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VIII
the film from front to back which is desirable for improved carrier collection.
These improvements eventually allow for solar cells fabrication. There are a
variety of other growth techniques currently being explored. Many of these
techniques focus on low cost, large area, easily scalable processes. Low
temperature growth allows for the use of cheaper substrates including flexible
materials and is also a major area of interest. In general, these growth methods
involve the deposition of the initial metal layers and this book discusses six
ternary thin films grown through chemical solution technique and equally
analyses their optical properties and other solid state properties.
IX
TABLE OF CONTENTS
DEDICATION ... V
ACKNOWLEDG
EMENT ... VI
PREFACE ... VII
CHAPTER ONE ... 1
THIN FILMS ... 1
Introduction
... 1
Benefits of Thin Films
... 4
Cadmium Sulphide thin films
... 5
Electrical properties of CdS thin films
... 7
Optical properties of CdS thin films
... 9
CdS-PbS based photovoltaic Cells
...14
CHAPTER TWO ... 15
THEORY OF THIN FILMS ... 15
Semiconductor thin films
...15
Energy bands in solids
...15
Energy band structure in semiconductors
...17
Intrinsic semiconductors
...18
Extrinsic Semiconductors
...20
Semiconductor transport carriers
...23
Optical phenomena in thin films
...26
Photoconductivity in thin films
...27
Thin film applications
...28
The p-n junction
...28
A p-n homo-junction
...29
A p-n hetero-junction
...31
Photovoltaic cells
...31
Photovoltaic cell operation
...33
Strengths and limitation of thin films for photovoltaic cells
...35
CHAPTER THREE ... 36
OPTICAL SOLID STATE PROPERTIES OF THIN FILMS ... 36
Optical and Solid State Properties of Thin Film
...36
Band Gap and Absorption Edge
...40
Dispersion
...46
Photoconductivity
...46
Luminescence
...47
Electrical Conductivity
...48
X
Thermal Conductivity
... 49
Spectral Selective Surfaces
... 49
Semiconductor- Metal Tandems
... 51
Heat Mirrors
... 52
Dark Mirrors
... 52
Anti-reflection Coatings
... 52
Spectral Splitting and Cold Mirror Coatings
... 53
Radiative Cooling Materials
... 54
Window Coatings
... 54
Solar Control Coatings
... 54
Window Coatings with Dynamic Properties
... 56
CHAPTER FOUR ... 57
METHODS AND MATERIALS FOR TERNA
RY THIN FILMS ... 57
Cleaning of the substrates
... 57
Thermal Evaporation
... 57
Epitaxial Growth
... 59
Chemical Vapour Deposition
... 64
Plasma Technique
... 67
Sol -gel Thin Film Formation
... 68
The solution Growth Technique
... 70
Thin Films Condensation Formation Mechanism
... 76
CHAPTER FIVE ... 78
THIN FILM MEASUREMENT AND CHARACTERIZATION TECHNIQUES ... 78
Measurement Techniques of Thin Film Characteristics
... 78
Film Thickness
... 78
Gravimetric Technique
... 78
Optical Technique
... 79
Absorbance or Transmittance Measurements
... 80
Method of Determining the Composition of Thin Films
... 80
Atomic Absorption Spectroscopic Method
... 81
X-Ray Fluorescence
... 81
Infrared Spectroscopy
... 82
Chemical Analysis of thin films
... 83
Crystallographic Structure and Topography
... 84
Transmission Electron Microscopy
... 85
Surface Structure
... 86
XI
Leed Technique
...86
RHEED Technique
...86
Photo Electron Spectroscopy
...87
Optical Microscopy
...87
Methodology
...89
Growth of ternary thin films
...90
Deposition of cadmium zinc sulphide thin films (CdZnS)
...92
Deposition of lead sulphide thin films
...94
Optical and Solid State Characterization
...95
Photovoltaic cell characterization
... 100
CHAPTER SIX ... 102
OPTICAL BEHAVI
OUR OF TERNARY THIN FILMS ... 102
Optical properties of Iron Copper Sulphide
... 102
Solid State Properties of Iron Copper Sulphide
... 108
Optical Properties of Iron Zinc Sulphide ( FeZnS)
... 112
Solid State Properties of Iron Zinc Sulphide
... 119
Optical Properties of Lead Silver Sulphide (PbAgS)
... 122
Solid State Properties of Lead Silver Sulphide thin films
... 129
Optical Properties of Copper Silver Sulphide (CuAgS)
... 134
Solid State Properties of Copper Silver Sulphide thin films
... 140
Optical Properties Of Copper Zinc Sulphide ( CuZnS
)... 144
Solid State Properties of Copper Zinc Sulphide thin films
... 151
Optical properties of cadmium zinc sulphide thin films (CdZnS)
... 156
Optical properties of lead sulphide thin films
... 170
Photovoltaic properties of CdZnS / PbS cell
... 182
XII
CHAPTER SEVEN ... 185
OPTICAL ANALYSIS OF THIN FILM SOLID STATE PROPE
RTIES ... 185
The Spectral Analysis
... 185
Other Optical Properties
... 185
Solid State Properties
... 185
APPENDIX ... 209
1
CHAPTER ONE
THIN FILMS
Introduction
Thin films can be used to fabricate optoelectronic devices that can convert solar
energy into electrical energy for various uses. This can be achieved if their
structure, inter-band transitions and other optical properties are maximized to
harvest enough solar radiation to provide energy. Activities that take place
when electrons transit between energy bands in thin films are of fundamental
importance in harvesting solar radiation just like all fuels derive their source by
utilizing solar energy . Although solar energy is abundant it has not been
harvested well. Obtaining energy by use of solar cells does not require sophisti-
cated and expensive facilities.
Thin film nanotechnology has been able to fabricate cheap optoelectronic
devices that produce power for homes, small commercial uses or electric
current for other uses. It is a source of energy that is reliable, easy to maintain
and even install and because of some of these advantages over other forms of
fuels. Thin film materials with good photoelectrical properties in the visible
range and those that extend into the IR and UV regions for photovoltaic cells
are required. Photovoltaic cells are known to absorb light (photons) from the
sun and convert them directly into electricity. They consist of a p-type layer
which has a majority hole carriers and an n-type layer that has a majority
electron carriers as shown in Figure 1.1. These layers form a diode in the form
of a p-n or p-i-n junction that enables current to flow when electron-hole pairs
are created at the junction. When a photon with energy greater than the band-
gap of the semiconductor passes through such a cell, it may be absorbed by the
material and this takes the form of a band-to-band electronic transition produc-
ing an electron-hole pair.
2
Figure 1.1: p-type and n-type thin film cell
Several types of thin films have been fabricated and used to manufacture
photovoltaic cells. Various methods of preparing thin films for photovoltaic
applications have been used that include chemical deposition, liquid deposition
and chemical vapour among others. Chemical bath deposition (CBD) is one of
the noble methods devoted their efforts to this method because it is a non-
expensive method for thin film preparation. Through this method many noble
materials have been developed. Among these noble materials that are of great
interest include metal chalcogenides especially binary (2) elements such as CdS
and PbS from group II and group VI elements.
Doping them through CBD has been done to make them suitable for use as
window layers using different elemental dopants like boron, indium, arsenide
and chlorine to improve efficiency of their photovoltaic cells but these cells
have shown low efficiency due to their high spectral reflectance and resistance.
It has been proposed that if they are doped to take a ternary form and then be
used as thin films cells then their cells are expected to improve. Ternary
derivatives of CdS have generated a lot of interest because of their varied
applications in the field of optoelectronic devices. One such compound is
cadmium zinc sulphide (Cd
1-x
Zn
x
S) which is gaining prominence as a good
candidate for wide band gap materials for photovoltaic and photo-conducting
devices. Its band gap can be tailored to vary from 2.43 eV to 3.32 eV depending
on its constituents and preparation technique.
The addition of Zn to CdS is believed to enhance open-circuit voltage (V
oc
) and
short-circuits current (I
sc
) in hetero-junction devices as a result of the decrease
in the window absorption losses. It has also been proposed that to replace CdS
3
with the higher energy band gap ternary Cd
x
Zn
1-x
S may led to a decrease in
window absorption loss and a decrease in the lattice mismatch with the
Cu(In,Ga)Se, Cu
2
S and other absorber semiconductors and hence higher
efficient cells.
