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1 A STUDY OF HOT CARRIER COPPER INDIUM GALLIUM DISELENIDE BASED THIN FILM SOLAR CELLS By YIGE HU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR T HE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013
2 2013 Yige Hu
3 To my husband and my parents
4 ACKNOWLEDGMENTS First I would like to express my sincere gratitude to my advisor, Prof essor Gi js Bosman, for his dedicated support, advice and encouragement throughout my PhD research. I would also like to express appreciation to my comitte e members for their time commitment to see the completion of th is work: Prof essor s Jing Guo and Ant Ural of th e UF D ep ar t ment of Electrical and Computer Engineering and Prof essor Tim Anderson of the UF D ep ar t ment of Chemical Engineering, who also provided the CIGS devices and the expertise related to the deposition process, which is a key part of the work. I also like to thank the Florida Energy Systems Consortium, which has given continuous financial support and collaboration opportunity for the work during my PhD studies. I would like to express my warm thanks to my colleagues from the Noise Research group, Heman t Rao, Weikai Xu and Yanbin An for research discussions and time for solving problems. I am also grateful for my collaborators from the Chemical Engineering Photovoltaic Group; David Wood, Ranga rajan Krishna n Barrett Hicks, Chris topher Muz z illo and Zhi Li all who assisted me with photovoltaic material characterization and processing, and former member Jiyon Song from Global Solar, who helped me obtain important samples and information for th is work. Finally I would like to thank my parents and my husband Barrett, for encouraging me to be persistant in my efforts and loving me during the many challenging periods.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION OF HOT CARRIER SOLAR CELLS ................................ ........... 13 Solar Cell Background ................................ ................................ ............................ 13 Hot Carrier Solar Cell State of Art ................................ ................................ ........... 13 2 TRADITIONAL THIN FILM COPPER INDIUM GALLIUM DISELENIDE SOLAR CELL MODELING AND SIMULATION ................................ ................................ ... 22 Overview of Solar Cell Device Physics ................................ ................................ ... 22 Thin Film Copper Indium Gallium Diselenide Solar Ce ll Simulation Using Medici .. 23 3 COPPER INDIUM GALLIUM DISELENIDE BASED HOT CARRIER SOLAR CELL ................................ ................................ ................................ ....................... 30 Phonon Engineering in the Absorbe r Layer ................................ ............................ 30 Phonon Disperion Modeling ................................ ................................ ............. 32 Superlattice Phonon Dispersion Realization ................................ ..................... 36 Electrical Engineering Aspects of the Contacts and the Absorber Layer ................ 40 Energy Selective Contacts ................................ ................................ ............... 40 Esaki tun neling ................................ ................................ ........................... 41 Double barrier quantum well structure ................................ ....................... 42 Superlattice Absorber ................................ ................................ ....................... 45 4 EXPERIMENTS ON COPPER INDIUM GALLIUM DISELENIDE THIN FILM SOLAR CELL FOCUS ON HOT CARRIER EFFECTS ................................ ........... 57 Introduction ................................ ................................ ................................ ............. 57 Sp ace Charge Limited Current Model ................................ ................................ ..... 59 Space Charge Limited Current Model Basic Physics ................................ ....... 60 Space Charge Limited Current in a Copper I ndium Gallium Diselenide Solar Cell ................................ ................................ ................................ ................ 63 Electric Field Guiding Model ................................ ................................ ................... 67 Description of the Model ................................ ................................ ................... 67
6 Hot Carrier Effects in the Current Voltage Characteristic under Reverse Bias ................................ ................................ ................................ ............... 68 The Zener Tunneling Model ................................ ................................ .................... 70 The Impact Ionization Model ................................ ................................ ................... 71 Basics of the Impact Ionization Model ................................ .............................. 72 The Modified Impact Ionization Model ................................ .............................. 76 The Modified Shockley L ucky E lectron M odel ................................ .................. 79 5 MODIFICATION OF A CONVENTION COPPER INDIUM GALLIUM DISELENIDE SOLAR CELL WITH HOT CARRIER EFFECTS ............................ 102 Introduction ................................ ................................ ................................ ........... 102 Adding the Energy Selective Contact to the Device SC1 ................................ ...... 103 Barrier Model ................................ ................................ ................................ ........ 105 Barrier Location ................................ ................................ .............................. 106 Barrier Height Influence on the Performance ................................ ................. 106 6 CONCLUSIONS AND FUTURE WORK ................................ ............................... 117 Conclusions ................................ ................................ ................................ .......... 117 Future Work ................................ ................................ ................................ .......... 118 LIST OF REFERENCES ................................ ................................ ............................. 120 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 126
7 LIST OF TABLES Table page 2 1 Simulation parameters of CIGS cell  ................................ .............................. 27 3 1 CIS and CGS lattice parameters ................................ ................................ ........ 47 4 1 Simulation par ameters of n+ p n+ CIGS cell ................................ ...................... 83 4 2 Simulation parameters of the device SC1 ................................ .......................... 84 4 3 Simulation parameters of n ZnO/p CIGS cell ................................ ..................... 85
8 LIST OF FIGURES Figure page 1 1 Schematic presentation of a hot carrier solar cell ................................ ............... 21 2 1 CIGS solar cell device model ................................ ................................ .............. 28 2 2 Simulation results for the CIGS solar cell. ................................ .......................... 29 3 1 Phonon dispersion curve of CIS ................................ ................................ ......... 48 3 2 Linear chain model for CIS ................................ ................................ ................. 49 3 3 SL structure of CIS/CGS ................................ ................................ .................... 49 3 4 Phonon dispersion curve of CIS/CGS ................................ ................................ 50 3 5 Confined optic phonon dispersion curveswithin a SL reduced Brillouin zone 0
9 4 7 Photo current voltage characteristic s of the device SC1 ................................ .... 91 4 8 Normalized I V characteristics for nonlinearity anal ysis with different wavelengths ................................ ................................ ................................ ........ 92 4 9 Band diagram illustrating the hot carrier effect in the electric field guiding model ................................ ................................ ................................ .................. 93 4 10 Simulation of hot carrier J V characteristics using the electric field guiding model ................................ ................................ ................................ .................. 93 4 11 Reversed bias J V characteristics under different wavelength illuminzation. ...... 94 4 12 Medici simulated im pact ionization current density ................................ ............. 94 4 13 Multiplication factor of the device SC1 under 395nm, 455nm, 633nm and 740nm illumination, respectively, as a function of applied reverse bias. ............. 95 4 14. Voltage Electric Field relationship for parameter W 1 extraction. ......................... 96 4 15 Impact ionization rates versus maximum electric field inverse for the device SC1 ................................ ................................ ................................ .................... 97 4 16 Illustration for the modified impact ionization model ................................ ........... 98 4 17 Phonon mean free path extraction model for el ectrons with different energies .. 98 4 18 CIGS solar cell band diagram, electric field and photo generation rates as a function of distance to the top contact ................................ ................................ 99 4 19 CI GS solar cell band diagram(dashed lines) and photogeneration rate(solid lines) as a function of distance to the top contact for different wavelengths ....... 99 4 20 The ionization rates of different wavelengths of the device SC1 with the fitting function of and E av ................................ ................................ ......................... 100 4 21 Phonon mean free path plotted versus the kinetic energy E av after a initial rapid loss before phonon scatterings ................................ ................................ 101 5 1 AM1.5 spectrum  ................................ ................................ ......................... 112 5 2 The energies of photo generated carriers reaching the top contact determining by the field accele ration and phonon scatterings. ......................... 113 5 3 Medici simulated dark I V characteristics of the device SC1 structure (parameters in Table 4 2) with a barrier between the ZnO and CdS layers ...... 114 5 4 Medici simulated dark I V characteristics of the device SC1 structure (parameters in Table 4 2) with a barrier between the CdS and CIGS layers. ... 114
10 5 5 Medici simulated JV characteristic of the device SC1 without barrier and with barrier heights of 8kT, 10kT an d 14kT at different wavelengths ....................... 115 5 6 Band diagram for II VI and I III VI 2 compounds ................................ .............. 116
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A STUDY OF H OT CARRIER C OPPER I NDIUM G ALLIUM DI S ELENIDE BASED THIN FILM SOLAR CELLS By Yige Hu August 2013 Chair: Gijs Bosman Major: Electrical and Computer Engineering The photovoltaic (PV) industry has entered a period of record growth since the 90s. Most of th e commercial products are based on crystalline Si technology. However, there are fundamental limits to the ultimate Si costs that may inhibit it from achieving the desired level of contribution to worldwide energy production. In contrast, thin film PV tech nology can reach the desired cost performance outcome due to fast deposition rates and lower material cost. The research of this dissertation is focused on hot carrier solar cells for cell conversion efficiency improvement in a low cost, high throughput C uIn x Ga 1 x Se 2 (CIGS) system. The rapid thermalizaton loss of hot photo exited carriers interacting with the lattice can potentially be reduced through phonon engineering in the absorber layer; the subsequent extraction of the hot carriers may be realized th rough device engineering of energy selective contacts. Simulations and modeling are presented for a novel hot carrier solar cell design with a superlattice structured absorber consisting of copper indium diselenide/copper gallium diselenide( CIS/CGS ) and a quantum well structured energy selective contact of aluminum nitride/gallium nitride( AlN/GaN ) The discrete p honon dispersion curve of a CIS/ CGS absorber reduces the phonon decay possibility
12 and provides a phonon bottle neck effect to slow do wn the cooling process. The AlN/ GaN contact provides confinement for hot carrier extraction. Experiments were performed on the national renewable energy laboratory ( NREL ) conventional solar cell SC1. Comparison of the current voltage relationships of CIGS illuminated un der low energy and high energy photon wavelengths shows evidence of hot carriers contributing to the collection. A modified Shockley lucky electron model is developed to extract the initial carrier energies and the phonon mean free paths by applying the ho t carrier concept to the traditional thin film CIGS cell design. An improvement using the hot carrier theory is made by imbedding the traditional design with a barrier between the buffer layer and absorber layer for blocking the cold diffusion carriers whi le allowing most hot carriers to pass through A barrier consisting of Zn 0.3 Cd 0.7 S is proposed for optimal effectiveness.
13 CHAPTER 1 INTRODUCTION OF HOT CARRIER SOLAR CELLS Solar Cell Background Solar energy has been gaining a lot of attention since the 70 s of the last cen tury. There are few sources of energy that are as clean and environment ally friendly as photovoltaic While conventional fossil fuels such as natural gas are constantly found to 2 economical and not entirely safe. Traditional non CO 2 processes such as hydroelectric, wind and tidal are limited by the number of available sites and ma y have a negative photosynthesis efficiency of plants and consume agricultural resources. No alternative power production process can produce the energy per squaremeter the collec tion efficiency, to match modern high efficiency photovoltaic modules. In the last century this technology was mostly found in remote off grid locations and satellites. It was too expensive for other uses. Nowadays the cost per watt has greatly improved du e mainly to economy of scale   Hot C arrier S olar C ell S tate of A rt The design of a hot carrier solar cell should allow hot carriers to be collected before their energy is lost to the lattice. This is done by slowing the cooling in the absorber  and collecting the carriers in energy selective contacts  This ultimately leads to both higher open circuit voltage and short circuit current s, leading to an overa ll greatly improved efficiency.
