PERFORMANCE OF ADVANCED TRIPLE-JUNCTION (ATJ) SOLAR CELLS

PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE ESCUELA DE INGENIERIA PERFORMANCE OF ADVANCED TRIPLE-JUNCTION (ATJ) SOLAR CELLS ROLF ALLAN L�DERS MORALES Memoria para optar al t�tulo de Ingeniero Civil Electricista Profesor Supervisor: ANDR�S GUESALAGA MEISSNER Santiago de Chile, 2005 PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE ESCUELA DE INGENIERIA Departamento de Ingenier�a El�ctrica PERFORMANCE OF ADVANCED TRIPLE-JUNCTION (ATJ) SOLAR CELLS ROLF ALLAN L�DERS MORALES Memoria presentada a la Comisi�n integrada por los profesores: ANDR�S GUESALAGA MEISSNER JUAN DIXON ROJAS �LVARO SOTO ARRIAZA Para completar las exigencias del t�tulo de Ingeniero Civil Electricista Santiago de Chile, 2005 ACKNOWLEDGEMENTS I would like to express my gratitude to Francisco Calder�n, classmate and friend with whom we participated in the Life in the Atacama project representing Pontificia Universidad Cat�lica de Chile. This work is the result of many hours of discussions as part of our long-run teamwork to complete our respective theses. Both complementary works are the result of a common goal, which was to accurately characterize new ATJ solar technologies. This made us work together on both of our theses. I want to thank the Department of Electrical Engineering of the Pontifical Catholic University of Chile for allowing me to carry-out this research, specially to my professor and advisor Andr�s Guesalaga, who was always aware of my work and was at all times available when I needed his advice. I also want to show my appreciation to him for trusting in me and allowing me to participate in the Life in the Atacama project, which has opened many professional possibilities. I have to give special credit to James Teza, electrical engineer of the Field Robotics Center at Carnegie Mellon University (CMU), for his help in searching for specialized documents and papers relevant for this work. David Wettergreen, Michael Wagner, and the rest of the Life in the Atacama team from the Robotics Institute of CMU, merit particular gratitud for their unconditional support. ii CONTENTS P�g. ACKNOWLEDGEMENTS ......................................................................................... ii LIST OF TABLES ....................................................................................................... v LIST OF FIGURES..................................................................................................... vi RESUMEN.................................................................................................................. ix ABSTRACT................................................................................................................. x 1 INTRODUCTION .............................................................................................. 1 1.1 Objectives................................................................................................... 1 TECHNICAL BACKGROUND ........................................................................ 3 2.1 Semiconductor Basics ................................................................................ 3 2.1.1 Semiconductor Doping .................................................................... 5 2.1.2 P-N Junction Operation ................................................................... 9 2.1.3 Isolated P-N Junction ...................................................................... 10 2.1.3 Forward and Reverse Bias ............................................................. 12 2.2 Photovoltaic Cell Operation..................................................................... 15 2.2.1 Separation of Charge ..................................................................... 16 2.2.2 Isolated Photocell........................................................................... 17 2.2.3 Photocell with Load....................................................................... 17 2.3 Design Considerations ............................................................................. 18 2.4 Multi-Junction Solar Cells ....................................................................... 19 2.4.1 Construction Procedure ................................................................. 19 2.4.2 Advanced Triple Junction Solar Cells ........................................... 21 2.5 Definitions for the Characterization of Photovoltaic devices .................. 23 METHODS AND RESULTS ........................................................................... 26 3.1 Experimental Setup .................................................................................. 26 3.1.1 Central Experiment........................................................................ 27 2 3. 3.1.2 Pointing System ............................................................................. 31 3.1.3 Auxiliary Sensors........................................................................... 32 3.1.4 Physical Layout ............................................................................. 35 3.1.5 Control Software............................................................................ 36 3.2 Environmental Conditions during Experiments....................................... 39 3.3 General Considerations Used for Data Analysis...................................... 40 3.4 Results ...................................................................................................... 42 3.4.1 Overview of Electrical Characteristics .......................................... 42 3.4.2 Performance Under Varying Conditions ....................................... 44 3.4.3 Performance of ATJ Solar Cells on Earth versus Space................ 56 4. CONCLUSIONS .............................................................................................. 60 BIBLIOGRAPHY ...................................................................................................... 62 A P P E N D I X E S .................................................................................................. 