Tandem Solar Cell

8/13/2019 Tandem Solar Cell

1/67

Tandem Solar CellsDemonstration of tandem solar cell based on GaAs/GaInNAs/GaAsBi

Umair Ahmad Nasir

Supervisor: Prof. Naci Balkan

Date: August 2013

A thesis submitted for Masters in Electronic Engineering

Department of Computer Science and Electronic EngineeringUniversity of Essex

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


2/67

i

Acknowledgment

In the name of ALLAH, the Most Beneficent and the Most Merciful, Alhamdulillah, allpraises to ALLAH for the strengths and His blessing in completing this dissertation. I wouldexpress my sincere gratitude to my supervisor Professor Naci Balkan, for his supervision,advice and motivation throughout my research project.I am very grateful to my family for their support both emotionally and financially. My special

thanks go to Mr. Adrian Boland-Thoms for helping in clean room and the smooth running ofthe experiments by providing the benefit of his many years of experience and technicalexpertise with semiconductor devices and fabrication. I extend my thanks to the members ofthe Optoelectronics Research group whom helped in keeping up my morale when things werenot going smoothly.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


3/67

ii

Abstract

The efficiency of the single band gap solar cell is limited to 33% for the standard air mass 1.5(AM1.5) spectrum according to detailed balance limit given by Shockley and Queisser in1961. Tandem solar cells solar cells with several junctions of different energy gaps canimprove the efficiency of PV cells. The ability of GaInNAs and GaAsBi semiconductors tohave considerably lower band gaps than GaAs and to remain lattice matched with GaAs

makes them attractive materials for tandem solar cells.In the first part of this project band anti crossing model is used that enables us to show theband gap reduction effect in the GaAsN due to downward shifting of the conduction with theaddition of nitrogen content. In addition to this valence band anti crossing model is used toexpress the reduction in the GaAsBi band gap due to the upward shifting of valence band andincrement in the spin orbit splitting with the increase in the concentration of bismuth content.In the end a comparison is also done between band gap reduction effects in dilute nitride and

dilute bismide with the increase in the concentration of nitrogen and bismuth.

In the second part of this work we investigate GaInNAs, GaAsBi multiple quantum well andGaAs control solar cells. Initially the fabrication of GaInNAs, GaAsBi MQW and GaAscontrol cell is carried out in the clean room. After fabrication process current-voltage (I-V)and spectral response measurement were conducted for all solar cells. The GaInNAs deviceexhibit efficiency of 3.6% with the fill factor of 38% at AM1.5 G. The GaAsBi and GaAscontrol cells does not shows any diode like characteristics in dark and under illumination.Spectral response measurements performed on the GaInNAs MQW samples express that theirspectral response is prolonged to the effective band gap of the GaInNAs quantum wells. Onthe other side the GaAsBi solar cells exhibits a small response only for wavelength near theband gap of GaAs and it is also not extended to the higher wavelength, which indicates thepoor quality of the dilute bismide layers in the intrinsic region of the MQW solar cells.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


4/67


5/67


6/67

1

1 IntroductionThe increase in world energy consumption and the reduction of conventional energy sourcesdemands a renewable, infinite and economical energy source. World energy consumption ispredicted to grow by 56% between 2010 and 2040. The total world energy use will rise from1.53 1018 J (1.53 EJ) in 2010 to 1.84 1018 J (1.84 EJ) in 2020 and to 2.39 1018 J (2.39EJ) in 2040 [1].Currently fossil fuels supply almost 80 % of world energy while renewable energy sourcesaccount for 14.3 % and nuclear power for 5.7 % [2]. Renewable energy is the world's fastestgrowing energy source, increasing by 2.5 % per year [1].One of the most suitable ways to cope with the worlds energy crisis is to use the solarenergy. The solar energy reaching earth every day is over 1.5 1022 J (15000 EJ), while thedaily world energy consumption is equal to approximately 1.3 EJ [3]. Photovoltaic devices

specifically are receiving wide attention, as they can convert solar radiation into electricalpower.The efficiency of the single band gap solar cell is limited to 33% at band gap (Eg) of around1.4eV for the standard air mass 1.5 (AM1.5) spectrum according to detailed balance limitgiven by Shockley and Queisser in 1961 [13].The multiband gap solar cells with several junctions of different energy gaps attractedincreasing attention to improve the efficiency of PV cells because each of them can convertsolar energy into electricity more efficiently and permit to achievement of solar cellefficiencies beyond the Shockley Queisser detailed balance limit for a single junction [3].

Up to the present time the GaAs based tandem cells have the highest efficiency, achievingefficiencies of 35.8 % for global AM1.5 (1000 Wm-2) and 42.3 % for the direct beam AM1.5spectrum at a cell temperature of 25oC [4].GaAs has the significant property of alloying with other group III and V elements. In 1995Kondow et al. revealed that incorporation of a small amount of nitrogen in GaAs causes alarge band gap reduction effect by lowering the conduction band. In a similar way to thedilute nitrides, the addition of Bismuth in III V semiconductors (e.g. GaAs) is expected todisplay a valence band anti-crossing effect causing a large band gap bowing [21]. The abilityof dilute nitride (GaNAs) and dilute bismide (GaAsBi) to have significantly lower band gapand to be lattice matched with GaAs makes them interesting material for III-V tandem solarcells.The aim of this thesis is to design, fabricate and study a three junction tandem solar cell,GaAs /GaAsBi/GaAsN.This dissertation is structured in the following sections:

Chapter 2 presents most of the key background topics and reviews beginning with the solarspectra, fundamental concepts of semiconductors, PN junction, solar cell equivalent circuitsand the operation and main design characteristics of single band gap, tandem solar cells. Thegrowth techniques and properties of dilute nitrides and dilute bismide alloys will bediscussed. In the end, reviews about the design of the GaAs solar cell are presented.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


7/67

2

The fundamental experimental techniques used in this project to investigate both electricaland optical properties of the GaAs, dilute nitride and dilute bismide solar cells are containedin Chapter 3. It starts with reviews of epitaxial growth techniques and moves on to molecularbeam epitaxy. The processes used to fabricate a hall bar and mesa structures on the solar cells

and the various experimental techniques used in the research are also explained in detail.In chapter 4, the theory of the band gap bowing effect in dilute nitrides and dilute bismides isexplained using the conduction band and valence band anti crossing model respectively.The performance of GaAs/GaAsBi/GaInNAs solar cells is evaluated by AM1.5G IVcharacteristics and spectral response measurements in chapter 5. In order to evaluate thecarrier density and mobility in the GaAs solar cells, study is carried out using Hallmeasurement.Chapter 6 presents the conclusions of the work undertaken, and gives suggestions for futurework on dilute bismide and dilute nitride tandem solar cells.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


8/67

3

2 Background

2.1 Solar SpectrumThe photovoltaic cells convert light energy incident on them into electrical energy. Accordingto Planks theory light is made up of quanta of energy, known as photons. The energy ofphotons depends (inverse relationship) only on the frequency of light. In the solar cellapplications, usually the source of light is the sun. The nuclear fusion reactions at the sun areresponsible to produce light ranging from the ultraviolet & visible to infrared wavelengthsportion of the electromagnetic spectrum [5].

