Solar Cell Device Physics

Solar Cell Device Physics

by Stephen Fonash

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There has been an enormous infusion of new ideas in the field of solar cells over the last 15 years; discourse on energy transfer has gotten much richer, and nanostructures and nanomaterials have revolutionized the possibilities for new technological developments. However, solar energy cannot become ubiquitous in the world's power markets unless it can become


There has been an enormous infusion of new ideas in the field of solar cells over the last 15 years; discourse on energy transfer has gotten much richer, and nanostructures and nanomaterials have revolutionized the possibilities for new technological developments. However, solar energy cannot become ubiquitous in the world's power markets unless it can become economically competitive with legacy generation methods such as fossil fuels.

The new edition of Dr. Stephen Fonash's definitive text points the way toward greater efficiency and cheaper production by adding coverage of cutting-edge topics in plasmonics, multi-exiton generation processes, nanostructures and nanomaterials such as quantum dots. The book's new structure improves readability by shifting many detailed equations to appendices, and balances the first edition's semiconductor coverage with an emphasis on thin-films. Further, it now demonstrates physical principles with simulations in the well-known AMPS computer code developed by the author.

*Classic text now updated with new advances in nanomaterials and thin films that point the way to cheaper, more efficient solar energy production

*Many of the detailed equations from the first edition have been shifted to appendices in order to improve readability

*Important theoretical points are now accompanied by concrete demonstrations via included simulations created with the well-known AMPS computer code

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Solar Cell Device Physics

By Stephen J. Fonash

Academic Press

Copyright © 2010 Elsevier Inc.
All right reserved.

ISBN: 978-0-08-091227-1

Chapter One


1.1 Photovoltaic Energy Conversion 1 1.2 Solar Cells and Solar Energy Conversion 2 1.3 Solar Cell Applications 7 References 8


Photovoltaic energy conversion is the direct production of electrical energy in the form of current and voltage from electromagnetic (i.e., light, including infrared, visible, and ultraviolet) energy. The basic four steps needed for photovoltaic energy conversion are:

1. a light absorption process which causes a transition in a material (the absorber) from a ground state to an excited state, 2. the conversion of the excited state into (at least) a free negative-and a free positive-charge carrier pair, and 3. a discriminating transport mechanism, which causes the resulting free negative-charge carriers to move in one direction (to a contact that we will call the cathode) and the resulting free positivecharge carriers to move in another direction (to a contact that we will call the anode).

The energetic, photogenerated negative-charge carriers arriving at the cathode result in electrons which travel through an external path (an electric circuit). While traveling this path, they lose their energy doing something useful at an electrical "load," and finally they return to the anode of the cell. At the anode, every one of the returning electrons completes the fourth step of photovoltaic energy conversion, which is closing the circle by

4. combining with an arriving positive-charge carrier, thereby returning the absorber to the ground state.

In some materials, the excited state may be a photogenerated free electron-free hole pair. In such a situation, step 1 and step 2 coalesce. In some materials, the excited state may be an exciton, in which case steps 1 and 2 are distinct.

A study of the various man-made photovoltaic devices that carry out these four steps is the subject of this text. Our main interest is photovoltaic devices that can efficiently convert the energy in sunlight into usable electrical energy. Such devices are termed solar cells or solar photovoltaic devices. Photovoltaic devices can be designed to be effective for electromagnetic spectra other than sunlight. For example, devices can be designed to convert radiated heat (infrared light) into usable electrical energy. These are termed thermal photovoltaic devices. There are also devices which directly convert light into chemical energy. In these, the photogenerated excited state is used to drive chemical reactions rather than to drive electrons through an electric circuit. One example is the class of devices used for photolysis. While our emphasis is on solar cells for producing electrical energy, photolysis is briefly discussed later in the book.


The energy supply for a solar cell is photons coming from the sun. This input is distributed, in ways that depend on variables like latitude, time of day, and atmospheric conditions, over different wavelengths. The various distributions that are possible are called solar spectra. The product of this light energy input, in the case of a solar cell, is usable electrical energy in the form of current and voltage. Some common "standard" energy supplies from the sun, which are available at or on the earth, are plotted against wavelength (λ) in W/m2/nm spectra in Figure 1.1A. An alternative photons/m2-s/nm spectrum is seen in Figure 1.1B. The spectra in Figure 1.1A give the power impinging per area (m2) in a band of wavelengths 1nm wide (the bandwidth δλ) centered on each wavelength λ. In this figure, the AM0 spectrum is based on ASTM standard E 490 and is used for satellite applications. The AM1.5G spectrum, based on ASTM standard G173, is for terrestrial applications and includes direct and diffuse light. It integrates to 1000 W/m2. The AM1.5D spectrum, also based on G173, is for terrestrial applications but includes direct light only. It integrates to 888 W/m2. The spectrum in Figure 1.1B has been obtained from the AM1.5G spectrum of Figure 1.1A by converting power to photons per second per cm2 and by using a bandwidth of 20nm. Photon spectra φ0(λ), exemplified by that in Figure 1.1B, are more convenient for solar cell assessments, because optimally one photon translates into one free electron-free hole pair via steps 1 and 2 of the four steps needed for photovoltaic energy conversion.