64 Appendix A: Recombination Processes in Semiconductors ..................................... 65 Appendix B: Absorption in Direct Bandgap and Indirect Bandgap Materials ........ 68 LIST OF TABLES Table 3.1: Main characteristics of the SCTU sensors connected to the generalpurpose data logger ..................................................................................................33 Table 3.2: Average temperature of solar cells under horizontal position testing ............48 Table 3.3: Conversion Efficiencies and Fill Factors........................................................51 Table 3.4: Electrical characteristics of ATJ solar cells operating in space compared to operation on earth ................................................................................................58 v LIST OF FIGURES Figure 2.1: Position of Fermi level in a metal, insulator and semiconductor ....................3 Figure 2.2: Fermi-Dirac distribution function....................................................................5 Figure 2.3: Extra energy levels due to doping in a n-type semiconductor and in a ptype semiconductor. Efn and Efp are the new Fermi levels of the n-type and ptype semiconductors respectively due to doping .......................................................6 Figure 2.4: Junction in final equilibrium (isolated) ...........................................................9 Figure 2.5: Energy diagrams, reverse (left) and forward bias (right) ..............................13 Figure 2.6: Schematical cross-section diagram of a single-junction solar cell................15 Figure 2.7: Optimal bandgap for single junction solar cell [2]........................................18 Figure 2.8: Lattice Constant and Bandgap Energy for Commonly Used Semiconductors [2] ..................................................................................................20 Figure 2.9: Cross-sectional schematic diagram of the n/p InGaP/InGaAs/Ge ATJ cell ............................................................................................................................21 Figure 2.10: Typical external quantum efficiency for the ATJ cells ...............................22 Figure 2.11: Typical I-V Curve........................................................................................24 Figure 3.1: Block Diagram of the SCTU .........................................................................26 Figure 3.2: Electrical circuit and temperature measuring system of the main experiment................................................................................................................28 Figure 3.3: ATJ solar cell set used in the SCTU (embedded thermocouples are shown) ......................................................................................................................30 Figure 3.4: SCTU mobile platform pointing to the sun ...................................................32 vi Figure 3.5: Top-view mechanical layout diagram of SCTU mobile platform.................35 Figure 3.6: Main components of the MASS/SCTU mounted in the field........................35 Figure 3.7: Layout of components in the Primary and Secondary Electronics Enclosure..................................................................................................................36 Figure 3.8: Flowchart of the general software operation .................................................38 Figure 3.9: Solar Irradiance of the Day............................................................................40 Figure 3.10: I-V Curves of ATJ and Si solar cells...........................................................42 Figure 3.11: I-V curves along the day for the ATJ set (blue) and silicon set (red). Horizontal position. Maximum power points are marked by an asterisk (*)...........46 Figure 3.12: I-V curves along the day with temperature compensation (28�C) for the ATJ set (blue) and silicon set (red). Horizontal position. Maximum power points are marked by an asterisk (*) ........................................................................47 Figure 3.13: I-V curves with sun tracking and temperature compensation for the ATJ set (left) and silicon set (right) .................................................................................49 Figure 3.14: Conversion efficiencies during test day ......................................................51 Figure 3.15: Efficiency degradation with respect to the angle of incidence of the radiation for the ATJ solar cells...............................................................................52 Figure 3.16 : Efficiencies of ATJ solar cells in horizontal and pointing to the sun positions along the day.............................................................................................53 Figure 3.17: Efficiencies along the day, with different temperature compensations, from 0� to 80� C........................................................................................................55 Figure 3.18: Conversion efficiency vs. temperature at maximum insolation instant. .....56 Figure 3.19: I-V curve of ATJ solar cells operating in space under AM0 conditions (1353 W/m2) at 28�C ................................................................................................57 vii Figure 3.20: I-V curve of ATJ solar cells operating on earth, with the solar cells pointing to the sun, compensated at 28�C ................................................................57 Figure 3.21: Solar spectra in space and on earth during experiments (Measured spectra was scaled for comparison purposes) ..........................................................59 Figure A.1: Auger recombination with associated excess energy given to an electron in the conduction band: In the recombination process, the electron collides with another electron in the conduction band (1). After that, the second electron gains energy which is then dissipated as a phonons (2), no light is emitted............65 Figure A.2: Two step recombination process via a defect energy level, situated in the forbidden gap. The electron