Lead chalcogenides thin films deposited by CBD have been investigated and
they have shown to possess a well-defined band structure in which their energy
gap varies continuously between 0.41 eV to 2.7 eV depending on the method of
preparation. Since their band gap ranges within the optimum theoretical band
gap for maximum absorber material of about 1.5 eV, they can be used to
fabricate photovoltaic cells. To obtain good quality and cheap semiconductor
thin films of Cd
x
Zn
1-x
S and PbS for photovoltaic cells using CBD the influence
of factors like temperature and concentration need to be optimized.
Thin films are crystalline or non-crystalline materials developed two dimen-
sionally on a substrate's surface by physical or chemical methods. They play
vital role in nearly all electronic and optical devices. They have been used as
electroplated films for decoration and protection. They have long been used as
anti-reflection coatings on window glass, video screens, camera lenses and
other optical devices. These films are less than 100 nm thick, made from
dielectric transparent materials and have refractive indices less than that of the
substrate. However, the use of techniques which have been developed over the
last few years show that much of the thin films are of recent origin. They are in
use in various ways, such as in solar energy conversion. Thin film of thickness
of less than 100 nm, now serve as anti-reflection coatings on solar energy
collectors.
Semi-transparent films in Schottky barrier solar cells, combinations of thin
films in photo-thermal devices that generate low or high grade heat and thin
semiconductor films on metal or glass substrate form a promising type of low
cost solar cells. In industrial, scientific and technical applications of thin films,
their physical properties such as optical, chemical and electrical are investigat-
ed which results in variety of devices such as solar energy devices, xerography,
4
switching devices, high resolution lithography, optic memories, photo-detectors
etc.
Thin films deposition for optical, electronic and optoelectronic device applica-
tion has become an industry in most advanced countries using highly techno-
logical, sophisticated and very expensive techniques. However, in third world
countries, the high technological and sophisticated techniques are not easily
achieved because of their complexity and the poverty of the third world
countries. Hence, considerable efforts are put into developing simple and cheap
techniques of depositing the films. The solution growth technique offers the
simplest, cheapest, most economical and affordable method of depositing thin
films like Halide and Chalcogenide.
Benefits of Thin Films
Thin films could be used to produce solar panels which in turn could be used to
produce clean and quiet electricity. Such alternative source of cheap electricity
will reduce electricity bills, guard against rising energy costs, protect the
environment, add comfort, security and value to homes; and provide uninter-
rupted power supply. Because, there are no moving parts, there is little or no
breakdown in the provision of such systems. The systems have long life times.
The solar panels themselves are guaranteed for 20 30 years. There is virtually
no maintenance on the panel. Distribution can be decentralized. It can be used
to supply DC or also AC by using an inverter. The main component of a solar
panel is the solar cell which is made from thin films. Hence the main thrust of
our work is to grow thin films of competitive standard.
For the technological development of any nation, cheap semiconductor materi-
als as well as into energy are required, efficient, high yield and low cost
technique for the deposition of thin films which, when characterized properly
will find its way into one of the following applications: electronics, optoelec-
tronics, photo-voltaic, photo-thermal, photo electromagnetic, photo-
electrochemical and photo-biochemical. When there is a breakthrough in low
cost solar cell technology through solution growth techniques, large-scale rural
5
electrification, using solar cell modules will be feasible and rural development
will be a reality.
Many thin films have been developed for solar radiation absorption and glazing
which are used for photo-thermal devices. However they are not yet fully
developed for temperate and tropical environments to be used for heating and
cooling in buildings. This could be due to lack of understanding of the need and
prospects of selective glazing for buildings. There is also lack of interest due to
the high of the films that have been developed for these applications. Many
scientists all over the world are now occupied with into ways of improving the
performance of solar energy devices to provide comfort in buildings and
automobiles. The separation of the input solar radiation from the emitted
thermal radiation by an absorbing material is needed in order to obtain higher
collector efficiency in this wise.
A material which is capable of separating thermal (infrared) radiation from the
input solar radiation is a spectral selective surface. Energy could be conserved,
and an acceptable level of comfort is achieved inside buildings, when a suitable
thin film is deposited directly onto the window glazing. This is referred to as
solar control coatings or heat mirrors. Solar control coatings are expected to
play the role of a conventional air conditioner, but passive selecting only filters
certain solar radiation that is required and screen of the infrared radiation (heat)
from inside of buildings in warm climate. For solar control coatings, there must
be controlled optical transmittance which ranges between 10-50% and low
reflectance which is less than 10% in the visible region (0.4m 0.7m) and
high reflectance in the infrared region (> 0.7m). With this, there is the cooling
of the inside of buildings as the infrared portion of the solar radiation which
causes heating is screened off and there is also adequate illumination of the
inside of the same buildings.
Cadmium Sulphide thin films
Group II-VI metal chalcogenide semiconductors particularly CdS, CdSe and
CdTe have been of interest because they have high photoconductivity in the
6
visible region. CdS has the best photoconductivity and is widely used in a large
number of solid state device applications. Today CdS is considered as the best
suited window material for CdTe and CIGS
solar cells. As the applications of
CdS thin films increases their study also becomes popular among because of
their merits such as their smallness and lightness, their easiness of fabrication
and the possibility of forming thin film circuits. Focus on the enhancement of
the optical and electrical properties of pure and doped CdS films to produce
high efficiency photovoltaic cells. This enhancement has been in progress for
some time now and efforts to deposit large grain CdS films on low cost
substrates are still on-going. The type of substrate used also plays an important
role during the initial growth stages of CdS thin films.
In most cases CdS thin films grow as n-type semiconductors due to the donor
centres formed during deposition. Vacancies of sulphur cause deviations from
stoichiometry during its formation hence surface quality depends on the
method used in preparation and it is important that the films be free of voids,
grain frontiers etc. CdS is one of the semiconductors to investigate. A large
variety of deposition techniques have been utilized to obtain photovoltaic cell
quality layers like those that will be discussed in chapter three. It is important
to note that there are some problems in each method. For example, it is difficult
to obtain stoichiometric CdS by the evaporation technique while in spray
deposition high temperatures are required.
Zinc has been used to dope CdS thin films to obtain CdZnS. Cd
1-x
Zn
x
S ternary
semiconductors form a continuous series of solid solution allowing systematic
variation of the band gap from 2.43 eV for CdS to about 3.7 eV for ZnS by
adjusting the composition. In CdS/CdTe solar cells, the replacement of CdS
with a higher band gap ternary (Cd,Zn)S film can lead to a decrease in window
absorption losses and an increase in the short-circuit current. The first well
characterized deposition of a true (CdZn)S alloy film prepared by chemical
bath deposition (CBD) was in 1988. In this work Cd and Zn acetates were used
in various ratios complexed with ammonia, TEA and thiourea at 90-95 °C.
Interestingly, Zn was more heavily complexed than Cd in its solution which
showed that the mechanism of deposition was not only based solely on solubili-
7
ty product of the sulphides. Chemical Bath Deposition (CBD) in the prepara-
tion of sulphide thin films on soda-glass substrates including Cd, Zn and Cd-Zn
mixed sulphide films and reported uniform films. Adhesion of CdS films to the
substrate was found to be dependent on the [Cd]:[S] ratio in the starting
solution. The small crystals of pure ZnS and the larger ones of pure CdS
suggested a cluster mechanism and an ion-by-ion mechanism respectively.
Electrical properties of CdS thin films
Electrical properties of CdS thin films depend on the deposition condition.
Evaporated films prepared for solar cell applications usually have resistivity in
the range of 1 to 1000 -cm. They are usually n-type in conductivity dominat-
ed by the deviation from stoichiometry which influences the films to have S
vacancies or Cd excess. Resistivity decreases as the thin film thickness in-
crease. In thermal evaporation the [Cd]:[S] ratio during evaporation influences
the electrical properties as does when doping. For CdS films doped with indium
(CdS:In), the best electrical properties are obtained at a [Cd]:[S] ratio of 1:5 at
which the films also exhibit resistivity values as low as 10
-3
cm on CdS:In
[1.5%)] samples.