The temperature at the surface of the sun is about 6000K. The extra-terrestrial spectrumresembles black body spectrum at 5760K. A blackbody absorbs all radiation incidents on itssurface and releases radiation depending upon on its temperature. The blackbody sources that

emit light in the visible region are attractive for photovoltaic cells. The spectral irradiancefrom a blackbody can be expressed following function [7];

(2.1)where: is the wavelength of light,T is the temperature of the blackbody, andh, c and kare constants.

Figure 2.1 : Black body spectrum compare with AM0 and Am1.5 Spectrum [6]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


9/67

4

The amount of the radiant energy received from the sun per unit area per unit time as afunction of wavelength is called solar irradiance [5]. The solar irradiance is strongest in thevisible wavelength range (300 - 800 nm) with maximum value in the blue to green range. Thepower density of the solar radiation on the surface of the Sun is 62 MWm-2. This density is

reduced to 1353 Wm-2

at a point outside the Earths atmosphere. When light passes throughthe atmosphere, some portion of light are absorbed and dispersed by numerous atmosphericelements, so that the spectrum received at the surface of earth has attenuation at differentpoints. Oxygen, Ozone and Nitrogen filter out the light with wavelength less than 300nm.Water and CO2 are mainly responsible for the absorption of the infrared and in consequenceproduce the sudden drops in the spectrum at 900, 1100, 1400 and 1900 nm (due to H2O) andat 1800 and 2600 nm (CO2) [5].

The attenuation of the spectrum is dependent on the distance the light travels through theatmosphere, therefore is dependent on the location on the earth surface and the earths

position in orbit. The solar light spectrum is defined by the air mass index (AM). It is theratio of the path length of the solar radiation through the atmosphere at a given angle to thepath length when the sun is directly overhead [7].

!"#$ (2.2)

Figure 2.2 : The air mass representing the portion of atmosphere that the light passes (Y) before reaching

the Earth comparative to overhead path length (X) [7]

The standard spectrum is Air Mass 1.5 or AM1.5, when the sun is at angle of elevation of420. The solar spectrum is attenuated to a mean irradiance value of almost 900Wm-2 due tothe atmospheric thickness. However, the standard spectrum (AM1.5) is regulated to1000Wm-2because of the convenience of the round number and due to the fact that there arenatural variations in incident solar light [5].

The performance of a PV cell depends on both the power and the spectrum it receives. TheAmerican Society for Testing and Materials defines different standard (AM0, AM1.5G andAM1.5D) spectrums. The standard spectrum AM0 is used to evaluate the performance of

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


10/67

5

solar cells for space applications. The AM1.5G and AM1.5D spectrums are used to predictthe solar cells performance on the Earths surface. The letter D (direct) declares that thisspectrum contains only the direct radiations and letter G (global) includes the direct as well asthe scattered radiation. AM1.5G is used for conventional terrestrial cells; while when

designing a concentrator system, the AM1.5D spectrum is used [7].

2.2 Semiconductor Basic Concepts

2.2.1 Band TheoryWhen a couple of atoms are combined together to form a molecule, their atomic orbitscombine together to create the molecular orbits. When a large numbers of atoms combinetogether in a solid, then the mutual electrons of atoms combine together to form a crystalstructure, also known as a crystal lattice. The orbit of each atom splits into a large number ofenergy levels close enough that they produce an energy band. The highest occupied band isknown as the valence band (VB), whereas the lowest unoccupied band is known as theconduction band (CB) [5].

Figure 2.3 : Energy Band Gap Diagram of Semiconductor

If the lowest occupied band (VB) is partially occupied or if it overlaps with conduction band(CB) then the solid is known as metal. If the valence band is fully occupied and does notoverlap with the conduction band (separated by an energy gap), then the solid is asemiconductor or insulator. The minimum amount of energy required to excite an electronfrom the highest occupied band to the lowest unoccupied band is called the band gap (Eg).Semiconductor materials usually have a band gap between the 0.5 to 3 eV [5].Semiconductor conductivity in the dark is minute because a smaller number of electronstransfer from the valence band to the conduction band in the dark. The conductivity of thesemiconductor decreases with the increase in the band gap whereas the conductivity of theinsulator is negligible because of the large band gap [5].

Conduction band

Valence band

Band gap E n e r g y

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


11/67

6

2.2.2 Fermi LevelThe electrons always attempt to be energy efficient. They always try to keep their energy aslow as possible. At absolute zero temperature the electrons contain no kinetic energy andalways try to reside in the lowest available energy levels. The energy up to which the

available states are filled is called the Fermi energy, EF. In a semiconductor the valence bandis fully occupied and the conduction band is fully empty, at the absolute zero temperature.This indicates that the Fermi level lies in the centre of the band gap Eg [5].

The vacuum level, E vac , is the energy to which electron must to be shifted to free from allforces of the solid. The electron affinity is the minimum amount of energy required to

remove an electron from solid [5].The concentration and nature of semiconductor carriers can be changed by adding a certainamount of impurities by a process, known as doping. A semiconductor which is doped to risethe concentration of electrons with respect to holes is known asn-type and if it is doped toincrease concentration of holes relative to electrons, then is known as p-type . After dopingthe semiconductor the Fermi level is shifted from the middle of the band gap, nearer to theconduction band E c in n type doped materials and nearer to the valence band E v in p type doped materials [5].

Figure 2.4 : Intrinsic Semiconductor Fermi Level [5]

Figure 2.5 : Fermi Level of N and P type semiconductor [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


12/67

7

2.2.3 Band StructureThe graph of the band energies against the wavevectork is known as the crystal bandstructure. If the valence band maximum and conduction band minimum are present at samevalue of wavevectork then the semiconductor is known as direct band gap material [8].

GaAs is the most important semiconductor with the direct band gap structure.If the valence band maximum and conduction band minimum occur at different values ofwavevectork , then the semiconductor is known as an indirect band gap materials [8]. TheSilicon (Si) is the well-known semiconductor material with the indirect band gap. The figure2.6 shows the band structures of GaAs and Si.

2.2.4 Electrons and Holes GenerationGeneration is the electronic excitation process which results in the increase in the amount ofmobile carriers (electrons and holes) available to carry the charge, through the absorption oflight. Generation may include the shifting of the electron from the valence band to theconduction band, which creates both electron and hole, or from valence band into thelocalised state in the band gap, which generates only a hole, or from a localised state intocondition band which generates only electrons [5].

Figure 2.6: Band Structure GaAs and Si [8]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


13/67

8

The basis of a solar cell is to generate the photocurrent by absorbing the light. The efficiency

of the solar cell is calculated equilibrium between light absorption, current generationand the charge recombination processes [5]. When light impinges upon the surface of thesolar cell it is either reflected or absorbed. On the other hand if it fails to do the above processthen it is transmitted through the material. The reflection and transmission processes do notcontribute to the photocurrent and result in a loss for the solar cell efficiency. The energy ofthe photon is the main factor responsible for the absorption or transmission of the photon.When the electron has enough energy (equals or greater than band gap) to stimulate theelectron from the valence band to the conduction band then it is absorbed. This absorption ofphotons creates the electron and hole pair. The electron and hole pair releases their excessenergy in a very small time (femto seconds) by emission of phonons and relaxes to the edgesof the bands. If the energy of photon is less than band gap of the solar cell then photon willpass through the semiconductor considering it as a transparent material [9].