relaxes to an intermediate defect energy level (1), then recombines with a hole in the valence band (2)...............................................66 Figure A.3: Surface states lying within the forbidden bandgap at the surface of a semiconductor ..........................................................................................................67 Figure B.1: Schematical energy-momentum diagram for a direct bandgap material ......68 Figure B.2: Schematical energy-momentum diagram for an indirect bandgap material .69 Figure B.3: Energy-momentum diagram for silicon ........................................................70 viii RESUMEN Las celdas solares ATJ (Advanced Triple Junction) InGaP/InGaAs/Ge son uno de los dispositivos fotovoltaicos mas eficienctes disponibles en el mercado. En este trabajo se presenta su desempe�o en la superficie terrestre, obteni�ndose resultados notoriamente superiores a las tecnolog�as convencionales en todas las pruebas realizadas. Se determinan sus caracter�sticas el�ctricas, par�metros de modelaci�n relevantes (eficiencia y factor de llenado, dentro de otros) y se analiza el efecto de factores externos en su desempe�o (�ngulos de incidencia, efectos de la atm�sfera y efectos de la temperatura). El estudio realizado utiliza celdas solares ATJ comerciales las cuales a la fecha s�lo est�n disponibles para aplicaciones satelitales. El an�lisis de los resultados obtenidos se realiza en comparaci�n a la tecnolog�a convencional de silicio, la cual fue sometida a pruebas equivalentes. Se demuestra que las caracter�sticas espec�ficas para la operaci�n en el espacio de las celdas ATJ en algo degradan su desempe�o en la tierra, pero a�n as� se obtienen resultados ostensiblemente superiores respecto a la tecnolog�a de silicio. La metodolog�a de an�lisis considera el desempe�o de las celdas solares bajo condiciones atmosf�ricas cambiantes a lo largo de un d�a. Se captura informaci�n de voltaje, corriente y temperatura de las celdas, adem�s de variables relevantes del entorno como el espectro solar incidente, la irradianza total y variables meteorol�gicas. Las celdas solares de prueba se instalan sobre una plataforma m�vil capaz de orientarlas a posiciones arbitrarias incluyendo el seguimiento continuo del sol, permitiendo aislar el efecto coseno en la radiaci�n incidente. Este documento comienza con un an�lisis te�rico para entender la tecnolog�a convencional mono-capa y la tecnolog�a multi-capa de las celdas ATJ. Posteriormente se muestran los m�todos utilizados para la realizaci�n de los experimentos. A continuaci�n, se analiza el desempe�o de las celdas solares a lo largo del d�a considerando los distintos factores que la afectan. Finalmente, se compara el desempe�o real obtenido en la tierra con los resultados en el espacio obtenidos por el fabricante. ix ABSTRACT Advanced Triple Junction (ATJ) InGaP/InGaAs/Ge solar cells use stateof-the-art photovoltaic technologies whice are based on multiple semiconductor junctions. This work analyzes their performance on the surface of the earth, obtaining noticeably-improved results compared to conventional technologies in all performed tests. The analysis takes into account the solar cells electrical characteristics, relevant modeling parameters (efficiency and fill factor, among others) and the effect of external factors affecting the performance (angles of incidence, effects of the atmosphere and temperature dependence). This study uses commercial ATJ solar cells which are currently available only for satellite applications. Obtained results are compared to conventional silicon solar cells which are exposed to equivalent tests. It is demonstrated that specific space-construction characteristics of ATJ solar cells partially degrade their performance on earth, but anyway noticeably exceed the performance of the silicon technology. The applied methodology considers the performance of the solar cells under varying atmospheric conditions along a day. Voltage, current and solar cell temperature are logged together with relevant environmental information such as the incident solar spectrum, total irradiance and weather variables. All solar cells are mounted on a mobile system capable of arbitrarily orienting their position (including sun-tracking), what allows to distinguish the cosine effect from the influence of the atmosphere in the incident radiation. This document first presents a theoretical analysis to understand the single-junction (silicon) and multi-junction (ATJ) semiconductor technologies. After that, shows the applied methods to perform the solar cell characterization. Next, analyzes the performance of the solar cells along the day considering all factors that affect performance. Finally, compares the obtained results on earth to the results in space obtained by the manufacturer. x 1 1 INTRODUCTION Currently, more efficient photovoltaics devices are needed for the further development of market-competitive solar powered mobile devices, such as robots or automobiles. Today's standard technologies, such as silicon solar cells, have efficiencies that are not high enough to satisfy the high-power needs of mobile applications. Thus, more efficient technologies such as the ones used in space must be considered. This work analyzes the performance of Advanced Triple-Junction (ATJ) InGaP/InGaAs/Ge solar cells built for satellite use, when they are used on the surface of the earth. This study is developed as part of the NASA-funded "Life in the Atacama" project, developed by Carnegie Mellon University with the collaboration of Pontificia Universidad Cat�lica de Chile among other institutions. The Life in the Atacama project seeks to develop technology in support of robotic astrobiology for NASA while conducting useful Earth science in the Atacama Desert of northern Chile [Wett03]. Its purpose is to develop technology relevant to Mars in the form of an autonomous rover capable of traversing extremely long distances finding basic forms of life without direct human intervention. The final objective of this study is to characterize ATJ solar technology used in Zoe robot during field expeditions of years 2004 and 2005. 