INVESTIGATION OF OPTOELECTRONIC PROPERTIES IN THIN-FILM AND CRYSTALLINE CADMIUM SULFIDE
Mithun Bhowmick
A Thesis
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 2007
Committee:
Bruno Ullrich, Advisor
Lewis P. Fulcher
Robert I. Boughton
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ABSTRACT
Bruno Ullrich, Advisor
Photocurrent (PC), transmission and photoluminescence (PL) properties were measured in cadmium sulfide (CdS). A thin-film (G69) and a single crystal of CdS were used for the measurements. These measured spectra were compared to theoretical values using two different models. In each of the comparisons, a theoretical absorption spectrum was used for the analysis.
Along with these experiments, reflectivity of the material was measured to find the thickness of the film. The PL spectrum was used to determine crystal orientation. Based on these measurements, efficiency of the model as well as the material was verified.
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To my parents, Dinesh Chandra Bhowmick and Renukana Bhowmick.
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ACKNOWLEDGEMENTS
I would like to express sincere gratitude to my advisor, Dr. Bruno Ullrich, for guiding me throughout the entire project. I have learned numerous technical skills from him. His ideas, enthusiasm, and encouragement have made significant changes to this thesis and I am grateful for that.
I would like to thank Dr. Lewis Fulcher and Dr. Robert Boughton for evaluating this thesis as committee members. Their suggestions have made important additions to the thesis and their comments made during discussions were very helpful for me to understand my research.
I feel indebted to Mr. Marco Nordone for his assistance in Mathematica programming.
Additionally, I would like to thank Mr. Chinthaka Liyanage and Mr. Krishna Acharya for their valuable suggestions and help.
I am thankful to Dr. John Laird and the faculty and staff of the Department of Physics and
Astronomy at Bowling Green State University for their continuous support to my graduate education and research. I am also grateful to Mrs. Kimberly Spallinger of ESL department whose valuable comments made this thesis more organized.
Finally, I am grateful to my family and friends for supporting me throughout the academic career.
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TABLE OF CONTENTS
Page
CHAPTER 1 INTRODUCTION ……………………………………………………...... 1
1.1 History of semiconductors …………………………………………………………...1
1.2 Semiconductors : fundamental concepts ………………………………………...... 2
1.3 Purpose of the project ……………………………………………………………...... 3
1.4 Future of semiconductor devices …………………………………………………….4
CHAPER 2 STRUCTURE AND PROPERTIES OF THE SAMPLE USED…………...... 6
2.1 Structure and properties of CdS…………………………………………………...... 6
2.2 An overview of the samples used ……………………………………………………9
CHAPTER 3 INVESTIGATION OF PHOTOCURRENT ……………………………….13
3.1 Theory of photocurrent generation in a photoconductor ……………………………13
3.2 Experimental set-up …………………………………………………………………16
3.3 Results: photocurrent spectra ……………………………………………………...... 19
a] Measurements with CdS thin-film (G69) ………………………………………...19
b] Measurements with CdS single crystal …………………………………………...22
CHAPTER 4 INVESTIGATION OF TRANSMITTANCE ………………………………25
4.1 Theoretical overview of transmittance and absorption coefficient ………………….25
4.2 Experimental setup for the transmittance measurement …………………………….26
4.3 Experimental results …………………………………………………………………27
CHAPTER 5 INVESTIGATION OF PHOTOLUMINESCENCE FROM
SINGLE CRYSTAL ……………………………………………………………………….30 vi
Page
5.1 Theory of photoluminescence: Van Roosbroeck-Shockley equation ……………...... 30
5.2 Experimental set-up for measuring photoluminescence ………………………….....30
5.3 Results ……………………………………………………………………………….31
CHAPTER 6 COMPARISON OF PHOTOCURRENT, TRANSMISSION, AND
PHOTOLUMINESCENCE MEASUREMENTS…………………………………...…...34
6.1 Comparison of calculated and measured photocurrent from thin-film……….…...... 34
6.2 Comparison of calculated and measured transmittance obtained from thin-film……35
6.3 Comparison of measured and calculated photoluminescence data using Van
Roosbroeck-Shockley relation …………………………………………………………..37
6.4 Comparison of photocurrents measured from the thin-film and single crystal…...... 38
6.5 Comparison of Transmission coefficients from thin-film and single crystal………..38
6.6 Comparison of absorption coefficients calculated from the photoluminescence
and photocurrent measurements through the single crystal …………………………….39
6.7 The photocurrent fit obtained for the crystal ………………………………………..40
CHAPTER 7 ANALYSIS AND RELATED DISCUSSIONS ……………………………42
7.1 Discussions on photocurrent data collected and fitted for the thin-film …………….42
7.2 Discussions on the transmittance data collected and compared with theory ………..42
7.3 Analysis of the theoretical and measured photoluminescence from CdS crystal ...... 42
7.4 Discussion on the photocurrent measurements from thin-film and crystal …………43
7.5 Analysis of the plot showing thin-film and crystal transmission measurements ……43
7.6 Calculation of effective thickness of thin-film using transmittance data ………...... 43
7.7 Comparing photoluminescence and photocurrent of crystal through absorption …...44 vii
Page
7.8 Discussion on photocurrent fit found for the crystal ……………………………...... 44
7.9 Determination of the crystal orientation from photoluminescence data …………….44
CHAPTER 8 CONCLUSION……………………………………………………………...46
APPENDIX…………………………………………………………………………………47
BIBLIOGRAPHY…………………………………………………………………………..49
REFERENCES……………………………………………………………..………………50
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LIST OF FIGURES
Figure Page
Figure 1.1: Typical Energy band diagram of a semiconductor …………………………...2
Figure 2.1: A typical zinc blende unit cell …………………………………………...... 6
Figure 2.2: A typical wurtzite unit cell …………………………………………………...7
Figure 2.3: Hexagonal CdS crystal structure ……………………………………………..7
Figure 2.4: Thin film of CdS ……………………………………...... 11
Figure 2.5: CdS crystals used for the measurements …………………………………....12
Figure 3.1: Photocurrent generation in a semiconductor ………………………………..14
Figure 3.2: Top view of a diffractive monochromator ……………………………….....16
Figure 3.3: Path of light rays in a diffractive monochromator ……………………….....17
Figure 3.4: The front panel of lock-in-amplifier (SR 530) …………………………...... 18
Figure 3.5: Internal circuitry of a Lock-in Amplifier …………………………………...18
Figure 3.6: Block diagram of the photocurrent setup …………………………………...19
Figure 3.7: Photocurrent plot from CdS thin-film before correction ……………...... 20
Figure 3.8: Monochromator output plotted for different wavelengths ……………...... 21
Figure 3.9: Responsivity curve of the calibrated diode ……………………...……...... 21
Figure 3.10: Corrected photocurrent from CdS thin-film ……………………………….22
Figure 3.11: Photocurrent from the crystal before correction ………………………...... 23
Figure 3.12: Photocurrent from the crystal after correction ………………………...... 23
Figure 3.13: Magnified part of the plot around the band-gap …………………………...24
Figure 4.1: A schematic diagram of the process inside the spectrometer ……………….26 ix
Page
Figure 4.2: Experimental set up for transmission measurement from crystal …………..27
Figure 4.3: Transmittance plot of thin-film CdS (G69) …………………………………27
Figure 4.4: Transmittance of the CdS crystal …………………………………………...28
Figure 4.5: Experimental set-up for the measurement of reflection coefficient R ……...29