2.2.5 Electrons and Holes RecombinationRecombination processes are known as the loss of free electrons or holes through the shiftingof an electron from the higher energy level to a lower energy level. The recombination mayinclude a decay from conduction band to the valence band, eliminating an electron-hole pair,or it may be from conduction band to localised state (trap) removing an electron or fromlocalised state (trap) to the valence band resulting in the loss of a hole. The excited electronin the conduction band remains there for limited period of time, known as the life time,before it stabilizes to the lower energy state (valence band) by recombining with the hole.The energy released can be given up as photon (radiative recombination), as heat throughphonon emission (non radiative recombination) or as kinetic energy to another free carrier(Auger recombination) [5]. The important forms of recombination are shown in figure 2.8.

Figure 2.7: Photon absorption and electron and hole pair generation process [9]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


14/67

9

The band to band recombination process (Radiative recombination) dominates in direct bandgap semiconductors materials (e.g. GaAs). In this process an electron moves directly from theconduction band to the valence band, recombines with the hole and generates the photon. Thetrap assisted recombination also known as Shockley-Read-Hall or SRH recombinationhappens because of the impurities in the material. This recombination process involves a trapor localized energy level in the band gap. If the trap state captures a free carrier and thiscarrier can be escaped by thermal activation. On the other hand, if another carrier of reversepolarity is transported to the same energy level before the previous carrier is released then thetwo carriers recombine. The Auger recombination comprises of three carriers when twocarrier of similar polarity collide then one carrier is excited to a higher kinetic energy, and therecombination of other carrier occurs across the band gap. Auger recombination is significantin low band gap materials with higher carrier densities [5]. The average distance a carriertravels between the generation and recombination process is known as the diffusion length. Itcan be expressed by the following formula:

% & '( (2.3)

where D is the diffusivity in m/s and is the lifetime in seconds.

Figure 2.8 : Band to band, trap assisted and Auger Recombination [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


15/67

10

2.3 PN Junction FormationThe photon generated current in the photovoltaic cells is achieved by the process of electron-hole pair generation, their separation and transportation. The charge separation requires somedriving force to move the carrier. This purpose is accomplished by the formation of a p-n

junction which is created by combiningn-type and p-type semiconductor materials, as shownin figure 2.9.

The work function of the p-type semiconductor is higher than the n-type semiconductortherefore the electrostatic potential is greater on the p-side than the n-side, and an electricpotential is established at the junction. The density of electrons comparative to holes is higherin the n-type region while the density of positive charge carrier (holes) comparative tonegative charge carrier (electrons) is higher in the p-type region. The holes (electrons) fromthe p-type (n-type) region diffuse into the n-type (p-type) side and this diffusion process willlast until the concentration of electrons and holes on the two sides becomes equal [5].

Figure 2.9 : (a) Band profile of n-type and p-type semiconductor. (b) Band profile ofthe p-n junction in equilibrium. [5]

Figure 2.10 : An ideal model of p-n Junction without bias [10]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


16/67

11

In the p-n junction carriers diffusion across the junction leaves behind a layer of fixed ionisedatoms on the both sides as shown in figure 2.10. These space charges establish an electricfield which opposes the further diffusion across the junction. This region is known as the"depletion region" because it is depleted of free carriers. A built in voltage)*+ due to thiselectric field is produced at the junction. The p-n junction region always presents a highresistance to majority carriers and a small resistance to the minority carriers. The movementof minority carriers across the depletion region causes a drift current. The net current is equalto zero for both electrons and holes because of the fact that the diffusion currentcounterbalances the drift current for both carriers [10].The built in voltage at the junction can be expressed by the equations

)*+ ,-./ 01234356 (2.4)

)*+ ,-./ 01785849 (2.5)

where nn and n p are the electron densities in the n-type and p-type regions andk B isBoltzmanns constant.The width of the depletion in the n-type and p-type regions can be given by the following setof expressions:

:4)*+ ; ?@?A?A B ?@CDE FG (2.6)

:5)*+ ; ?A?@?A B ?@CDE FG (2.7)

where Na and Nd are the uniform doping densities of the acceptors and donors.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


17/67

12

2.4 Solar Cell Equivalent CircuitThe solar cell can be modelled electrically as a current source in parallel with a nonlineardevice, such as a diode. When there is no light, the solar cell behaves like an ordinary diode.When the solar cell is illuminated with light, excess electron and hole pairs are generated and

hence photocurrent relative to the intensity of light and temperature flows through the device[12]. This current is divided between the diode resistance and the load resistance. When theload resistance is high, a small amount of current flows through the load, and the majority ofphotocurrent will flow through the diode that will result in a higher potential differenceacross the solar cell terminals.

The potential difference across the terminals of the cell produces a current which flows in thereverse direction to the photocurrent and the total current is decreased by its short circuitcurrent value. This reverse current is known as the dark current. This current is analogous tothe current which flows through the device under an applied voltage in the dark [5].

H@AIJ) HK / LMJNO (2.8)

Figure 2.11 : Ideal Solar Cell Model and I-V characteristics [5]

Figure 2.12 : Dark and Light Current [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


18/67

13

The net current can be expressed as:

H HPQ K / LMJNO

(2.9)

The fill factor is a essential parameter to measure the quality of the solar cell. The fill factoris defined as the ratio of maximum power to the theoratical power (Product of open circuitvoltage and short circuit current density) [5].

RR S)S HPQ)KQ (2.10)

where:

J sc is the short circuit current density.

V oc is the open-circuit voltage.

The efficiency is the most important factor to examine the performance of the solar cell. It isdefined as the ratio of electrical power output from the solar cell to input power from the sun[5].

T HS)SUP

(2.11)

The characteristic resistance is known as the output resistance of the PV cell at which it givesmaximum power. If the load resistance is equivalent to the characteristic resistance, then themaximum power is delivered to the load and the PV cell functions at its maximum powerpoint [11].

Figure 2.13 : Characteristic Resistance of solar cell [11]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


19/67

14

It is given by the expression:

VWX )YWZ[W (2.12)

In a practical solar cell power is dissipated through the contact resistance and through leakagecurrents of the solar cells. These effects can be expressed by the equivalent parasiticresistance in series and in parallel [12]. The series resistance represents contact resistance andthe cell material resistance to the flow of current from the front surface to the contacts. Theshunt (parallel) resistance expresses the leakage current around the boundaries of the deviceand between contacts with different polarity [5].