Standard spectra are needed in solar cell research, development, and marketing because the actual spectrum impinging on a cell in operation can vary due to weather, season, time of day, and location. Having standard spectra allows the experimental solar cell performance of one device to be compared to that of other devices and to be judged fairly, since the cells can be exposed to the same agreed-upon spectrum. The comparisons can be done even in the laboratory since standard distributions can be duplicated using solar simulators.

The total power PIN per area impinging on a cell for a given photon spectrum φ0(λ) is the integral of the incoming energy per time per area per bandwidth over the entire photon spectrum; i.e.,


where an example φ0(λ), expressed as photons/time/area/bandwidth, is plotted in Figure 1.1B. In Equation 1.1 the quantity h is Planck's constant and c is the speed of light. The electrical power POUT per area produced by the cell of Figure 1.2 operating at the voltage V and delivering the current I as a result of this incoming solar power is the product of the current I times V divided by the cell area.

Introducing the current density J defined as I divided by the cell area allows POUT to be written as

POUT (1.2)

A plot of the possible J-V operating points (called the "light" J-V characteristics) of the cell of Figure 1.2 is seen in Figure 1.3. The points labeled Jsc and Voc represent, respectively, the extreme cases of no voltage produced between the anode and cathode (i.e., the illuminated solar cell is short-circuited) and of no current flowing between the anode and cathode (i.e., the illuminated solar cell is open-circuited).

At any of the operating points seen in Figure 1.3, POUT is given by the JV product.

The quantity POUT has its best value at the maximum power point labeled by the current density Jmp and the voltage Vmp on the light J-V characteristic in Figure 1.3. This operating point gives the maximum obtainable current density-voltage product. Therefore, the best thermodynamic efficiency of the photovoltaic energy conversion process for the cell of Figure 1.2 is:

η (Jmp Vmp)/pIN (1.3)

which assumes the photon impingement area and the area generating the current are the same, as in Figure 1.2. For cells collecting light over a larger area than that generating the current (i.e., for concentrator solar cells), this expression is replaced by


where AS is the solar cell area generating current and AC is the area collecting the photons. The advantage of a concentrator configuration lies in its being able to harvest more incoming solar power with a given cell size.

As can be seen from Figure 1.3, the ideally shaped J-V characteristic would be rectangular and would deliver a constant current density Jsc until the open-circuit voltage Voc. For such a characteristic, the maximum power point would have a current density of Jsc and a voltage of Voc. A term called the fill factor (FF) has been invented to measure how close a given characteristic is to conforming to the ideal rectangular J-V shape. The fill factor is given by


By definition, [is less than or equal to] 1.

The J-V characteristics seen in Figure 1.3 merit one additional comment. What has been plotted is that part of a cell's J-V characteristics for which power is being produced. Put simply, in this first quadrant plot, conventional current is emerging from the anode of the cell. Conventional current enters the anode of the archetypical power-consuming devices, the resistor and the diode. In this book, the power-producing quadrant of a solar cell will henceforth be switched to the fourth quadrant, to be consistent with resistor and diode plots, which will be in the first and third quadrants.


Solar photovoltaic energy conversion is used today for both space and terrestrial energy generation. The success of solar cells in space applications is well known (e.g., communications satellites, manned and unmanned space exploration). On earth, solar cells have a myriad of applications varying from supplementing the grid to powering emergency call boxes. However, the need for much more extensive use of solar cells in terrestrial applications is becoming clearer with the growing understanding of the true cost of fossil fuels and with the widespread demand for renewable and environmentally acceptable terrestrial energy resources. As long as 120 years ago, visionaries looking through the soot and smoke of the early industrializing world saw the need for a renewable and environmentally acceptable energy source. Writing in 1891, Appleyard foresaw "the blessed vision of the Sun, no longer pouring his energies unrequited into space, but, by means of photo-electric cells and thermo-piles, these powers gathered into electrical storehouses to the total extinction of steam engines, and the utter repression of smoke." It is interesting to note Appleyard's specific mention of what he calls photo-electric cells. This energy conversion approach was known even then due to Becquerel's discovery of photovoltaic action in 1839.