Resistivity of doped evaporated films is insensitive to substrate temperature
during deposition which contrasts the strong dependence of the resistivity of
un-doped films on deposition temperature. CdS thin films evaporated for
photovoltaic cell applications have carrier concentrations in the range 10
16
to
10
18
cm
-3
and minority carrier diffusion lengths in the range 0.1 to 0.3 m and
films grown at higher rates exhibit higher carrier concentration that increase
with increase in film thickness. Those doped with indium increases their carrier
concentration by almost three orders of magnitude up to a concentration of
about 2% by weight and thereafter the carrier concentration does not increase.
It is noted that at low indium concentrations, the carrier concentration and
mobility decreases.
Chlorine has been used to dop CdS thin films. It has been reported that the CdS
films doped with chlorine gas present very low photoconductivity at room
8
temperature and their Hall mobility decreases with heat treatment. Those
prepared by evaporating CdCl
2
mixed CdS powders increases in resistivity and
carrier concentration. A rapid incremental behaviour of mobility for the pure
and low-doped films below 0.05% CdCl
2
concentration was also noted. The
electrical properties in spray deposited CdS films are dominated by the chemi-
sorption of O
2
at the grain boundaries which reduces both the carrier concentra-
tion and mobility. The films are invariably n-type with resistivity varying over
a range as much as 10
8
-cm. Post deposition annealing in air increases the
resistivity of CdS films to about 10
7
-cm and makes them highly photo-
conducting.
A photoconductive gain from 10
6
to 10
7
with response time of about 1 ms under
50 mW cm
-2
illumination has been reported. In vacuum annealing, the resistivi-
ty decreases to 1 - 10 -cm and the photoconductivity is quenched indicating
the reversibility of chemisorption and desorption of oxygen. Electrical proper-
ties of CdS thin films grown by Closed-Space Vapour Transport [CSVT] show
strong dependence on growth conditions especially substrate temperature. The
films showed that the carrier concentration increased exponentially with
increase in substrate temperature and exhibited very high mobilities while their
resistivity varied from 10
-3
to 1 -cm as a function of the substrate temperature.
Un-doped epitaxial CdS films grown by CVD exhibit resistivity between 10
and 100 -cm.
Annealing them in H
2
/Ar at 400 °C reduces resistivity values to between 0.01
and 0.05 -cm and when doped with indium the films possess carrier concen-
trations of 10
18
cm
-3
and Hall mobility of 65 cm
2
V
-1
s
-1
. The as-deposited
sputtered CdS films exhibit a high resistivity up to 10
8
-cm while co-
sputtering them with indium yields films with resistivity of about 1 -cm and
changes their conductivity to p-type with hole mobility of 6 - 15 cm
2
V
-1
s
-1
and
a carrier concentration of about 7×10
18
cm
-3
.
In most cases chemically bath deposited CdS films are n-type and have
resistivity in the range 10
7
to 10
9
-cm and on annealing them in a vacuum
their resistivity decreases to about 1 to 10 -cm. This reduction is attributed to
9
desorption of O
2
from the films. When annealed in air they exhibit high
photosensitivity, have a carrier concentration of about 10
14
cm
-3
and a mobility
of 5cm
2
V
-1
s
-1
measured under normal illumination. As-deposited CdS films
show a higher resistivity than those annealed due to the creation of number of
sulphur vacancies in the films. Similar observations for CBD prepared films
but after annealing at 200 °C in a vacuum and in argon that showed resistivity
decreasing from 10
5
-cm to about 10 cm were also reported. Similar results
exist of resistivity for films thinner than 0.5 m.
Resistivity of CdS films decrease with increasing thickness. These reports also
add that an increase in carrier concentration with reduced carrier mobility is
observed for any increase of cadmium ion concentration. Observed results
show that growing films with increasing cadmium ion concentration in the bath
incorporate more cadmium (Cd) in the deposited films. This makes the re-
sponse of the films when under illumination reduce their resistivity between 3 -
5 orders of magnitude. Co-deposition of CdS-ZnS films by CBD at 80
0
C
causes sheet resistance to increase linearly.
In a similar the resistivity of (CdZn)S thin films on soda-lime glass substrates
grown by CBD for CGS solar cells and their resistivity varied linearly on a log
scale from 10
9
-cm (CdS) to 10
14
-cm (ZnS). Using ammonia-complexed
metal iodide and thiourea at pH 10 produced films whose properties depended
on the temperature of deposition. Their resistivity decreased with an increase in
Zn content from 10
10
-cm for CdS to 10
6
-cm for a 90% solution concentra-
tion of Zn and then increased to 10
9
-cm for a pure ZnS. The films were
photoconductive with resistivity decreasing as a function of composition up to
about 5 x 10
3
for the 90% Zn films.
Optical properties of CdS thin films
Optical properties of CdS films are determined to a large extent by the micro-
structure of the films themselves and also by the deposition conditions. Cadmi-
um sulphide thin films have high visible transmittance and a good near-IR
reflectance. It has been found that the optical absorption edge of CdS films
prepared by vacuum evaporation (VE), screen printing (SP) and CBD shifts to
10
higher wavelengths as the film thickness increase. Thin evaporated CdS films
are smooth and specularly reflecting. Their surface roughness increases with an
increase in thickness leading to a large diffuse scattering component in thick
films.
The optical constants n and k have been determined for evaporated thin films
over the wavelength range of 0.25 m to 2.0 m by measuring normal inci-
dence reflectance and transmittance and taking into account surface roughness.
Analysis yielded direct transitions in the range of 2.42 eV to 2.82 eV and it
combined both direct and indirect transitions beyond 2.82 eV. The n and k
values were observed to be dependent on the substrate temperature during
deposition. At higher substrate temperatures the refractive index approached
that of single crystal material. It has also been reported that refractive index
increases with increase in film thickness while the extinction coefficient
decreases rapidly with an increase in wavelength in the range 400 - 600 nm
because thickness increases optical density.
Sputtered CdS films have a sharp optical transmission cut-off near 0.52 m
corresponding to the band gap of CdS but in spray deposited films the band gap
and the fundamental optical absorption edge are not affected by the microstruc-
ture. Diffuse scattering and transmittance depend on film thickness, substrate
temperature, [Cd]:[S] ratio and increase in film thickness but reduced by
increasing deposition temperature. Different band gap values of CdS thin film
have been reported from 2.30 eV 2.60 eV depending on the deposition
conditions, thickness and annealing temperature. The thickness of the film
increase the absorption edge shifts towards lower energy region (higher
wavelengths) and becomes much sharper (i.e. the band gap decrease).
It has also been
reported that films present a steep absorption edge at a wave-
length of 500 nm with a band gap value of about 2.45 eV and their refractive
index was of about 2 eV for the higher wavelengths while after annealing the
absorption edge undergoes a slight shift towards the higher wavelengths. It has
been reported that CBD grown CdS films prepared from different sources of
cadmium (chloride or acetate) present high transmissions 70 - 80% and
11
therefore it has been deduced that very thin CdS films allow a high transmis-
sion even at wavelengths below 500 nm that corresponds to CdS energy gap
until the stronger absorption detected at 300 nm due to the glass substrate.
Average transmittance in the 400 - 800 nm wavelength range mainly depends
on the cadmium sulphide thickness as a consequence of the higher absorption
occurring in the films. Experimental data demonstrate that in CdS-SnO
2
bi-
layer transmission is more dependent on the type of SnO
2
substrate than on
thiourea concentration used during the CdS deposition process and thus
absorption coefficient [ ] in the order of 1 to10 cm for energies greater than 2.4
eV has been achieved. A direct forbidden energy gap of about 2.48 eV,
refractive index that follows Mayer's law equal to 2.116 for the high wave-
lengths has also been attained. A band gap range of 2.45 - 2.50 eV at the
absorption edge has also been reported.
When zinc is used as an impurity, the CdZnS thin films deposited by diffusing
Zn into CdS have band gap energy of 2.64 eV (Cd
0.74
Zn
0.26
S) which exceeds
the band gap of CdS of 2.43 eV. It was concluded that inter-diffusion in
Zn/CdS structures at temperatures exceeding melting point of Zn is accompa-
nied by the formation of Cd
1-x
Zn
x
S ternary compounds. These films had an
optical transmittance of 80% and a direct band of 2.49 eV. Guoshi and co-
workers observed that Zn
2+
ions in chemical bath doping regulate the growth
rate and the formation of ternary CdZnS films and also Zn
2+
cause the band gap
of CdS to be tunable depending on its concentration in the bath. When spray
pyrolysis is used it is observed that CdZnS films have optical transmittance
above 65% in the wavelength range 450 800 nm and direct band gap of
between 2.47 3.04 eV.