14 In a conventional single junction cell, a photon at or greater than the band gap energy is absorbed to excite an electron from the valence band up into the conduction band, leaving a hole in the valence band. If equal, a carrie r arrives at the band gap edge. If greater, as is most often the case for the solar spectrum, energ y in excess of the band gap directly convert s in these high energy carriers defines a hot carrier tempera ture, T H The kinetic energies and hot carrier temperature are related by E kinetic = 3/2 kT H where k is the B oltzmann co nstant Of course, the hot carrier temperature is higher than the ambient temperature T 0 Ultimately the excess kinetic energ y is dissipa ted as heat until the carrier temperature equals the ambient temperature. Hot electrons and holes will collide with the lattice relaxing the energy in the form of phonons until electrons and holes reach the conduction band and valence band edges. Because o f this transition, the energy exceed ing the band gap is not utilized to generate electrical power but waste d as heat. For this reason the open circuit voltage is limited to the absorber band gap potential. Moreover, the short circuit curren t is limited by heat dissipation and small carrier density because th e small separation between conduction band and valence band leads to a high recombination rate. Hot carrier solar cell s should be designed in such a way that T H d ecay s to T 0 at a slow enough rate for the hot carriers to be collected without significant thermal loss. Photon energy is ke pt within the carrier system instead of becoming useless device heat. The resulting open circuit voltage is therefore not limited b y the band gap potential. The open circuit voltage is rather the potential difference between the quasi Fermi levels of the high energy e lectrons and holes as shown in F igure1 1 The short
15 circuit current is also improved because of a reduction in the reco mbination rate. This is due to the fact that high energy electrons and holes are separated farther than the edges of the conduction and valence bands. Also, point and extended defects in cry stal structure, polycrystalline or impurities in hot carrier devi ces are less of a problem since the high velocity carriers often have energies in considerable excess of trap states and barrier heights, thus reducing capture or scattering cross sections. This implies lower recombination rates as well easy transport acro ss grain boundaries and other extended defects. This characteristic is important since it suggests that lower cost polycrystalline absorber layers will be nearly as effective as single crystal absorbers. A typical hot carrier solar cell structure is schema tically displayed in Figure 1 1. An efficient cell design must perform two critical functions. First the design should ensure that the high energy photo excited carriers in the absorber do not transfer the energy to the ambient environment. Secondly, these carriers should be collected without energy lost. The first function is achieved by phonon engineering in the absorber layer. Hot carriers transfer the excess energy to the lattice in the form of an optic phonon. An optic phonon typically decays into two equal energy acoustic phonons, known as the Klemens mechanism   Optic phonons are high energy stationary lattice waves and are actually able to transfer energy back to the carriers to keep them hot. Acoustic phonons on the other hand are low energy propagatin g waves. Once energy is in the form of an acoustic phonon, it cannot be recovered to re heat carriers and thus will not contribute to electrical power generation Phonon engineering may be used to block the Klemens mechanism and to keep the high energy pho to exited carriers hot longer
16 Hot carrier collection is achieved by using energy selective contacts (ESC). T he se contact s are required to be very thin so that carriers are collected before they intera ct with the lattice. T he device design should allow col lection of carriers at an optimal energy range. Carriers having energies outside this range w ill be rejected to prevent scattering loss. Carriers in the ambient temperature device contacts at energ ies below the ESC energy are prevented to flow into the hot absorber and reflect from the lower band edge of the contact. Carriers at energ ies above the ESC energy are reflected back into the absorber by the upper energy structure of the contact. Many III V material systems have been used to demonstrate hot carrie r solar cell technology. A major breakthrough was achieved by group at the University of South Wales where modeling and simulat ion of phononic bandgap s for blocking the Klemens transistion in GaN, indium nitride( InN ) and indium phosphide( I nP ) were performed  The s imulations were done for superlattices and quantum dots with high phonon confinement using a semi empirical force constant mode l and a rigid ion approximation. The quantum dots of a sc ale of only a few atoms result in a degeneracy that success fully b l ock s the Klemens mechanism The experimental values for the mini gaps and car rier cooling rates were later measured using Raman spectroscopy and time resolved photoluminescence  using indium arsenide( I nAs ) quantum dots fabricated by the University of Tokyo  The dots were embedded in a gallium arsenide( GaAs ) strain reduction layer, which makes a superlattice. The hot carriers are collected from the phonon engineer ed absorber by use of the ESCs. Tunneling current peak position s of the hot carriers from the III V solar cell with the ESCs were extracted from the I V measurement  The maximum calculated
17 efficiency of a hot carrier solar cell is limited to 37.1% when the realistic transport properties of energy selective contacts are used  However, an argument made in  states that a carrier temperature high enough to make a difference in cell performance can only be achieved by realiz ing extremely long phonon lifetimes that are not realizable with current semiconductor technology In a study on GaAs/AlGaAs quantum wells the photogeneration energy balance model is used to extract the carrier temperature reaching the contacts T he energ y balance model states that the photogeneration energy loss rate equals the sum of the phonon energy loss rate and carrier recombination loss rate  The carrier temperature versus time behavior was given by an E nsemble Monte Carlo simulation based on t he energy balance model with an assumption of a 5 ps phonon life time T he temperature time behavior shows that the additional current from a hot carrier population resulting from the phonon bottle neck effect is not enough to improve the overall collectio n current. However, t his conclusion is reached from M onte C arlo simulation only where the many assumptions may not accurately reflect the physics Another approach to hot carrier solar cell study is a variation in the thickness of the ESCs  The study is based on InAs, which is a potential hot carrier solar cell absorber material. T he k ey of a hot carrier absorber (HCA) selection is a high absorption coefficient a low electron effective mass and a high hole effective mass so that the energy from photons is mostly di stributed to the electrons Furthermore, a m aterial with a low ratio of electron effective mass to hole effective mass in a superlattice absorber layer results in a high quantum confinement which is advantageous for several reasons. The absorp tion layer can be thick for better
18 absorption. Also the diffusion of hot carriers is suppressed, resulting in localized hot carriers that slow down the cooling  The c ontact material wa s selected for compatibility with the hot carrier absorber. A Monte Carl o simulation was used to analyze how the thickness variation and hot electron carrier scattering angle to the interface of the contact and the absorber would interfer e with the energy selection and contact conductivity. Another recent approach for improving the efficiency of hot carrier solar cells is the use of an optimally thin absorber layer, as demonstrated in a recent theoretical report on a gallium antimonide( GaS b ) absorber  In hot carrier solar cells a thinner absorber layer has more potential for reduction of thermalization loss and a fast extraction of carriers before cooling. However, ultrathin absorber layers do not absorb much light. So the thickness must be optimized between these two variables. Also, the light is engineered to scatter in a complex way s o absorption is possible An algorithm was used to comp ute the hot carrier collection  The conclu sion was that an absorber layer of 25 to 50 nm is theoretically capable of absorbing between 67 and 71% of the contain a statement about the carriers being hot, but it is assume d that the carriers would be quite hot if measured. Qu antum dots (QD) are another technique applied to hot carrier solar cells. At the University of Texas in Austin, the transfer of hot carriers from lead selenide( PbSe ) nanoparticles to titanium dioxide( TiO 2 ) was observed in real time using time resolved optic al second harmonic generation  The process occurred in the sub 50 femto second range. In a s eparate study of PbSe nanoparticles, a well ordered array of particles was created and tested for the property of preventing newly generated bi
19 excitons from recombining via the Auger mechanism  In a well ordered array, quantum dots have the tendency to couple. In doing so, a bi exciton pair in one QD will distribute one of the pairs to the other QD before the Auger recombination occurs. The multiple carrier collection demonstrated solar cells based on these arrays could yield quantum collection efficiencies in excess of 100%. The object of this research is to develop a practical hot carrier solar cell design that improves the efficiency of CIGS solar cells. In Chapter 2, the key parameters of a traditional CIGS solar cell are introduced for cell performance evaluation. Simulation results of a standard CIGS device structure are shown for studying the device physics and planning experiments to reveal hot carrier effects. In Chapter3, the HC princi ple is applied to the CIGS absorber. First, the phonon dispersion relationship of CIS is used to explain the phonon loss mechanism. Second, A CIS / CGS superlattice structure ve. Third, a quantum well structure of AlN / GaN is found to be the compatible contact for the CIGS absorber. The tunneling possibilities with varying contact thickness for selecting different energies are simulated using the principle of resonant tunneling. In Chapter 4, experiments are set up to study the hot carrier effects in CIGS thin film solar cells. Different mechanisms are used to extract the phonon loss information in the CIGS solar cell, including a space charge limit ed current model, the electric field guiding model, the Zener tunneling model and the impact ionization model. Chapter 5 discuss the modification on the conventional CIGS solar cell to use the hot carrier effect for efficiency improvement First, the energy selective contact is construct ed by calculating the energies reaching the contact with the obtained phonon mean free path relationship.
20 Second, a barrier inserted in the absorber is proposed to help hot carrier collection by blocking cold carriers flowing in.
21 Figure 1 1. Schemati c presentation of a hot carrier solar cell
22 CHAPTER 2 TRADITIONAL THIN FILM C OPPER I NDIUM G ALLIUM DI S ELENIDE SOLAR CELL MODELING AND SIMULATION Overview of Solar Cell Device Physics To understand how hot carriers are able to improve the efficiency, it is very important to study the basic device physics and equations of the traditional solar cells. In its basic form, the solar cell is just a simple PN junction diode when there is no light. The current density versus voltage characteristic of a solar cell i n the dark is given by (2 1) where J 0 is the reverse bias saturation current density. It is a function of the minority structure. The factor n equals 1 when there is no recombination and equals to 2 when there is a lot of recombination inside the junction space charge region of width W. With light, the solar cell generates a current density J L (2 2) wh ere G is the photo generation rate, and L n and L p are the minority carrier diffusion lengths of electron and holes, respectively. The solar cell current density versus voltage characteristic under illumination becomes then (2 3) Short circuit current density J sc open circuit voltage V oc fill factor FF and energy c are the key parameters for solar cell performance characterization.
23 The short circuit current density J sc is defined as the current density of the solar cell when V=0. The open circuit voltage is the out put voltage of the solar cell when J=0. The fill factor FF is defined as (2 4) where J m and V m are the solar cell current density and voltage, respectively, for delivering maximum electric power per unit of cell area The conversio c is described as (2 5) where P in is the incident light power density. D evice modeling and simulation are used in the following to study the device characteri stics for planning experim ents on CIGS devices with an eye on hot carrier cell design Thin Film C opper I ndium G allium Diselenide Solar Cell Simulation Using M edici A typical and often used  CIGS solar cell structure model is shown in Figure 2 1 The first layer is a 50 nm n type zinc oxide ( ZnO ) with an electron band gap energy of 3.3eV the second layer is a 30 nm n type cadmium sulfide ( CdS ) with a band gap energy of 2.4eV followed by a 30 nm inverted CIGS layer before the final CIGS absorber layer T his inversion layer is due to the diffusion of Cd + ions from the bath solution into th e CIGS films and substituting Cu 2+ ions during the deposition process   C a d mium is oxidized in the +2 state and Cu is oxidized in the +1 state. For this reason Cd acts as an electron donor and inverts the CIGS interface region from p type to n type. Also, an indium rich n type layer is observed on the surface of CIGS, further adding to the effect of inversion  Th e inverted layer reduces the hole population at
24 the defect rich interface and hence reduces the surface r ecombination rate. The next layer is a 2m p type CIGS absorber layer. The p ty pe CIGS absorber with the n type ZnO and CdS layers form a PN junction so that photo generated carriers can be separated by the build in electric field. Recombination centers are present in these devices. For modeling purposes defect centers and deep traps are placed at mid gap energies of the ZnO, CdS and CIGS; and in the interface of the inverted CIGS surface, respectively. The top contact is a commonly used transparent conductive oxide (TCO): ZnO:Al. The Al doped ZnO contact provides a planar pathway for electrons at the top of the CIGS structure to laterally transfer to the metalized grid. Spacing in the grid can be up to 2 .5 mm  to minimize blocked light, requiring the TCO to be highly conducti ve. It must also be transparent over the absorbed spectrum so that the photons are not prevented going to the CIGS absorber. The back contact usually is a molybdenum (Mo) layer. Mo is one of a few metals which stay stable under the high temperature CIGS la yer process  In Medici 1D simulations the ZnO:Al and Mo are not specifically applied because the front and back contacts are treated as ideal electrodes. All parameters us ed in our simulations are listed in Table 2 1  Simulations are carried out by using the Medici program. The band diagrams in equilibrium and under illumination are shown in Figure 2 2 A and B respectively. In equilibriu m, the Fermi level is aligned for all the layers. Under illumination, the quasi Fermi levels separate for the n side and the p side of the PN junction because the photon generated electron hole pairs change the carrier populations. The photon generation ra te is plotted as a function of distance in Figure 2 2 C. Most electron hole pairs are generated in the absorber layer surface. ZnO and CdS absorb a low
25 percentage of the solar spectrum, where most of the energy is below 3.2eV. The high band gap of ZnO allo ws this energy to pass through, and CdS is a thin layer with only a moderate coefficient of absorption for photons of energies above its band gap of 2.4 eV. On the other hand, CIGS is a direct band gap material with an extremely high absorption coefficien t of 10 5 /cm  and rapidly absorbs the bulk of the solar spectrum. Therefore, most absorption occurs on the CIGS surface. This makes thin film technology possible. The el ectric field formed in the space charge region (SCR) is shown in Figure 2 2 D. The slope of the electric field plot relative to the depth of the device is proportional to the charge density. The electric field increases in the n region since n type materia ls lose electrons across the junction and are charged positively. It decreases in the p region since the p type material accepts electrons and contains negatively ionized acceptors and thus becomes charged negatively. The charge density is discontinuous at the band edge, and creates spikes at depths of 50nm and 80nm. The photon generated carriers are swept out by the build in electric field in the SCR and are collected at the top and bottom contacts of the solar cell. Electron hole pairs generated outside t he SCR traverse towards the SCR by the diffusion process and are separated by the electric field before they recombine. The current density is plotted as a function of the depth of the device in logarithm scale at zero bias, as shown in Figure 2 2 E. Accor ding to the solar cell current density versus voltage characteristic expressed in equation 2 3 the photo generated current is obtained when the bias is zero. The electron and hole current densities are 310 2 A/cm 2 and 610 6 A/cm 2 respectively at the Z nO contact. The e lectron current starts to fall at a depth of 0.08m, which is the interface of the CdS and CIGS layers. At a depth of 0.15 m, the hole current density
26 becomes greater than electron current density. A large dip in the electron current dens ity appears at a depth of 0.8m and is due to the combined effects of vertical, lateral and horizontal currents in the 3D structure. The current density versus the voltage is shown in Figure 2 2 F. The short circuit current is 27mA/cm 2 and the open circuit voltage is 0.74V. The fill factor is 83% and the efficiency is 17%.
27 Table 2 1. Simulation p arameters of CIGS cell  Layer parameters ZnO CdS Inverted surface CIGS absorber Thickness(nm) 50 30 30 2000 Band gap E g (eV) 3.3 2.4 1.24 1.24 4.0 3.75 3.83 3.83 Electron mobility n (cm 2 /Vs) 50 6 300 300 Hole mobility p (cm 2 /Vs) 5 3 30 30 Type N N N P Carrier density (cm 3 ) 510 17 610 16 810 16 810 16 Dielectric constant 9 10 13.6 13.6 Effecti ve density N c (cm 3 ) 10 19 10 19 310 18 310 18 Effective density N v (cm 3 ) 10 19 10 19 1.510 19 1.510 19 Recombination center (s) n =10 6 p =10 6 n =10 6 p =10 6 n =10 9 p =10 10 n =10 6 p =10 6 Interface trap (s) n =410 9 p =410 10
28 Figure 2 1. CIGS solar cell device model
29 A B C D E F Figure 2 2. Simulation results for the CIGS solar cell A) Band diagram at dark. B) Band diagram at illumination. C) Photogeneration rate. D) Electrical field. E) Current density. F) CIGS solar cell JV chara cteristic.
