterised. Theoretical Eg (10K) = 0.617 eV . We can observe
the great change in PL spectra as we remove the cladding layer.
23
Fig. 4.2: PL spectra of GaInSb QW sample V809 at 10K with varying intensity.
iii) O-1 GaAs
In Fig 4.3, the sample peak is at 1.45 eV. The broad peak suggests interface localized
states. Theoretical Eg (10K) = 1.52 eV
24
Fig. 4.3: PL spectra of GaInSb QW sample V809 at 10K with varying intensity.
iv) GaSb Bulk
Fig 4.4, There are two peaks for GaSb bulk. First peak at 0.725 eV is thought to be due to
defects within the sample whereas the second at 0.78 eV is accorded to sample curve
maxima. Theoretical Eg (10K) = 0.812 eV. The sample peak disappears as we decrease
the laser intensity. This seems to suggest that all the recombination takes place in the
defect states.
25
Fig. 4.4: PL spectra of GaSb bulk sample at 10K with varying intensity.
4.3 TEMPERATURE DEPENDENCE
As V812 (5QWs+ GaSb + cladding layer) is the most suitable sample to study
thermalisation, further results would be taking only V-812 in consideration. In fig 4.5, we
have fixed intensity at 100% and we look at the temperature dependence of the PL
spectra. The peak moves to the right as we increase the temperature of the cryostat (10 K
= 0.727 eV, 30K = 0.726 eV, 50K = 0.724 eV). Also the width of the luminescence
spectrum becomes narrower and more intense as the temperature decreases.
26
Fig. 4.5: PL spectra of GaInSb QW sample V812 at 10K, 30K and 50K.
Fig. 4.6: Theoretical Bandgap for GaInSb bulk material according to Varshni
Formula [Varshni (1967)] according to Lattice Temperature. .
27
The Band Gap – Temperature graph for the Ga0.8In0.2Sb was calculated using the formula:
Eg(Ga1-xInxSb) : (1-x) Eg (GaSb) + x Eg(InSb) - c x(1-x)
Here, x = 0.2 and c is the bowing contant and for GaInSb, c = 0.415. The compression
factor has not been taken into consideration which ought to be taken into consideration
for a more precise calculation of Eg. Also, this Eg does not reflect the band gap energy of
V812, because it does take into consideration the Quantum Well effect. Which broadens
the spectra and shifts the bandgap.
Fig. 4.7: Comparision of theoretically calculated bandgap and the experimentally
observed peak maximas.
28
In the Eg – peak maxima figure, we can see the curve position shift is in accord between
theory and experiment. The theoretical figure has been calculated using Varshni formula.
Taking into consideration the ‘bending effect’.
4.4 HOT CARRIER TEMPERATURE
The Hot carrier temperature is calculated using the relation [Wurfel (1982)]
12 1))(exp().(
−
−−−=
KT
µEEEAI pl
Equation 4.1
I pl is the PL intensity, u is transition potential of the bandgap, A(E) is the absorption
factor and E is energy in eV. In which the effect of the transition potential has been
ignored and the equation reduces to
)exp().( 2
KT
EEEAI pl −≈ Equation 4.2
And the temperature is extracted from the slope by;
KCT
1= Equation 4.3
And logIpl is proportional to –E/KT which would give us the slope as: C = (logIpl/E) ; the
falling slope of the PL spectra, q is electronic charge and K is boltzmann constant. To
look how well it reciprocates with the carrier temperature, we will generate the absorption
graph from these temperatures.
4.4.1 ABSORPTION CURVE
The absorption curves were calculated using Matlab according to the formula used to
extract hot carrier temperature, i.e. Equation 4.2.
29
Where A is the Absorptivity factor, including the absorption coefficient, geometrical
factor and losses. The curves obtained show a plateau which corresponds to the linear
region of the falling slope of PL spectra. The curves have been normalized.
Fig. 4.8: Absorptivity determined from carrier temperature at 10K,30K and 50K.
The slight shift in the absorption curves in fig 4.8, at different temperatures corresponds
to the shift in the peak maximas at different temperatures in accordance with the
temperature shifts of band gaps in the Varshni Formula.
30
Fig. 4.9: Absorptivity determined from carrier temperature at 10K for varying
incident laser intensity.
The rising slopes at lower intensities do not reflect the absorption but only the rise in the
factor exp (E/KT) in Fig 4.9. Thus these absorption graphs show that the carrier
temperatures are projecting the probable temperatures of the excited carrier distribution
which is independent of the chemical potential µ. Which seem to validate our method of
extracting the carrier temperatures and rendering them more credible. Thus the carrier
temperatures are given as:
31
Fig. 4.10: Rise in carrier temperature at 10K,30K and 50K lattice temperatures with
increasing absorbed laser power.