The increase in the series and decrease in the parallel resistance cause a decrement in the fillfactor and thus efficiency as shown in figure 2.15

Figure 2.14 : Solar Cell Model with series and shunt resistance [5]

Figure 2.15 : Effect of Series and Shunt Resistance on Efficiency and Fill Factor [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


20/67

15

2.5 Single Band Solar CellThe main function of a photovoltaic cell is to convert the solar radiation into the electricalpower. In this quantum energy conversion method packets of light energy (photons) are usedto produce the electron hole pairs and these electron hole pairs are separated by the p-n

junction to make them work in the external circuit [14]. The solar cell efficiency is animportant factor to compare the performance of solar cells. In the ideal case (only radiativerecombination) the efficiency of the solar cell depend on band gap (Eg) and the incidentspectrum. If the solar spectrum is stable then the PV cells efficiency depends only on theband gap. The efficiency of the single band gap solar cell is limited to 33% for a band gap(Eg) of around 1.4eV for the standard air mass 1.5 (AM1.5) spectrum according to thedetailed balance limit given by Shockley and Queisser in 1961 [13].

A large portion of the suns energy is lost because of solar cell failure to absorb the photonshaving energy smaller than the band gap. The efficiency is highest for photons having energycloser to the band gap and it is zero for photons with energy lower than band gap (E>Eg). The efficiency of PV cellswith very small (very large) band gaps decreases because of small values of voltage(photocurrent) [5].

2.6 Tandem Solar Cell

2.6.1 Strategies to Improve EfficiencyThe multiband gap system with several junctions of different energy gaps is an idealapproach to enhance the efficiency of solar cells. Another technique is to increase the numberof electron hole pairs generated by a photon using impact ionisation solar cells [16]. Theefficiency of the photovoltaic cells can be improved by absorbing the photons of differentenergies in cells of different band gap. The efficiency of a single band gap solar cell improvesconsiderably with monochromatic light which is adjusted to the band gap. If the solarspectrum is divided into different wavelength and guided into photovoltaic cells of differentband gaps then more of the solar spectrum can be coupled and higher power could beextracted from the same spectrum [15].

Figure 2.16 : Single band solar cell Limited Efficiency at AM1.5 [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


21/67

16

2.6.2 Principles of tandem solar cellsThe tandem solar cells can be arranged in different ways, such as independent spectrumsplitting, mechanically stacked cells and monolithically grown cells, to cover the desiredspectrum [16].

In the first technique the photons of different energies are filtered by using dichroic mirrorsand directed on the respective cells with different band gap. In practice it is very difficult toefficiently split up the spectrum. A more well-designed strategy is to arrange solar cells withdifferent band gap junctions in series using mechanical stacking or a monolithical growthtechnique. In these strategies larger band gap cells are placed at the top to filter out themajority of the lower wavelength photons, while higher wavelength photons pass through tosmaller band gap materials below. The mechanically stacked cells method is simplest but thecells should be thin to minimize the absorption losses and a perfect alignment of grids isdesirable [16].

For the two solar cell tandem system, two different wiring configurations (two, fourterminals) can be achieved. The four terminal arrangements require independent contact totop and bottom a cell which is difficult to attain in practice. A more well-designedorganization is to connect all the cells in series. The problem with this arrangement is thatsame current is flowing through each cell so this limits the band gaps that can be usedbecause of the need to keep the current as close as possible (current matching) [15].

Figure 2.18 : Two and Four Terminal Solar Cell [5]

MechanicallyStacked

MonolithicalConfiguration

Spectrum Splitting

Figure 2.17: Mechanically stacked, monolithical and optically integrated configuration of solar cells [17]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


22/67

17

In monolithically grown cells different layers of materials are grown on the same substrate.The two junctions are connected in series with help of a tunnel junction or metal deposit.Series connected cells are easier to fabricate. The lattice constant and thermal coefficient

matching of different materials needs to be considered before monolithical growth. Theoptical losses in this configuration are minimized [16].

2.7 III V SemiconductorThe group III atoms of the periodic table combine with the atoms of group V to formcrystalline semiconducting compounds, known as III V semiconductors. III Vsemiconductor alloys contains equal numbers of atoms (1:1 atomic ratio) from groups III andV atoms. The group III and V atoms donate three and five valence electrons respectively toform a tetrahedral covalent bond. The majority of III V compounds including the GaAs,InP, AlSb etc. have a zinc blende crystal structure [5].

III V compounds are grown by a variety of epitaxial techniques such as molecular beamepitaxy (MBE), liquid phase epitaxy (LPE), metal organic vapour phase epitaxy(MOVPE) and metal organic chemical vapour deposition (MOCVD). The most famousand extensively used of III V semiconductor is gallium arsenide (GaAs) and other relevantternary alloys such asGallium Arsenide Bismide (Ga 1-x AsBi x) or Gallium Arsenide Nitride(Ga 1-x AsN x), where a portion x of gallium atoms in GaAs replace the Bismuth (Nitride) atom[5]. The GaAs semiconductor bonding structure and band gap is shown in figure 2.19.

GaAs has a direct band gap structure with band gap of 1.42 eV, which is close to the idealband gap for the standard solar spectrum and has 31 % theoretical efficiency. The absorptioncoefficient of GaAs is approximately ten times higher than that of silicon as shown in figure2.20, therefore a thinner (few m) active layer of the PV cell is required, that makes theGaAs solar cell suitable for the space activities because of the lower weight.

Figure 2.19 : GaAs Bonding Structure and Band Gap Diagram [5]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


23/67

18

Carrier mobilities are also higher in GaAs materials (Electrons: 8500 cm2 /V s, Holes: 420cm2 /V s) [19]. The most significant advantage of GaAs is the possibility of substitutingcertain group III atoms with the atoms of other group III elements with the intention ofchanging the composition of crystal to vary the band gap. Another benefit is that the majorityof these compounds are direct band gap semiconductors. The lattice constant difference ofdifferent GaAs alloys is very minute therefore these alloys can be grown epitaxially uponeach other to create a highly efficient device.

Figure 2.20 : Absorption Coefficients of Silicon and GaAs at different energy/eV [5]

Figure 2.21 : Lattice Constant and band gap relationship of III-V compounds [18]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


24/67

19

Solar cell efficiency has a tendency to decrease with the increase of temperature, due toincrease in carrier recombination and a reduction in the band gap. GaAs also has the bettertemperature coefficient as compared to silicon and germanium as presented in the figure 2.22.

2.7.1 DopingIn GaAs, n type doping is done by incorporating a controlled quantity of silicon duringgrowth process. The silicon atoms usually substitute some of the gallium atoms, and create adonor state because of the addition of an electron. Another tetravalent element, Tin can beused for n type doping [5].

On the other hand carbon is the most generally used as an impurity for p type doping.Carbon, the same as silicon is also a tetravalent element but under particular growthconditions it has a preference to replace arsenic atoms in the lattice structure, and creates anacceptor state because of the shortage of an electron. Otherwise beryllium (Group II) can beused, which forms an acceptor state by replacing Ga atoms. Doping is done by diffusion ofelements or directly during the epitaxial growth techniques [5].