A study on (CdZn)S thin films grown on soda-lime glass substrates by CBD
process for applications in copper gallium selenide [CGS] solar cells. Optical
absorbance (A) and transmittance (T) spectra measured over the wavelength
range of 300 to 1100 nm showed that 30 % of Zn in the solution had better than
80 % transmittance for wavelengths longer than 600 nm and thickness less than
50nm. Energy band gaps obtained were 2.40, 2.55 and 2.70 eV for Zn- content
12
of 0, 30 and 50 %, respectively. The band gap calculated from optical absorp-
tion spectroscopy varied almost linearly with composition between that of CdS
(2.4 eV) and ZnS (3.6 eV). An analysis of the absorption spectrum indicated
the formation of CdZnS compound with the largest value of energy band gap
up to 2.64 eV.
The spectrum of CdS film showed allowed direct band gap with single slope
while the spectrum of the Zn/CdS could not be characterized by one slope but
rather presented a curve with changing slopes. Considering the findings
reported here it is made clear that zinc doped CdS offers good photovoltaic
properties that need to be optimized and consequently be used to fabricate an
efficient photovoltaic cell. A choice of an easy and cheap deposition technique
was of essence.
Lead sulphide is an important direct narrow gap semiconductor material with
an approximate energy band gap of 0.4 eV at 300K and a relatively large
excitation Bohr radius of 18 nm. These two properties make PbS films very
suitable for infrared detection and solar cell applications. It is a material that
has also been used in many fields such as photography, Pb
2+
ion selective
sensors
,
solar absorption etc. These properties have been correlated with the
growth conditions and the nature of substrates used. CBD prepared PbS thin
films are reported to have a cubic centered structure with a preferential orienta-
tion of [200] perpendicular in direction to the plane of the substrate as well as
being amorphous with lower spectral reflectance and transmittance [below
40%] in the wavelength range of 300 1800 nm. This is due to diffuse reflec-
tions from the surface of the thin films while their dark electrical resistance is
in the range of 10
10
10
11
/cm for `nano-crystalline' and 10
5
10
6
/cm for
`standard' films. Both cases the films were of p-type conductivity. Popescu and
co-workers reported on the photosensitivity of PbS films after a long thermal
treatment at 90
0
C in air as being 23.75 % to 50 %.
A non-linear relationship between CBD deposition time and absorbance on as-
deposited PbS films for varied deposition times has been observed. Infrared
transmissions and photoluminescence spectroscopy show a tunable band gap
13
for bulk and nanostructures as from 0.41eV - 0.48eV when deposited on GeAs
coated substrates. The blue shifts in both absorbance and emission peaks of the
nano-structured layers are obtained due to quantum size effects and the band
gap edge. CBD deposited PbS films in the wavelength range of 240 840 nm
at temperature ranges of 10 30
0
C and established values of dielectric
constant ( ) that were attributed to the empty spaces between the aggregates.
The AFM analysis showed a mixture of PbS and voids but the structure was
similar to the one reported.
Characterized nano-crystalline PbS thin films sensitised by CBD and reported
crystal sizes of 2.0 - 4.4 nm with a band gap range of 1.9 - 2.6 eV. Those
deposited by sono-chemical methods showed an increase in photosensitivity
due to thermal treatment while An absorption band in the infrared range [1250 -
2400 nm] of 1.23 eV 1.28 eV from absorption measurements and a 0.93 eV
1.0 eV from photocurrent measurement. High absorbance levels at lower
wavelength range of 350 500 nm i.e. above 60% absorbance has been
reported. Direct allowed transitions in the energy range 1.88 2.28 eV and a
decrease in dc resistivity with grain size has been observed. The films were p-
type with crystals similar to those deposited using sol gel and spin coating
methods but with direct band gap of 0.41 eV and a dc electrical conductivity of
10
5
- 10
6
cm
-1
. PbS thin films with optical absorption in the range of 70
75% for wavelength range [350 850 nm] have good absorbance in the visible
region.
CBD is attracting considerable attention as it does not require sophisticated
instrumentation and it is relatively inexpensive, easy to handle, convenient for
large area deposition and capable of yielding good quality thin films. Since the
AFM analysis showed a mixture of both PbS quantum dots and voids in their
structure while an absorption band in the infrared range [1250 - 2400 nm] of
1.23 eV 1.28 eV from absorption measurements and a band gap of between
0.93 eV 1.0 eV from photocurrent measurement. It suggested that PbS thin
films can be optimized and provide a good absorber material for both infrared
and visible light spectrum.
14
CdS-PbS based photovoltaic Cells
CdS and PbS semiconductor materials are the most widely investigated by
chemical deposition technique and especially CBD. Starting in 1969 into
1970's, photovoltaic cells of CdS/PbS have been reported with V
oc
of up to 450
mV and J
sc
less than 1 mA/cm
2
. However, further reports on this type of cells
are scarce. The CdS/PbS cells and the photovoltaic junction fabricated present-
ed a photovoltaic behaviour of distinctive cell structures prepared by chemical
deposition; [glass/CdS/PbS/Ag, SnO
2
:F/CdS/PbS/Ag, and SnO
2
:F/CdS/(Bi
2
S
3
or/and CdSe)/PbS/Ag]. Depending on the cell type, V
oc
of greater than 500 mV
or J
sc
greater than 3 mA/cm
2
were reported under illumination of 1-3 kW/m
2
.
Any new technology for producing photovoltaic cells is now based on the use
of materials with very thin film geometry. This ensures that there is a low cost
for solar energy conversion, less material consumption and easiness to obtain
very small integrated modules. This study is investigating the performance of a
CdZnS/PbS photovoltaic cell with an intention of opening up the possibilities
of developing simple photovoltaic cell structures by sequential chemical
deposition of doped CdZnS and PbS layers for harvesting both the visible and
infrared light spectrum.
15
CHAPTER TWO
THEORY OF THIN FILMS
Semiconductor thin films
Semiconductors materials exhibit a number of useful but also unique properties
related to their electronic structure. Semiconductors can be fabricated to be in
bulk, wafer or in thin film forms. A semiconductor material is said to be in thin
film form only when it is built up as a thin layer on a solid support called
substrate by a controlled condensation of the individual atomic, molecular, or
ionic species. Thin films are also regarded as two dimensional materials
fabricated by the process of condensation of atoms, molecules or ions. This is
what makes them have unique properties significantly different from their
corresponding bulk materials. These unique properties are as a result of the
changes that occur in their physical dimensions, geometry and microstructure.
Thick films are prepared either by a direct application of solution dispersion or
by a paste of the material on a substrate and then letting them dry irrespective
of their thickness. In thin films there are deviations from the properties of the
corresponding bulk materials that arise because of their small thickness, large
surface-to-volume ratio and their unique physical structure which is a direct
consequence of the growth process. Most of the new thin film technologies
coming up are based on the use of materials with very thin film geometry
because they tend to lower costs and also lower material consumption. It is
currently known that a relatively small group of elements and compounds have
an important electrical property called `semi-conduction'. This is a property
where they are neither good electrical conductors nor good electrical insulators
but instead their ability to conduct electricity is intermediate and that is why
these materials are called semiconductors.