Figure 5.1: Photoluminescence measurement setup …………………………………….31
Figure 5.2 Plot showing the total output data for the PL measurement ………………....32
Figure 5.3 The polynomial which corresponds to the laser line, particularly in the PL region ……………………………………………………………………………………32
Figure 5.4 Subtracted function for the total output spectrum …………………………...33
Figure 5.5 Corrected photoluminescence output after subtraction and magnification ….33
Figure 6.1: Theoretical fit found using Mathematica for thin-film photocurrent ……….35
Figure 6.2: Theoretical absorption spectra used to fit measured PC ……………………36
Figure 6.3: Comparison of theoretical and experimental transmittance ………………...36
Figure 6.4: Normalized theoretical and measured photoluminescence spectra …………37
Figure 6.5: Normalized photocurrent plots for thin-film and single crystal …………….38
Figure 6.6: Normalized transmission plots for thin-film and single crystal …………….39
Figure 6.7: Comparison of absorption coefficients calculated from the PC and PL measurements in a normalized form …………………………………………………….40
Figure 6.8: Photocurrent fit obtained for the measurement using single crystal ………..41
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LIST OF TABLES
Table Page
Table 2.1 Important physical properties of CdS ……………………………...8
Table 4.1 Results from reflectivity measurement ……………………………29
CHAPTER ONE
INTRODUCTION
This chapter deals with the fundamental concepts of semiconductors and the significance of a project involving measurement of optoelectronic properties of semiconductors:
1.1 History of semiconductors
According to their ability to conduct electricity, solids are primarily divided into three groups, i.e., as insulators, metals, and semiconductors. Semiconductors are materials having conductivities in between metals (conductors) and insulators (bad or non conductors). The discovery of selenium photoconductivity in 1870 started the trend which now is called semiconductor device exploration. Even though, the development almost stopped due to widespread use of electronic tubes. The situation changed just before World War II, when investigators started to look for new crystal devices with smaller inter electrode capacitances than electron tubes. In 1949, amplification effects were discovered in semiconductors which led to the development of transistor. Shortly after this, in 1950, Ioffe predicted that gray tin is a semiconductor 1. This inspired many scientists to start investigations of the electrical properties of a large number of binary compounds that belong to the groups of the periodic table equidistant from Group IV. Thus there are fifteen III-V, eighteen II-VI, and four I-VII compound semiconductors summing up to thirtyseven 1, to date.
1.2 Semiconductors : Fundamental concepts
To understand the basic properties of a semiconductor, it is useful to focus on the energy band structure. An energy band structure (sometimes referred to as energy band diagram) is a pictorial representation of different allowed and available 2 energy levels which an electron can occupy. These states are the outcome of the solution of
Schrödinger equation that satisfy the required boundary conditions. The most important concept in the energy band diagram is the shape of the bands and their mutual energy separation.
Following is a rough sketch of a typical energy band diagram of a semiconductor:
E Conduction band
Eg k
Valence band
Figure 1.1: Typical Energy band diagram of a semiconductor
As illustrated in the above diagram, the energy bands have a parabolic shape due to the energy-mass relation E= h 2k2/4 π2 m* , where h is Planck’s constant, k is the wave vector, and m* is the effective mass of the carrier, electrons or holes.
The separation between the highest point of valence band (which is the completely filled band with electrons having highest amount of energy) and the lowest point of the conduction band (which is the unfilled band corresponding to the lowest energy state) is called the band gap
(E g). Depending upon the conservation of the space vector k, semiconductors are termed either direct or indirect materials. In a direct band gap semiconductor, both energy and momentum are conserved. However, for indirect band gap semiconductors the momentum is not conserved and phonons are involved. Phonons are quanta of lattice vibrations which supply the additional 3 amount of energy accounted for the momentum loss. Direct gap semiconductors are useful due for their possible applications in both sensor devices and light emitting devices. Another useful way to classify semiconductors is as intrinsic and extrinsic materials, depending on the purity.
Nowadays, extrinsic (impure or “doped” semiconductors) find more applications due to their flexibility in composition.
Most applications using semiconductors involve the band to band transition of electrons.
When a photon supplies an electron with enough energy (usually equal to or higher than the band gap energy), in a simple case, the electron jumps to the conduction band and contributes to the conductivity of the material, leading to the generation of photocurrent (PC). This property is the basis for developing light active sensors. If the electron returns to the valence band after recombination, then there is a possibility of electromagnetic waves radiation thus giving rise to light generation which is termed photoluminescence (PL). PL is useful in making light emitting devices, typically LEDs and lasers. Other than these two, there are numerous optical and electronic properties for which semiconductor devices are one of the most rapidly expanding fields of research.
1.3 Purpose of the project
Many projects have been started to investigate II-VI compound semiconductors, particularly cadmium sulfide 2 (CdS). In spite of having a relatively large band gap, CdS is suitable for use as a sensor material due to its broad spectral response and sensitivity. CdS is widely used as a detector of radiation in the visible range. The band gap of CdS is approximately
2.44 eV, which corresponds to green light in the visible spectrum, thus making it useful in detecting visible radiation. In 1958, the fundamental absorption edge 4 was measured and the temperature dependent edge shift was reported by Dutton 3. After this, a series of experiments were conducted by researchers to measure the basic absorption processes in CdS. In most of the work, photocurrent or photoluminescence spectra were measured along with transmission spectra, which is another way to understand surface and bulk semiconductor physics. In 1991, probable switching applications using CdS were proposed by Ullrich 4. This observation led to a new concept called “hybrid logic” which uses optical bistable systems to realize logic gates. Thus, most projects have been designed to investigate bistable properties of
CdS in order to make modern data communication and data processing faster. Since there were always some materials which showed greater promise in terms of optoelectronic properties, measurements on the fundamental properties (other than switching) of CdS almost stopped. Even though there was a need to explore the polarization properties of the material, very few experiments had been designed 5. With the invention of the laser, measurements with CdS grew faster and experiments were designed to understand previously ignored facts.