Figure 2.22: Energy Band gap dependence on temperature of GaAs, Si and Ge [20]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


25/67

20

2.8 Dilute Bismide

Bismuth is the heaviest (atomic mass of 208 amu) element of group V of the periodic tablewith the large atomic radius. The atomic size and core electronic structure of Bi is different

from those of P and As atoms. It is therefore obvious that alloying Bi with III-V materialsresults in unusual alloy properties [22].In recent years different elements (Bi, N, etc.) of group V have been incorporated into the III-V alloy, which ends up with interesting properties. Bismuth containing materials have causedremarkable interest because of the fascinating properties such as, band anti crossing effect inthe valence band that cause a large band gap bowing effect, when a small amount of bismuthis incorporated into III V semiconductors (e.g. GaAs). The incorporation of bismuth in III V compounds creates Bi defect states close to the valence band edge of the hostsemiconductor. The Bi incorporation also increases spin orbit splitting energy due to the largesize of the bismuth atom [21].

The spin orbit splitting energySO, increases rapidly with the increase in the atomic numberof group V elements. Due to the large size of bismuth atom it is theoretically predicted thatGaBi should have the largest spin orbit splitting energySO(2.2 eV), as shown in the figure2.24.

Figure 2.23 : Group V elements of periodic table

Figure 2.24 : Increase in spin orbit splitting energy of III-V compoundwith group elements atomic number [21]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


26/67

21

The band gap bowing effects due to Bi can be modelled by using the band anti crossingmodel (BAC). In BAC the incorporation of Bi produces a Bi resonant level and its interactionwith the valence band maximum (VBM) leads to band gap bowing effect due to theformation of E+ and E valence sub bands as show in figure 2.25.

The decrease (increase) in the band gap Eg (SO) with the fraction of bismuth in the dilutebismide is expressed in figure 2.26. The figure shows that the band gap decreases rapidlywith increasing Bismuth content at a rate of 60 meV/Bi% approximately [21].

Figure 2.26 : Effect of increase in bismuth incorporation on theband gap and spin orbit splitting [21]

Figure 2.25 : Band anti crossing model of GaAsBi [55]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


27/67

22

The spin orbit splitting larger than the band gap (SO > Eg), has the advantage of reducingthe fundamental carrier losses such as CHSH Auger recombination (in which a recombiningelectron-hole pair give their energy to a second hole which is excited to a higher energy band)or hole leakage and optical losses such as Inter Valence band absorption (IVBA). The carrier

leakage losses (thermal escapes) can be eliminated by higher valence (Ev) and conduction( Ec) band offsets [23]. In figure 2.26 spin orbit splittingSO surpasses band gap Eg with theBi fraction of ~9% on GaAs. Thus in the dilute bismide with Bismuth content more than 9%,the Auger recombination loss is eliminated and therefore optimum band structure is obtained.

The sensitivity of the band gap of dilute bismide (GaAsBi) to temperature is slightly reducedin comparison with the GaAs [22]. The figure 2.27 indicates that the band gap dependence ofGaAs on temperature is almost similar with the GaAsBi having bismuth contents up to 3.1%,and has minute effects on the band gap dependence on temperature.

2.8.1 Growth of Dilute Bismide

The growth ofGaAs 1-x Bi x with high Bi incorporation by molecular beam epitaxy (MBE)has some limitations due to the weak reactivity of the bismuth (Bi) with the Gallium (Ga) and

the great tendency of Bi to surface segregate because of the large size of bismuth atom [24].The growth ofGaAs 1-x Bi x alloys, results in the formation of metallic surface droplets underconventional MBE III-V growth conditions. The sizes and densities of the droplets isapparently dependent on the Bi flux, growth rate, III-V ratio and growth temperature [27].The incorporation of Bi content in growth of theGaAs 1-x Bi x depends on following differentparameters.

Figure 2.27 : Effects on band gap of GaAs (without and with Biconcentration) on temperature [22]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


28/67

23

2.8.1.1 Dependence of Bi content on Bi : Ga BEPR

The Bi incorporation is directly proportional with the Bi : Ga beam equivalent ratio pressure(BEPR). It grows linearly with the Bi:Ga BEPR and then the Bi content becomes constant

and shows no change with the increase in Bi : Ga BEPR, as shown in figure 2.28. After thisphase the Bi incorporation is determined by the As2 : Ga BEPR and the growth temperatureof devices [26].

Figure 2.28: Bi content as function of Bi : Ga BEPR [26]

2.8.1.2 Dependence of Bi content on As 2 : Ga BEPR

The Bi incorporation is inversely proportional with the As2 : Ga flux ratio / BEPR [26]. Thefigure 2.29 shows that the Bi content becomes constant when the As2 : Ga BEPR isdecremented below 2.25 and further decrease in BEPR does not affect the Bi concentration.

On the other hand Bi content decreases rapidly with increase in As2 : Ga BEPR from 2.25 to3.6. When As2 : Ga BEPR is increased above 4.5, then no Bi incorporation was detected.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


29/67

24

Figure 2.29: Bi content dependence on As 2 : Ga BEPR [26]

2.8.1.3 Dependence of Bi content on growth temperature

The Bi incorporation also has an inverse relationship with growth temperature as the Bicontent increases very rapidly with the decrease in the growth temperature. It is clear fromfigure 2.30 that the Bi concentration was less than ~10% and then it reaches to ~22% at thetemperature 200oC. Lewis et al grew samples at the range of 0.81 1.7 As2 : Ga BEPR, at

which the Bi incorporation is constant (as shown in figure 2.29). The solid data points weregrown at large Bi : Ga BEPR (0.59), at which Bi incorporation has saturated (as shown infigure 2.28).

Figure 2.30: Bi content as a function of growth temperature [26]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


30/67

25

2.8.1.4 Dependence on the Growth Rate:The Bi incorporation is not affected by the growth rate. But the growth rate is a significantfactor for controlling the development of Bi droplets. The low growth rates enable the growthof GaAs 1-x Bi x with higher Bi concentrations and smaller Bi droplet density. When the Biatoms are incident on the substrate it can do one of following three actions (as shown in theinset of figure 2.30).

Incorporate into the substrate Evaporate back into the vapour Attach to the Bi droplet

In order to minimize the chances of the formation of Bi droplets, the flux rate of Bi should beless than the sum of the incorporation and the evaporation rate [25]. According to Vardar etal, Ga- richGaAs 1-x Bi x growth results inGa-Bi droplets whereas on the other hand, As-rich, GaAs 1-x Bi x growth produces a droplet free surface [27].

2.9 Dilute Nitride

When a small quantity of nitrogen is incorporated into GaAs to form dilute nitride alloy aprofound effect on fundamental band gap is exhibited as compared to conventional

semiconductor alloys [28]. Although the GaN band gap is 2 eV higher in comparison toGaAs, it is monitored that band gap energy decrease with the increasing contents of nitrogenand reduction of almost 205 meV for 1 % of nitrogen is observed [29].

Semiconductor alloys create by substituting a small percentage of host atoms with the atomsof other element having different electronegativity and/or sizes are known as highlymismatched alloys (HMA). The properties of HMAs are intensely changed e.g. they showlarge band gap decrement and their electronic structure are extremely different from theirhost materials [30]. The lattice constants of GaAs mismatched with GaN by 20%, and thenitrogen atom has higher tendency to attract electrons in relation to arsenic atom. These

mentioned features encourage a distortion of the electrostatic potential in the crystal and thusresults in the non-linear behaviour of the band energy gap [29].