Energy bands in solids
Most semiconductors occur in solid form. These solids are made up of atoms
which in turn contains electrons. From quantum mechanics it is clear that
e
n
l
m
a
b
t
I
p
c
t
t
c
m
b
b
s
b
t
k
16
electrons o
number of
levels split
merge toget
approaches
by a region
tion band (C
Figure
In conducto
partially fil
courses the
top of the v
they gain k
conductors.
moderately
bonds and
band gap o
some electr
band leavin
the electron
kinetic ener
f an isolate
atoms are b
to form a b
ther to form
equilibrium
n called the
CB) and the
e 2.1: Band-
ors (i.e. met
led or over
uppermost
valence band
kinetic ener
. In semicon
strong. W
free electro
f a semicon
rons will be
ng holes in t
ns in the con
rgy and con
ed atom ca
brought tog
band. As th
m a single b
m distance t
forbidden g
e lower band
-gaps for me
tals) as show
rlaps the va
t electrons i
d to move t
rgy. Throug
nductors the
When therma
ons along w
nductor is n
e able to m
the valence
nduction ba
nduct electri
an have onl
gether to fo
he inter-atom
band. When
the band sp
gap, E
g
. Th
d is called th
etals, semic
wn by figure
lence band
in the parti
to the next h
gh this, cur
e bonds bet
al vibration
with free ho
not as large
move from th
e band. If an
and and the
icity.
ly discrete
orm a cryst
mic spacing
n the distanc
lits again in
e upper ban
he valence
onductors a
e 2.1, the co
so that the
ally filled b
higher avail
rrent condu
tween neigh
ns occur th
oles are pro
e as that of
he valence
n electric fi
holes in the
energy lev
al their dis
g decreases
ce between
nto two ban
nd is called
band (VB).
and insulato
onduction b
re is no ban
band or ele
lable energy
uction readi
hbouring ato
hey break s
duced. Tha
an insulato
band to the
eld is appli
e valence ba
els. When
crete energ
these band
these atom
nds separate
the conduc
ors.
band is eithe
nd-gap. Thi
ctrons at th
y level whe
ly occurs i
oms are onl
some of th
at is why th
or. Therefor
e conductio
ed then bot
and will gai
a
gy
ds
ms
ed
c-
er
is
he
en
in
ly
he
he
re
on
th
in
17
The valence electrons form strong bonds between neighbouring atoms in
insulators. These strong bonds are difficult to break. This means that there are
no free electrons to participate in current conduction. This courses the band gap
in an insulator to be large. When you consider the band gap in an insulator,
thermal energy or any external applied electric field cannot raise the uppermost
electron in the valence band to the conduction band. Using the energy parame-
ters we get that in the donor case;
E
C
- E
F
= KT ln (
) (2.1)
and in the acceptor case;
E
F
- E
V
= KT ln (
(2.2)
where the symbols have their usual meanings.
Electron and hole densities in extrinsic semiconductors can therefore be
expressed as:
n = n
i
exp{ (E
F
-E
i
)/KT} (2.3)
p = n
i
exp {(E
i
- E
F
)/ KT} (2.4)
When both the donor and acceptor impurities are present simultaneously, the
Fermi level adjusts itself to preserve charge neutrality according to the mass
action law.
Energy band structure in semiconductors
Materials are classified as direct or indirect semiconductors depending on the
band structure. In the figure 2.2 (a) the maximum in the valence band occurs at
P = 0 while the minimum in the conduction band occurs along the [100]
direction at P = p
C
. The electron at the conduction band (minimum) with zero
kinetic energy can have crystal momentum different from zero (i.e. P = p
C
).
When an electron makes a transition from the valence band to the conduction
band it requires then, not only an energy change greater than E
g
but also some
change in the crystal momentum, P. This makes such semiconductors to be
indirect semiconductors because a change in crystal momentum is required in
their transitions.
I
c
a
c
a
b
t
I
T
m
o
t
o
v
t
18
In figure 2
conduction
an electron
can do so w
are classifie
band to the
the electron
Intrinsic se
These are
materials is
occurs due
the bottom
of the elect
valence ban
the gap can
F
(E)
.2 (b) the m
band occur
making a t
without a ch
ed as direct
conduction
n.
Figure
emiconduct
pure cryst
s due to the
to the elect
of the cond
trons across
nd. These a
then be cal
= 1/ [ 1+ ex
maximum i
rs at the sam
transition fr
hange in the
semicondu
n band does
e 2.2: (a) Dir
tors
tals of sem
intrinsic pr
trons that ar
duction ban
s the band
are called h
lculated from
xp (E-E
F
)/K
in the valen
me crystal m
rom the val
eir momentu
ctors becau
not require
rect and (b)
miconductor
rocesses wit
re excited fr
nd by therm
gap leaves
holes. The n
m the Ferm
KT] (
nce band an
momentum,
lence band
um, P value
use their tran
e a change in
) Indirect tra
r materials
thout the in
from the top
mal energy. T
some vaca
number of e
mi-Dirac prob
(2.5)
nd the mini
, p = 0 and
to the cond
e. Such sem
nsition from
n crystal mo
ansition
. Conducti
fluence of i
p of the vale
The promot
ant electron
electrons ex
bability dis
imum in th
in this case
duction ban
miconductor
m the valenc
omentum fo
on in thes
impurities. I
ence band t
tion of som
n sites in th
xcited acros
tribution as
he
e,
nd
rs
ce
or
se
It
to
me
he
ss
s:
T
d
l
n
h
T
e
t
e
U
t
i
w
b
s
e
d
The Fermi l
den gap. Th
levels at thi
nator of eq.
hence the Fe
Figure
The unity (
exponential
thermal ene
electron occ
F
(E)
Using the b
the electron
n =
in a similarl
p =
where, N
C
,
bands respe
semiconduc
electrons in
density. Sin
np =
level (E
F
)
fo
he probabilit
is point are
(2.5) is equ
ermi level i
e 2.3: Fermi
(1) factor in
term beca
ergy (KT) at
cupying ene
= exp [-E
g
/2
bottom of co
n density in t
N
C
exp [(E
ly way, hole
N
V
exp [- (
N
V
,
are the
ectively. As
ctor contain
n the condu
nce the mass
n
i
2
for an intrin
ty of findin
forbidden.
ual to E
g
/2,
is shown in
i level in an
n the denom
ause of the
t room temp
ergy level E
2KT]
onduction b
the conduct
E
C
-E
F
)/KT]
e density in
(E
F
E
V
)/ K
effective d
each excite
ns an equal
uction band
s action law
nsic semicon
ng an electro
This means
where E
g
is
figure 2.3.
n intrinsic se
minator can
fact that (
perature. Th
E becomes;
(2.
band as E
C
a
tion band ca
(
the valence
KT]
density of st
ed electron
l number o
(i.e. n = p
w is given by
(2.9)
nductor lies
on here is 50
s then that
s the magni
emiconducto
n be ignored
(E - E
F
) va
herefore the
6)
and the top
an then be g
(2.7)
e band can b
(2.8)
ates in the c
leaves behin
of holes in
p = n
i
) wher
y;
s midway in
0% even th
(E - E
F
) in
itude of ene
or
d in compa
alue is larg
e probability
of valance
given by;
be given by
conduction
nd one hole
the valenc
re n
i
is intr
1
n the forbid
ough energy
the denomi
ergy gap an
arison to th
ger than th
y F(E) of an
band as E
V
y;
and valenc
e an intrinsi
ce band an
rinsic carrie
9
d-
y
i-
d
he
he
n
V
,
ce
ic
d
er
2
t
g
d
d
w
e
s
v
E
I
c
e
q
p
(
t
I
a
a
20
this means t
given temp
ductor unde
density can
n
i
= (
where E
g
excited into
states avail
valence ban
Extrinsic S
If a dopant
changes an
energy leve
quantities o
process resu
(electrons)
these electro
If the dopin
atoms are c
acceptor en
that the pro
erature. Th
er thermal e
be written
N
c
N
v
)
1/2
exp
(E
C
E
V
).
o conductio
lable in the
nd move but
Semiconduc
t (impurity)
nd becomes
els are intro
of impurities
ults in n-typ
then the im
ons are call
Figure 2.4:
ng process
called accep
nergy levels
oduct of the
his law is v
equilibrium
as;
p [-E
g
/2KT
When an e
on band by
e conductio
t in a direct
ctors
) is introdu
s an extrins
oduced. The
s to a pure
pe semicond
mpurity atom
led the dono
: Doped sem
a
results int
ptors and th
(E
A
) as sho
(n-type)
two types o
alid for bot
condition. U
] (
external fie
y thermal m
on band. A
ion opposit
uced into a
sic semicon
e process o
semiconduc
ductors due
ms are calle
or energy le
miconductor
acceptor hol
to a p-type
he energy le
own in figu
of carriers w
th intrinsic
Using eq. (
(2.10)
eld is applie
means accel
At the same
e that of the
an intrinsic
nductor. Th
of deliberate
ctor is calle
to the addit
ed donors a
evels (E
D
).
r with a don
le
semicondu
evels of the
ure 2.4 (a). T
will remain
and extrins
2.9) the intr
ed the electr
lerate using
e time the h
e electrons.