1.1 Objectives This study determines the performance and electrical characteristics of ATJ solar cells operating under the influence of the ambient conditions on the surface of the earth. To achieve this, the performance of the ATJ solar cell is compared with that of traditional silicon solar cell designed for use on earth. Experiments consist in exposing ATJ and silicon solar cells samples to normal outdoor ambient conditions, applying them several tests. They include an electrical characterization (current-voltage curve acquisition with a variable load), temperature measurements of the solar cells, and characterization of the environment (incident irradiance, incident spectra, and others). The solar cells and instruments are mounted on a mobile platform that can be oriented arbitrarily to quantify the 2 influence of the angle of incidence of the sunlight in the performance of the solar cell. The data obtained from the tests is used to determine performance parameters such as conversion efficiencies, fill factors, temperature sensibilities and others. These choice of parameters are meant to simplify the comparison and characterization of the solar cells. In order to understand the results in detail, this document presents a complete overview of basic concepts related to solar cell operation and specific ATJ solar cell concepts. Chapter 2 describes a general technical background including topics related to semiconductor basics, the photoelectric effect, construction characteristics of ATJ solar cells and technical definitions commonly-used for solar cell characterization. Finally, chapter 3 describes the methods used and the results obtained in this study. 3 2 TECHNICAL BACKGROUND Before reviewing the technical characteristics of the Advanced-TripleJunction (ATJ) solar cells, the basic operation of a single-junction cell will be discussed. 2.1 Semiconductor Basics When discussing single atoms, electrons have their own discrete energy levels. In a solid state, however, these energy levels interfere with each other, resulting in energy bands, broader energy states that can be occupied by electrons. These energy bands are separated from each other by a zone with forbidden energy levels (bandgap). The energy band below the bandgap is called valence band, above the bandgap lies the conduction band. (See Figure 2.1). At zero Kelvin, the electrons start to fill up the energy bands from the lowest level upwards, to a certain value, called the Fermi level. All energy bands above this level are empty. The position of this Fermi level and bandgap size determines whether a material is an electrical insulator, a semiconductor or a metal (electrical conductor). Energy of Electrons
Conduction Band Fermi Level Eg1
Fermi Level Conduction Band Conduction Band
Fermi Level Overlap Eg2
Valence Band Valence Band Valence Band Conductor Insulator Eg1 > Eg2 Semiconductor Figure 2.1: Position of Fermi level in a metal, insulator and semiconductor 4 From Figure 2.1, it follows that a metal is a very good electrical conductor, since the conduction band overlaps the valence band. Virtually no excess energy is needed to achieve electrical conductivity here, since electrons can freely move from one allowed level to another. In an insulator, however, the bandgap is very large, making it almost impossible to provide electrons with enough energy to make the transition to the conduction band1. On the other hand, in a semiconductor the Fermi level is also located in between both bands, but the bandgap is smaller, therefore the probability of electrons crossing the bandgap is higher. Additionally, crystalline semiconductors have a rigid/ordered nature arrangement of the molecular/atomic setup named the crystal lattice. The ordered lattice gives these materials properties similar to single atoms. In solid states, at temperatures higher than absolute zero, electrons will occupy levels above the Fermi level (only in the allowed energy levels of the material). The distribution of electrons over the different energy levels is then given by the Fermi-Dirac formula, which represents the probability a certain energy level is occupied, f (E) = 1 1+ e
E - EF k BT , (2�1) in this formula, kB is the Boltzmann constant (1.38 x 10-23 JK-1), and T is the absolute temperature. The distribution is schematically drawn in Figure 2.2. At room temperature, some electrons will be in the conduction band, leaving an open position in the valence band. These positions are referred to as holes. In this situation, the material can conduct electricity, since electrons can freely move from one allowed 1 The fact that the Fermi level in a semiconductor or insulator is located in the middle of its gap, does not mean there exists an electron population at that energy level. The population depends on the product of the Fermi function and the electron density of states. Therefore, in the gap there are no electrons since the density of states is zero. Also, at zero Kelvin, the conduction band is empty even though there are plenty of available states, but the Fermi function is zero, therfore, according to the Fermi-Dirac distribution no electrons will have that energy. 