30 CHAPTER 3 C OPPER I NDIUM G ALLIUM DISELENIDE BASED HOT CARRIER SOLAR CELL Phonon Engineering in the A bsorber Layer The traditional solar cell models do not consider hot carrier effects, as hot carriers are thought to be too short lived to play a ny significant role in the energy collection The mechanics of phonon scattering are very efficient for dispersing the excess energy of hot carriers. However, phonon engineering in the absorber shows it is possible to block most of the phonon scattering los s mechanisms and increase the life time of the hot carriers. The approach of phonon engineering starts from the basics of phonon physics. A crystalline lattice is composed of tightly al igned atoms. Chemical bonds from the lattice exert forces on the atoms, which keep each at om in an equilibrium position. If the lattice is impacted by an external force, atoms move away from their equilibrium position s The electronic bonds in a spring like action will resist the displacement. All connecting bonds of the latt ice b ehave in a spring like manner. Therefore the displacement of one atom transfers force to its neighboring atom, transferring force to the next to neighbor ing atom and so on. The displacements of many atoms from their respective equilibrium positions re sult in the formation of a lattice vibration wave. The energy of a wave can vary great ly depending on what the wave mode is. If a wave mode causes two neighboring atoms to stretch in opposite directions, the energy involved is very high. It is called an op tic mode because the vibration wave contains the energy of a visible, near UV or near IR light wave depending on how energetic of an impact the atoms received. If the displacements of neighboring atoms change gradually, there is less energy involved. This type of wave is classified as the acoustic mode. To
31 describe a wave, the wave vector q wavelength of the vibration al wave. The wave formed from atoms perturbed in this mode has a discr e ti z ed energy that is expressed as E=(n+1/2) (3 1) where is the reduced Planck constant, is the phonon energy and n is the phonon number. The phonon is introduced to describe the quantization of lattice vibration energy. The coupling of wave energy and the wav e vector depends on media properties such as the force constants between atoms. This relationship can be expressed in a phonon disp ersion curve. It has the information and the corresponding phonon energy as y axi s as shown on Figure 3 1. The phonon energy is proportional to the frequency For this reason the angular is often the y axis. The wave group velocity v g is defined as This is the slope of the phonon dispersion curve. An acoustic phonon branch typically has a group velocity on the order of the sound velocity which means that the wave propagates approximately at the speed of sound. phonon o riginates from this fact. An optic phonon branch usually has a very low group velocity, and therefore is effectively a stationary wave. Sometimes the y axis of the dispersion curve is also expressed in terms of a wave number, which is the inverse wavelength of an energy equivalent optical light wave The unit is cm 1 The reason for using wave numbers is that we then can map the phonon energy to the optical spectrum in spectroscopic studies
32 Phonon Disperion Modeling A phonon dispersion relation i s obtained by expressing the wave motion in terms of the displacement. A simple model called the linear chain model is used to establish s l aw, the force on an atom depends linearly on the displacement of its nearest neighbor s only. Effects from distant atoms are considered negl i g i l aw t he force can also be expressed as the dis placement acceleration the second derivative of the wave displacement with respect to time. T he force is therefore associated with the wave angular frequency. Thus, the relationship between the wave angular frequency and the wave vector is established. CI GS is a hybrid compound of the two ternary compounds CIS and CGS. For simplicity the two pure compounds are modeled to show their phonon dispersion curves. The linear chain model  of a CIS lattice is shown in the Figure 3 2. The atomic mass of copper, indium and selenium are M 1 M 2 and M 3 respectively The copper selenium atomic force constant and the atomic spacing are K Cu Se respectively, and the indium selenium constant and spacing are K In Se respectively. The displacement of an atom is noted as U. Different atoms usually have different amplitude s: (3 2)
33 The r epeating structure gives that (3 3) Forces impacting on atoms can be expressed b l aw and l aw: (3 4) Solving e quations 3 2and 3 4 gives the relationship of the and wave vector q as : (3 5) The atomic mass of copper, indium and selenium, the atomic spacing between atoms and the atomic force constants between copper selenium and indium selenium are list ed in the Table 3 1 The bulk phonon dispersion curve of CIS i s simulated in Matlab using a three atom unit (Cu, I and Se) linear chain model, plotted in the Figure 3 2 T he wave vector q is plotted on the x axis and the phonon energy is plotted on the y axis The C I S bulk phonon dispersion curve contains one acousti c branch, which curves and goes through the origin, and three optic branches, which are above the acoustic curve and do not go through the origin. For a crystal lattice containing a base of N
34 atoms, there will be N 1 longitudinal optic modes and one longit udinal acoustic mode  CIS contains a base of four atoms resulting in three optic branches plus one acoustic branch as shown in the F igure 3 1 The highest energy optic mode is at 0.032 eV and flat, and the others are in the range of 0.024 to 0.28 eV and 0.15 to 0.02 3 eV, respectively. The acoustic mode has energies ranging from 0 to 0.011eV. The phononic gap between the highest acoustic phonon energy a nd the lowest optic phonon energy is 0.004eV. For a real wave vector q, t he left side of the Equation 3 5 is a cosine function always within the range of plus and minus one. Frequencies that make the absolute value of the right side of the equation exceed one are not solutions. These frequencies form a forbidden band. Any wave introduced at a forbidden frequency in this band will be strongly damped. In a hot carrier solar cell, materials with high phononic band gaps are favorable due to the eck effect"    phenomenon where optic phonons are reabsorbed by electrons. The emission of hot optic phonons generates a hot non equilibrium distribut ion. The high optic phonon concentration reheats the carriers, thus slowing cooling. However, optic phonons can rapidly decay to acoustic phonons. Unlike stationary optic phonons, acoustic phonons will propagate energy away at the speed of sound. Moreover, acoustic phonons have low energ ies and are not likely to reheat the carriers. For significant energy to transfer back to the carriers, hundreds of acoustic phonons must transfer their energ ies at the same time. Statistically this is highly improbable. To utilize the bottleneck effect for hot carrier population, the decay process must be blocked. The probability of an optic phonon decaying into two equal energy longitude acoustic phonons is much greater
35 than decay into one transverse optic phonon and one lo ngitude acoustic phonon known    or other decay mechanism s If a material ha s a phononic band gap that is as large as the maximum acoustic phonon energy, the split of an optic phonon into two equal energy acoustic phonon s is blocked. The energy of the resulting two acoustic phonons falls in the forbidden gap, which means there is not an available acoustic energy level. Ideal solar materials having both big phononic gaps blocking the optic phonon decaying and solar matched optic al band gaps are unfortunately extremely rare. For example, the phononic band gap of InN is 0.0135eV, whic h is 1.8 times greater than its maximal acoustic phonon energy   However, the optical band gap of InN is only in a range of 0.7eV to 0.95eV  which is too low to efficiently collect from the solar spectrum. The phononic band gap of GaN is 1.2 times greater than its maximal acoustic phonon energy  But its optical band gap is 3.4eV, which is too high to efficiently collect from the solar spectru m. CIGS is known to be a good material for thin film solar cell absorber s The direct band gap gives a ver y high absorption coefficient. The band gap is tunable by the ratio of gallium to indium, from 1.0 eV for pure CIS to 1.7 eV for pure CGS (30% Ga at 1.3 eV is an excellen t match for AM1.5 radiation). It holds the record efficiency for thin film solar cells, 21%  However the phononic gap is not big enough to block the Klemens decay. Thus p honon engineering should be u sed to modify the bulk properties of this material. P honon engineering can build up more mini forbidden gaps in the acoustic mode by acoustic fol ding and discreti zing the optic mode by confinement. Mini gaps in the acoustic branch are observed in low dimen sional material structures   Those mini
36 gaps create extra forbidden gaps for the optical decay process, thus lowering the decay probability. Also, as the dimension decreases optic modes become discrete. The likelihood of a decay transitio n is reduced since the available optic phonons are reduced. A carefully engineered device structure will have a desirable phonon dispersion relationship. Hot carrier solar cell researchers have use d a superlattice (SL) structure to create a low dimension al confinement  SL structures are nano scale repeating material layer patterns. Tuning the material combinations and layer thicknesses gives an optimal phonon dispersion relation that maximally limits the transitions from optic phonons to acoustic phonons. The UNSW research group uses a silicon based SL structure in the hot carrier solar cell  Super l attice Phonon Dispersion Realization Phonon engineering in the absorbe r includes engineering in both the acoustic mode and the optic mode. First, mini gaps in the acoustic branch of the SL structure are analyzed Two models are used. One is called the linear chain model  as shown on Figure 3 3 The monolayer spacing is noted as The length and wave vect or of the CIS layer are d 1 and q 1 respectively. For CGS, the respective parameters are d 2 and q 2 The wave vector of the overall SL is q. The period of the SL is d: d=d 1 +d 2 The wave propagates in the z direction. Within the CIS layer, the displacements of each atom are: (3 6)
37 Defining and (3 7) and can be expressed as functions of q 1 equation 3 8 simultaneously: (3 8) Similarly, within the CGS layer, displacements are as fo llows: (3 9) and are functions of q 2 and by solving the wave equation 3 9 with CGS parameters At the interface of the CIS and CGS the impact forces must match. The wave m ust be allowed to behave as if it is in a uniform medium with displacement and stress continuity at the boundaries Therefore, the displacement continuity is kept at z=0: or (3 10)
38 and at z=d 2 : or (3 11) Stress continuity at z=0: or (3 12) and at z=d 2 : or (3 13) Let , and (3 14) Solving the equations 3 6 to 3 1 4 the SL phono n dispersion relationship becomes : (3 15) Another model that predicts mini gaps in the acoustic phonon branch of the SL structure is called the Elastic Continuum model  For acoustic modes having wavelengths significantly longer than the lattice spacing, the atomic displacements are effectively a continuum so that the propag ation of elastic waves across the SL layers gives a phonon dispersion relation as follows:
39 (3 16) B y using equation 3 16 an acoustic phonon dispersion curve of the CIGS based SL structure of one atomic l ayer of CIS over two atomic layer of CGS is plot ted as shown in Figure 3 4 The densities and sound velocities of CIS and CGS are listed in Table 3 1 The mini gaps in the acoustic mode of the SL structure are due to the fact that two slightly different ma terials have different force constant s and lattice constant s at the boundary. Next the optic phonon confinement is utilized. A bulk optic phonon wave vector is in the range of The minimal wave vector where L is the material thickness. Therefore the wave vector of a bulk material can be considered continuous within the above range since the bulk material is very thick. However, in a SL structure, the wave vector becomes clearly discrete as illuminated in Figure 3 5 where d 1 is the thickness of the material in a unit of the SL structure. Therefore, the corresponding phonon energies are limited to few possibilities. This phenomenon is also due to the mismatch between the materials of the SL so that some waves in the bulk material cannot propagate in the SL structure. Hence, p honons are spatially confined. The optic pho non branches of the SL become discrete further reducing the likelihood of Klemens transitions. A complete picture of the acoustic and optic modes of the CIGS SL structure is shown i n Figure 3 6 with 1 nm of CIS alternating with 2 nm layers of CGS. Mini ga ps in the acoustic phonon branch of the SL structure are simulated by using the elastic
40 continuum model. Optic branches become discrete due to optical confinement in the superlattic structure. The simulation results show that the phononic gap increases to 0.006eV and t he decay of an optic phonon with energy of 0.015eV is blocked because the two resulting acoustic phonons having energies of 0.0075eV via the Klemens mechanism are in the forbidden mini gap. The available optic phonon energies are discrete, whi ch makes the engineering less complicated. Electrical Engineering Aspects of the Contacts and the Absorber Layer Energy Selective Contacts The next stage of the hot carrier solar cell design is to collect the hot carriers without energy loss using energy selective contacts (ESCs) Firstly, the contacts need to be very thin so that phonon interactions are limited and the high energy is confined in the carrier system. Secondly, the contacts are to collect only carriers of a very narrow energy range so that n o energy loss occurs inside the system. The carriers of lower energy are rejected to prevent cooling the other hot carriers already collected. The carriers of higher energy are also rejected so their energies are not wasted. Thirdly, the energy range is op timized to match the most likely energy of the hot carriers so that more carriers are available for efficient collection Therefore, the quasi F ermi level of the electron contact is above the conduction band and the quasi F ermi level of the hole contact is below the valence band. The output voltage of the hot carrier solar cell, which equals the difference between the quasi Fermi levels, is enhanced. The ESCs structures are proposed to be a n inter band degenerate tunneling structure or a resonant tunneling structure 
