Third Generation Photovoltaics, Notas de estudo de Engenharia Elétrica

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springer series in photonics

Series Editors: T. Kamiya B. Monemar H. Venghaus Y. Yamamoto

The Springer Series in Photonics covers the entire f ield of photonics, including theory, experiment, and the technology of photonic devices. The books published in this series give a careful survey of the state-of-the-art in photonic science and technology for all the relevant classes of active and passive photonic components and materials. This series will appeal to researchers, engineers, and advanced students.

1 Advanced Optoelectronic Devices By D. Dragoman and M. Dragoman

2 Femtosecond Technology Editors: T. Kamiya, F. Saito, O. Wada, and H. Yajima

3 Integrated Silicon Optoelectronics By H. Zimmermann

4 Fibre Optic Communication Devices Editors: N. Grote and H. Venghaus

5 Nonclassical Light from Semiconductor Lasers and LEDs By J. Kim, S. Somani, and Y. Yamamoto

6 Vertical-Cavity Surface-Emitting Laser Devices By H. Li and K. Iga

7 Active Glass for Photonic Devices Photoinduced Structures and Their Application Editors: K. Hirao, T. Mitsuyu, J. Si, and J. Qiu

8 Nonlinear Photonics Nonlinearities in Optics, Optoelectronics and Fiber Communications By Y. Guo, C.K. Kao, E.H. Li, and K.S. Chiang

9 Optical Solitons in Fibers Third Edition By A. Hasegawa and M. Matsumoto

10 Nonlinear Photonic Crystals Editors: R.E. Slusher and B.J. Eggleton

11 Waveguide Nonlinear-Optic Devices By T. Suhara and M. Fujimura

12 Third Generation Photovoltaics Advanced Solar Energy Conversion By M.A. Green

13 Thin Film Solar Cells Next Generation Photovoltaics and Its Application Editor: Y. Hamakawa

Professor Martin A. Green University of South Wales Centre of Excellence for Advanced Silicon Photovoltaics and Photonomics Sydney, NSW, 2052, Australia

Series Editors:

Professor Takeshi Kamiya Ministry of Education, Culture, Sports, Science and Technology, National Institution for Academic Degrees, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan

Professor Bo Monemar Department of Physics and Measurement Technology Materials Science Division Link¨oping University 58183 Link¨oping, Sweden

Dr. Herbert Venghaus Heinrich-Hertz-Institut f¨ur Nachrichtentechnik Berlin GmbH Einsteinufer 37 10587 Berlin, Germany

Professor Yoshihisa Yamamoto Stanford University Edward L. Ginzton Laboratory Stanford, CA 94305, USA

ISSN 1437-

ISBN-10 3-540-26562-7 Springer Berlin Heidelberg New York ISBN-13 978-3-540-26562-7 Springer Berlin Heidelberg New York

ISBN 3-540-40137-7 Springer Berlin Heidelberg New York ( -Cover Edition)

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To Judy, Brie and Morgan

VIII Preface

there alternative, more elegant approaches to increased performance, perhaps more compatible with the thin silicon on glass technology we had helped develop? Both to answer this question and to meet the more mundane need to differentiate future research from work funded in the past, we were led to the concept of a third generation of photovoltaics. This would be differentiated from the two earlier generations by higher performance potential than from single junction devices. Other key criteria were that it use thin-films, for low material costs, and abundant, non-toxic materials. Although silicon is ideal in this regard, progress with molecularly based systems such as organic and dye sensitised cells and with nanostructural engineering in general, suggested other comparably attractive material systems may become available by 2020. The first phase in our attempts to identify third generation candidates was to gain a clear understanding of the strengths and weaknesses of approaches suggested in the past for improving performance. It was also hoped that this re- examination might stimulate new ideas. This book documents the results of this phase. Taking a very broad view of photovoltaics, almost as broad as “ electricity from sunlight ”, advanced photovoltaic options are analysed self-consistently with key features and challenges for successful implementation assessed. Although radiative inefficiencies readily can be incorporated, the main focus is on performance in the radiative limit. The rationale for this is that all successful photovoltaic devices must evolve towards this limit as argued above. I would like to thank all who have stimulated my interest in photovoltaics since the early days, either by direct contact or by published work. I particularly thank those who took my postgraduate course on advanced photovoltaics during 2000, acting as guinea pigs for developing the text’s first draft. Andrew Brown, Nils Harder and Holger Neuhaus deserve special mention for constantly challenging the material presented and for several graphs and tables in the text. I also thank Richard Corkish, Thorsten Trupke and Stuart Wenham and the high profile researchers on the Advisory Committee of the Centre formed to explore third generation options, particularly the longest serving members, Professors Antonio Luque, Hans Queisser and Peter Würfel. As the reader will note, the book also benefits from their past work. I also thank the Humboldt Foundation for a Senior Research Award and Professors Ernst Bücher, Ulrich Gösele and Rudolph Hezel for hosting associated visits during 2001 and 2002 where, amongst other activities, the manuscript was finalised. Finally, I thank Jenny Hansen for tireless efforts in producing diagrams plus many drafts of the text and Judy Green for support and companionship over the period this book was developed.