In 1995 Kondow et. al. revealed that incorporation of small quantity of nitrogen in GaAsexhibits a band gap reduction effect, due to small size ionic radius of nitrogen. Thedependence of the energy band gap on the nitrogen (N) concentration in the dilute nitride hasbeen the explained by many theoretical techniques. The band anti crossing (BAC) model isused to theoretically model the structures of the dilute nitride as show in the figure 2.31.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


31/67

26

The band gap energy of dilute nitride (GaNAs) reduces with the rise in temperature and therate of this reduction becomes lower and lower, when the nitrogen concentration is increases.The addition of 1% of nitrogen (N) content reduces the band gap by ~205 meV at roomtemperature, and ~250 meV at lower temperature [29]. The band gap difference for thetemperature 15K and 300K declines from 110 meV in case of GaAs to 70 meV for theGaAsN with nitrogen concentration of 1.5%, as shown in figure 2.32.

The growth of dilute nitride semiconductor is challenging task, they are usually grown by

either metal organic vapour phase epitaxy (MOCVD) or gas source molecular beamepitaxy (GSMBE) [28].

Figure 2.32 : Energy band gap response to the temperature and the Nitrogen concentration [29]

Figure 2.31 : Band Anti Crossing model of dilute Nitride [54]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


32/67

27

2.10 Quantum Wells

In the order to get higher efficient PV cells the structure of solar cell continues to evolve. Thesingle band solar cell only absorbs photons with energies larger than or equal to their bandgap. Hence, the remaining lower solar spectrum is lost. Tandem solar cells improve theabsorption characteristics of solar cells. However their efficiency still far short of thetheoretical efficiency of 42% to 52%. One of the limitations of the tandem solar cell is thatthe current matching. The other challenge with the tandem cells is the diffusion length islower than the depletion layer which reduces the current.

There are several epitaxial growth techniques of changing the band gap of semiconductors byformation of materials with a different chemical composition. Initially, the development ofthe growth techniques focus on the formation of homojunctions comprising of semiconductor

material having the same composition with different impurities and carrier concentrations.Subsequently, the interest shifted toward heterojunctions, containing two semiconductormaterials of different band gap [33].

A double heterostructure is formed when a thin layer (whose thickness varies from ~250 to~ 10) of narrow band gap semiconductor placed between the bulk semiconductors of largerband gaps. A quantum well is created, if the thickness of the thin layer becomes comparableto the De Broglie wavelength (~10nm) of the carriers. In this case larger band gap act asbarriers to electron flow, which traps the mobile carriers in the resulting quantum well. Thecarriers in the thin layer start to behave according to particle in a potential well. Now theconduction band energy levels are quantised and only definite values are allowed to exist[33].

The main purpose of quantum well solar cells (QWSCs) is to control the open circuit voltageby reducing the recombination in the bulk material (barriers), while the lower band gapmaterial sections, known as the wells, absorb low energy photons that the bulk material

cannot utilise [35]. The carriers produced by the extra photons absorbed in the well escape tothe barriers and produce the additional current. There is some voltage loss, but the

Figure 2.33 : Energy structure and single-particle wave function for singlequantum well solar cell [33]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


33/67

28

improvement in current of the QWs is enough to overweight the voltage losses. Hence, thewells can improve efficiency of solar cells compared with conventional cells [31].

If the quantum well structure repeats itself in a periodic routine it is known as a multiplequantum well (MQW) [33]. The quantum well solar cell (QWSC) is a diverse technique toachieve the multi-band gap solar cells where a multi quantum well system is generated in theintrinsic region of a pin structure [34]. The p-i-n designed addresses the defect of shortdiffusion lengths of carriers in tandem solar cells.

The output voltage of the quantum well solar cells depends on the width of barrier, therecombination rate in the wells and the interface between barrier and wells. Whereas theshort-circuit current is subject to the width and depth of the quantum well. Deeper quantumwells can absorb longer wavelength light and generate a higher photocurrent. On the otherhand, deeper wells has higher recombination rate that results in a reduction of the outputvoltage. Therefore, quantum wells depth creates a trade-off between the output voltage andthe photocurrent [34].

The increment in the thickness of the well increases the absorption per well, but a lessernumber of wells can accommodate in the solar cell. Alternatively, a thinner well absorbsfewer photons but a larger number of wells can be accommodated in the intrinsic region.Moreover, the wider quantum well has the higher recombination ratio and as a result theopen-circuit voltage declines. On the other hand increase in the number of the wells canabsorb more photons that results in increment in the photocurrent but the recombination inthe interfaces also rises that cause a reduction in the output voltage. Due to mentionedreasons, it is essential to enhance the design of QW solar cell so that attain higher efficientsolar cells [34].

Figure 2.34: Schematic energy band diagram of a QWSC [31]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


34/67

29

Imperial College of London demonstrated that quantum wells can improve the efficiency ofconventional bulk tandem solar cell by building a tandem quantum well structure whichattained the efficiency of 30.6% under 54 suns AM1.5G [32]. Later they were successful inshowing that both the short circuit current and open circuit voltage can increase for multi

quantum well solar cells [31].

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


35/67


36/67

31

An MBE system usually contains three vacuum chambers: a growth chamber, an analysischamber and a small sample load lock chamber. The metal sealed or Viton sealed gatevalves are used to separate these chambers from one another [36].

The growth chamber is the most significant module of an MBE system. A growth chamberusually consists of effusion cells, shutters, a substrate manipulator, cryopanels, and somesurface analysis equipment [36]. The most common sources for molecular beams are effusioncells, also known as Knudsen Cells. These cells are made of graphite pyrolytic boron nitride(PBN) [37]. The effusion cells are usually 7.5 12 cm long and have a diameter of 2.5 cm[36]. In solid phase source MBE, all elements including Bi, group III elements In, Ga and Al,and dopants Te, Si, Be, in ultra-pure form, are placed in effusion cells and heated by tantalum(Ta) heating elements, in separate effusion cells until they start to slowly evaporate [37]. Thegaseous elements are then incorporated into the substrate. The effusion cells are surroundedby the water cooling system to reduce the chances of heat transfer between the cryopanelsand the Knudsen cells. The beam flux is controlled by accurate control of the temperature.The flux arriving at the substrate is monitored by using a beam flow gauge placed behind thesubstrate holder. The substrate is mounted on molybdenum (Mo) holder, and because of itshigh thermal conductivity, a constant temperature can be attained across the substrate. Indium(liquid at the MBE growth temperature) is used to bind the wafer to the molybdenum (Mo)holder [37].The rotary substrate manipulator is used to turn the substrate at a speed up to 125 rpm duringgrowth for uniform epitaxial film thickness and doping uniformity. The substrate outgassingis achieved by heating the substrate up to 300 C to remove gasses which would otherwise

contaminate the growth chamber.One of the distinctive features of MBE is its capability to rapidly switch the growth elementfrom one source to another. This property allows one to accurately control materials ofdifferent layers and their thickness. The switching of the growth elements beam is usuallydone with the mechanical control shutters [37].To avoid contamination, a sample load lock is used to place and remove the wafers from theMBE growth chamber with minimum disturbance of the vacuum conditions [36].A majority of analysis devices are used to observe the structure of the epitaxially grown