41 Esaki tunneling An Esaki diode is an interband degenerate tunneling structure. It provides an energy select feature since only carriers with a certain energy can tunnel through the diode. The band diagram of a cadmium sulfide (CdS) Esaki diode is shown in Figure 3 7 A p type CdS layer is heavily doped so that the quasi Fermi level (Ef p ) is a few KT below its valence band and the quasi Fermi level (Ef n ) of the heavily doped N type CdS layer is a few KT above its conduction band. An important assumption is that all states above the quasi Fermi level are empty and that all states below the quasi Fermi level are filled At equilibrium the voltage bias V is zero. A p ositive voltage value is defined as introducing a positive bias at the p side and a negative voltage is defined as having a negative bias at the p side. The Ef p and Ef n are al igned in equilibrium, as shown in Figure 3 7 A. When the diode is under forward bias, where V>0, electrons accumulate on the n side. The quasi Fermi levels Ef n and Ef p are separated by qV electron volts, as shown in the Figure 3 7 B. Electrons in t he fille d states on the n side below the Ef n now can tunnel to the p side above the Ef p and below the valence band, where empty states are available. A small amount of tunneling current is generated, as shown in the Figure 3 7 D. The maximum is given when the Ef n is aligned to the valence band of the p side and the Ef p is aligned to the conduction band of the n side. The diode thus provides a selective range between the valence band of the p side and the conduction band of the n side via the tunneling channel. The narrow tunneling path prevents scattering loss. As the applied bias increases this property is lost. T he Ef n will be above the p side valence band and Ef p below the n side conduction band. The tunneling current decreases since the filled states under the Ef n are cut off by the p side forbidden gap. If the applied bias further increases the difference between the n side and the p side conduction band
42 decreases so that the electrons of the n side may overcome the reduced band potential resulting in a curre nt increase, as shown in the Figure 3 7 D. A proposed devic e structure is shown in Figure 3 8 [3 2] Two Esaki diode contacts are used to selectively collect carriers of specified energies. However, a few shortcomings of the structure need to be explained. Conventional solar cells work in the forward bias domain where the p side of the junction coll ects holes and n side of t he junction collects electrons. But current in the Esaki diode contact of the proposed device structure flows backwards, where holes are collected in the n side and electrons in the p side. This creates problems. Firstly, holes en tering an electron rich n region will rapidly recombine, causing an internal leakage current. Secondly, the n side always has a lower voltage, where external currents prefer to flow in and not out. Also, restrictions on the tunneling energy band width limi t the collection of high energy carriers. The tunneling energy band is limited by the degeneracy level, which allows a quasi Fermi level just a few KT above the conduction band or below the valence band (1 KT = 25 .9 meV at room temperature). However, in or der to let high energy carriers tunnel through, the optimal selective energy band needs to be a few electron volts high. High energy tunneling bands are thus hard to realize by Esaki diode contacts. Also, large amounts of electrons generated by light will raise the Ef n to be higher than the p side valence band, and the tunneling channel is lo st. A double barrier quantum well structure as presented in the next section alleviates many of these drawbacks. Double barrier quantum well structure A double barrier quantum well (DBQW) structure is a resonant tunneling structure where the transmission probability goes towards one within the resonant energy band and falls towards zero outside the band The simplest DB QW structure is
43 made of a low potential energy well confined by two high potential energy barriers. In classical mechanics, the probability of transmission across the barrier is zero if the particle energy is less than the barrier potential energy and one if the particle energy is greater In quantum mechan ics, however, the probability of a particle crossing the barrier is rarely zero or one, but a number in between this range. The transmission probability is obtained by first solving the Schrodinger equation in the barrier and well regions independently and applying the boundary conditions of a continuous wave function and wave function derivative to the solutions The square DB QW tunneling probability depends on the barrier potential energies the incident energy of the particle and the well width  : where and (3 17) The sine function causes the tunneling probabili ty to oscil lat e. The incident energies with high transmission probabilities form resonant bands at the maximum of the oscillation which provide the energy selections. The calculation of transmission tunneling probabilit ies across arbitrary potential energ y barriers is given in  Assume the arbitrary potent ial energy profile can be represented as a sequence of N small step potentials U l Transmission between each segment is described by the matrix M l defined as where (3 18)
44 E is the electron incident energy and m* is the effective mass. The overall transmission is: (3 19) The transmission amplitude is: (3 20) The transmission probability is (3 21) The CIGS absorber has a composition dependent electron affinity in the range of 4.1eV for CGS to 4.48eV for CIS and respective band gaps ranging from 1.68 eV to 1.04 eV Electron affinity measures how strongly an atom binds its outermost electron The band diagram shows this to be the energy between the conduction band and the vacuum level as indicated in the Anderson model  Figure 3 9 The DB QW structure contact requires a potential barrier to form between the absorber and the contact itself. Therefore, the contact barrier material needs to have a lower electron affinity and a greater band gap relative to CIGS based on the Anderson m odel. Cold cathode materials are known to have low electron affinities  Some material candidates include diamond films with a surface electron affinity in the range of 0.38eV to 1.27eV depending on the hydrogen coverage of the surface  and a band gap of 5.47eV b oron carbon nitride(BCN) films with an electron affinity from negative to 1.2eV  and a bandgap range from 5.3eV to 3.4eV  depending on the carbon composition ratio of the films and AlN films reported to have a positive electron affinity of 2.1eV  and a band gap of 6.3eV. An AlN film is a good candidate for adapting to the CIGS absorber,
45 as nitride compounds can be deposited on many materials. The well material is chosen to be GaN which is compatible with the absorber and also has a high electron affinity to form a suitable w ell between two AlN cladding films Also, GaN has a wide band gap of 3.4eV and thus is transparent for the sunlight to be absorbed The electron transmission probability of a n Al N /GaN/AlN DB QW contact is shown in the Figure 3 10 A and B Calculations perfo rmed with a varied barrier and well thickness result in different resonant band locations. In Figure 3 10 A, the thickness of the AlN barrier is 4nm and the thickness of GaN well is 2nm. Seven resonant bands appear for electrons with energies ranging from 0eV to 3 .5eV. In Figure 3 1 0 B, the thickness of the AlN and GaN layers are 2nm and 4nm, respectively. There are still seven resonant bands for incident energies ranging from 0eV to 3 .5 eV. However, more resonant bands are locate d below 2eV T he resonant ba nds locat ed above 2eV are broadened Therefore, optimization of the DB QW structure results in desirable energy selections for the hot carrier solar cell domain of operation. The hole transmission probability of the respective AlN DBQW contact is shown in t he Figure 3 1 0 C and D. The hole contact is not important since there are not many hot holes. Super l attice A bsorber The CIGS SL absorber was studied previously; mainly from the phonon engineering point of view. Here, the electrical properties are investiga ted. A SL structure is also a resonant tunneling structure. Only carriers within the resonant bands can tunnel through the whole absorber and arrive at the contacts. Careful tuning of the structure not only gives the benefit of slowing the rate of hot carr ier cooling, but also provides carriers with se lective energies for the ESCs. An absorber structure consisting
46 of alternating stack of five 2 nm thick CGS layers with four 1 nm thick CIS layers was simulated, and t he results are shown in Figure 3 1 1 The b and diagram is shown in Figure 3 1 1 A. The resonant bands for electrons are located in the range of 0.22eV to 0.4eV, and abov e 0.8eV as shown in the Figure 3 1 1 B. For holes, the first resonant band located at 1.15eV and the second one located at 1.35eV, as shown in Figure 3 1 1 C. The resonant bands reduce the probability of recombination. Electrons and holes will only recombine by the mechanism of electrons in the first electron resonant band re combining with holes in the first hole resonant band, or the second with the second and the third with the third and so on. The optical band gap of the absorber is no longer the band gap of CIS or CGS but the difference of the first resonant bands. Tuning the structure can give different band gaps for the absorpti on. Therefore, the optimization can be done with a large amount of freedom.
47 Table 3 1 CIS and CGS lattice parameters I III VI2 CIS CGS Atomic mass of I(kg) 1.055310 25 1.055310 25 Atomic mass of III(kg) 1.906710 25 1.15810 25 Atomic mass of VI(kg ) 1.311210 25 1.311210 25 Atomic spacing of I VI(m) 2.4610 10 2.4610 10 Atomic spacing of III VI(m) 2.5610 10 2.5610 10 Atomic force constant of I VI(N/m)  54.8 59.8 Atomic force constant of III VI(N/m)  120.7 129.3 Density(g/cm 3 )  5.77 5.57 Sound velocity(m/s)  2.210 3 3.0210 3
48 Figure 3 1. Phonon dispersion curve of CIS
49 Figure 3 2. Linear chain model for CIS Figure 3 3. SL structure of CIS / CGS
50 Figure 3 4. Phonon dispersion curve o f CIS / CGS
51 Figure 3 5. Confined optic phonon dispersion curves( solid line) within a SL reduced Brillouin zone 0
52 Figure 3 6. Phonon dispersion curve of CIGS bulk and SL structure. Black Solid lines represent the CGS b ulk phonon dispers ion curve; blue solid lines represent the CIS bulk phonon dispersio n curve; green, purple, and red lines are the phonon dispersion curves for the SL structure of 1nm CIS with 2 nm CGS
53 A B C D Figure 3 7. Esaki tunneling band diagram A) At zero bias. B) at 0.1 Volts. C) at 1 Volts. D) JV characteristic.
54 Figur e 3 8. Proposed hot carrier solar cell with Esaki diode contacts Figure 3 9. Anderson Model for the DBQW contact
55 A B C D Figure 3 10. Transmission probability of an AlN DBQW contac t A) Electron contact with 4nm barrier and 2nm well. B) Electron contact with 2nm barrier and 4nm well. C) Hole contact with 4nm barrier and 2nm well. D) Hole contact with 2nm barrier and 4nm Well.
56 A B C Figure 3 11. SL absorber tunneling A) Potent ial. B) Resona nt bands for electrons. C) R esonant bands for holes.
57 CHAPTER 4 EXPERIMENT S ON C OPPER I NDIUM G ALLIUM DI S ELENIDE THIN FILM SOLAR CELL FOCUS ON HOT CARRIER EFFECTS Introduction The theoretical analysis shows nano scale structures would ultimately achieve the goal of improving the hot carrier lifetime a nd collection. But the fabrication of a nanostructure CIGS device is a very advanced process. The traditional device is relatively much simpler, yet has evolved from years of efforts from NREL and other research groups. The optimization of layer thicknesse s and processing conditions have been done to achieve the best performance. The more advanced nanostructure device would be a much greater undertaking. The previous modeling work established the proof of concept for more advanced work to follow. First expe rimental research is necessary to investigate the possible presence and characteristics hot carrier effects in a conventional device. Photo current measurements as a function of applied bias were carried out on the device SC1 fabricated by NREL to search f or the presence of hot carrier effects already present in bulk CIGS The device SC1 consisting a semiconductor material stack from the top starting with 450nm ZnO, 30nm CdS layer, 30nm inverted CIGS layer and 2m CIGS absorber layer and ending with Mo I n the reverse bias region, the photo current density was observed to increase with voltage whereas the standard curve is relatively flat. Th e observed nonlinearity with wavelength dependency is proposed to be a hot carrier related effect. First, s ome other possible mechanisms need to be discussed and possibly eliminated One possible mechanism for the nonlinearity is the potential barrier between the CdS and CIGS layers varying in height depending on the wavelength of light entering
58 the device. A red light distortion is observed i n  where the barrier blocks current generated in forward bias resulting from a higher barrier under red light, resulting in the distortion. T he CdS layer has acceptor like defects trapping donor electrons, raising the conduction band of the CdS layer relative to the Fermi level U nder short wavelength illumination the photon energy is high enough to generat e EH pairs in the CdS layer which gives extra electrons to the conduction band in an amount that is possibly greater than what the traps are able to trap and recombine This lowers the conduction band of CdS layer and the barrier height. Thus current flow is not inhibited by the barrier, and does not appear to have a distortion at short wavelengths However the nonlinearity trend in the device SC1 is observed in both the red and blue light experiments. Therefore the CdS deep level trap theory cannot explai n the nonlinearity A model that explains both the red light and the blue light distortions is that for a material with a small absorption coefficient in the depletion region, th e absorption coefficient will be affected by the applied bias significantly, causing the rate of current increase to deviate from the normal exponential trend  T he increased electric field under increased reve rse bias may result in an increased absorption coefficient which is called the Franz Keldysh effect  If the absorption coefficient of the absorber is low the photocurrent will significantly increase under th is effect But CIGS has a large absorption coefficient in the junction and the effect s hould be minimal below our detection limit. Therefore the Franz Keldysh model does not seem to explain the current nonlinearity observed in CIGS A nother potential explanation of the nonlinearity is that the photocurrent may increase at a greater rate und er certain biases due to the bias extending the length of
59 the space charge region, which results in an increased collection volume of photogenerated carriers  The SCR does not extend far into the n side due to the heavy doping, but on the p side it extends far due to the light doping Under blue light exposure t he CIGS absorption region is smaller than th e SCR. Under red light exposure the absorption region is comparable to the length of the SCR The theory suggests that a red light current increase would be seen due to the SCR being extended to better cover the absorption region under red light. However t he current increase is not observed just under red illumination. In fact the red light photo current increases less than the blue light photo current. A lso, the current increase due to the SCR widening is only a square root law whereas the observed trend is greater. Therefore the theory of the SCR widening collection volume does not seem to match the observed data. Next, several models are discussed that potentially could explain the wavelength dependent IV measurements. A space charge limit ed current mode l and the Zener tunneling model are used to determine if the nonlinear effect in reverse bias is due to traditional carrier injection and tunneling or to a hot carrier effect. The electric field guiding model, the modified impact ionization model, and the modified Shockley lucky electron model are used to interpret the current voltage characteristics of the bulk CIGS solar cell under different wavelength illuminations to possibly identify and quantify hot carrier effect s. Finally, the modified Shockley luck y electron model is used to extract the mean free path of hot carriers between successive phonon collisions. Space Charge Limited Current Model The dark current density of a diode is commonly modeled as (4 1)