In the current project, the PC and PL spectra of CdS were measured and fitted with the help of a model of absorbance spectra. Thin-film and single crystal CdS were used to measure PC and PL signals respectively. From the measurements, it was possible to determine the effective thickness of the film and that of the crystal. Another interesting feature of a material is its polarization properties. This project is focused on that property by suggesting the probable crystal orientation from the experimental results.
1.4 Future of semiconductor devices
Though researchers have been investigating several possible applications of semiconductors for the last few years, this field is still far from well understood. One of the main reasons is the advent of new technologies. Thus, completion of an existing project is creating opportunities for 5 several new research projects. It is clear from the results of current project that materials like cadmium sulfide deserve more investigations, especially in this era of lasers.
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CHAPTER TWO
STRUCTURE AND PROPERTIES OF THE SAMPLE USED
The material used for the measurements is CdS. This chapter explains various structural aspects and important properties of CdS along with a brief overview of different forms of the materials used.
2.1 Structure and properties of CdS
A semiconductor made of elements from group II and group VI of the Periodic Table is called a II-VI compound semiconductor. CdS and zinc sulfide (ZnS) are typical II-VI compound semiconductors which may take either a cubic zinc blende or a hexagonal wurtzite form, depending upon the thermodynamic parameters. With a band gap of 2.45 eV 5,6 , CdS finds a place in the class of wide gap semiconductors. The wavelength corresponding to the band gap energy is approximately 512 nm, green, i.e. in the visible range of the electromagnetic spectrum, which makes it a potential visible light emitting material. Thus CdS can be used for making light emitting diodes (LED) and lasers.
Figure 2.1: A typical zinc blende unit cell 7
In a zinc blende crystal, like most typical face centered cubic (f.c.c) structures, there are four units of ZnS per unit cell (Figure: 2.1). This structure does not have a
7 center of inversion at the mid-point of a line connecting nearest neighbor atoms. There is a distinction in ZnS in terms of two interpenetrating f.c.c sublattices composed of entirely different atoms, i.e., Zn and S.
Figure 2.2: A typical wurtzite unit cell 7
Wurtzite is the common form of CdS with a hexagonal structure
(Figure 2.2-2.3) with Cd and S atoms stacked together.
Figure 2.3: Hexagonal CdS crystal structure 7
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Typical CdS is a hexagonal, yellowish crystal with specific gravity of 4.82 and Mohs
hardness of 3.8. Some properties of CdS are given below:
Cadmium sulfide
Crystal Color: Yellow/ Orange
General Greenockite , Other names Cadmium(II) sulphide
Molecular CdS formula Molar mass 144.46 g/mol
Yellow-orange Appearance solid.
CAS number [1306-23-6] EINECS 215-147-8 number
Properties
Density and 4.82 g/cm 3, solid. phase Solubility in Insoluble water
Melting point 1750°C at 100 bar Boiling point 980°C subl.
Crystal Hexagonal structure
Table 2.1 Important physical properties of CdS 6
As discussed earlier, CdS can take either the zinc blende or wurtzite form with lattice parameter at room temperature of 0.5833 nm and the X-ray density of 4.835 g/cm 3.
Though the wurtzite form is a high temperature allotrope, it is the common form of CdS.
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Both cubic and wurtzite forms are direct band gap semiconductors with band gaps of 2.31eV and
2.41eV, respectively, at 300 K. The room temperature electrical conductivity for the cubic form varies between 10 -9 S/cm and 10 S/cm. The electron and hole Hall mobilities in undoped n-type bulk wurtzite CdS are between 300 cm 2/V.s and 350 cm 2/V.s. The thermal conductivity of the same crystal is found to be 0.20 W/cm.K.
2.2 An overview of the samples used
In semiconductor research, both thin films and single crystals are widely used for measuring different parameters. In the thin-film deposition technique, a thin layer of material is deposited on a substrate. A typical thin film has a thickness close to one micrometer. According to the nature of the deposition, thin films can either be a chemically deposited, physically deposited type, or a combination of both. In a chemical deposition, a fluid is used to indirectly deposit a solid layer on a surface after undergoing a chemical change. Chemically deposited thin films can be classified further into two sub-groups as plated and chemical vapor deposited (CVD). If a metal-organic chemical vapor is used, the corresponding process is called metal-organic chemical vapor deposition (MOCVD).
On the other hand, a physically deposited thin-film is produced when a solid layer is formed either thermally or mechanically. Most optoelectronic measurements use physically deposited thin films, particularly films formed by physical vapor deposition (PVD). In the PVD technique, the evaporated material is deposited on a relatively cooler surface using either high pressure or heat generated directly or indirectly by an electron gun, a laser system, a plasma gas, or even a simple electrical heater. Several of the techniques currently used are electron beam evaporator, pulsed-laser deposition (PLD), sputtering, or thermal evaporation. In an electron beam evaporator, a high energy beam from an electron gun evaporates a very small part (typically 10 point size) of the material. The entire process is carried out in a vacuum chamber. The rate of deposition in this technique is ideally 10 nanometers per second. The PLD technique relies on a high intensity laser beam to generate enough heat on a material to boil it off from the surface.
The vapor thus produced is then converted to plasma and is deposited on the substrate forming the thin-film. When the plasma of a noble gas (e.g. Argon) is used to displace a layer of atoms from the target material, a sputtered film is formed. Thermal evaporators are probably the simplest of all the above mentioned processes. Here, an electric resistance heater is used to melt the material in a low pressure chamber and the vapor is deposited on the target. The process requires enormous care to avoid impurities or scattering.
There are some processes where a combination of chemical and physical techniques is used.
Reactive sputtering qualifies in this category, along with molecular beam epitaxy and topotaxy.
In reactive sputtering, plasma of the depositing material is produced and then mixed with a non- noble gas before the reaction takes place on the substrate. Molecular beam epitaxy is a very popular technique to form thin films by depositing one layer of atoms at a time. In this process, a stream of slow moving material impinges on the substrate to form a layer of atoms on it.