Figure 3.1: Schematic layout of the main chamber of MBE system [38]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


37/67

32

layers throughout the growth process. The analysis chamber comprises of the surface analysisequipment. An auger electron spectrometer (AES), a secondary ion mass spectrometer(SIMS), an X-ray photoelectron spectroscope (XPS), and a scanning electron microscope(SEM) are used to examine the sample surface [36]. The surface analysis of the sample is

performed during growth by using reflective high energy electron diffraction (RHEED)apparatus. RHEED is used to observe the structure, thickness and surface morphology of thegrowing film. In this process an electron gun generates a high energy electron beam (5 50keV), which strikes the surface of the substrate at a small angle (1 2o). Electrons arereflected from the substrate surface and strike a fluorescent screen forming a diffractionpattern which allows observation of the growth of the layers [37].

3.2 Fabrication Process

The fabrication process consists of photolithography techniques and several chemicalprocesses that can produce extremely complicated electronic devices. The metallic contactsare constructed on the sample for the electrical characterisation of solar cells. Therefore, byusing the photolithography process, either the cylindrical mesa structure or the Hall barsstructure pattern (for Hall Measurements) contacts are made on the solar samples. Figure 3.2shows the structure of the most common cylindrical mesa [39] and the Hall bars structures.[40]

3.2.1 CleavingThe solar cell device (cylindrical mesa structure) used for the experiments has a diameter ofless than 2 mm. Therefore in the first stage of fabrication, a large-sized wafer is cleaved intothe required size of sample (~5mm) to fabricate the desired device.

After measuring the required size (5mm) of the sample with the help of a ruler, a scriber isused to make a tiny scratch at the edge of the front side of the sample. The sample is thenturned over and a small amount of pressure is applied to the back side (substrate side) in theexact position of the scratch. This will result in a straight crack across the semiconductorwafer.

Figure 3.2: Cylindrical Mesa and Hall bars Structure

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


38/67


39/67

34

are applied to the sample. The sample is then left to soak in photoresist for 1 minute toeliminate air bubbles before the sample is spun at 4000 rpm for 30 seconds.

Soft BakingAfter the spin coating process, the sample is removed from the spin coater and placed on thehot plate at 95 C for 60 seconds for soft baking, to make the photoresist thinner andphotosensitive.

MaskingThe sample with the photoresist coating is then employed on the mask aligner and a photomask with the required pattern is used. The sample is aligned with the pattern using the micropositioners. When the sample and masking pattern are aligned, the mask is lowered down sothat it touches the sample, to minimize diffraction effects. Then the sample is exposed to ultraviolet (UV) light through the mask for 10 seconds [50].

3.2.6 Developing

After ultra violet (UV) illumination, the sample is developed using a Sodium Hydroxide(NaOH) and water (H2O) solution prepared with 1 and 10 proportions, respectively. Thesample is placed in the solution until the photoresist is developed and the pattern becomesvisible. When the pattern becomes clear, the sample is removed from the developer, rinsedwith deionised water and dried with nitrogen gas (N2) [50].

Figure 3.5 : Applying BPRS 150 positive photoresist

Figure 3.6 : Sample with the mask after developing

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


40/67

35

3.2.7 Oxide RemovalBefore the process of evaporation, oxides are removed again from the sample using thesolution of aqueous ammonia (35% NH3). The sample is then rinsed with deionised water anddried using nitrogen gas (N2). At the end, the sample is exposed to UV light for blanket

exposure.

3.2.8 EvaporationIn this process the metallic contacts are evaporated onto the sample using an Edwards E306Avacuum coating unit. For the n-type materials Au/Au:Ge/Ni/Au contacts are used, whereas forthe p-type materials Au/Zn:Au/Au contacts are most commonly used. The Ti / Au contacts areused for the heavily doped (because it bond to the top of the device) devices. The requiredmetals are loaded into Tungsten (W) baskets (Ti, Ni, Zn) or Molybdenum (Mo) boats (Au,Ge), so that they can be evaporated by heating [50].

Once the sample is loaded within the coating unit, Firstly the system is pumped to 10-2millibar with help of rotary pump and then after this it is driven to 10-6 millibar using adiffusion pump. When the required vacuum pressure is achieved, the metals are evaporated inthe correct layers order by applying current. At the end of this process, the coating unit is leftto cool down for a minimum of 30 minutes before opening.

3.2.9 Lift offAfter the evaporation process the sample and glass slide are completely covered with themetal. To achieve the desired pattern with the metal on it, the sample is soaked in acetone.This will dissolve the photoresist, leaving behind a clear area, while the metal contactsremain on mask pattern areas. After achieving a perfect contact pattern, the sample is rinsedin deionized water to stop the lift off operation and dried with nitrogen gas (N2).

3.2.10 AnnealingBefore the annealing process the sample is removed from the class slide by putting it on thehot plate (150oC) and crystal bond is removed with acetone. This process is done to diffusethe Au/Zn:Au/Au or Au/Au:Ge/Ni/Au contacts into the device. The samples are annealed at

temperature of 350 C for the p-type or 400 C for then-type contacts for 15 to 30 seconds.

Figure 3.7 : Sample after evaporation and Lift off Processes

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


41/67

36

3.2.11 EtchingThe simplest and most frequently used etching technique is wet chemical etching, in whichthe sample is drenched in a chemical that removes the semiconductor material layers fromselected areas [10]. In the etching process steps 3 (Mounting) to 6 (Developing) are repeated

again using the etching mask. The area which needs to be removed is exposed to ultra violet(UV) light and those not to be etched are covered with positive photoresist. Once the desiredpattern is transferred from a mask to a wafer, the material from selected regions is removedor etched to define a fixed active area for the solar cell and the contacting layer of the sampleis also removed so that light directly fall on the window layer.

Hard BakingOnce the sample is developed, it is placed on the hot plate at 150 C for 1 minute for hardbaking to make sure that the photoresist is resistant to etchant and to enhance adhesion ofphotoresist to the surface of the sample.

Active Area EtchingIn order to do the active area etching the etchant H2SO4:H2O2:H2O is prepared in the ratio1:8:80 respectively. The H2O2 behaves as the oxidizing agent whereas the H2SO4 dissolvesthe resulting oxide [42]. This solution has an etch rate of 500 nm/minute. The thickness ofthe photoresist is measured with the help of surface profiler. Then the sample is put in theetchant for a time long enough, to reach the substrate. The depth of the etched area is thenchecked using the surface profiler.

Contacting Layer EtchingIn order to make it possible for the light to hit directly the AlGaAs window layer, the GaAscontacting layer is etched away. The sample is cleaned using acetone and then placed insolution of Citric acid and H2O2 prepared in the ratio 10 to 1. The etch rate of this solution is200 nm/minute for GaAs but has an etch rate of 2 nm/minute for AlGaAs.