60 where J 0 =J 01 +J 02 is the diode saturation current density. (4 2) is the diffusion related component and (4 3) is the trap assisted generation recombination related component. J 02 dominates via generation in the depletion width the reverse dark current density for a non ideal device. The depletio n width therefore J 02 follows a square root dependency on reverse bias. However, the experimental dark current density in CIGS solar cells reported in the literature is observed having a linear characteristic at low reverse bias and becomes superlinear at high reverse bias  Mechanical scratches were proposed to explain the linear behavior since the reverse current increases dram atically with the increase of the load of scratches and the reverse current varies linearly over 1/T 1/4  In the experiment on the device SC1 the reverse dark current (Figure 4 1) shows neither the expected square root nor linear bias dependence. The generation related Space charge limited current (SCLC) via pinholes in the ZnO and CdS layers consisting of a metal CIGS molybdenum structure was proposed as contributing to the reverse bias leakage current   Space Charge Limited Current Model Basic Physics The current density has a linear dependence on voltage when the mobile charge is a constant, as: (4 4)
61 In this case, the surface potential and the electron and hole concentrations are fixed. But if the electrode injects carriers resulting in the tot al carriers exceeding the number of carriers generated from the dopants, the linear relation of the current and voltage no longer holds. The resulting SCLC is proportional to the square of the voltage   Assuming the capacitance between the two parallel electrodes is a constant (4 5) where is the applied voltage and is the excess charge injected from the electrodes. The density of injected free electrons is written as: (4 6) where is the cross section area of the parallel electrodes and is the distance between the electrodes. The resulting SCLC is therefore expressed as (4 7) A numerical coefficient of was obtained by Mott and Gurney from detailed calculations, and is added to the equation for a more accurate predictions. Law equation 4 4 dominates at low applied voltage, where is the electron density from thermal generation. In semiconductors, it equals the donor density N d in n type materials. As the applied voltage increases, the excess carrier density n s from the electrode increases linearly with voltage. There is a cro ssover voltage, V T point, the injected carrier density is high enough to offset the thermal equilibrium density. Also at this crossover voltage the transit time of the exce ss carriers t transit equals the carrier relaxation time,t ohmic Beyond V T the excess carriers do not relax quickly
62 enough and reach the surface of the opposing parallel plate contact. V T can be calculated as follows: (4 8) A Medici simulation is carried out to check if the software can handle SCLC phenomena where specifically the contact boundary conditions play an important role. The parameters used in the simulation are listed in Table 4 1. The heavily doped n type CIGS, modeling a metallic pinhole shorting the contact to the absorber layer, provides excess electrons for injecting into the lightly doped p type CIGS. The dark current density versus v oltage is shown in Figure 4 low bias and the square law in the high bias regime, as shown by the trend lines with log slopes of 1 and 2, respectively. The doping density of the p type CIGS used in the simulation is 610 11 /cm 3 At V= 10 3 ( 4 9) The plot in Figure 4 2 reads a current density of 510 2 A/cm 2 at the same voltage. The increased current density comes f rom the fact that the carrier density of the lightly doped p region is conve r ted to n type by the adjacent heavily doped n + regions. The electro n density is plotted in Figure 4 3 The heavily doped n + contacts make that the effective carrier density betwee n the contacts becomes 10 14 /cm 3 due to diffusion and the effective distance between contacts reduces to 1 m. The current density is then calculated as ( 4 10)
63 The crossover voltage equals 1.2 V as calculated from Equation 4 8 In Figure 4 2, the point at where the extrapolated lines cross agrees with this value. At the crossover voltage, the total current density is twice the corresponding ohmic current density, since it is where the SCLC from the excess carriers equals the ohmic current from the thermal carriers. The total current density is the sum of these two components. The SCLC of the simulated n + p n + CIGS cell under illumination is shown in Figure 4 4. Currents at two different illumination intensities are plotted. In the ohmic region, the more intense illumination results in a greater current. However, as the voltage reaches the crossover point, the curren ts are the same regardless of illumination intensity. As seen in the space charge equation for current calculation equation 4 7, it is not a function of the carrier concentration. This is because the current is limited by the injection of carriers from the parallel electrodes, which is a function of voltage only. However, at the higher illumination intensity the crossover point occurs at a higher voltage The crossover voltage is determined by not only thermally ionized dopants but also illumination g enerated carriers. At the higher illumination intensity, this sum is greater and increases the V T Space Charge Limited Current in a C opper I ndium G allium Diselenide Solar Cell The dark current voltage characteristic of the device SC1 has a log scale slope between 1 and 2 ( Figure 4 1 ) under reverse bias and is symmetric with respect to the origin in the voltage range of 0.2 volts ( Figure 4 5 ) However, in a normal diode we would expect to see the reverse bias current relatively flat and the forward bias cu rrent exponential. Therefore, SCLC is proposed to explain the data   since the SCLC has a square law dependence on the voltage and a symmetric structure through the origin.
64 In a CIGS solar cell, the contact metal may pe netrate the thin layers of ZnO and the CIGS directly. In addition the CIGS layer may have regions with low densities of acceptor sites. If the pinholes contact an area of low carrier density in the CIGS they form a SCLC structure T he low carrier density causes the crossover voltage to occur at relatively low voltage values and the metal electrodes are abundant electron carrier sources. Pinhole current causes a parasiti c loss in a CIGS device. The total current is expressed as a sum of current through the pinholes and current through the rest of the device contact area: I total =J SCLC A SCLC +J solar A solar (4 11) where A SCLC and A solar are the overall effective pinhol e area and the solar cell area, respectively. Under reverse bias, the total current is dominated by the SCLC giving a weak voltage dependence. The SCLC matching with the device SC1 dark current versus reverse bias voltage is shown in Figure 4 6 where the measured reverse bias dark current is compared to the simulated dark current using the pin hole model. The pinhole area is calculated by A SCLC =I total /J SCLC in the reverse bias section. I total is the experiment dark current and J SCLC is obtained by the Med ici program with the parameters listed in Table 4 1. The resulting calculated effective pinhole area is 0.147m 2 which makes up only 1/10 7 of the solar cell contact area. The modeled dark current for device SC1 is the sum of the simulated dark SCLC curren t plus the simulated dark solar cell current The dark SCLC current is caculated by multiplying the simulated pinhole current density, J SCLC with the pin hole area, A SCLC The solar cell current is simulated by the M edici program
65 with the parameters list ed in Table 4 2 Figure 4 6 shows that there is a good match between the experiment and the model IV curves In the next few paragraphs the dark SCLC current, obtained above, is applied to a method of extracting the photo generated current from measured CI GS data, which is more rigorous than th e basic solar cell performance characterization: photo current, I L is extracted by subtracting dark current density I d from the measured total current density I tot under illumination as shown in Figure 4 7 I L is th eoretically flat because the rate of photo generation is a constant and the cell is a thin film, so that the active photo absorption region is limited by the film thickness. However the I L obtained by the traditional method is not flat. The likely reason i s the model does no t consider the effects of SCLC. The model taking the SCLC into consideration for photo current density is extracte d as follows: The measured current under illumination, I opt_tot is written as I opt_tot =I L +I diode +I sclc_opt (4 12) where I L I diode and I sclc_opt are the photo generated current, the diode current and the optical SCLC current, respectively. The measured dark current is written as I dark_tot = I diode +I sclc_dark (4 13) where I sclc_dark is the dark SCLC current. Th erefore, the photo generated current I L equals the difference between the measured illumination current and the dark current plus the difference between the dark SCLC current and the optical SCLC current. Hence: I L =I opt tot I d ark_tot +I sclc_dark I sclc_opt (4 14)
66 However, the experiments are not designed to extract the effects of the fourth term, which is linear in the region of the IV curve measured in experiments. The number of photo generated carriers pushes the crossover voltage beyond the range me asured, as previously discussed. Therefore I sclc_opt is believed to not contribute to the photo current in a non linear manner. To study the nonlinear contribution of the SCLC, equation 4 14 is modified as: =I opt tot I dark_tot +I sclc_dark (4 1 5) is not an exact photo current, but is the nonlinear part of the photo current, which is useful for the following experimental analysis. The device SC1 is exposed to LED sources of wavelengths 365nm, 455nm, 630nm and 740nm, respectively. The LED light intensity at each wavelength is different as controlled by the supply current. Although a best effort was made to have an approximately consistent distance of LED to solar device and LED power (photons/s), the equipment used was not accurate enough t o guarantee that the current was 100% consistent. However the information from the I V curve that characterizes the hot carrier collection lies in the relative rate of increase of the current with voltage. Therefore the calculated photo generated photo curr ent, is normalized to its value at a voltage of V= 0 to eliminate the the difference due to the light intensity variation as shown in Figure 4 8 in logarithm scale. For 630nm and 740nm wavelengths illumination the current increases gradually with the bias. For 395nm and 455nm wavelengths illumination, the current rapidly increases at high bias. The IV curve analysis at different wavelengths is used to determine if nonlinearities observed in the data are due to SCLC effects. In the log log plot, tw o
67 different types of curves are expected to be seen depending on the type of dominant current. If photogeneration current is dominant, the curve is expected to be flat. If SCLC current is dominant, the slope of the curve is expected to be between 1 and 2 a t lower voltages. As the bias increases, curves will all merge to slope 2 independent of wavelengths and intensities. In Figure 4 8 the slope s of the plot are less than 1 in the region where V<0.1 volt indicating the current is not SCLC dominated, as I SCL C has a slope of at least 1 in all cases. This is expected, as small voltages result in small SCLC currents that cannot compete with the photo current. When V>0.1 volt the slopes of the plot s are in the range of 1 to 2 which is possibly a transition from Ohmic to SCLC dominated current. For an Ohmic device, the IV has a wavelength dependency because the conductivities change with carrier densities for different photogeneration rates at different wavelengths. But the observed wavelength dependent IVs are n onlinear, where as an Ohmic effect sustains a linear trend. Therefore the data is not ohmic possibly SCLC dominated. However, the current s measured at the four different wavelengths should merge together as the SCLC slope 2 region is only a function of v oltage regardless of wavelength or photon intensity But the observed currents at different wavelengths are diverging. The refore, the nonlinearity observed above V=1 is not from the SCLC slope 2 component. Electric Field Guiding Model Description of the Mo del The following model where the bias dependent electric field in the space charge region of the solar cells affects the collection of high energy carriers differently than low energy carriers, explains how the photo current can be nonlinear and waveleng th dependent. For a given field strength, low energy, thermally generated or thermalized
68 carriers will be directed to their collecting contacts, but the hot carriers with initially randomly directed velocities may overcome the field effect and scatter into opposing contacts reducing the photo current in this way. Hence via a simple device physical model, a relationship between initial hot carrier energy, electric field in the space charge absorber region, and photocurrent has been established from which the relative density of hot electrons if present, can be determined from measured current voltage data Hot Carrier Effects in the Current Voltage Characteristic under Reverse Bias The hot carrier effect in a current voltage characteristic is illustrated in Figure 4 9. Light comes from the left. Photo generated carriers are separated in the space charge region by the build in and applied electric field. Typically electrons are collected in the n type region contact and holes are collected in the p type regio n contact. However, the high energy photo generated electrons have excess energy to overcome electric field deceleration reaching possibly the p type region. These electrons reduce the overall current. In the model hot carriers generated within the region x 1 will bounce from the conduction band E c and will be subsequently be collected in the n region contributing to the photo current; hot carriers generated within the region of W x 1 have a 50% chance of going to the p region therefore only 50% are contributi ng to the photo current. W is the width of the depletion region. X 1 is the thickness of the region where the potential barrier is high er than the electron energy. W X 1 is the region where the electron energy is high enough for hot electrons to enter the p type region. The resulting electron photo current is written as (4 16) where the photon generation rate g op is assumed constant in the depletion region.