5 position to another allowed position in the conduction band (electron conduction). On the other hand, an electron in the valence band can move from its position to a vacant hole position, leaving a hole at its original position. It appears like the hole has moved in the opposite direction, a process called hole conduction. Figure 2.2: Fermi-Dirac distribution function 2.1.1 Semiconductor Doping Yet another method for improving the electrical conductivity of a semiconductor by orders of magnitude is known as doping. In a pure semiconductor material like silicon, the atoms are all ordered in a specific lattice, forming covalent bonds with the neighboring atoms. Since silicon has four electrons in its outer shell, four covalent bonds are formed. Minor electrical conduction occurs when such a covalent bond is broken. The electron that is freed can move through the solid, the hole that is left behind can move due to hole conduction. The doping process, in which the pure material is `contaminated' with strange atoms, can enlarge this electrical conductivity by orders of magnitude. Two types of doping can be distinguished: n-type and p-type doping. In n-type doping, a pure semiconductor, 6 like silicon, is mixed with tiny amounts of an element that has one extra electron in the outer shell (donor atoms). An example of such an element is phosphorus (P). The phosphorus atoms are incorporated in the specific silicon lattice by replacing Si atoms (substitutional). As a result, four of the five electrons in the outer shell of phosphorous form a covalent bond with electrons from the silicon atoms. The fifth electron is very loosely bound and can be freed quite easily. n-Type silicon is electrically neutral, since the pure silicon is mixed with electrically neutral phosphorus atoms. However, the electrical conductivity has greatly improved, due to the doping process. In p-type doping, a pure semiconductor material like silicon is `contaminated' with an element with only three electrons in its outer shell (acceptor atoms), for example boron (B). The three electrons form a covalent bond with the outer electrons of the silicon atoms, leaving a hole at the place where a fourth electron would fit in. The hole conduction mechanism can provide electrical conductivity in this situation. Just as n-type material, p-type material is electrically neutral. Ec
Extra allowed level due to donor impurity Efn Ec
Extra allowed level due to acceptor impurity Ev Ev Efp N - type Semiconductor P - type Semiconductor Figure 2.3: Extra energy levels due to doping in a n-type semiconductor and in a p-type semiconductor. Efn and Efp are the new Fermi levels of the n-type and p-type semiconductors respectively due to doping The addition of n-type or p-type impurities to a pure semiconductor like silicon, allows new energy levels in the bandgap. The extra energy level due to n- 7 type doping, is situated just below the conduction band. This occurs since the fifth electron is very loosely bound and little energy is needed to promote the electron to the conduction band. In an analogous way, the extra energy level due to p-type doping, is situated just above the valence band, so that very little energy is required to achieve hole conduction (see Figure 2.3). Also, the Fermi level of the n-type material is now situated in between the new extra level and the conduction band in the bandgap. Analogously, in the p-type semiconductor, the Fermi level is located below the new extra energy level and over the valence band (see Figure 2.3). At room temperature, there is some thermal energy available to the electrons in the lattice due to vibrations. If an electron absorbs some of this energy, it may be promoted to a higher energy level (e.g. from the valence band to the conduction band). In n-type materials two different "kinds" of electrons are present (called majority carriers): those that begin at the donor level, and those that begin in the valance band. There are far more electrons in the valance band than at the donor levels. However, the energy needed by the valance electrons to traverse from the band gap to the conduction band is far greater than the energy needed by the electrons at the donor level to get to the conduction band. In n-type materials, when donor level electrons are thermally promoted to the conduction band, a donor level is left empty. These electrons are called majority carriers (for n-type materials) nM, and is given by the Boltzmann statistics approximation2 (in this estimate, electrons promoted from the valence band are neglected, since their number is insignificant in comparison to the number of electrons from the donor level ), 2 n1 The Boltzmann statistics, is given by: =e n2 - ( E2 - E1 ) kT , and approximates the concentration of carriers at some energy level E, where n1 and n2 are the concentration of carriers at potential energies E1 and E2. This approximation can be used since the concentration of electrons in the conduction band is never large enough to consider the Pauli exclusion principle important. In this work the concentration of carriers is addressed as number of carriers for simplicity. 8 ( E cn - E fn ) nM = AM e kT , (2�2) where Ecn is the energy at the bottom of the conduction band in the n-type material, Efn is the Fermi level in the n-type material, and Am is the number of n-type dopant atoms. Conversely, the number of valance electrons promoted to the conduction band is small. Note that when a majority carrier is promoted from a donor level, the lattice itself is unaffected. However, when a valance electron is promoted, it leaves a hole behind in the lattice. The hole is called a minority carrier. The number of minority carriers, nm, is given by the Boltzmann statistics,
E fn nm = Am e kT , (2�3) where Am is the number of atoms in the lattice. In p-type materials, electrons from the valence band are being promoted either to the conduction band or to the acceptor levels, leaving conducting holes behind in the valance band. To determine the number of holes, the number of electrons that were promoted to create the holes must be obtained. In p-type materials, the number of majority carriers, or holes created by electrons getting promoted to the acceptor levels, is hM, and is given by,