Repeating the same procedure multiple times produces a film of the desired thickness. Topotaxy is very similar to epitaxy except that the formation of crystalline layers three dimensionally forms the film. A typical thin-film (Figure 2.4) has a layer of coated material over a substrate along with Al contacts for measuring electrical properties (e.g. current or voltage). The thin-film measurements were conducted on a laser ablated 14 cadmium sulfide (CdS, sample number G-69) thin-film with a glass substrate. 11
Figure 2.4: Thin-film of CdS used in the measurement
Crystalline substances can be either single crystals (sometimes called monocrystals) or polycrystals. In a single crystal, the material is uniform in terms of crystal structure and has the same lattice parameters throughout the mass. Single crystals are extremely rare in nature and very useful for their unique chemical, electrical, and electronic properties which make them highly desirable in industrial research projects. Typical single crystals are grown in a number of ways, such as slow evaporation, slow cooling, vapor diffusion, solvent diffusion, sublimation, reactant diffusion, and, sublimation. If the material does not tend to form crystals by any of the above methods, it is recommended to try some complex methods such as ionization to their crystals. Growing perfect single crystals is difficult, but can be avoided by ordering commercial single crystals from various manufacturers. This project does not attempt to focus on the fabrication of the material, rather, it deals with the measurement and analysis of the optoelectronic properties of the sample. 12
Figure 2.5: CdS crystals used for the measurement 8
Figure 2.5 shows two commercial CdS single crystals which can be derived from a huge mass of the same material by specifying the desired dimensions like size, shape etc. The lattice constant and orientation are very important parameters to know for a single crystal. It is possible to order a single crystal with the desired orientation and lattice constant values.
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CHAPTER THREE
INVESTIGATION OF PHOTOCURRENT
This chapter describes the theoretical derivation, methodology, and results of photocurrent measurements made with a thin-film and a single crystal.
3.1 Theory of Photocurrent generation in a photoconductor
A photoconductor is a device that converts the absorbed light into a current that is referred to as the photocurrent. The current is detected by an ammeter. The entire technique is divided into three steps 9:
[1] Absorption of optical energy and generation of carriers.
[2] Transport of generated carriers.
[3] Collection of carriers.
A more detailed qualitative and quantitative description of the process is given in the following section.
The generation of photocurrent depends entirely on the semiconductor and the type of light used.
When photons with greater energy than the bandgap illuminate the material, the material absorbs the light and electron-hole pairs are formed. If the energy supplied is sufficient, then the generated electron jumps to the conduction band, thereby increasing the material conductivity.
For a photoconductor, an applied electric field has to be present which moves the electron (in the conduction band) and holes (in the valence band) in opposite directions. These carriers are collected at the electrodes. This movement of carriers gives rise to the photocurrent which persists until both carriers are collected at the electrodes or until they recombine in the bulk of the semiconductor before reaching the respective electrodes. 14
Quantitatively, the process can be demonstrated (Figure 3.1) by considering a piece of semiconductor of length L and area A with two electrodes to collect the carriers. It is to be noted that the length L is actually the distance between the two electrodes formed on the material.
Figure 3.1: Photocurrent generation in a semiconductor 7
It is clear that the amount of photocurrent is directly proportional to the number of carriers generated in the material, which in turn, varies directly with the amount of light that impinges on the sample. The number of photons incident on the semiconductor per second is Pin /h ν, where
Pin is the incident optical power. If all the incident photons are absorbed, and the carrier generation rate is G, then the internal quantum efficiency of the material is given by,
ηin = G V h ν/ P in (3.01) where V is the volume of the semiconductor. The incident optical power can be used to derive both the dc and ac photocurrent equations. If the optical power is incident on the surface of the material with thickness d, then the light power leaving the sample is,
-αd P(d) = P in e (3.02) where α is the absorption coefficient of the material. Using the above two equations, the quantum efficiency can be rewritten as
-αd η= ηin (1- e ) (3.03) 15
If all the carriers are collected before recom bining, then the photocurrent can be expressed as
Iph = q G V Г (3.04) where q is the elementary charge and Г is the gain which can be written as a ratio of two quantities, the minority-carrier recombination time ( t1) and the transit time of the electrons (t 2).
Thus the gain is given by
Г= t 1/t 2 (3.05)
These two quantities are connected to the mobility of the carriers and are of great importance in determining the sustainability of photocurrent. In this context, the so-called transit time is important
t2= L/ (µn F) (3.06) where F is the electric field applied. Using all the above equations the net photocurrent can be derived as
I ph = q G (t 1/t 2) (1+ µ p/µ n) A L (3.07)
For the derivation of the ac photocurrent the incident power needs to be altered by introducing a complex factor to represent an amplitude modulated signal. It can be proved in this way that the net photocurrent is equal to the summation of two current terms, the dc component given by equation 3.07 along with an ac term.
However, the photocurrent equation used in calculating and analyzing the measurements taken in this project is slightly different in form. In this formula, when light carrying energy hν
13 illuminates a sample having surface intensity I0, the corresponding photocurrent generated is :
I τ − αL 1 I = 0 Aq ([ 1− exp( −αd)] − 1( + SR ) 1 d × 1{ − exp[ −d(α + ]}) (3.08) Ph ν τ α + h Ph Ld 1 Ld
Where A= 2x10 5 cm -1(eV) -1/2 corresponds the saturation value of absorption of CdS, d is the thickness, τSR is the surface recombination time, τPh is the bulk carrier lifetime, and, Ld is the 16 characteristic absorption length. This equation can be derived in different approaches. One of them is given in appendix.
3.2 Experimental set-up :
The photocurrent measurements were done using a standard setup having a monochromator and a lock-in amplifier. In order to understand the function of each component used, it is required to discuss briefly some of their key features.
Monochromator : A monochromator is a device, which can select and transmit a particular wavelength of light from a spectral range. Monochromators can be divided broadly into two categories, according to their principle of operation. A dispersive monochromator uses a prism to separate different wavelengths. However, a diffractive monochromator (Figure 3.2) relies on a diffraction grating for the same action.
Figure 3.2: Top view of a diffractive monochromator 7
In the photocurrent experiment, a diffractive monochromator was used to select a range of wavelengths and corresponding signals were recorded by the lock in amplifier. A typical diffractive monochromator consists of a grating and a pair of spherical mirrors to collimate and 17 focus rays of light. A beam of white light is reflected from the collimator to be incident on a diffraction grating from where it is dispersed into component wavelengths (Figure 3.3). The individual wavelengths are then refocused to form strong
Figure 3.3: Path of light rays in a diffractive monochromator 7 monochromatic beams of light and a desired ray is selected for the measurements.
Lock-in Amplifier : For the photocurrent measurements, an important concern is the amplitude
of the signal from the sample. In the worst case, the signal is obscured by noise with much
greater amplitude than the signal. A lock-in amplifier (LIA) uses a technique called phase-
sensitive detection to separate the desired component of a tiny signal. The process is
accomplished at specific phase and frequency, which is called the reference frequency. In a
typical photocurrent measurement, the reference frequency is set by a mechanical chopper. The
LIA normally measures alternating current signals (A.C) as low as pico-amperes. The output
from the LIA is a vector which refers to a circle in a two dimensional complex coordinate space
for the in phase and the out of phase components of the AC signal. Among the three available
modes (Figure 3.4), the mode “A” gives the actual input, “A-B” determines the potential drop 18
between two specific points ‘A’ and ‘B’ in the circuit. “I” records the current measurements by
converting the obtained voltage using a factor of 10 6 V/A. The photocurrent was measured using
the “A-B” mode using a shunt of 1k Ω.