Figure 3.8 : Spin coating, applying etching mask and expose to UV, developing and etching process

UV

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


42/67

37

3.2.12 Contact on the back SideAfter the etching process the front side of the devices is completed and now contacts aremade on the back side of the device. To do this process, step 2(Sample Cleaning), step3(Mounting), step 4(Oxide Removal) and step 8(Evaporation) are repeated with the substratefacing up.

3.3 Experiments

3.3.1 I V Measurements

The solar cell characterization comprises measurement of the solar cells electricalperformance characteristics to calculate the conversion efficiency and different parameters ofthe equivalent circuit. The Current Voltage (I V) characteristic of a solar cell under lightand in dark are the most important experimental results in order to know about the

performance of the solar cell under normal operational conditions. In this technique theshort circuit current density (JSC), open circuit voltage (VOC), fill factor (FF) and theefficiency () of the PV cells are measured. All of these critical performance factorsdepend on both the illuminating light spectrum and the temperature of the solar cell [43].Therefore, for comparison of results, these experiments are performed using standardoperating conditions (spectrum and temperature range). The standard terrestrial solarspectrum, the AM1.5 regulated to give a total output power of 1000 W/m2 and the experimentperformed at 25 C temperature. In order to standardize the output of the beam equal to 1000W/m2, initially a GaAs and Si sample solar cells were used as a reference to regulate thesimulator output before doing any measurement [50].In this experiment a Newport96000 solar simulator is used, which contains a xenon lampwhich produces light in a similar wavelength range to a solar spectrum. The light beampasses through an AM1.5G filter which filters out part of the xenon lamps spectrum to give aspectrum closer to the solar spectrum. The figure below shows the comparison of the AM1.5and Xenon lamp spectrum.

Figure 3.9 : Comparison of AM1.5 (green) , Xenon lamp without filter (blue)and Xenon lamp with filter (brown) spectrum [44]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


43/67

38

To maintain the solar cell temperature at 25 C during the solar simulator illumination aconventional approach is used. A block of copper is used to make the back side contact of thesolar cell and also acts as a cooling element. The temperature of this copper block iscontrolled by a Peltier Temperature Controller by monitoring the temperature of a thermistor

inserted between two pieces of GaAs substrate. One piece of GaAs is connected with thecopper cooling block and the other is illuminated by the simulator to get the temperature asclose as possible to that of the solar cell [50]. A probe is used to make contact with the ringsof the solar cell, in order to avoid the need for wire bonding. The figure shows the structureof the probe station.

The IV characteristics measurement is made using a Keithley 238 source measurement unit,which sweeps a voltage across the terminals of the solar cell and measures the resultingcurrent. The dark Current Voltage (I V) characteristic of a solar cell is also measured bysimply covering the sample. The experimental setup for this I V measurement is presentedin figure 3.11.

Connection fortemperature controller

Clip for thermistor

ThermistorCopper Block Solar Cell

Contacting Probe

Clip to hold solar cell

Figure 3.10: Probe Station for the I-V measurement [50]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


44/67

39

Figure 3.11 : Experimental Setup of I-V measurement [50]

3.3.2 Spectral Response

The spectral response is theoretically analogous to the quantum efficiency. The quantumefficiency is given by the number of electrons generated by the solar cell relative to thenumber of photons incident on the sample, whereas the spectral response is defined as theratio of the current produced by the photovoltaic cell to the power of incident radiation on thePV cell [48].In the spectral response experiment, light of a specific wavelength is incident on a solar cellsample and the resultant current is measured. The spectral response not only givesinformation about the wavelength range over which the device responds, but is also useful asan effective diagnostic and analytical technique, specifically in a device research and design[47].The experimental setup for the spectral photoconductivity is shown in figure 3.12.

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


45/67

40

A Tungsten Halogen Lamp is used as source of light for the wavelength range 500 1200nm, the spectrum of this lamp is shown in figure 3.13. A Xenon Arc Lamp is used for thelower wavelengths [47]. A M300 monochromator is used to scan through the preferredwavelength range.

A chopper is used to chop the light beam from the monochromator at specific frequency andthen the resultant light signal is incident on the sample. The chopper controller is used to setthe chopping frequency of the chopper. The current generated in the solar cell due to the light

is measured with a Stanford research systems SR510 lock in amplifier.

Figure 3.12 : Experimental set up for spectral response [50]

Figure 3.13 : Tungsten lamp spectrum without the filter (left) and with filter (right) [46]

U P :

2 2 / 0 8 / 2

0 1 3

- 0 8

: 4 9

: 3 7

W M :

2 2 / 0 8 / 2 0 1 3

- 0 8

: 4 9

: 3 9

M : C E

9 0 1

- 7

- S U A :

1 2

a 1

R :

1 2 0 2 4 3 5

C :

3 0 8 3

F 4

0 E

5 A

7 8 8 1 3 8 2 3

E A

0 C

0 B

2 B C D B

3 6

0 8 3 6

E D

4 C

8


46/67

41

# $odelling

4.1 Band Anti-Crossing ModelThe band structure of a semiconductor is most significant for solar cells, as the wavelengthbelow which it absorbs light is determined by the band gap. Consequently it has a directimpact on the photocurrent of the solar cell. A band anti-crossing (BAC) model was proposedby W. Shan et al. to describe the characteristics of IIIV dilute nitrides and other highlymismatched alloys. This model is used to determine the electronic structure of HMAs bytaking into account the interface between the localized states of the impurity and the extendedstates of the host semiconductor [52]. In this project the BAC model is used to calculate theband gap ofGaAsBi and GaAsN with a different concentration of bismuth and nitrogenrespectively.

4.1.1 Conduction band anti crossing

When nitrogen (N) is added to the GaAs, an isolated N atom substitutes an As atom andcreates a localized state with the energy level E N , caused by the large difference inelectronegativity and atomic size of the N and As [54]. In general, this level is positionedvery close (0.25 eV) beyond the conduction band edge in GaAs. The incorporation of aslightly higher nitrogen content into III-V compounds considerably changes the electronicband structure that results in decrease of the fundamental band gap, substantial increase in theelectron effective mass and reduction in electron mobility [53]. The interaction between thelocalised state at energy level E N and the extended conduction band states results in thereduction of the band gap energy in dilute nitride alloys. This conduction band dispersioneffect can be characterized by the following eigenvalue expression [53].

\] , ]Q , )^_) _ ], ]_\ ` (4.1)

E c(k) is the energy of the GaAs conduction band, E N is the energy of the localized state fromthe top of the GaAs valence band andV MN is the matrix element, which expresses theinteraction between the localized N state and extended conduction band state. The E c(k) andV MN can be written as follow [53].

]Q, ]a BbF,F


47/67

42

The solution to the eigenvalue equation can be given as

]g, ]_ B]Q , gh ]_ ]Q, F Bi)^_F

< (4.

Date post:	04-Jun-2018
Category:	Documents
Upload:	umairahmadnasir
View:	220 times
Download:	0 times

Tandem Solar Cell

Documents