Efp hM = AM e kT , (2�4) where Efp is the Fermi level in the p-type material, and AM is the number of p-type acceptor atoms in the lattice. When an electron is promoted from the valance band all the way to the conduction band, it leaves behind a conducting hole which becomes a conducting agent itself. Electrons in the conduction band of p-type material are called minority carriers, and their number, hm is given by, 9 (Ecp - Efp ) hm = Am e kT , (2�5) where Am is the number of atoms in the lattice and Ecp is the energy at the bottom of the conduction band in the p-type material. 2.1.2 P-N Junction Operation In a p-n junction, p-type material is in contact with n-type material in the same integral crystal. The Fermi level of the p-type material is much lower than that of the n-type material with respect to the top of the valance band in the n-type material (see Figure 2.3). Therefore, when the two are juxtaposed in an integral substance, the Fermi levels must equilibrate. This equilibration occurs because the electrons residing in the donor levels of the n-type material are exposed to lower energy levels. Electrons always seek the lowest energy level, so they begin to diffuse over to fill the acceptor and valance levels in the p-type material, where the density of electrons is lesser (analogously, holes seek higher energy levels, therefore the opposite occurs). Electric Field E n-type p-type Conduction Band Ecp Ecn Ef Valence Band Distance Space Charge or Depletion Region Figure 2.4: Junction in final equilibrium (isolated) 10 Fermi levels begin to move closer to each other until finally, they meet in the middle (see Figure 2.4). At this point, the contact potential difference between the two material types is just enough to prevent further diffusion of electrons and holes across the junction. When the Fermi levels have equilibrated, there are no longer lower energy levels in the vicinity for n-type electrons to occupy, so they stop migrating, and the system is again in equilibrium. There is now only one Fermi level (Ef) and the whole crystal has undergone through what is known as band bending. The Fermi level was equilibrated, and all of the rest of the bands in each type of the semiconductor moved relative to it. The depletion region is the region in the crystal in which the bands are bent. As shown in Figure 2.4, the bottom of the conduction band in the p-type material is now higher than the bottom of the conduction band in the n type material. This potential difference between energy levels in the depletion region grows until it is just large enough to oppose further movement of majority carriers. The contact potential is what displaces the p-type and n-type bands, and its electric field points in the direction that a positive charge would be inclined to move. 2.1.3 Isolated P-N Junction In an isolated p-n junction, the majority carriers on the n-type side (electrons) will not move toward the p-type side, because in order to do so, they would have to move up to a higher energy level. The minority carriers (holes) on the n-type side, on the other hand, will move easily to the p-type side, since holes seek higher energy levels. On the p-type side, the majority carriers are holes. They will be deterred from crossing the depletion region, since at the other side the energy levels would be lower. Conversely, the minority carriers in the p-type side (electrons) easily move down to the n-type, since there the energy levels are lower. As a final result, the vast majority of mobile carriers are not able to cross the junction. The thermally generated minority carriers can easily flow across the junction, creating what will be referred as the thermal current (It). The thermal current from the p-type side is proportional to the number of electrons thermally promoted to the conduction band. Therefore, from Equation 2-5, 11 ( Ecp - E f ) I m = Ce kT , (2�6) where C is an experimentally determined constant of proportionality related to the dopant concentration. In the n-type material, the thermal current is from holes moving across the junction, so the n-type contribution to thermal current is proportional to the number of hole minority carriers in the n-type material which comes from Equation 2-3. Then,
Ef I m = Be kT . (2�7) The total thermal current is also called the reverse saturation current, or the dark current. Note that because Itp is due to electrons flowing from the p-type material to the n-type material and Itn is due to holes flowing from the n-type material to the p-type material, they are additive (have same sign). Then total thermal current, IT, is the sum of the two. In an electrically isolated situation, there can be no net current through the junction. Thus, there must be another component of current that opposes the thermal current. This component is called the recombination current, and is comprised of majority carriers traversing the p-n junction in the "wrong" direction. Only majority carriers that have been thermally promoted to a high enough energy level, such that the energy level of the other side "looks" desirable, will cross the junction. More specifically, an electron on the n-type side of the material (majority carrier), would merely move to the p-type side if it could gain a lower potential by doing so. This means, it would have to be in an energy level in the n-type conduction band with a higher potential than the top of the conduction band in the p-type material ( >Ecp). The opposite occurs with the majority carriers (holes) in the p-type side. Quantitatively, the recombination current is proportional to the number of majority carriers that can cross the junction. In the n-type material, the 12 contribution to the recombination current is proportional to the number of electrons that can cross to the p-type side of the junction,
( Ecp - E f ) I m = Ce kT , (2�8) where C is the same than in equation 2-6. Analogously, the contribution to the recombination current due to holes crossing the junction to the n-type side of the material is proportional to the number of holes that are created in the p-type side at energies below the top of the n-type valance band. This contribution is