69 A 450nm n doped ZnO and a 2m p doped CIGS diode with 455nm incident photons based on this model is simulated using Matlab. All parameters used in the simulation are listed in Table 4 3. Photo current density versus reverse bias voltage is plotted in the Figure 4 10. At low bias, hot carriers can overcome the barrier scattering and reach both contacts. Only half of them are collected on the electron contact. Therefore the current density considering this hot carrier effect is half of the one without a hot carrier effect. As bias in creases, more of the hot carriers bounce back from the E C potential energy barrier and are collected via the n side contact. Therefore the current density increases rapidly, as shown in the Figure 4 10 for reverse bias voltages larger than 0.6 V. Experime nts on the device SC1 are carried out to study the hot carrier effect. The device is illuminated with 455nm and 740nm wavelengths under reverse bias, respectively. In a parallel theoretical study, the n ZnO/p CIGS diode is simulated under the same conditio n. The photo current density is normalized to the current density value at a voltage of V=0 to obtain the relative rate of increase due to the hot carrier effect and eliminate other effects such as light intensity variation. Figure 4 1 1 shows the photo cur rent density versus voltage relationship of the experimental and simulation results. The photon energy of 455nm wavelength is 2.7 eV, which is about 1.4 eV higher than the CIGS optical band gap and is able to generate high energy, hot electron hole pairs. The photon energy of 740nm wavelength is only 1.8eV. The generated electron hole pairs are closed to the conduction band edge and are more likely to relax as cold carriers. As shown, the experiment with 455nm wavelength illumination reveals a rapidly incre asing current density at high bias while the experiment with 740nm wavelength
70 illumination show s an weaker effect. The trend of the experimental data matches with the model prediction. At 0. 6 volts in the simulation the current increases suddenly at a much steeper slope, creating a cusp in the plot. The 455nm wavelength experiment data does not show the predicted sharp cusp Also the overall slope is more extreme than predicted by the electric field guiding model. Therefore the lacking of electric field gui dance on low bias for hot carriers is not the only theoretical phenomena governing the current changing nonlinearity. The Zener Tunneling Model The observed photo current increases with bias may be a type of Zener effect, which is a type of electric al brea kdown that can occur under reverse bias conditions. As the bias increases, the p side valence band moves above the n side conduction band. When this happens the p side valance band electrons could tunnel to the n side conduction band empty states, if there are available valence band electrons, available conduction band states and the space charge region is narrow enough for the electrons to tunnel through the depletion region. The current density is proportional to both the number of p side valence band ele ctrons and the number of empty n side conduction band states A small change in the bias near the breakdown voltage can cause an exponential increase in the current density. However, the large size of a typical CIGS solar cell space charge region is unlike ly to allow tunneling of p side valence band electrons. The typical depletion region width that Zener tunneling is known to occur in is smaller than 10 6 cm  whereas the space charge region of the device SC1 is on the order of 2010 6 cm. In addition to a thick barrier to tunneling, when CIGS is under illumination the photo generation reduces the number of valence band electrons on the
71 p side and increases the number of conduction band electrons on the n side. As a result, the probability of Zener tunneling is reduced. The Impact Ionization Model Impact ionization is another phenomenon that could be a factor in the observed photo current increase in the reverse bias region. The increased electric field and widened SCR allows some carriers to accelerate to the ionization threshold energy within a scattering mean free path The hot carrier may transfer th e extra energy to ionize a val e nce band electron, leaving a hole behind and thus creating an extra EH pair. Th e process of extra EH pair generation results in the impact ionization current A Medici simulation was performed to extract the impact ionizatio n current by comparing the difference in reverse bias currents when the impact ionization is considered and not considered. The Medici simulation uses the parameters listed in Table 4 2 under 4 5 5nm and 633nm wavelengths respectively. The impact ionization current density is shown in Figure 4 1 2. It varies with bias and wavelength in a rapidly increasing manner. However the impact ionization current density is only 0.1% of the total photo current density when impact ionization model is not considered in the simulation, whereas the increase of the photo current density in the previous device SC1 experiment shown in Figure 4 7 gives a larger value F urthermore, the Medici simulation result gives a more rapid increas e for long wavelength than for short wavelengt h, whereas the trend shown in Figure 4 7 indicates a more rapid increase for short wavelengths than for long wavelengths. One shortcoming of the Medici impact ionization simulation is that it does not consider the possibility of photo generated hot carrier s The shortcoming is a result of the Medici assumption that all the photo generated carriers are relaxed to the band gap
72 edge independent of the stimulating photon energy. The only source of energy gain for hot carriers is acceleration in the electric fie ld: where W is the effective acceleration distance. W is equal to the lesser of two: the length of the SCR or the photon penetration depth. As the bias increases, the electric field increases and the SCR is widen ed in the direction of the light ly doped CIGS layer Under 455nm wavelength illumination, the SCR is longer than the penetration depth. Therefore the W is limited by the penetration depth The energy gain increasing is due to the increasing electric field only. It does not benefit from t he SCR becoming wider. Under 633nm wavelength illumination, the SCR changes from less than the penetration depth to larger than penetration depth with increasing reverse bias. The energy gain increasing benefits both from the increasing field and widening of the SCR. Therefore the red illumination is more responsive to the increased SCR width and gives higher impact ionization current The i mpact ionization model need s to be modified for hot carrier solar cells. Basics of the Impact I onization M odel The t h reshold energy E th can be calculated as follow s : (4 17) where is the ratio of the hole effective mass , and the electron effective mass For CIGS with an optimal band gap of 1.24eV, the impact ionization threshold energy for electrons and holes is then 1.4 3 eV and 2.36eV respectively The higher thres hold of the hole is due to its larger effective mass relative to the electron, resulting in a lower probability of impact ionization
73 The m ultiplication factor M is a convenient way to eliminate the difference due to the illumination intensity variations It is defined as the ratio of the electron (or hole) current coming out of the impact ionization region to the electron (or hole) current going into the region U nder a low breakdown voltage M can be written as  ( 4 18) The multiplication factor for the device SC1 is shown in Figure 4 13 The i onization rate is defined as the electron hole pairs generated per carrier per u nit distance travelled  The relationship between and M is given as follows: (4 19) where W is the SCR width  W hen the electron ioni zation rate is a lot larger than the hole ionization rate, the total ionization rate is written as  ( 4 20) F or CIGS the hole multiplication factor, M p is equal to 1 under the assumption that the hole impact ionization is negligible for the followin g reasons First the hole effective mass is 10 time larger than the electron effective mass Second, the acceleration is not big enough to have hole impact ionizat ion. The hole does not reach the threshold energy in the SCR, as the energy gained from the 1 00nm SCR is not enough, and it does not reach the threshold in the 2 m p type region either as any additional energy gain is small due to the low electric field. Equation 4 18 gives the multiplication factor based on the total current. However, since hole multiplication is negligible, all of the multiplication comes from electrons, hence:
74 M n = (4 21) T he parameter W 1 in equation 4 20 is a fitting constant that defines the relationship of the bias across the junction V, and the SCR region width, W by the way of : ( 4 22) The unit is cm/V 0.5 Another relationship is given in terms of the bias, maximum electric field and the SCR width as : ( 4 23) Equations 4 22 and 4 23 are combined and re arranged as follows : ( 4 24) The maxim um field and voltage from Medici simulations with parameters listed in Table 4 2 are plotted in Figure 4 1 4 to extract parameter W 1 where the x axis is E m and the y axis is The plot is linear, and W 1 is the obtained slope The ionization rate i s obtained by plugging W 1 and E m into Equation 4 20 W 1 M p and E m are obtained from previous discussion and M n is obtained from I V measurements on the device SC1 The experimentally obtained ionization rates are shown in Figure 4 1 5 When 1/E m is below 5.5 10 6 cm/V, the ionization rate drops down for 395nm. The reason is unknown, as the ionization rate is expected to continue to go up. F or wavelengths of 395nm and 455nm, both impact ionization rates are independent of the electric field wh en 1/E m ranges from [5.5 6.2 ] 10 6 cm/V. The ionization rate is also observed to be independent of the electric field over [6 8.5] 10 3 V /cm  when an indium antimonide( InSb ) photo diode is exposed to 1100K blackbody radiation. The
75 reason for the flat trend is not explained in the paper. The impact ionization rates for wavelengths of 633nm and 740nm in the device SC1 go up as 1/E m increase from [8 10] 10 6 cm/V. The trend is contrary to the expectation of a continued decrease with the decreasing bias. An explanation is possibly an inaccurate multiplication factor that shows up in low bias. The ionization rate s for short wavelengths are in the order of 10 5 /cm which indicates a minimum acceleration distance of 10 0 nm for impact ionization to occur Considering that the SCR is 100 to 200 nm long, most short wavelength photogenerated carriers in the SCR are expected to initiate impact ionization. The ionization rate s for long wavelength s are in the range of 2 to 8 10 4 /c m, resulting in an acceleration distance of 125 to 500 nm. Impact ionization is not expected to take place at low bias due to t he long acceleration distance required, but at high reverse bias the e lectric field increases and the SCR expands, thus impact ionization is expected to occur. The observed ionization rate difference for short and long wavelengths is due to the respective differences in carrier temperatures. The higher the initial energy, the lower the acceleration distance that is needed, The design of experiments for observing impact ionization should maximize the carrier acceleration distance. Electron impact ionization tests are usually done by illuminating the p side so that electrons have a long accelerati on distance, and hole tests by illumination from the n side. But in the above CIGS experiment, illumination is only possible from the n side. As a result, electrons do not have a long acceleration distance and are therefore not expected to have impact ioni zation due to the field. T he observed impact ionization is a result of the high energy the initiating energy electrons
76 received from the short wavelength photons, which is helpful for revealing phonon loss information since reaching the ionization threshol d electron energy is determined by phonon energy loss and field gain. The M odified I mpact I onization M odel The traditional source of the impact ionization energy is the electric field, but t he proposed additional source is the photon energy Under illumina tion an electron can reach the threshold energy under an relatively small electric field in comparison to dark current conditions due to the help of the photon energy. In this model, the difference in electric field energy needed for the onset of impact io nization at two different wavelengths is simply the difference in photon energy at the two different wavelengths, as seen in a voltage fall off in t he illustration shown in Figure 4 1 6 The point of electrical breakdown due to the field alone is shown unde r the dark condition, where the black line starts to fall at the dark threshold voltage V 3 which provides an acceleration energy E 3 (V 3 ). For red light and blue light the breakdown voltages V 2 and V 1 are respectively decreasing in magnitude The threshold energy for electrical breakdown, E th is the same with or with out illumination because it is a material property. The E th not only comes from the field acceleration energy, but it also considers the photo n energy and the phonon loss If h igher photon ener gies contribute to reaching the threshold energy then less energy is needed from the field acceleration. For the dark current with phonon loss, the threshold energy is: E th =E 3 E ph (4 25) and the required field acceleration energy is E 3 (V 3 )=E th +E ph (4 26)
77 For the current under red illumination, there is an extra term, E opt_red considering the extra energy from the red light contributing to the calculation of the threshold : E th =E opt_red E g E ph +E 2 (4 27) The required field accelerat ion is, E 2 (V 2 )=E th E opt_red +E g +E ph (4 28) For blue light th e required field energy is: E 1 (V 1 )=E th E opt_blue +E g +E ph (4 29) There are some differences between the predictions and the experiment results from Figure 4 7 The first difference is the absence of a hard breakdown. The data appears to be a soft trend The second difference is the lines are not set apart by differences in voltage that directly correspond to the differences in the photon energies. Besides the differences, the data tren d shows that blue light current onset impact ionization ahead of the red light current. The trend is due to how much the added photon energy and phonon loss affect the carrier acceleration towards breakdown. Information about electron energy loss to phonon s is contained in the impact ionization data Below a theory is presented for revealing the phonon loss information from the data. T he illustration in F igure 4 1 7 shows for different photon energies the electron energies at the peak generation point are re lative to the impact ionization threshold energy. Electrons w ith low photon energ ies cannot get enough energy for ionization even without phonon scattering loss, as shown Figure 4 17 A) In the case of high photon energy the electron has energy above the im pact ionization threshold energy even without the help from the electric field shown in Figure 4 17 C ). T he impact ionization occurs even at zero reverse bias. With moderate photon energy, the
78 case in Figure 4 17 B ) the energy gain from the photon and el ectric field electron minus phonon scattering loss results in an energy value just above the impact ionization threshold energy at the edge of SCR. I mpact ionization may or may not occur depending on the amount of energy loss due to phonon scattering whic h is determined by the phonon scattering mean free path. Information about the phonon scattering loss is contained in the onset conditions whe n M is larger than 1. An analysis for revealing the phonon mean free path is performed w he re the highest density o f photo generated electron s is expected The electron distribution around the peak generation point is narrow due to the high absorption coefficient of CIGS. Therefore the location of the photo generation can be accurately estimated. The initial energy is known based on the photon wavelength and the energy gained from the field based on the location within the SCR The initial energy above the onset, E in Figure 4 17 B), represents the maximum amount of phonon scattering loss that can occur and still have impact ionization. The minimal phonon scattering mean free path can be calculated from the maximum phonon scatterings within distance x, the distance between the peak generation and the edge of the field. The mean free phonon scattering path can be direct ly calculated as follows: (4 30) This analysis only works for the case B in Figure 4 1 7 A CIGS solar cell is a more complicated heterojunction device than the simple diode illustration in Figure 4 17 In Figure 4 1 8 the CIGS solar cell ban d diagram, electric field and photon generation rate are shown as a function of distance to the top contact predicted by Medici using the device SC1 structure and the parameters listed in
79 Table 4 2 The first observation is that the peak carrier generatio n occurs at the interface of CIGS and CdS. The second observation is that the interface is 50 nm from the edge of the SCR. Therefore the peak photo generated carriers will not get much acceleration help from the field. In Figure 4 1 9 the impact ionization threshold energy is plotted in the CIGS solar cell band diagram with the photon generation rate in the CdS layer and the CIGS layer I mpact ionization is un likely to happen over the CdS buffer layer due to its high threshold energy Therefore the electron s are only expected to have impact ionization while they are still in the short section of CIGS before the interface. The possibility of impact ionization is low. The initial kinetic energy of the electrons gain ed from 395nm and 455nm wavelengths are plott ed as green dash lines i n the band diagram s in Figure 4 19 For high level photons, the carrier already is above the threshold energy and the impact ionization is expected to already occur at zero bias The experiment al data shows onset at zero bias, but i n this case, the phonon scattering mean fre e path cannot be calculated by the modified impact ionization model The M odified Shockley L ucky E lectron M odel T o extract the value of the mean free scattering path from impact ionization data an initial model developed by Shockley is used to study the probability of an ing up kinetic energy to the impact ionization level The lucky electron does this by means of not scattering while accelerating in the field so that it retains all the kinetic energy until the threshold level is obtained The percentage of electrons that participate in impact ionization is related to the probability of an robability of an electron scatter ing within a distance dx is considered. This probability is proportional to dx and inverse ly proportional to : hence
80 (4 31) The p robability of an electron not scattering over the distance l the impact ionization mean free distance, is calculated by sectioning l into lengths of dx, calculating the probability of not scattering over each lengt h and calculating the overall probability by the product (4 32) For a given choose dx<< (4 33) The kinetic energy gained from the field by accelerating over distance l to reach the threshold energy is given by (4 34) which allows the impact ionization rate to be written in terms of the field: (4 35) If the equation 4 35 is re arranged as (4 36) it is noticed that the right hand side of equation 4 36 is negative since the terms E th q, which indicates < Because is always less than the impact ionization rate is limited by the electric field. However, t he ionization rate shown in Figure 4 1 5 is much higher than allowed by the field. Therefore electrons are believed to have an initial e nergy higher than room temperature to compensate for lacking energy from the electric field for ionization.