semicondu
his is becau
e addition o
ed doping. I
tion of nega
and the ener
nor electron
uctor then t
ese holes ar
The additio
constant at
sic semicon
rinsic carrie
rons that ar
g the vacan
holes in th
uctor then
use impurit
of controlle
If the dopin
ative charge
rgy levels o
n/
the impurit
re called th
on of impuri
(p-type)
a
n-
er
re
nt
he
it
ty
ed
ng
es
of
ty
he
i-
t
i
I
e
i
3
T
f
i
e
i
e
t
l
ties (doping
illustrated in
Figure
In general
energy para
its observed
3.4 (c);
To excite e
from accept
is required.
electrons is
in the same
energy of a
temperature
level holes
g) greatly
n the figure
2.4: (b) Mo
when an e
ameters used
d that their
Figure
electrons fro
tor level int
As shown
approxima
e crystal. W
an impurity
e a large fr
are excited
increases t
2.4 (b);
ovement of
extrinsic sem
d to describ
interactions
2.4: (c) Ene
(b) p-ty
om the don
o valence b
n in figure
ately the sam
When it is
y atom is
action of th
into the co
he conduct
f electrons a
miconducto
be semicond
s can be de
ergy interac
ype doped m
nor level int
band (VB), e
2.4 (c), the
me as the io
compared
very small
he donor le
onduction an
tivity of m
and holes du
or is analys
ductors [(E
c
,
monstrated
ctions in (a)
materials
to conducti
energy know
e ionization
onization en
to the ener
l. This mea
evel electro
nd valence
most semico
uring condu
sed in term
, E
D
, E
F
,
E
A
as shown i
n-type,
ion band (C
wn as ioniz
n energy (E
nergy of ac
rgy gap, th
ans then th
ons as well
band respec
2
onductors a
ction
ms of all th
A
, E
i
, and E
V
in the figur
CB) or hole
ation energy
E
i
) of dono
ceptor hole
he ionization
hat at room
as accepto
ctively. Thi
1
as
he
V
]
re
es
y
or
es
n
m
or
is
22
fraction is much larger than the fraction of electrons excited from the valence
band or that of holes created by these electrons due to the intrinsic process.
The product of the number of electrons in the conduction band and the number
of holes in the valence band must be constant for any semiconductor according
to the law of mass action. For an n-type semiconductor this condition drastical-
ly reduces the number of holes and therefore electrons in the conduction band
become the majority charge carriers. In a similar way, the number of electrons
in the p-type semiconductor is reduced causing the holes in the valence band to
become the majority charge carriers. From the figure 2.4 (c) it can be seen that
the Fermi level (E
F
) with higher donor concentration (E
D
) will move closer to
the bottom of the conduction band and in the same manner the one with a
higher acceptor concentration will move closer to the top of valence band.
Therefore when the semiconductor is under complete ionization condition (i.e.
when n = N
D
and p = N
A
) we obtain the Fermi level in an extrinsic semiconduc-
tor as follows:
In donor case,
E
C
E
F
= KT ln [N
C
/N
D
] (2.11)
in acceptor case,
E
F
E
V
= KT ln [N
V
/N
A
]. (2.12)
Also electron and hole densities in extrinsic semiconductors can then be
expressed as:
n = n
i
exp[(E
F
-E
i
)/KT] (2.13)
p = n
i
exp [(E
i
-E
F
)/KT] (2.14)
If both the donor and acceptor impurities are present simultaneously, the fermi
level must adjust itself in such a way so as to preserve charge neutrality.
23
Semiconductor transport carriers
Carrier transport in semiconductors thin films is temperature sensitive. At room
temperature electrons in a semiconductor are considered to be moving in all
directions. The thermal velocity then at this temperature for any individual
electron is caused by random scattering from collisions with the lattice atoms,
or with impurity atoms, or with other scattering centres or all of them simulta-
neously. If an electric field ( ) is applied to the semiconductor thin film, then
each electron will experience a force from this field and it will be accelerated
along the field (say on x-axis) and a hole in the opposite direction (- x-axis) of
it.
The electrons under this field will have a velocity called the drift velocity, V
d
.
The relationship between the drift velocity (V
d
) of electrons and the electric
field ( ) applied to a semiconductor is then obtained as;
d
=
n
(2.15)
where
n
is the electron mobility and it is given by;
n
= q
c
/m
n
(2.16)
where
c
is the mean free time (the average time between collisions) and m
n
is
the effective mass of electrons. Electron mobility is greater than hole mobility
because of their effective masses i.e. an electron is smaller than a hole. This
equation also applies to drift velocity for holes as:
v
p
=
p
(2.17)
where
p
is the hole mobility. When a transport carrier is under the influence of
an applied electric field ( ) it produces a current called the drift current (J).
Therefore electron current density (J
n
) caused by electron mobility is written
as:
J
n
= qpv
n
= qn
n
(2.18)
and, the holes current density (J
p
) due to hole mobility is likewise given as:
J
p
=qpv
p
= qp
p
(2.19)
24
where, q is the electronic charge, n and p are the concentration of electrons and
holes per unit volume respectively. The total current density (J) in the semi-
conductor sample is given by the sum of electron and hole mobility current
densities:
J = J
n
+ J
p
= ( qn
n
+ qp
p
) (2.20)
This total current summed up can also be written as:
J = (2.21)
Where conductivity, is given by;
= qn
n
+ qp
p
(2.22)
where, is the conductivity of the semiconductor which depends on the
concentration of charge carriers n and p. The numbers of charge carriers are
dependent on temperature in an exponential way and therefore conductivity
increases exponentially and hence the corresponding resistivity which is a
reciprocal of is given by;
= 1/ = [1/{qn
n
+ qp
p
}] (2.23)
Equation 2.22 can be used to describe the conductivity of extrinsic semicon-
ductor especially the doped ones. The only difference is that the number of
electrons in the conduction band and the number of holes in the valence band
are not equal in the case of an extrinsic semiconductor. One of the two (p or n)
dominates depending on the type of the extrinsic process but the mass action
law is maintained as;
(np = n
i
2
)
If both the donor and acceptor impurities are present simultaneously, then the
impurity that is present in a greater concentration determines the type of
conductivity in the semiconductor. Therefore eq. 2.22 can be written for n-type
semiconductor as;
=1/qn
n
(2.24)
and for p-type semiconductor as:
=1/qp
p
(2.25)
25
Sheet resistance, R
s
is an important parameter in thin films and it is used to
characterize both wafers and thin doped layers. It is easier to measure the sheet
resistance rather than the resistivity of thin film materials. The sheet resistance
of a uniformly doped layer with a resistivity, , and thickness, t, is given by
their ratio;
R
s
= /t (2.26)
while the unit of the sheet resistance is Ohms, it is usually referred to as Ohms
per square. This is because when the resistance of a rectangular piece of thin
film material with length, L, and width, W, is to be obtained, it is taken to be
equal to the product of the sheet resistance and the number of squares:
R = R
s
L/W (2.27)
where the number of squares equals the length L, divided by the width, W.
Transport carriers move from a region of high concentration to a region of low
concentration when a spatial variation of carrier concentration exists in any
semiconductor material. Diffusion currents emanates from this random thermal
motion of carriers due to a concentration gradient. This motion causes a certain
current to flow without the influence of an electric field and therefore it
diffuses freely. This current is called diffusion current. This current for electron
carriers (n) can be given by:
J
n
= [qD
n
] dn/dx (2.28)
where, q is the electronic charge, D
n
is the diffusivity and the term dn/dx is the
spatial derivative of the electron density. The diffusivity, D
n
according to
Einstein relation is given as:
D
n
= [KT/q]
n
(2.29)
From eq. 2.20 the diffusion current is proportional to the spatial derivative of
the electron density. When both electric field and concentration gradient are
present, both drift and diffusion currents flow. The total electrons current
density will then be the sum of these two current components:
J
n
= qn
n
E + [qD
n
]dn/dx (2.30)
26
and for total holes current density:
J
p
= qp
p
E [qD
p
]dp/dx (2.31)
The total conduction current density (J
cond
) is given by the sum of eq. 2.30 and
2.31 as:
J
cond
= J
n
+ J
p
(2.32)
Optical phenomena in thin films
When a semiconductor is illuminated photons are absorbed to create electron-
hole pairs if their energy is equal to or greater than the band-gap energy (h =
E
g
). If h is greater than E
g
, then an electron-hole pair is generated and the
excess energy (h E
g
) is dissipated as heat. Both processes are called intrinsic
transitions (or band-to-band transitions). If h is less than E
g
, a photon will be
absorbed only if there are available energy states in the forbidden band gap due
to chemical impurities or physical defects. This process is called extrinsic
transition. This is also generally true when an electron at the conduction band
edge combines with a hole at the valence band edge resulting into an emission
of a photon with energy equal to that of the band gap.