Ef I m = Be kT , (2�9) where B is the same than in equation 2-7. The Boltzmann statistics considers here the energy difference between Ecn=0 and the acceptor levels. Note that the thermal current from the p-type side (Equation 2-6) is equal to the recombination current from the n-type side (Equation 2-8), and the thermal current from the n-type side (Equation 2-7) is equal to the recombination current from the p-type side (Equation 2-9). This ensures that the total junction current will be zero (the constants B and C are also equal if the p-type and n-type dopants have been added in equal proportions). It is useful to note that while thermal current depends only on temperature, total recombination current depends on temperature and on the external voltage (forward or reverse bias, see next section). 2.1.3 Forward and Reverse Bias To make the junction reversed biased, the positive lead of a battery is connected to the n-type side and to ground (potential=0) and the negative lead to the p-type side (see Figure 2.5, "Reverse Bias"). In this case, the potential on the n-type side remains constant at zero, but the potential of all the energy levels on the p-type side are raised by an amount eV, where e is the charge of the electron and V is the value of the applied potential. Therefore, the energy hill becomes even steeper, and it becomes even less likely for majority carriers to cross the junction (note that the Fermi level is still continuous, but is bent by the applied potential). The net junction current is no longer zero, since the thermal current remains essentially constant, but 13 the recombination current shrinks proportionally to the increase in potential difference. Electron Energy n-type Conduction Band p-type Electron Energy n-type Conduction Band p-type Ep+eV EFermi Ep+eV EFermi Valence Band Distance Valence Band Distance REVERSE BIAS N P FORWARD BIAS N P + - - + Figure 2.5: Energy diagrams, reverse (left) and forward bias (right) If the junction instead is forward biased, by attaching the negative end of the battery to the n-type side and ground, and the positive battery lead to the p-type side (see Figure 2.5 "Forward Bias"), the opposite occurs. Every energy level on the p-type side is reduced by an amount eV, making it more probable that majority carriers will cross the junction. In fact, if the potential applied is great enough, the potential hill will become flat or even reverse its direction, making it energetically favorable for majority carriers to cross the junction. In this case, the semiconductor will conduct electricity. In a forward biased situation, the thermal current remains constant, but the recombination current grows in proportion to the applied potential. The new recombination current has two parts; one is from the n-type side, and is given by, 14 (Ecp - E fn -eV ) I rnfb = Ae kT . (2�10) The contribution to the current from the p-type side will be,
(E fp -eV ) I rpfb = Me kT , (2�11) which is bigger than the recombination current from the p-type side in the unbiased junction (Equation 2-9). Upon inspection, it can be found that the total forward biased recombination current is just the unbiased recombination current multiplied by the Boltzmann factor ( e kT ), with E = eV resulting,
E I Rfb = I R e , eV kT (2�12) where here, IR is the total recombination current in the isolated cell, and is equal to the total thermal current IT. From here, the total net electron current through the forward biased junction may be found. If we consider a cell that has been carefully doped so that the constant coefficients of the current terms are equal, we can calculate the total current in a forward biased junction. The total junction current must be the thermal current plus the recombination current,
I j = I Rfb + I T . (2�13) When the coefficients are equal, IRfb can be written in terms of IT, as mentioned above, so that, finally, the total junction current in a forward biased junction is simply,
eV I j = I T e kT - 1 . (2�14) 15 2.2 Photovoltaic Cell Operation photon (light) e front contact grid n-type e-h e E p-type e-h rear contact e Figure 2.6: Schematical cross-section diagram of a single-junction solar cell A single-junction photocell is just a p-n junction with metallic rear and front contacts that allow electron conduction to an external load. The front contacts cover only partially the semiconductor to allow the light to enter. In Figure 2.6 a schematical cross-section diagram of a single-junction solar cell is displayed. In order to promote an electron into the conduction band, an incoming photon must have energy at least equal to the band gap (assuming all the electrons in the donor levels have already been thermally promoted). Therefore, photons of wavelength less than hc/Eg (h is the Planck constant, c the speed of light, and Eg the bandgap energy) will make no contributions to generate electricity in the cell. However, photons with sufficient energy will promote electrons with a certain efficiency rate (see Recombination Processes in Semiconductors appendix in pg. 65) and they will, in the presence of an external load, produce a current through the cell. This current is called the photocurrent, and is given by, 16 IP = eF , Tr (2�15) where e is the charge of the electron, F the total number of carriers produced each second by absorbed photons (the efficiency is implicit in F), is the effective lifetime of the carriers, and Tr is the transit time, or the time spent by the carriers in moving to the electrode of the cell. Tr is a quantity that groups several terms, L2 Tr = , �V (2�16) where L is the electrode spacing, � is the drift mobility (another quantity that has to do with efficiency) and V is the applied voltage. 2.2.1 Separation of Charge When photons enter the semiconductor to which no external voltage has been applied (see Figure 2.4 and Figure 2.5), they add a form of energy in addition to heat. The photons interact with atoms in the lattice, in general, a single photon collides with a single electron, imparting its energy to the electron. When h > E g ( h is the photon energy, where is its frequency), the electron is promoted to a higher energy level if the electrons have the right momentum (See Absorption in Direct and Indirect Bandgap Materials appendix in pg. 68). On the n-type side, they promote electrons into the conduction band, leaving holes in the valance band that can see the junction field and be swept across to the p-type side. Once they reach the p-type side, however, they cannot re-cross the junction; to do so would be to oppose the field. In the p-type material, electrons become promoted to the conduction band and roll easily down the "hill" into the n-type side, but once they are there, they cannot re-climb the hill. This is analogous to an increase of the thermal current. Separation of charge begins to build up, because an excess of electrons become trapped on the n-type side while an excess of holes are trapped on the p-type side. This separation of charge competes with and eventually overcomes the junction field and forms a forward biased junction. 17 2.2.2 Isolated Photocell If the junction is electrically isolated, the forward bias will not last. Also the net current must be zero, so the recombination current must somehow compensate. The sum of the total junction current (Equation 2-14) and the newly created photocurrent must be zero, so that,