Figure 3.4: The front panel of Lock-in Amplifier (SR 530) 7
In the phase sensitive detection process, the output ac signal is expressed by the difference in phases of the input signal and reference giving a signal to noise ratio (SNR) of approximately twenty. The sensing of phase is done by a phase locked loop (Figure 3.5) which makes the measurement very accurate due to considerable noise reduction.
Figure 3.5: Internal circuitry of a Lock-in Amplifier 7
The block diagram (Figure 3.6) of the photocurrent setup has a monochromator sending out light of wavelength ranging from 480 nm to 700 nm. The monochromatic ray then passes through the 19 chopper and illuminates the sample, which is connected to the LIA to record the signal that is coming out of it. Both the monochromator and the LIA are connected to a computer through
GPIB bus in order to control and customize the measurements.
Monochromator 460nm Filter Chopper Lens
Sample
Computer Lock-in Amplifier
Figure 3.6: Block diagram of the photocurrent setup
3.3 Results: Photocurrent spectra a] Measurements with CdS thin-film (G69)
Using the above experimental set-up, the photocurrent from the thin-film and the crystal were measured. The PC measurements were taken for different frequencies keeping electric field constant (20 V). The data obtained from the experiment with thin-film are plotted in the figure below: 20
Uncorrected PC spectra 0 .0 0 1 7 1 H Z 1 5 0 H Z 2 7 1 H Z 3 4 8 H Z 0.0 00 8 4 4 5 H Z 5 7 8 H Z 6 7 3 H Z 8 3 5 H Z 0.0 00 6 1000H Z
0.0 00 4
0.0 00 2 Uncorrected thin-film PC(V) thin-film Uncorrected
0 450 500 550 600 650 700 W avelength(nm)
Figure 3.7: Photocurrent plot from CdS thin-film before correction
However, this photocurrent data needs to be corrected because of the variable output of the monochromator. For this purpose, the monochromator output (IPC,Si ) was measured with the help of a calibrated Si diode. In this process, a calibration curve (C) of the diode responsivity was used to correct the photocurrent. The correction formula is
IPC,Corr = I PC,uncorr x C/I PC,Si (3.09)
Figures 3.8-3.10 show the monochromator output, responsivity, and the corrected graph, respectively. 21
0.3
0.25
0.2
0.15
0.1 Si-diode PC (V) PC Si-diode
0.05
0 450 500 550 600 650 700 Wavelength(nm)
Figure 3.8: Monochromator output plotted for different wavelengths
0 .5
0 .4 5
0 .4
0 .3 5
0 .3
0 .2 5
0 .2
Responsivity of the Responsivity of (A/W) Si-diode 450 500 550 600 650 700 W avelength(nm)
Figure 3.9: Responsivity curve of the calibrated diode
22
0.0014 corrected_71 corrected_150 0.0012 corrected_271 corrected_348 corrected_445 corrected_578 0 .001 corrected_673 corrected_835 corrected_930 0.0008 corrected_1000
0.0006
0.0004
0.0002
Responsivity of the thin-film CdS (A/W) thin-filmthe CdS of Responsivity 0 450 500 550 600 650 700 Wavelength(nm)
Figure 3.10: Responsivity of the thin-film CdS b] Measurements with CdS single crystal
The photocurrent obtained from the crystal was corrected in a similar manner as was done in case of the thin-film. Figures 3.11-3.12 depict the photocurrent obtained from the crystal before and after correction, respectively. The photocurrent signal from the crystal was relatively weak around the band gap. For this reason, the lower wavelength part of the entire plot is magnified and represented as a new graph (Figure 3.13). 23
0.02 Uncorrected_1V Uncorrected_2V Uncorrected_3V Uncorrected_4V Uncorrected_5V 0.015
0.01
0.005 Uncorrected single crystal PC(V) single Uncorrected crystal
0 480 520 560 600 640 680 Wavelength(nm)
Figure 3.11: Photocurrent from the crystal before correction
0.01 corrected1V corrected2V corrected3V 0.008 corrected4V corrected5V
0.006
0.004
0.002
0 450 500 550 600 650 700 750 Responsivity of the single crystal CdS (A/W) singleCdS the of crystal Responsivity Wavelength(nm)
Figure 3.12: Responsivity of the CdS crystal 24
corrected1V corrected2V corrected3V corrected4V corrected5V 0.0005
0.0004
0.0003
0.0002 Responsivity (A/W) Responsivity 0.0001
0 480 490 500 510 520 530 Wavelength(nm)
Figure 3.13: Magnified responsivity around the band gap
25
CHAPTER FOUR
INVESTIGATION OF TRANSMITTANCE
The objective of this chapter is to focus on the transmittance measurements and to compare them with the absorption coefficient obtained theoretically.
4.1 Theoretical overview of transmittance and absorption coefficient
The transmittance is defined as the ratio of transmitted to the incident power. The transmittance of a sample depends on α, d, and the reflectivity ( R). Out of these three factors, d and R are almost constant. Thus, the nature of the transmittance spectrum depends mostly on the absorption coefficient. The absorption coefficient can be calculated using the density of states with a careful consideration of the continuity conditions obeyed by the two different functions, the root function (or, the density of states) and the Urbach’s rule. The root function is valid when
10 h ν ≥ E cr , and takes the form
α (h ν) = A hν − Eg , (4.01)
5 -1 -1/2 where A =2 x 10 cm (eV) is the saturation value of the CdS absorption coefficient, Eg is the band gap energy, and Ecr represents the crossover energy at which the two functions meet. Using the slopes of the two intersecting functions, the expression for the crossover energy is obtained 10 ,
Ecr = E g+ kT/(2 σ) (4.02) where kT denotes the thermal energy and σ is a dimensionless phenomenological parameter used for fitting
10 the curve. Urbach’s rule defines the function for the other part of spectrum, i.e., when h ν ≤ Ecr ,
kT σ α(h ν)= A exp[ (hν − E )] (4.03) 2σ kT cr
Using the above expressions for the absorption coefficient, the transmission takes the form 11 :
1( − R)2 exp( −αd) Tr = x 100 % (4.04) 1− R2 exp( −2αd) 26
For a large value of the product αd , the second term of the denominator can be neglected and the expression becomes:
2 -αd T r ≈ (1 − R) e x 100 % (4.05)
4.2 Experimental setup for the transmittance measurement :
The measurement of transmittance of the thin-film was easier than that of the single crystal. A spectrometer was used to measure the transmittance in a way very similar to the photocurrent measurement (Figure 3.6). The wavelengths were controlled by the computer and the corresponding transmittance was recorded for each wavelength.