When a film is illuminated by a light source with h greater than E
g
and a
photon flux of
is absorbed, the fraction of the photons absorbed is propor-
tional to the intensity of the flux. Therefore the number of photons absorbed
within distance (d) is given as;
(d) =
e
d
(2.33)
where is the absorption coefficient and is a function of h , d is the film
thickness, the negative sign indicates decreasing intensity of the photon flux
due to absorption. The absorption coefficient decreases rapidly at the cut-off
wavelength
c
given as;
c
= 1.24m /E
g
(2.34)
since the optical band-to-band absorption reduces to become negligible for h
< E
g
, or >
c
. The complex index of refraction is defined as;
27
n
c
= n ik (2.35)
where n, is the refractive index and k, is the extinction coefficient. The complex
index of refraction is related to the velocity of propagation by;
v = c/n
c
(2.36)
The absorption coefficient is related to the extinction coefficient k by;
= 4 k/ , (2.37)
where, is the wavelength of the light in a vacuum. The dielectric constant ( )
is related to conductivity by the relations;
n
2
k
2
= , (2.38)
nk = /v, (2.39)
where, is the frequency, is also defined to be complex as:
i , (2.40)
This then implies that;
n
2
k
2
=
1,
(2.41)
2nk =
1
, (2.42)
The knowledge of n and k determines
1
and
2
, and vice versa. A plot of
versus photon energy hv has generally the same shape as a plot of
2
and n,
because n usually does not vary greatly with energy.
Photoconductivity in thin films
Photoconductivity can be defined as an increase in electric conductivity with
the absorption of light or other suitable radiation and it is experienced in all
semiconducting materials. The change in conductivity (
) upon illumination
results only when absorption of light increases the values of the dark free-
carrier densities n and p and/or the dark mobilities
n
, and
p
. Thus;
= q( n
n
+ p
p
) (2.43)
28
A change in mobility ( ) upon illumination occurs if n and p are not uniform
throughout. Photoconductivity in semiconductors may also be due to either
intrinsic or extrinsic excitations. When the incident radiation has energies
greater than the band-gap energy (E
g
) resulting into a creation of electron-hole
pairs, then it is regarded as intrinsic photoconductivity. Extrinsic photoconduc-
tivity behaviour results when free carriers are photo-excited from impurity
centres with energy levels within the forbidden energy gap.
Thin film applications
Thin films are widely used in a large number of solid state devices. Some of
these applications include photoconduction which is the change in the electrical
conductivity of a substance as a result of absorbing electromagnetic radiation,
xerography which is the process of forming an image by the action of light on a
specially coated charged plate, in electroluminescent devices, piezoelectric
transducers, photovoltaic solar energy conversion and other optoelectronic
devices. The current investigation is the novel applications in which conversion
of solar energy into electrical energy through photovoltaic effect cause photons
that contain various amounts of energy corresponding to different wavelengths
of light according to the expression;
E = hv = hc/ , (2.44)
be converted to electricity where h is Plank's constant and v is frequency of
radiation dependent on wavelength, .
The p-n junction
A p-n junction is a metallurgical and electrical junction between p and n
materials. When the materials are the same, the result is a homo-junction and if
they are dissimilar then it is a hetero-junction. A p-type material contains a
large concentration of holes with few electrons while an n-type material
contains a large concentration of electrons with few holes.
29
A p-n homo-junction
A homo-junction is essentially one semiconductor with two regions of different
conductivity types (n-type and p-type). It is formed at the region where the
conductivity changes from one type to another. This junction can be termed as
an abrupt or graded junction depending on whether the impurity concentration
in the semiconductor changes abruptly or gradually from acceptor impurities
(N
A
) to donor impurities (N
D
)
respectively. If N
A
>> N
D
in thermal equilibrium,
a one-sided abrupt (p + -n) junction is formed and conversely when N
D
>>N
A
,
an (n + -p) junction is formed. While the p-type region contains a large
concentration of holes with few electrons, the opposite is true for the n-type
region.
When we have large carrier concentration gradients at the junction, carrier
diffusion occurs. Holes from the p-side diffuse into the n-side and electrons
from the n-side diffuse into the p-side. As holes continue to leave the p-side
some of the negative acceptor ions (N
A-
) near the junction are left uncompen-
sated since the acceptors are fixed in the semiconductor lattices while the holes
are mobile. Similarly some of the positive donor ions (N
D+
) near the junction
are left uncompensated as the electrons leave the n-side. The charge due to the
ionized donors and acceptors causes an electric field which in turn causes a
drift of carriers in the opposite direction. The diffusion of carriers continues
until the drift current balances the diffusion current thereby reaching thermal
equilibrium and therefore at thermal equilibrium net current flowing across the
junction is zero.
For each type of carrier the drift current due to the electric field must exactly
cancel the diffusion current due to the concentration gradient. For the net holes
current density;
J
p
= J
p
(drift) + J
p
(diffusion) = 0 (2.45)
Similarly, for the net electrons current density;
J
n
= J
n
(dift) + J
n
(diffusion) = 0 (2.46)
3
F
c
I
r
v
f
T
b
a
30
For a condi
constant thr
V
bi
, termed
q
V
V
bi
It is noted t
refer to the
value, and V
fore;
V
Thus, the h
by;
p
no
=
and
n
po
=
ition of zero
roughout th
as the diffu
V
bi
= E
g
[V
i
= {KT/q} l
= {KT/q} l
that at equil
e type of se
V
n
and V
p
V
bi
= KT/q l
= KT/q ln[
hole and ele
= p
po
exp[-q
= n
no
exp[-q
Figure 2.
o net electro
he sample a
usion potent
V
n
+ V
p
]
ln[n
n0
p
n0
/n
i
2
ln[N
A
N
D
/n
i
2
librium, n
no
emiconduct
are the elec
ln[p
po
/p
no
]
[n
no
/n
po
]
ectron densi
(V
bi
/KT)]
(V
bi
/KT)]
5: Drift and
on and hole
as shown in
tial can be e
(2
2
]
2
]
o
p
no
= n
po
p
p
tor and (o)
ctron and h
ities on eith
d diffusion d
e currents, t
n figure 2.5
expressed by
2.47)
(2.48)
(2.49)
po
[where th
refers to t
hole potenti
(2.50)
her side of
(2.51)
(2.52)
directions fo
the Fermi le
5. The built
y the relatio
he subscript
the thermal
als respecti
the junction
or currents
evel must b
t-in potentia
on:
s (n) and (
p
equilibrium
ively. There
n are relate
be
al
p)
m
e-
ed
31
A p-n hetero-junction
This is a junction formed between any two semiconductors having different
energy band gaps. If the conductivity type is the same in any of these two
semiconductors, then it is called an isotype hetero-junction while in an aniso-
type the conductivity type is different in the two semiconductors. The use of a
hetero-junction (HJ) with a large band-gap window material and a small band-
gap absorber material is a means of minimizing surface recombination losses
that might otherwise dominate in direct band-gap materials. Thin film technol-
ogy uses HJ to expand semiconductor material possibilities for solar and
photovoltaic cell applications enormously.
Hetero-face photovoltaic cells [where a p-n homo-junction is interfaced with a
lattice matched material of larger band gap] have achieved extremely high solar
efficiencies. The carrier transport properties of HJs are generally dominated by
phenomena in the interface of p-n region. The current transport in the depletion
layer is usually attributed to recombination, tunnelling, or a combination of
both involving energy levels near the interface. The requirements for the
formation of a good quality hetero-junction are:
(i)
the lattice constant of the two materials should be nearly equal,
(ii)
the electron affinities should be compatible, and
(iii)
their thermal expansion coefficients should be close.
If there is a mismatch of lattice constants and thermal expansion coefficients
then interfacial dislocations at the hetero-junction interface occur which gives
rise to interface states that act as trapping centres.