eVoc I j = I p = I T e kT - 1 , (2�17) where Ip flows from the n-type side to the p-type side, while Ij flows from the p-type material to the n-type material. In the above equation, the applied potential Voc is the potential difference set up by the photocurrent. It is the voltage created by the photons, and it is called the open circuit voltage. Physically, the majority carriers cross the junction until a situation has been reached in which the difference in potential between the p-type side and the n-type side has "unbent" the bands exactly. In such a situation, there is no preferred direction for carriers to go, and the system reaches an equilibrium. Then the open circuit voltage must be exactly equal to the contact potential in the junction. Experimentally, this is exactly the case. The open circuit voltage of silicon photovoltaic cells is between 0.5 V and 0.7 V, which is the range of "turn-on potential" in silicon diodes. From this realization, the current equation (2-14) can be solved to find the open circuit voltage, which gives,
Voc = kT e Ip ln + 1 . I T (2�18) 2.2.3 Photocell with Load If the cell is connected to an electric circuit with some load a net current will flow through the junction. It is more energetically favorable for the charge build-up to dissipate through a load than for the recombination current to increase by as much as it is necessary for the junction current to match the photocurrent. Therefore, when connected to a load, the photocurrent will in fact discharge across it, creating useful electrical energy. The current through the load will be, 18 IL = I p - I j . (2�19) We can again solve this equation for V to find the potential drop across the cell, or the effective "battery voltage" created by the photocell, Ve =
2.3 kT I p - I L ln + 1 . e IT [Angr92] (2�20) Design Considerations Design restrictions include selecting an optimal energy bandgap of the semiconductor. This yields in a tradeoff between absorbing a small number of highenergy photons versus absorbing a wider spectra of photons with higher thermal losses. Figure 2.7 shows maximum allowable efficiencies for different bandgap energies and corresponding well-known semiconductors used in solar cells. Figure 2.7: Optimal bandgap for single junction solar cell [Nrel00] Relevant electrical parameters of a solar cell depend both on the number of freed electrons and on their energy. Voltage levels are proportional to the bandgap energy difference; current levels are proportional to the number of electrons freed to the conduction band. Therefore, choosing an energy bandgap implies a tradeoff between high voltages (high energy bandgaps) or high currents (low energy bandgaps). 19 2.4 Multi-Junction Solar Cells Multi-junction solar cells use multiple semiconductors junctions, each with different bandgap energies to minimize losses of low-energy photons and excess energy of energetic photons. Each individual semiconductor absorbs photons at specific wavelengths, with the resulting solar cell absorbing a broader spectum with higher efficiencies due to reduced thermal losses. Physically, the different semiconductors are stacked together ordered according to their bandgap energies. Incident photons first strike materials with the largest bandgap, absorbing the more energetic photons. Lower-energy photons travel across the semiconductor and are absorbed in successive layers with lower bandgap energies. If the bandgap of the semiconductor is larger than the energy of the photon, the material will be transparent. 2.4.1 Construction Procedure There are two major approaches to the construction of multi-junction solar cells. The mechanically stacked approach physically stacks independentlygrown layers. This system finds its main applications in optical concentrator systems. But the bulkiness, additional expense, and heat-sinking challenges make these multijunction cells a less-desirable alternative [Nrel00]. The second approach is the monolithically grown, where each semiconductor is sequentially grown on top of the other as one single piece. Monolithically-grown solar cells and their design restrictions will be analyzed with further details due to its importance for understanding ATJ solar cells. Monolithically-grown multi-junction solar cells are expected to work at higher voltages and lower currents than a single-junction solar cell. The presence of specific semiconductors junctions for specific bands of the spectra yields in that each material individually absorbs fewer photons (e.g. a narrow band of the spectra), therefore generating lower currents. On the other hand, the series architecture and the absorption of more energetic electrons in several stages yields to higher voltages. 20 All semiconductors used in monolithically grown solar cells must have a similar crystal structure (e.g. lattice constant3) in order to produce optical transparency and maximum current conductivity between the top and bottom cells. A mismatch in the crystal lattice may produce mechanical defects and potentially constitute a source for electron-hole recombinations (see appendix A, Recombination Processes in Semiconductors, pg. 65). Figure 2.8 shows commonly-used semiconductors in solar cells (III-V materials). Semiconductors with different bandgaps and similar lattice constants are desir

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PERFORMANCE OF ADVANCED TRIPLE-JUNCTION (ATJ) SOLAR CELLS