81 A new, modified lucky electron model includes a term for the initial energy of electrons as a result of generation by a high energy photon. The imp act ionization threshold comes from the field acceleration and the initial kinetic energy E av : (4 37) where E av is the electron kinetic energy from high energy photons after a rapid initial loss: E av =E photon E g E raploss (4 38) For the modification to include the E av it is convenient to have a new term for the energy d erived from the field, that distinguishes from the real threshold energy, E th Eqn 4 37 becomes as follows: (4 39) The ionization rate equation 4 35 is modified as: (4 40) The terms and are used as fitting parameters for the ionization rates at different wavelengths in the device SC1 which is shown in Figure 4 20. For wavelengths of 395nm and 455nm in the 1/E m range of 5.5 to 6.2 10 6 cm/V, the fitting curves and the data diverge It is unknown why the ionization rate data is independent of the field in this range, but the independent trend is also observe d and not explained for in  For wavelengths of 633nm and 740nm, the fitting curves are below the data when 1/E m is above 8.5 10 6 cm/V. It might be that the ionization rate data is inaccurate due to a distorted multiplication factor when the bias is close to zero.
82 The initial electron energy, E av is extracted from the data by the difference of in CIGS layer and as shown in equation 4 39. The ionization in the ZnO and CdS layers are not considered as: first, th e ionization threshold energies of ZnO and CdS are too high to allow impact ionization; second, the photo generation rates in the ZnO and the CdS layers are low; third, the high doping density in ZnO layer makes that W n <
83 Table 4 1. Simulation p ar ameters of n + p n + CIGS cell Layer parameters n + CIGS p CIGS n + CIGS Thickness(nm) 50nm 2m 50nm Band gap E g (eV) 1.24 1.24 1.24 3.83 3.83 3.83 Electron mobility n (cm 2 /Vs) 300 300 300 Hole mobility p (cm 2 /Vs) 30 30 30 Typ e n p n Carrier density (cm 3 ) 510 17 610 11 510 17 Dielectric constant 13.6 13.6 13.6 Effective density N c (cm 3 ) 310 18 310 18 310 18 Effective density N v (cm 3 ) 1.510 19 1.510 19 1.510 19
84 Table 4 2 Simulation p arameters of the device SC1 Layer parameters ZnO CdS Inverted surface CIGS absorber Thickness(nm) 450 30 30 2000 Band gap E g (eV) 3.3 2.4 1.24 1.24 4.0 3.75 3.83 3.83 Electron mobility n (cm 2 /Vs) 50 6 300 300 Hole mobility p (cm 2 /Vs) 5 3 30 30 Type N N N P Carrier density (cm 3 ) 510 17 610 16 810 16 810 16 Dielectric constant 9 10 13.6 13.6 Effective density N c (cm 3 ) 10 19 10 19 310 18 310 18 Effective density N v (cm 3 ) 10 19 10 19 1.510 19 1.510 19 Recombination center (s) n =10 6 p =10 6 n =10 6 p =10 6 n =10 9 p =10 10 n =10 6 p =10 6 Interface trap (s) n =410 9 p =410 9
85 Table 4 3 Simulation p arameters of n ZnO/p CIGS cell Layer parameters ZnO CIGS Thickness(nm) 450 2000 Band gap E g (eV) 3.3 1.24 4.0 3.87 Electron mobility n (cm 2 /Vs) 50 300 Hole mobility p (cm 2 /Vs) 5 30 Type N P Carrier density (cm 3 ) 510 17 810 16 Diele ctric constant 9 13.6 Effective density N c (cm 3 ) 10 19 310 18 Effective density N v (cm 3 ) 10 19 1.510 19 Recombination center (s) n =610 9 p =610 9 n =610 9 p =610 9
86 Figure 4 1 Experimental reverse dark current vo ltage characteristic of the device SC1
87 Figure 4 2 Space charge limited current density voltage characteristic of a n + p n + CIGS cell with parameters in Table 4 1 T
88 Figure 4 3 Electron density versus distance in a n + p n + CIGS cell with parameters i n Table 4 1
89 Figure 4 4 Space Charge limited current density voltage characteristic of the n + p n + CIGS cell with parameters in Table 4 1 under 455nm illumination with different intensity. The red line and black line are for i ntensities of 0.0125mW/cm2 and 0.5688mW/cm2 respectively.
90 Figure 4 5 Dark current voltage characteristic of the device SC1
91 Figure 4 6. Space charge limited current compared with the measured CIGS r everse biased dark current The black line is the measured data and the red dashed line is the Medici simulation data based on pin hole model. Figure 4 7. Photo current voltage characteristics of the device SC1
92 Figure 4 8. Normalized I V characteristics for nonlinearity analysis with different wavelengths. The purple, blue, orange and red lines are used to indicate illumination under 395nm, 455nm, 633nm and 740nm wavelengths, respectively.
93 Figure 4 9 Band diagram illustrating the hot carrier effect in the electric field guiding model Figure 4 10. Simulation of hot carrier J V characteristic s using the electric field guiding model
94 A) B) Figure 4 1 1 Reversed bias J V characteristics under different wavelength illuminzation. A) 455nm wavelength illumination and B) 740nm wavelength illumination. The current density on the y axis is normalized to the current density valu e at V=0. The blue line on A) and the red line on B) are the experimental data. They refer to the blue axis and the red axis respectively. The black solid line and black dash line are simulation results assuming photo generated carriers staying hot 100% an d 0% respectively. Both refer to the black axis on the left. Figure 4 1 2. Medici simulated impact ionization current density. The blue and red lines represent for 455nm and 633nm illumination, respectively.
95 Figure 4 1 3. Multiplication factor of the device SC1 under 395nm, 455nm, 633nm and 740nm illumination, respectively, as a function of applied reverse bias.
96 Figure 4 1 4. Voltage Electric Field relationship for parameter W 1 extraction.
97 Figure 4 15. Impact ionization rates versus maximum electric field inverse for the device SC1
98 Figure 4 1 6. Illustration for the modified impact ionization model Figure 4 1 7. Phonon mean free path extra ction model for electrons with different energies. A) L ow energy B) M oderate energy C) H igh energy.
99 A ) B ) Figure 4 18. CIGS solar cell band diagram, electric field and photo generation rates as a fu nction of distance to the top contact. A ) CIGS solar cell band diagram (dashed lines) and electric field (red solid lines). B ) CIGS solar cell band diagram (dashed lines) and photo generation rate for 395nm(blue solid line) and 740nm(red solid line) respectiv ely Band energies refer to the black axis and the photogeneration rates refer to the red axis. A ) B ) Figure 4 19 CIGS solar cell band diagram (dash ed lines) and photogeneration rate (solid lines) as a function of distance to the top contact for different wavelengths. A ) 39 5nm B ) 455 nm
100 A B C D Figure 4 20. T he ionization rates of different wa velengths of the device SC1 with the fitting function of and E av A) 395nm. B) 455nm. C) 633nm. D) 740nm.
101 Figure 4 21 Phonon mean free path plotted versus the kinetic energy E av after a initial rapid loss before phonon scatterings
102 CHAPTER 5 MODIFICATION OF A CONVENTION COPPER INDIUM GALLIUM DISELENIDE SOLAR CELL WITH HOT CARRIER EFFECTS Introduction Carrier cooling and other loss mechanisms result in the conventional CIGS device collecting only 25% of energy in the absorbable range of the spectrum. The absorbable spectrum has an upper limit of about 375 nm, limited by the ZnO and CdS layers, and a lower limit of about 1100 nm due to the absorber bandgap cutoff. This range contains 70% of the energy of the solar spectrum, as shown in Figure 5 1  Although most of the energy will not be collected by the single junction structure, hot carrier s may carry excess energies in a conventional CIGS device that can allow some improvement that is not thought possible traditionally The wavelength dependent ionization rates sugges t that the photo generated carriers do not lose all the energy above the bandgap. Hot carriers may reach the top contact under operating forward bias under the assumption that carriers travel in a direct path towards the contact. In addition to the excess initial energy, h ot carriers have a net energy gain due to the accelerating electric field and a net loss due to phonon scattering and impact ionization. For each phonon scattering with a mean free path a carrier loses energy, creating a phonon; for each impact ionization with a mean free path of a carrier loses energy to create an addition electron and hole. The Shockley luck y electron model gives the initial energies of photo generated carriers and the phonon scattering mean free path, which are used to predict the phot o generated electron energy at any location between the point of generation and the contact. The calculated energy allows a traditional solar cell to utilize the hot carrier effect for a more efficient collection by modifying the c ontacts or buffer layer.
103 Adding the Energy Selective Contact to the Device SC1 One way to collect the existing hot carriers in a conventional cell is an ESC. The quantum well structure design can be tuned to any energy window for electrons to pass through The window is determined by the energies of photo generated carriers reaching the top contact from the region between the CIGS surface and the back edge of the SCR, where most of the photons are absorbed. Most carriers reach the contact with the energy of E peak corresponding to t he peak generatio n point at the CIGS surface. Moving away from the CIGS surface at first the added field energy is less than the energy loss in scattering and ionization and a m ini mum energy, E m in is reached. Towards the back of the SCR, the field acceleration energy gain outweighs the overall scattering and ionization loss due to the longer acceleration distance Carriers from the back reach the top contact with a m axi mum energy, E m ax The analysis under forward bias, where solar cells generate power, can be translated directly to practical designs that improve efficiency. Photo generated carriers from 4 5 5nm and 633nm wavelengths are analyzed at a bias of 0.5 88 3 V, where the maximal electric field is half of the one in the dark wit hout bias, to estimate the energy with which the carriers arrive at the contacts. The carriers experience electric field acceleration and different type loss es One simplicity of the analysis is that ionization loss is not a factor unde r the bias of 0.5 88 3 V. The predicted ionization rates under the bias are below 510 4 /cm and 210 4 /cm for 455nm and 633nm, respectively, as shown in Figure 4 15 which translate to impact ionization mean free paths on the order of 200nm and 500nm, respectively. Both mean free paths are larger than the SCR region, which is on the order of 100 nm under 0.5883V Therefore the carriers are unlikely ionize within the SCR. Also, impact ionization loss is not considered outside of the SCR.
104 First, the electric field drops greatly and second, in the ZnO and CdS layers the threshold energies are too high due to the higher bandgaps. The only loss mechanism is phonon loss over every which is the phonon loss mean free path. T he carrier energy reaching the contact is determined by calculati ng the phonon scattering loss and the field acceleration at each scattering point as shown in Figure 5 2 The mean free scattering path used to p redict the scattering points is obtained from Figure 4 21 based on the initial kinetic energy of the photo generated carriers. The electric field energy gain is integrated over the distance between scattering points by the following formula: where is the electric field profile The electric field profile for calculating the energy gain under 0.5 88 3 V is obtained from the M edici simulation with the parameters listed in table 4 2 The phonon loss is assumed to be 35meV, which is the average optic pho non energy of CIS and CGS from Figure 3 6 The energy at the top contact is obtained by repeating the calculation between scattering points from the origin of the electron to the contact. For photo generation under 455nm wavelength, the model predicts elec trons generated at the CIGS surface to reach the n side contact with an energy of 0. 8658 eV E peak The upper and the lower bound limits, which are previously termed as E max and E min are 1.1064 eV and 0. 8658 eV, respectively, for the 455nm wavelength. T he values of E peak E max and E min for 633nm wavelength are 0. 5108 eV 0. 7360 eV and 0. 4762 eV respectively However the top transparent n type ZnO layer is not completely depleted in the solar cell operation quadrant. The cold majority electrons in the n ty pe ZnO layer cool down the hot electrons that make it to the top contact. Therefore a conventional
105 CIGS solar cell needs to be modified to utilize the hot electrons for efficiency improvement. Barrier Model The solar cell design should maximize the photo c urrent and minimize the diffusion current. Under forward bias the output current is the sum of the two opposing current components: the diffusion and drift current. The photo generated current is drift current and is canceled by the diffusion current. The diffusion current consists of thermal electrons from the n type ZnO region that overcome the weakened electric field and diffuse to the p type CIGS, resulting in an electrical current directed from the p side to the n side under forward bias. This current component goes up exponentially with the bias. Under dark conditions the forward bias I V characteristic is dominated by the diffusion current. Under illuminated conditions, the photo generated carriers are separated by the electric field, which creates an electrical drift current from the n side to the p side. The photo current, determined by the photo generation rate and absorption volume, is independent of the bias. Since the thermal current component is the diffusion current, which subtracts from the ph oto current in calculating the total current, the lower the value of the thermal current the more the optical output survives. The solar cell efficiency can be greatly improved by suppressing the thermal carrier diffusion current. A barrier layer design is proposed for suppressing the thermal carrier current while not affecting the photo current. The barrier is inserted between the CIGS layer and the n ZnO layer to prevent thermal carriers in the ZnO layer from diffusi ng to cancel photo current The barrier could be placed either in front of or behind the CdS layer as modeling results presented in the next section will demonstrate.