Photovoltaic cells
The choice of semiconductors for photovoltaic conversion is based on a
number of requirements. Some of the requirements include;
1. A direct band gap with nearly optimum values for either homo-
junction or hetero-junction devices.
2. A high optical absorption coefficient to minimize the requirements
for high minority carrier lengths.
32
3. The possibility of producing n- and p-type material so that the for-
mation of homo-junction or hetero-junction devices is feasible. Most
suitable window materials have an n-type window character and a p-
type absorber needed in a hetero-junction device.
4. A good lattice and electron affinity match with large band gap (win-
dow) materials such as CdS or ZnO so that hetero-junctions with low
interface state densities can be formed.
The above requirements are fulfilled by a number of II-VI compounds. Accu-
rate knowledge of the band gap (E
g
), refractive index (n) and absorption
coefficient ( ) of semiconductors is important for the design and analysis of
various optoelectronic devices. If a p-n junction of a photovoltaic cell is
exposed to the solar spectrum, current flows at zero applied external voltage. In
such a case a photon that has energy less than the band-gap
makes no contribu-
tion to the cell output and the one with energy equal to band gap
contributes an
energy E
g
to the cell output. Energy greater than E
g
is wasted as heat.
What actually happens in the photovoltaic cell when illuminated is demonstrat-
ed in the current-voltage (I-V) characteristics of the junction given by the
equation 2.53:
I = I
s
(e
qV/nKT
-1)-I
L
(2.53)
where the source I
L
results from the excitation of excess carriers by solar
radiation, I
s
is the diode saturation current. In Figure 2.6, the fill factor (FF) of
the cell and the square figure of the power of it show a higher quality cell. Its
square figure portrays good cell parameters.
P
I
a
t
t
W
p
f
T
t
g
P
T
c
n
C
b
p
i
t
Figure
Performan
In the mode
a growing n
the infrared
taic cells ab
When a ph
passes throu
form of a b
This transiti
the properti
grain bound
Photovoltai
The photocu
cell is opera
nated throu
Cd
x
Zn
1-x
S/ P
back electr
photons can
increasing t
the cell is v
2.6: Curren
ce of photo
ern world w
need for thi
d and ultra v
bsorb light (
oton with e
ugh the cell
band-to-ban
ion determin
ies like shor
daries and fi
ic cell oper
urrent gene
ated in the
ugh the wi
PbS that ha
odes, thick
n be reduce
the minority
very rough a
nt-voltage c
ovoltaic cell
where cheap
in film mat
violet region
(photons) fr
energy grea
l, it may be
nd electroni
nes the perf
rt-circuit cu
ill factor (ff
ration
erated in a p
front-wall
indow] par
as been fab
kness of th
d and the c
y carrier dif
and the sur
haracteristi
ls
and clean f
terials with
ns to be use
rom the sun
ater than th
e absorbed
ic transition
formance of
urrent densi
f).
photovoltaic
mode [thro
rticularly in
bricated. By
he absorber
collection ef
ffusion leng
rface topogr
cs of a cell
forms of ene
good photo
ed for photo
n and conve
he band-gap
by the mat
n producing
f a photovo
ity (J
sc
), abs
c cell also d
ough the ab
n hetero-jun
y using high
r material r
fficiency ca
gth. In thin f
raphy is ma
under illum
ergy are nee
oelectrical p
ovoltaic cell
ert them into
p of the sem
terial and th
g an electro
ltaic cell as
sorption coe
depends on
bsorber laye
nction sola
h-reflection
required to
an be increa
film cells th
ade up of py
3
mination
eded there i
properties in
ls. Photovol
o electricity
miconducto
his takes th
on-hole pair
s observed in
efficient ( )
whether th
er, or illumi
ar cells lik
n coatings a
absorb th
ased withou
he surface o
yramids an
3
is
n
l-
y.
or
he
r.
n
),
he
i-
ke
as
he
ut
of
d
34
therefore the actual area of the junction is much larger than the corresponding
geometrical flat plane area.
Since such a surface is non-reflecting, J
L
increases. However the reverse
saturation current also increases with the junction surface lowering V
oc
and FF.
In hetero-junctions a dislocation field at the junction interface arises caused by
lattice mismatch between the two materials counteracting at a space. This
means that the charge state, the capture cross-section, and the density of these
interface states strongly influence the photocurrent through the junction and
hence determine the magnitude of the field. It is also known that matching of
electron affinities is important. The potential barrier height is reduced by the
degree of band mismatch and the total short-circuit current density depends on
the intensity and spectral distribution of the incident radiation striking the thin
film. Different spectra give rise to different carrier generation profiles and
therefore different photocurrent magnitudes.
The design and optimization of a photovoltaic device of any particular material
requires a delicate balance between several conflicting requirements. Since the
basic material properties differ from material to material, no single design is
applicable to all photovoltaic systems and therefore each device design has to
be optimized depending on the material properties. Common loss mechanisms
experienced in most photovoltaic cells range from photon losses, carrier losses,
voltage losses and power losses. Heavy doping is favourable for the top layer
especially when it is the window layer.
It is desirable that it should have low surface recombination velocity and
sufficient thickness to prevent undue series resistance. At the same time the top
contact grid should have sufficient number of grid lines to reduce R
s
but
maintain high optical transmission and good ohmic contacts with a good anti-
reflecting coating or a textured surface to reduce reflection losses. The material
should also be transparent in the active range of the cell, solar spectrum and
impermeable to water vapour and oxygen. The rear contact should be transpar-
ent and highly conducting. The base material should have a long minority
carrier diffusion length if it absorbs the incident photons significantly and
35
sufficient thickness to prevent shorts through grain boundaries. The layer
should be properly doped to allow development of the desired space charge
region and a good electron affinity match with the top absorber layer. The
absorber layer should have low surface recombination, long minority carrier
diffusion length and sufficient thickness to absorb completely near band gap
photons after reflection from the rear contact.
Strengths and limitation of thin films for photovoltaic cells
Thin films have gained a tremendous advantage in the photovoltaic energy
industry because their photovoltaic cells record low costs of fabrication, large
area devices, and even have the possibility of integrating them with other solar
energy conversion devices like light sensors, lasers, xerographic imaging
devices and other optoelectronic devices. Desirable properties like a band gap
(E
g
) in the region of 1.1eV to 1.5 eV for absorber layers, high absorption
coefficient ( ), large minority carrier diffusion length (L), low density of
recombination centres, matching electron affinities and lattice parameters are
easily achieved.
One more advantage of thin film photovoltaic cells is that it is possible to
further develop the tandem structure approach into a more sophisticated
version. A factor which now limits the performance of thin film photovoltaic
cells is the polycrystalline nature of thin films in general. The grain boundaries
present in polycrystalline films provide recombination surfaces for minority
carriers and thus degrade the performance of the device. These grain bounda-
ries affect the device operation by allowing inter-diffusion of certain atomic
species or diffusion of a particular element (dopant) from one surface to
another, creating shorting paths.
36
CHAPTER THREE
OPTICAL SOLID STATE PROPERTIES OF THIN FILMS
In this chapter, a detailed discussion is made on solid state properties of most
types of thin film materials. This ranges from smart window materials to
photovoltaic materials used for both solar cells and solar coatings and ant-
coatings.
Optical and Solid State Properties of Thin Film
The optical and solid state properties studied in this work include: Absorbance
(A), Transmittance (T), Reflectance (R), Absorption coefficient ( ), Optical
density (O.D). Others are the band gap, optical constants, refractive index (n)
,extinction coefficient (k), the dielectric constants- real (
r
) and imaginary (
i
),
Optical conductivity (
o
), dispersion and Electrical conductivity (
e
).
Transmittance
The transmittance (T) of a specimen is defined as the ratio of the transmitted
flux (I
t
) to the incident flux (I
o
) as;
T = (3.1)
Reflection at surfaces are usually taken into consideration, hence transmission
is corrected for reflection and for scattering as well. With the corrections, the
transmittance is called internal transmittance. If a specimen has a thickness d,
an absorption coefficient, and a reflectivity, R, the radiation reaching the first
interface is (1R)I
o
, the radiation reaching the second interface is;
(1R)I
o
exp (- d)
and only a fraction,
(1R)(1R)I
o
exp(- d)
emerges.
The portion internally reflected eventually comes out considerably attenuated.
The end result is that overall transmission is given as:
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