To Source Computer after receiving
Figure 4.1: A schematic diagram of the process inside the spectrometer
However, the crystal did not fit into the cavity of the spectrometer very well, and so an different method was employed to measure the transmission. The sample was illuminated by the output of the monochromator (Figure 4.2) and then the transmitted signal was traced by a combination of calibrated silicon diode and a lock-in amplifier. Thus the signal recorded by the lock-in amplifier is only the transmitted part from the sample. This setup is almost the same as the photocurrent measurement except for the presence of the diode. Also, instead of measuring current or voltage, the transmitted light through the sample was measured after exciting it by monochromatic light.
27
Lens Monochromator 460nm Filter Chopper
Sample
Diode
Computer Lock-in Amplifier
Figure 4.2: Experimental set up for transmission measurement from crystal
4.3 Experimental results
The transmission of the thin-film for different wavelengths when plotted takes the form shown in figure 4.3.
80
60
40
20
0 Thin-film transmission (%) Thin-film
-20 100 200 300 400 500 600 700 800 900 Wavelength (nm)
Figure 4.3: Thin-film CdS (G69) transmission 28
The transmission through the crystal took the form shown below (Figure 4.4). The range of wavelengths used was different due to the different methodologies used for the measurements.
As discussed earlier, the thin-film measurement was taken using the spectrometer. However, the crystal measurement shows the data collected by using the diode-sample combination.
Apart from these two measurements, a set of data was recorded to measure the reflection coefficient R. The experimental set-up used contained a laser source, a calibrated diode, a beam splitter, and an ammeter (Figure 4.5).
15
10
5 Transmission (%) Transmission
0 450 500 550 600 650 700 Wavelength (nm)
Figure 4.4: Transmission of the CdS crystal 29
Laser Beam-splitter Sample Diode
Diode Ammeter
Figure 4.5: Experimental set-up for the measurement of reflection coefficient R. The dotted line represents a reflected beam focused on the diode.
The results obtained from the above experiment are given in the table (Table 4.1) below:
Input Reflected Average Average Reflectance % R
signal signal Input (mA) reflected
(mA) (mA) (mA)
0.369 0.061 0.39 0.0881 0.225897 22.59
0.375 0.093
0.397 0.106
0.406 0.0945
0.403 0.086
Table 4.1: Results for the reflectance measurement
30
CHAPTER FIVE
INVESTIGATION OF PHOTOLUMINESCENCE FROM SINGLE CRYSTAL
This chapter concentrates on the photoluminescence properties of cadmium sulfide crystal.
5.1 Theory of photoluminescence: Van Roosbroeck-Shockley equation
As in the case of the transmission, the photoluminescence spectrum depends on the absorption coefficient. With the help of the root-function and Urbach’s rule, discussed in the previous chapter (equations 4.01-4.03), the photoluminescence model given by Roosbroeck-Shockley takes the form:
(hν )2α(hν ) I (hν ) ∝ 0 ν − exp( h / kT ) 1 (5.01) where I0(h ν) is the emitted spectrum for a particular value of energy E (=h ν), α is the absorption coefficient, k is the Boltzmann constant, and Tc is the carrier temperature. Equation 5.01 is valid only for thin-films. For a sample of effective thickness d, the formula has to be slightly changed.
Assuming uniform recombination inside the crystal, the emitted intensity spectrum in a specific direction can be written as 12 :
1{ − exp( −α(hν )d)} I(hν ) ∝ I (hν ) 0 α ν (h )d (5.02)
Finally, substituting equation 5.01 in 5.02, the required photoluminescence formula becomes:
(hν )2 1{ − exp( −α(hν )d)} I(hν ) ∝ [exp( hν / kT ) − ]1 d c (5.03)
5.2 Experimental set-up for measuring photoluminescence
For the photoluminescence (PL) measurements an Argon laser was used, since the bandgap of the material is approximately 514 nm or 2.45 eV. A 458 nm interference filter was used to transmit the desired emission from the Argon laser output. Then a convex lens focuses the light 31 to a point at the edge of the crystal. As a result, PL was generated by radiative recombination process, i.e., when an electron-hole pair recombines to form light.
LASER CdS crystal
Interfer ence PL signal filter or prism
Optical Fiber
Figure 5.1: Photoluminescence measurement setup
The output signal was collected by an optical fiber connected to the computer. The most difficult part of this experiment was to determine the exact location of the optical fiber since the signal coming out from the crystal is very faint. The weak PL signal made the analysis difficult. Since the detected laser output was too strong when compared to the measured signal, consistent effort was made to distinguish the desired signal from the laser line.
5.3 Results
The PL measurement of the CdS single crystal is shown below (Figure 5.2). It is clear from the
plot that the PL signal obtained was much smaller than the laser line used. This problem was
solved by fitting a curve which takes the laser line as a background or baseline signal (Figure
5.3) and then subtracting the same from the whole spectrum (Figure 5.4). In this procedure, care
was taken to distinguish the PL spectra from the laser background and the fitting was done for 32 the extracted PL signal only.
5 0 0 0
4 0 0 0
3 0 0 0
2 0 0 0 PL
1 0 0 0 PL (arb. PL units)
0
-1 0 0 0 100 200 300 400 500 600 700 800 900 W avelength(nm )
Figure 5.2 Total output data for the PL measurement
1 1 0 4
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0 Plolynomial Function Plolynomial Fitted
0 100 200 300 400 500 600 700
W avelength(nm)
Figure 5.3 Polynomial fit for the laser background 33
4 0 0 0
2 0 0 0
0
-2 0 0 0
-4 0 0 0
-6 0 0 0 SubtractedFunction
-8 0 0 0
-1 1 0 4 100 200 300 400 500 600 700 800 900 W avelength(nm)
Figure 5.4 Difference between the measurement and the polynomial fit for the whole spectrum.
However, after magnifying the desired region of the spectrum, the output shows significant improvement (Figure 5.5).
400
350
300
250
200
150
100
50 Magnified Subtracted Function MagnifiedSubtracted
0 490 495 500 505 510 515 520 525 530 Wavelength(nm)
Figure 5.5 PL after correction and magnification 34
CHAPTER SIX
COMPARISON OF PC, TRANSMISSION, AND PL MEASUREMENTS
This chapter compares the measurements taken and plotted in the previous three chapters.
6.1 Comparison of calculated and measured photocurrent from thin-film
To determine the agreement between the theoretical and measured PCs, an equation was derived involving the absorption coefficient, the response time, and the lifetime of carriers. Then it was used to fit the data with the help of Mathematica. After adjusting the values of two fitting parameters A and σ, the fit obtained shows good agreement with the measured values (Figure
6.1). Details of the different variables and fitting parameters are given below.