From the graph , there are two main features, one the rise of carrier temperature. For all
temperatures, we see the rise of carrier temperature is almost linear. The minimum
temperature of the hot carriers should not be less than the lattice temperatures within the
margin of error. The error bars were determined by calculating the carrier temperature at
each segment of the slope and then finding the standard deviation of these temperatures.
We take the standard deviation of the carrier temperature and calculate the error bars. The
standard deviation was calculated by taking all the points on the slope considered and
finding the carrier temperature for each point. The mean value is taken as the carrier
temperature and the deviation from the mean is plotted as the error bar.
4.5 CARRIER COOLING BY LO PHONON
It has been shown experimentally that carrier cooling regime at high temperatures is
carried out by Optical Phonons. [Guillemoles(2005)] If we ignore the radiative
recombination. Then essentially all the absorbed power is used to increase the carrier
temperature from the relation:
32
Power absorbed ~ Qth ~ Q2 (Disintegration of optical phonon into acoustic phonons)
However, )(2 lCo TTQQ −= Equation 4.4
[Guillemoles(2005)]
Tc is carrier temperature and T1 is lattice temperature. And all the absorbed power
produces electronic excitations which in turn produce phonons. This formula is
empirically derived. It shows that at higher temperatures, it is infact the LO phonons
which cool the hot electrons. Therefore,
)( lCoabsorbed TTQP −= Equation 4.5
T
PQ absorbed
o ∆= Equation 4.6
Assuming that the carrier cooling takes place by LO phonon. The power delivered to hot
carriers is theoretically given by
)()exp( lCOLO
O
LO
e
LO
TTQkTcdt
dE −≈−−= ωτω ��
[Lyon(1986)] Equation 4.7
The Qo is equivalent to the thermalisation rate if we ignore the radiative recombination.
The carrier generation rate is proportional to the energy put into the sample, than inverse
of T will depend logarithmically on the laser power as:
ELoge
P
PKLog
TO
)(1
−= [Phillips(2004)] Equation 4.8
where P is the laser power, E is the energy put into the sample, and e is Euler’s number.
By inserting the expected energy of the LO phonon(28.4meV) in as E, one obtains a
formula for T vs. P for the LO phonon. By plotting this relationship in for various T
values found experimentally, one can determine from the intersection of the two curves
the range of electron temperatures over which the LO phonon dominates the cooling
process. We can see that as the lattice temperature increases, the slope of inverse carrier
temperature more closely resembles the LO phonon slope.
33
Fig. 4.11: Inverse carrier temperature at 10K,30K and 50K lattice temperatures with
increasing absorbed laser power. And the Phonon energy range.
4.6 THE MEANING OF Q FACTOR
The Q Factor represents the linear relation between absorbed laser power and the
increased carrier temperature. It is in fact the carrier thermalisation rate which governs the
hot carrier solar cell device efficiency. The hot photon results in the production of an
electron which in turn relaxes by the emission on an LO phonon which degenerates into
production of two LA phonons. [Lyon(1986)]
LALOeQQ
221
→↔→ −ν�
34
Power thermalised follows the conservation law. It is the flow of power which produces
the electron excitation and in turn the phonon.
The Q Factor is the limiting step at high intensity only. That is, when the carrier cooling is
carried out by optical phonons.
Fig. 4.12: Energy Loss Rate at 10K,30K and 50K lattice temperatures with
increasing absorbed laser power.
4.7 DISCUSSION
4.7.1 Hot carrier temperature
The decreasing slope (curve broadening at higher Intensity) in Fig 4.1 of V812 can be
explained by the fact that as we increase the laser intensity, we have greater number of
high energy incident photons which result in greater electron population (having higher
energies than Eg) in the conduction band. Simultaneous relaxation of this hot electron
35
population to the conduction band results in the curve broadening, showing greater
amount of higher energy radiative recombination.
By increasing the power, the total number of electrons that are excited into the conduction
band also increases, which means higher energies are being filled within the band
resulting in an increase of temperature of the electrons. The electron temperature, T, is the
deciding factor on how broad the emission peak is. Knowing that it only changes the
higher energies of the peak of the emission spectrum, T can be determined from this side
of the photoluminescence. This was the method employed to calculate the Hot carrier
temperature.
The method applied to extract the carrier temperature does not appear to be precise. In the
fig 4.10, it can be seen that the carrier temperature appears less than the lattice
temperature. There are 3 possibilities for such an error: The temperature recorded in the
cryostat is not the same as that of the sample lattice, the graphical methods employed to
determine the carrier temperature is imprecise or the chemical potential cannot be
ignored.