106 Barrier Location Two Medici models are constructed to simulate the way the forward bias dark current is affected by a 30nm barri er: one with the barrier between the ZnO and the CdS, and the other between the CdS and the CIGS. For simplicity, the barrier material is assumed to have the same material properties as CdS, except for the higher conduction band offset and a change in band gap that keeps the valence band of the barrier and the CdS lined up. There are several conduction band offsets selected for the barrier relative to CdS, which are expressed in terms of kT as 8kT, 10kT and 20kT. Other layer parameters are listed in Table 4 2 T he resulting dark IV characteristics are shown in Figures 5 3 and 5 4 for the barriers on the ZnO side and the CIGS side, respectively. Since the dark current under forward bias goes up exponentially, the currents are plotted in the nature logarithm sc ale to reveal linear trends. The results for barrier s on the ZnO side and the CIGS side each with the three different barrier heights, are compared to the result without a barrier. At a given barrier height, the CIGS side causes a current reduction that i s both larger and covering a greater range of the voltage than the ZnO side barrier. Also the CIGS side barrier reduction factor is a constant for a given barrier height, and changes with the height proportionally. Overall, for a given barrier height, the CIGS side barrier appears to be more effective than the ZnO side barrier. There is not yet an explanation as to why CIGS side location of the barrier makes a difference over the ZnO side barrier in the range of voltage over which the barrier is effective. Barrier Height Influence on the Performance With the material design selected, the height of the CIGS side barrier should be optimized for blocking sufficient thermal diffusion current while not reducing too much
107 hot photo current. A barrier height of 20kT as shown in Figure 5 4 results in a reduction of diffusion current by a factor of or about 3.3 million at 0.5V The next step is to determine the reduction factor of the photo current with different barrier heights, so that the barrier height may be optimized. But the photo current reduction is complicated by the broad range of the solar spectrum: hot electrons from different photons may or may not cross the barrier, depending on the height The effect of the barrier height on photo current is studied at four different wavelengths spanning the visible solar spectrum, which is about 70% of the energy in the entire spectrum, as shown in Figure 5 1. If the energy of the electrons reaching the barrier for these illumination wavelengths is greater th an the barrier, the electron will cross the barrier and contribute to the photo current. The energy is calculated by the initial energy, the acceleration from the electric field and the phonon scattering. In the case of the 20kT barrier previously mentione d, i f the photo current is not reduced by the barrier, the open circuit voltage is increased by 15kT, or about 0.38 volts. The photo currents at wavelengths of 395nm, 455nm and 633nm are expected to not be reduced since the barrier is lower than the result ing hot electron energy. However, the photo current at 740nm is expected to be reduced by the barrier. Only the portion of electrons generated where the acceleration from the field compensates the lack energy of the optical carrier relative to the barrier is contributed to the photo current. Since the barrier causes a dependence on the electric field profile, the 740nm photo current is now a function of the bias. A MATLAB program is used to calculate the portion of electrons generated by 740 nm wavelength that are able to pass through the barrier. Without the barrier, the
108 photo current density is the integration of the photo generation over the absorption region With the barrier, the photo current density is the integration of the photo generation over the region where electrons reach the barrier with energies higher than the barrier considering energy changes due to electric field acceleration and phonon scattering. The electric field profile and photo generation rate for 740nm wavelength are obtained from the previous Medici simulation s as shown in Figure 4 18 The scattering points are predicted by the initial kinetic energy versus phonon scattering mean free path relationship shown in Figure 4 21. The energies of carriers reaching the barrier from any p oint in the absorption region are obtained by repeating the calculation of the energy change between the scattering points. The region of electrons reaching the barrier with energies higher than the barrier contributes to the photo current. When the bias i s zero, 70 % of the photo current is able to pass the barrier. When the bias is 0.5V, where the maximum electric field is 50% weaker than the maximum electric field at zero bias, only 0.008% of the photo current gets through. As the bias increases, the elec tric field decreases. Hence, a longer acceleration is needed. However, the longer distance also gives a higher possibility of phonon scattering. The energy loss is larger than the field gain, which makes it impossible to overcome the barrier. The large los s of photocurrent limits the open circuit voltage to less than 0.5 volts at 740nm in spite of the reduction of diffusion current. To eliminate the bias dependency of the photo current at 740nm wavelength, the barrier height should be lower than the optical carrier energy of 0. 35 eV or 14kT. The JV characteristics show an added barrier between the CIGS and CdS layers improves the efficiency for different wavelengths and barrier heights. The total current
109 density under illumination is obtained by simulating th e dark and photo current densities separately, with and without a barrier, and subtracting the photo current density from the dark current density. The dark current density is simulated by M edici whereas the photo current density is an analytical result o f integrating the photo generation rate over the whole absorption region as the designed barriers are low enough to not block any photo generated carriers The photo generation rates are simulated in M edici using the given intensity at each wavelength in A M1.5  for solar cells with and without the barrier The J V characteristics with illuminations at wavelengths of 395nm, 455nm, 633nm and 740nm for barrier heights of 8kT, 10kT and 14kT respectively, an d the curve without a barrier a re shown in Figure 5 5. As the barrier height increases, the open circuit voltage increases. The 14kT barrier is best for increasing the open circuit voltage while not reducing the photo current in the wavelength range of 395 nm to 740nm. Although the wavelength range studied is not the complete CIGS absorption spectrum, the range does cover enough of the spectrum to be considered as representative for the full spectrum. For instance, the energy between 740nm and the bandgap cu toff is only about 10% of all the energy that CIGS absorbs, as shown in Figure 5 1. The current from this portion does not affect the total short circuit current greatly. The barrier height of 14kT is suitable for a large open circuit voltage while not cut ting off too much of the short circuit current. The barrier material should have a conduction band offset of 0.35 eV and not much valence band offset relative to the CdS layer. A suitable material is most likely to be found in the II VI system, as the comp ounds often have adjustable bandgaps and
110 offsets by tuning the mole fractions of one or both of the II or VI column elements. Also, the layer needs to be stable in the CIGS solar cell. An analytical band diagram of most known II VI compounds, many of which are potential alternative buffer layers for the CIGS abso rber, is shown in Figure 5 6  Zinc sulfide( ZnS ) has a higher conduction band than CdS and a valence band value that is similar to CdS. The desirable band offset can be obtained by changing the Zn and Cd mole fraction in a Zn x Cd 1 x S compound. Papers   show that the compound electron affinity and the conduction band value change linearly from CdS to ZnS with x changing from 0 to 1. The numerical number of the conduction band difference of CdS and ZnS i s 1.14 eV, predicted in figure 5 6. Therefore, with x=(0.35 eV)/(1.14 eV/mole fraction zinc) = 0.3 mole fraction zinc for the desired conduction band offset Zn 0.3 Cd 0.7 S provides the required barrier for maximal blocking the thermal carriers from the unde pleted ZnO layer while not limiting the hot photogeneration carriers from the CIGS layer. Zn x Cd 1 x S can be used in addition to the 30nm CdS layer in the device SC1 as a barrier for selectively blocking cold carriers. The modification is based on the phono n loss information of the device SC1 Zn x Cd 1 x S has been studied by other groups as a n alternative to CdS in CIGS with the primary motivations bein g to widen the bandgap of CdS  and to reduce or en tirely e liminate (x=1) Cd  Efforts have been made wit h band gap adjustable b uffer layers such as MgZnO  to show the effects of varying the band offset of the buffer layer in CIGS. To the best of our knowl edge the band gap offset variation of Zn x Cd 1 x S has not been studied for us e with the hot carrier effect. Future work can be performed on the CIGS device by depositing the Zn x Cd 1 x S barrier layer in between the CIGS and the existing CdS buffer layer while making the ZnO
111 layer thinner, to limit the thermal carriers from counteracting the hot carriers photo current
112 Figure 5 1 AM1.5 spectrum 
113 Figure 5 2. The energies of photo generated carriers reaching the top contact from the region between the CIGS surface and the back edge of the SCR determining by the field acceleration and phonon scatterings.
114 Figure 5 3. Medici simulated dark I V cha racteristics of the device SC1 structure (parameters in Table 4 2) with a barrier between the ZnO and CdS layers Figure 5 4. Medici simulated dark I V characteristics of the device SC1 structure (parameters in Table 4 2) with a b arrier between the CdS and CIGS layers.
115 A B C D Figure 5 5. Medici simulated J V characteristic of the device SC1 (parameters in Table 4 2) with out b arrier and with barrier between the CdS and CIGS layers for barrier heights of 8kT, 10kT and 14kT at different wavelengths. A) 395nm B) 455nm C) 633nm D ) 740nm
116 Figure 5 6. Band diagram for II VI and I III VI 2 compounds. Numerical values indic ate the positions of the valence band maximum( VBM ) and conduction band minimum( CBM ) in eV [60 ]
117 CHAPTER 6 CONCLUSION S AND FUTURE WORK Conclusions The preliminary study of the CIGS absorber phonon engineering shows that mini phononic gaps appear in acoustic and optic p honon branches of a CIS/ CGS superlattice structure. The mini gaps reduce the po ssibilities of optic phonons decaying to acoustic phonons, which propagate energy away as heat loss. The localized optic phonons transfer energy back to reheat the photo generat ed carriers. Therefore, the CIS/ CGS superlattice structure provides a way to sl ow down the carrier cooling rate. When hot carriers last long enough to be collected, one way of collecting the excess energy is believed to be an ESC. A quantum well structure of AlN/ GaN is chosen to be the ESC for a CIS/ CGS superlattice absorber. First, nitride materials are stable with the CIGS absorber. Second, the wide band gaps of AlN and GaN allow the layer to be transparent and not interfere with photons coming into the device. Third, the low affinity and high band gap of AlN create a b arrier betwe en the contact and the absorber so that cold carriers are confined while carriers with the selected energy can tunnel through. Simulations show the selected energy can be tuned by varying the AlN and GaN thicknesses. Hence, the AlN/ GaN quantum well is suit able to be the ESC of a CIGS based hot carrier solar cell that collects carriers with desirable energies preventing energy loss to cold carriers. T he CIS/ CGS superlattice absor ber and AlN/ GaN ESC are studied on the modeling level, as the fabrication of a nano structured CIGS device is beyond the scope of our current research facilities. While the modeling serves as a starting point for a nanostructured CIGS device to be fabricated in the future t here is a lot of information to
118 be gained about hot carriers in the traditional device. Current voltage characteristics of the conventional CIGS solar cell under four different wavelength illuminations are measured at reverse bias, where a rapid increase of current with increasing reverse bias is observed which can be attributed to the impact ionization of the hot carriers. The wavelength dependent impact ionization rates are extracted from the current voltage measurements to reveal the existence of hot carriers in a conventional solar cell. A modified Shockley lucky electron model is developed to extract the ionization data. This process is then used to obtain the initial energies and the phonon mean free paths of the photo generated carriers under different wavelength illuminations. The hot carrier effect is used to improve the solar cell efficiency by embedding a barrier in a traditional solar cell. The barrier locations and compositions were analyzed by simulating the corresponding open circuit voltage and short circuit current under four wavelength illuminations i n Medici. A barrier consisting of Zn 0.3 Cd 0.7 S embedded between the CdS and the CIGS layers is proposed for maximally blocking the cold diffusion carriers while allowing most of the CIGS absorption layer hot carriers to pass through. Future W ork The modeli ng shows the potential of nanostructures to utilize hot carrier energy. The start of developing a hot carrier solar cell is to first realize hot carrier related improvements in a conventional cell. Hot carriers effects were in fact observed in wavelength d ependent IV measurements. The information can be used to modify traditional solar cells in the short term. In the long term, cell improvements can be achieved by fabricating a superl attice CIS/CGS absorber and incorporating AlN/GaN quantum well contacts fo r efficient hot carrier collection
119 In this work the superlattice absorber is termed as CIS/CGS because the analysis of the phonon bottleneck effect was done on alternating layers of CIS and CGS. But for future work, more flexibility can be obtained by us ing a CuIn x Ga 1 x Se 2 superlattice structure where the alternating layers have two different mole fraction numbers. The composition and thickness for each layer can be tuned to optimally minimize the hot carrier cooling rate. The fabrication of a CuIn x Ga 1 x S e 2 superlattice structure has not yet been reported. Techniques need to be developed for interface abruptness and layer thickness controll in the CIGS superlattice. Once a real superlattice structure can be produced, a well tuned design can be developed th eoretically and experimentally by comparing the model predictions to the experimental results and refining the structure in an iterative process. Also, the AlN/GaN quantum well contact feature size and growth on the superlattice absorber can be further inv estigated. In the future, fabricating the complete device, including the nanostructure absorber and contacts, and characterizing the phononic and electrical properties of the real device by time resolved photoluminescence, Raman spectroscopy and IV measur ements may lead to an unprecedented efficiency of a single junction solar cell.
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126 BIOGRAPHICAL SKETCH Yige Hu was born in Nanning, China. She received a Bachelor of Science degree in e lectronics and c ommunication E ngineering from the Beijing Institute of T echnology, Beijing China in 2003. In Fall 2006 she joined the University of Florida for her graduate education where s he received t he Master of Science degree in electrical and computer e ngineering in 2009. After her graduation, she continued to work towa rd s her Ph.D degree. Her research interests include the modeling, simulation, measurement and material s characterization of advanced semiconductor devices including CIGS based hot carrier solar cells.