5 -1 -1/2 The band-gap was taken to be Eg= 2.44 eV with A= 2 x 10 cm (eV) , dimensionless
-4 -4 phenomenological parameter σ = 0.4, thickness d = 1 x 10 cm, absorption length Ld = 1 x 10 cm, surface recombination time τSR = 0.8 µsec, kT = 25 meV, and carrier lifetime τPh = 1 µsec. At this point, the value of d was assumed. Later, the accurate value
(2.69 x10 -4 cm) was measured using the transmission data.
35
PC (arb. units)
Responsivity Harb. units L Figure 4. Theoretical Fit for CdS Responsivity H1000 Hz L
1
0.8
0.6
0.4
0.2
Energy HeV L 2 2.2 2.4 2.6
Energy (eV)
Figure 6.1: Theoretical fit found using Mathematica for thin-film photocurrent. Energy in eV is plotted along X-axis and photocurrent in arbitrary units is plotted along Y-axis. The solid line represents the theoretical points and the dots are experimental data.
6.2 Comparison of calculated and measured transmittance obtained from thin-film
The absorption coefficient calculated to fit the photocurrent spectrum is shown in figure 6.2.
These absorption values were used to calculate the theoretical transmittance. The next step was to compare the theoretical and measured transmittance plot using the same set of axes (Figure
6.3). 36
4 1 0 5
3 1 0 5
2 1 0 5
1 1 0 5
0 Absorption coefficient (percm.) coefficient Absorption
-1 1 0 5 1 2 3 4 5 6 7 Energy (eV)
Figure 6.2: Theoretical absorption spectra used to fit measured PC
Calculated Transmission from Absorption Measured Transmission
0 .7
0 .6
0 .5
0 .4
0 .3
0 .2 Transmittance
0 .1
0
-0 .1 2 2.2 2.4 2.6 2.8 3 Energy (eV)
Figure 6.3: Comparison of theoretical and experimental transmittance
37
6.3 Comparison of measured and calculated photoluminescence data using
Van Roosbroeck-Shockley relation
The normalized PL data were plotted with the theoretical PL values to examine their agreement.
For calculating the theoretical PL spectra, Roosbroeck-Shockley relation was used. In the graph below, only a part of the total spectrum is shown to closely investigate the correlation between theoretical and experimental values (Figure 6.4).
Measured PL (normalized) Calculated PL (normalized)
1.2
1
0.8
0.6
0.4
PL (normalized) PL 0.2
0
-0.2 2.3 2.35 2.4 2.45 2.5 2.55 2.6 Energy (eV)
Figure 6.4: Normalized theoretical and measured PL spectra
38
6.4 Comparison of responsivities measured from the thin-film and single crystal
The photocurrent measurements were plotted on a graph after normalization. For convenience, photocurrent data corresponding to a small wavelength range (Figure 6.5) is magnified and plotted using the same set of axes.
normalized_crystal_PC normalized_thinfilm_PC
1.1
1
0.9 (b)
0.8
0.7
0.6 (a) Normalized responsivity units) (arb. Normalized 0.5 480 490 500 510 520 530
Wavelength (nm)
Figure 6.5: Normalized PC plots for (a) thin-film and (b) single crystal
6.5 Comparison of Transmission coefficients from thin-film and single crystal
The transmittance data collected for the thin-film and single crystal was plotted after normalization. Since the two transmission data were collected by different methods, the set of axes used to plot them were slightly different. However, after rescaling the plots, this ambiguity was removed (Figure 6.6). 39
crystal Transmission normalized Thin-film Transmission normalized
Wavelength for thin-film data (nm) 450 500 550 600 650 700
1 1 Thin-film (normalized)Transmittance
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2 Crystal Transmittance (normalized) Transmittance Crystal 0 0 450 500 550 600 650 700 Wavelength for crystal data (nm)
Figure 6.6: Normalized transmittance plots for thin-film and single crystal
The fringes in the thin-film measurement and the reflection data presented in chapter four were used later to find the thickness “d” of the film.
6.6 Comparison of absorption coefficients calculated from the photoluminescence and photocurrent measurements through the single crystal
The PL and the PC measurements for the crystal were fitted using respective absorption coefficients. Figure 6.7 shows a comparative plot of the two absorption associated coefficients.
40
Absorption from crystal PL (cm^-1) Absorption from crystal PC (cm^-1)
8 10 4
6 10 4
4 10 4
2 10 4
0
-2 10 4 2.35 2.4 2.45 2.5 2.55 2.6 Absorption coefficient of the crystal (cm^-1) crystal the of coefficient Absorption Energy (eV)
Figure 6.7: Comparison of absorption coefficients calculated from the PC and PL measurements in a normalized form.
6.7 The photocurrent fit obtained for the crystal
Using the absorption calculated in section 6.6, a photocurrent fit was obtained for the crystal data. The plot (Figure 6.8) was rescaled for the two datasets and does not use same coordinate axes.
41
Fitted PC from absorption coefficient Crystal PC for 5V
3 10 -14
0.00045 2.5 10 -14 Theoreticalresponsivity
0.0004 2 10 -14 (arb. units)
1.5 10 -14
0.00035units) (arb.
1 10 -14
0.0003 5 10 -15 Responsivity from PC frommeasurement PC Responsivity
0 2.4 2.42 2.44 2.46 2.48 2.5 Energy (eV)
Figure 6.8: Photocurrent fit obtained for the measurement using single crystal
42
CHAPTER SEVEN
ANALYSIS AND RELATED DISCUSSIONS
7.1 Discussions on photocurrent data collected and fitted for the thin-film
The PC measurement was compared to the theoretical results using Mathematica. To fit the theoretical curve accordingly, a phenomenological parameter σ was used. For σ = 0.4, the best fit was obtained. The two curves were represented simultaneously in a graph to illustrate the fitting
(Figure 6.1). The correlation between the two plots is close to 100% which validates the appropriateness of the theory used. Another important observation is the value of the fitting parameter found. In future, the same method can be used to find a fit of photocurrent spectra for other samples.
7.2 Discussions on the transmittance data collected and compared with theory
The absorption coefficients (used to fit the PC measurement of the thin-film) were used to find a transmittance dataset and taken as theoretical transmittance. The plot comparing theoretical and experimental transmittance (Figure 6.3) shows a good correlation. The band-gaps found from the two plots were 2.434 eV (509.38 nm) and 2.428 eV (510.64 nm) respectively, which showed good agreement between the theory and experiment.