To increase the use of terrestrial solar photovoltaics, more efforts are needed to enhance cell energy-conversion efficiency η, to increase module (a grouping of cells) lifetimes, to reduce manufacturing costs, to reduce installation costs, and to reduce the environmental impact of manufacturing and deploying solar cells. The last three may be combined into "true costs." Looked at it this way, increasing the use of terrestrial solar photovoltaics depends on increasing a "figure of merit" defined by

energy conversion efficiency/true costs x lifetime

Developing the knowledge base needed to further increase this figure of merit, and thereby bringing Appleyard's vision to fruition, are the objectives of this book.

Chapter Two

Material Properties and Device Physics Basic to Photovoltaics

2.1 Introduction 9

2.2 Material Properties 10 2.2.1 Structure of solids 10 2.2.2 Phonon spectra of solids 13 2.2.3 Electron energy levels in solids 18 2.2.4 Optical phenomena in solids 28 2.2.5 Carrier recombination and trapping 36 2.2.6 Photocarrier generation 45

2.3 Transport 46 2.3.1 Transport processes in bulk solids 46 2.3.2 Transport processes at interfaces 53 2.3.3 Continuity concept 58 2.3.4 Electrostatics 60

2.4 The Mathematical System 60

2.5 Origins of Photovoltaic Action 63 References 64


In order to conceive new photovoltaic energy-conversion schemes, improve existing configurations, develop and improve cell materials, and understand the origins of the technical and economic problems of solar cells, the basics behind photovoltaic device operation must always be kept in the forefront. With that in mind, an overview of the material properties and physical principles underlying photovoltaic energy conversion is presented in this chapter. The mathematical models for phenomena that are fundamental to solar cell operation, such as recombination, drift, and diffusion, are discussed rather than just presented. This is done with the firm conviction that awareness of the assumptions behind the various models better enables one to judge their appropriateness and to make adjustments as necessary, when analyzing and developing new solar cell structures. This is particularly the case for solar cells today, which can involve combinations of a variety of features or phenomena, such as nano-scale morphology, amorphous materials, organic materials, plasmonics, quantum confinement, and exciton-producing absorption.


Both solid and liquid materials are used in solar cells. Homojunction, heterojunction, metal-semiconductor, and some dye-sensitized solar cells use all-solid structures, whereas liquid-semiconductor and many dye-sensitized cells use solid-liquid structures. These materials can be inorganic or organic. The solids can be crystalline, polycrystalline, or amorphous. The liquids are usually electrolytes. The solids can be metals, semiconductors, insulators, and solid electrolytes.

2.2.1 Structure of solids

The solids used in photovoltaics can be broadly classified as crystalline, polycrystalline, or amorphous. Crystalline refers to single-crystal materials; polycrystalline refers to materials with crystallites (crystals or equivalently grains) separated by disordered regions (grain boundaries); and amorphous refers to materials that completely lack long-range order. CRYSTALLINE AND POLYCRYSTALLINE SOLIDS

The distinguishing feature of crystalline and polycrystalline solids is the presence of long-range order, represented by a mathematical construct termed the lattice, and a basic building block (the unit cell), which, when repeated, defines the structure of the lattice. The atoms or molecules of the crystal have their positions fixed with respect to the points of the lattice. Amazingly, there are only 14 crystal lattices possible in a three-dimensional universe. Four common ones are shown in Figure 2.1. Different planes in a crystal can have different numbers of atoms residing on them, as may be deduced by comparing, for example, the simple cubic and the body-centered cubic lattices in Figure 2.1. In solids that are compounds (e.g., the semiconductors CdS or CdTe), different planes can even be composed of different atomic species. Miller indices are a convenient convention for labeling different planes.

Polycrystalline solids differ from single-crystal solids in that they are composed of many single-crystal regions. These single-crystal regions (grains) exhibit long-range order. The various grains comprising a polycrystalline solid may or may not have their lattices randomly oriented with respect to one another. If there is correlation in the orientations of the grains, the material is referred to as being an oriented polycrystalline solid. The transition regions in a polycrystalline solid that exist between the various single crystals are what we termed grain boundaries. These regions of structural and bonding defects can extend for perhaps a fraction of a nanometer or more and may even contain voids. Grain boundaries can have a significant influence on physical properties. For example, they can getter dopants or other impurities, store charge in localized states arising from bonding defects, and, through the stored charge, give rise to electrostatic potential energy barriers that impede transport. The grain boundaries of polycrystalline materials can be broadly classified as either open or closed. An open boundary is easily accessible to gas molecules; a closed boundary is not. However, even a closed boundary is expected to be an excellent conduit for solid-state diffusion. Diffusion coefficients are generally an order of magnitude larger along such boundaries than those observed in bulk, single-crystal material.


Excerpted from Solar Cell Device Physics by Stephen J. Fonash Copyright © 2010 by Elsevier Inc.. Excerpted by permission of Academic Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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