The rise in the carrier temperature might be thought of as if the system is saturated and
working in the degenerate state. However, this was verified by plotting the integral of the
intensity versus the incident laser power and system was found to be unsaturated. The
absorption curves deduced from the carrier temperatures also seem to reflect their
validity. The linear plateau for which the absorptivity remains constant is the same region
for which the hot carrier temperature was approximated. And the shifts are well accorded
for. Therefore the slopes can be said to reflect the hot carrier phenomenon.
4.7.2 Carrier cooling
The plot of LO phonon cooling shows that as we increase the incident intensity the carrier
temperature comes within the range of optical phonon cooling range. However the most
important thing is that as the lattice temperature increases, which results in higher carrier
temperatures, meaning high energy electrons, then this slope approaches the same slope
36
as of the optical phonon energy. Which means that at higher energies, it is the optical
phonon which cools the hot carriers.
4.7.3 The Q Factor
The Q factor plot is only valid for electrons having sufficiently high temperature. Before
that the cooling mechanism is not LO phonon dominated and therefore will not give a
relatively constant value. Similar calculation done by Rosenwaks [Rosenwaks(1993)]
Such behaviour was observed as the initial values for Q were oscillating until sufficient
incident laser power was introduced. After this threshold intensity and thus resulting hot
carrier population, they became independent of the incident intensity. Also, its value
appears to be independent of the lattice temperature. Now this thermalisation rate Qo can
be used to predict the phonon emission time for the system using equation 4.7 as given
below:
Fig. 4.13: Cooling Time Constant for V812 against the carrier temperature at lattice
temperatures of 10K, 30K, 50K.
37
Furthermore, the thermalisation rate can predict the eventual efficiency of the hot carrier
device under ideal conditions. The simulation work on the efficiency of hot carrier device
with respect to the Qo has been carried out by Arthur Le Bris, in which the Q rate for real
material (GaAs etc) equalling 10 W/cm2/K has been considered as 1 on the graph.
Therefore we can see from the graph that if our device thermalisation rate is
approximated at 10 W/cm2/K, than the probable efficiency that can be achieved (at the
band gap of 0.7 eV) is above 50%. This is much higher than the fundamentally limited
efficiency of single threshold devices as determined by Shockley and Queisser.
Fig. 4.14: Efficiency of solar cell versus the band gap for different thermalisation
rates. (Here, Q = 10 => Qo = 1). Arthur Le Bris
38
My Solar Cell
CHAPTER 5
CONCLUSION
The goal of this internship was to characterize the solar cell samples and to determine
their hot carrier effects. The given samples did not have contacts therefore
Photoluminescence spectroscopy was used to characterise them. By varying the intensity
and lattice temperature, we were able to observe the changes in sample behaviour.
These photoluminescence data were further treated to extract the hot carrier effects. The
quantum well samples displayed sizable hot carrier effects. The method for extracting the
carrier temperature was validated by generating the absorption curves. Also, our
hypothesis of neglecting the chemical potential to extract the carrier temperature appears
to function.
Then, the cooling mechanism of these samples was treated. It was observed that at higher
intensities and corresponding higher temperatures, the cooling of these hot carriers was
carried out by the optical phonons. This is in accordance with the theory that higher
energy carriers are thermalised by the optical phonons.
Finally, the thermalisation rate was calculated which was is an important parameter for
determining the viability of the sample as a hot carrier solar cell. The Q factor should be
constant and it was found to be relatively constant for higher intensity regime. This is the
regime when hot carriers are cooled by the optical phonons.
The Q factor determines the efficiency of the hot carrier device. The closer it approaches
zero, higher is the efficiency. The quantum well sample gave a value of Q factor at
around 10 which suggests an efficiency of above 50% under full concentration and ideal
conditions.
39
5.1 FUTURE WORK
Hot carrier solar cell is only a theoretical concept. For its successful implementation a lot
of research must be carried out. First I shall state the work that I could be pursuing
immediately and then I shall give directions of further research.
- Connecting electrical contacts to the given contacts and observe their Current-
Voltage characteristics.
- We have assumed that all the excess energy is delivered to the electrons, which is a
close approximation to actual behaviour. In a more precise study of carrier
temperature, we can include the effective masses (modified in quantic confinement)
and get better approximated carrier temperatures.
- Model the Hot carrier solar cell. Initially, as an ideal absorber(no thermalisation,
immediate equilibration of photo-excited carriers: not equilibration with lattice but
within carriers, this ensures the energy distribution is represented by the Fermi
distribution at a high temperature), later introduce the effects of impact ionization (II)
and auger recombination (AR). [Wurfel(2005)]
- Introduction of a finite thermalisation time in the absorber and of a finite energy
selection width in the contacts. Also a finite equilibration time in the absorber must
be considered. [Takeda(2008)] [Takeda, Guillemoles, correspondance]
40
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