7.3 Analysis of the theoretical and measured photoluminescence from CdS crystal
The theoretical PL data were calculated using a complete theoretical absorption spectra and Van
Roosbroeck-Shockley equation. This yielded a band-gap of 2.453 eV (505.44 nm). The measured photoluminescence plot showed a band-gap at 2.467 eV (502.57 nm). Most of the points from the two dataset showed same shape after normalization and thus agreement between theory and experiment was successfully confirmed (Figure 6.4).
43
7.4 Discussion on the photocurrent measurements from thin-film and crystal
In figure 6.5, the normalized plots were presented showing responsivity spectra from a thin-film and a single crystal of CdS. The PC peaks were obtained at 508.05 nm and 498.05 respectively.
The magnitude of the PC obtained in the crystal was much smaller than that obtained from the thin-film. In spite of showing a shift in band-gap energy, the shapes of the two curves are fairly similar. Thus the two experiments are, to some extent, verified.
7.5 Analysis of the plot showing thin-film and crystal transmission measurements
Transmittance of the thin-film was measured using a spectrometer. However, due to the inconvenient size and shape of the crystal, a different method was employed for measuring crystal transmission. The measurement with the thin-film yielded excellent data showing almost every feature that was expected. On the other hand, transmission from the crystal was slightly steeper, as it was expected. For a single crystal the band gaps found from the two sets were
509.94 nm (thin-film) and 517.25 nm (crystal).
7.6 Calculation of effective thickness of thin-film using transmittance data
The thin-film transmittance data was used to determine the film thickness. The thickness of a thin-film can be calculated using the combined interference formula
λ λ d = 1 2 (7.01) λ − λ 2n( 1 2 ) where d = thickness of the film, n= refractive index of the material, λ1= interference fringe of order m, λ2= fringe of order (m+1).
Considering adjacent minima as fringes, λ1=713.07 nm, λ2 = 753.01 nm, n= 2.5, the thickness calculated from equation 7.01 was,
d = 2.69 µm
44
7.7 Comparing PL and PC of crystal through absorption
Figure 6.7 shows a comparison of absorption coefficients calculated from fitting two different measurements. One of them is the PL measurement of the crystal. The other is the PC measurement of the crystal. The fitted absorption curve for the PL measurement has a band-gap at 2.453 eV, whereas the absorption spectra found during the fitting of PC measurement shows a band-gap at 2.435 eV. The corresponding cross-over energies are 2.459 eV and 2.440 eV, respectively. The shift of 18 meV in the band-gaps can be taken as a result of mixed orientation.
The PL data corresponds to a mixed orientation causing the shift between the absorption spectra.
7.8 Discussion on PC fit found for the crystal
The PC fit found for the crystal is not as good as it was for the thin-film measurement. There are several reasons which might have contributed in the fitting procedure. First, the PC signal from the crystal was overwhelmed by the impurity PC. Thus the fundamental peak was almost invisible, though it showed slight improvement after correction. Another possible reason is the method of measurement. In this case, the PC spectra were measured from two opposite faces of the crystal instead of measuring from the surface, which was the case when PC from thin-film was measured. Finally, the calibrated diode may be considered a possible source of error for having a peak around the band-gap of CdS. For this reason, the PC correction process suffered at the band gap region. In spite of all these possible error sources, the fitted curve has significant correlation with the measurement.
7.9 Determination of the crystal orientation from PL data
As an attempt to determine the crystal orientation, the absorption coefficient calculated during the comparison of PL data was compared separately to the standard plots of absorption coefficients 3 of crystalline CdS with parallel and perpendicularly oriented crystal axes. The 45 absorption coefficient of the crystal at 300 K corresponding to the band-gap found (2.453 eV) is
4x10 4 cm -1. In the standard plot, the parallel crystal shows a value of 1x10 4 cm -1 as compared to a value of 5x10 4 cm -1. From these values, it can be predicted that the PL signal is neither linked to the perpendicular nor parallel orientation of the crystal and was caused by the experimental alignment.
46
CHAPTER EIGHT
CONCLUSION
Thin-film and single crystal CdS were used for PC and transmission experiments; PL was also measured on the crystal.
The PC and transmission measurements showed good agreement for the thin-film. The thin-film used was a PLD sample. Thus, the optoelectronic sensor potential of such materials was confirmed.
The PL and PC measurements were in agreement for the crystalline sample. Using the Van
Roosbroeck-Shockley equation and a standard PC equation, the PL and PC data were fitted.
Notably, these two different models yielded similar absorption coefficients during analysis.
Thus, the measurements were successfully confirmed. Using this verified information from the
PL measurement of the crystal, an approach was made to determine crystal axis of the sample.
After comparing the data with standard results, it was found that the crystal should have a perpendicularly oriented axis. However, the band gap and absorption coefficient found differed slightly from the typical values of a perpendicular crystal, due to the experimental arrangement of the PL setup.
To summarize, important optical parameters of thin-film and crystalline CdS were determined in this project.
47
Appendix
Derivation of the standard PC equation
If energy supplied by a photon= hν ( h= Planck’s constant, ν = Frequency) surface intensity = I0, Absorption coefficient = α, Effective thickness = d, surface recombination time = τSR , carrier lifetime = τPh , and characteristic absorption length = Ld, the corresponding generation rate is given by 13
G(z) = R( surface, z) + R( bulk, z) +R(impurity, z) (1) where, R represents the recombination rate and the second parameter gives the direction of consideration. The photocurrent is given by the integration over the thickness of the layer by evaluating
d = I Ph A∫ dj (z) , ( j= current density) (2) 0 with
dj (z) = q[G(z) − R(z)] dz (3)
R(z) τ − = 1( + SR ) 1 exp( −z / L ) (4) τ d G(z) Ph and
I G(z) = 0 α(hν )exp[ −α(hν )z] (5) hν
Assuming
τ = τ + τ 1{ − exp( −z / L )} SR Ph d (6) 48 the photocurrent can be derived by evaluating
d = τα −α I Ph ∫ exp( z)dz (7) 0 which, after a few rearrangements, gives
1 −d (α + ) τ −α τ − α I = τ 1( + SR )[( 1− e d ) − 1( + SR ) 1 1{ − e Ld }] (8) Ph Ph τ τ α + Ph Ph Ld 1
49
BIBLIOGRAPHY
• Singh, J., Semiconductor optoelectronics: physics and technology, (McGraw-Hill: New
York, 1995).
• Adachi, S., Optical properties of crystalline and amorphous semiconductors: materials
and fundamental principles , (Kluwer Academic Publishers: Massachusetts, 1999).
• Heavens, O. S., Optical properties of thin solid film, (Dover Publications Inc., New York
1995).
• Sze, S. M., Modern semiconductor device physics, (Wiley and Sons, New York 1998).
• Rosencher, E., Vinter, B., optoelectronics, (Cambridge University Press: Cambridge,
UK; New York, NY, 2002).
50
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