Bronte, Sydney Martin A. Green January, 2003

Table of Contents

• springer series in photonics
• 1.1 “Twenty-Twenty Vision” 1 Introduction
• 1.2 The Three Generations
• 1.3 Outline of Options
• 2.1 Introduction 2 Black-Bodies, White Suns
• 2.2 Black-Body Radiation.
• 2.3 Black-Body in a Cavity.
• 2.4 Angular Dependence of Emitted Radiation
• 2.5 Direct and Diffuse Efficiencies
• 2.6 Black-Body Emission Properties.
• 3.1 Introduction 3 Energy, Entropy and Efficiency
• 3.2 Energy and Entropy Conservation
• 3.3 Carnot Efficiency.
• 3.4 Landsberg Limit.
• 3.5 Black-Body Limit
• 3.6 Multi-Colour Limit
• 3.7 Non-Reciprocal Systems
• 3.8 Ultimate System.
• 3.9 Omnidirectional Global Converters
• 3.10 Summary
• 4.1 Efficiency Losses. 4 Single Junction Cells
• 4.2 Shockley-Queisser Formulation
• 4.3 Hot Photons (Chemical Potential of Light)
• 4.4 Einstein Coefficients
• 4.5 Photon Boltzmann Equation
• 4.6 General Cell Analysis
• 4.7 Lasing Conditions
• 4.8 Photon Spatial Distributions
• 4.9 Effect of Sample Thickness
• 4.10 Thermodynamics of Single Junction Cell
• 5.1 Spectrum Splitting and Stacking 5 Tandem Cells
• 5.2 Split-Spectrum Cells
• 5.3 Stacked Cells.
• 5.4 Two Terminal Operation
• 5.5 Infinite Number of Cells
• 5.6 Approximate Solution
• 5.7 Thermodynamics of the Infinite Stack
• 6.1 Introduction 6 Hot Carrier Cells
• 6.2 Relevant Time Constants.
• 6.3 Ross and Nozik’s Analysis
• 6.4 Simplification for E G = 0.
• 6.5 Würfel’s Analysis.
• 6.6 Possible Low Dimensional Implementation.
• 7.1 Introduction 7 Multiple Electron-Hole Pairs per Photon
• 7.2 Multiple-Carrier Photon Emission
• 7.3 Limiting Performance
• 7.4 Comparison with Würfel’s Analysis
• 7.5 Possible Implementation
• 7.6 Generalised Analysis
• 7.7 Raman Luminescence
• 8.1 Introduction 8 Impurity Photovoltaic and Multiband Cells
• 8.2 3-Band Cell
• 8.3 Photon Absorption Selectivity
• 8.3.1 Finite Bandwidths
• 8.3.2 Graded Absorption Coefficients
• 8.3.3 Spatial Absorption Partitioning
• 8.4 Absorption Leakage Loss
• 8.5 Other Possible Multigap Schemes
• 8.6 Impurity Photovoltaic Effect
• 8.7 Up- and Down-Conversion
• 9.1 Introduction 9 Thermophotovoltac and Thermophotonic Conversion
• 9.2 Solar Thermal Conversion
• 9.3 Thermophotovoltaic Conversion
• 9.3.1 Black-Body Source
• 9.3.2 With Narrow Passband Filter.
• 9.3.3 Solar Conversion: Cell/Receiver
• 9.4 Thermophotonics
• 9.4.1 Case with Filters Table of Contents XI
• 9.4.2 Without Filter
• 10 Conclusions
• A: Greek Alphabet Appendices
• B: Physical Constants.
• C: Fermi-Dirac and Bose-Einstein Integrals.
• D: List of Symbols
• E: Quasi-Fermi Levels
• F: Solutions to Selected Problems
• Index

1 Introduction

1.1 “Twenty-Twenty Vision”

Since the early days of terrestrial photovoltaics, many have thought that “first generation” silicon wafer-based solar cells eventually would be replaced by a “second generation” of inherently much less material intensive thin-film technology, probably also involving a different semiconductor. Historically, cadmium sulphide, amorphous silicon, copper indium diselenide, cadmium telluride and now thin-film silicon have been regarded as key thin-film candidates. Since any mature solar cell technology must evolve to the stage where cost is dominated by that of the constituent material, be it silicon wafers or glass sheet, it seems that high power output per unit area is the key to the lowest possible future manufacturing costs. Such an analysis makes it likely that photovoltaics, in its most mature form, will evolve to a “third generation” of high-efficiency, thin-film technology. By high-efficiency, what is meant is energy conversion values double or triple the 15-20% range presently targeted, closer to the thermodynamic limit upon solar conversion of 93%. Tandem or stacked cells provide the best known example of how such high efficiency might be achieved. In this case, conversion efficiency can be increased merely by adding more cells of different bandgap to a stack, at the expense of increased complexity and spectral sensitivity. However, as opposed to this “serial” approach, better-integrated “parallel” approaches are possible that offer similar efficiency to even a stack involving an infinite number of such tandem cells. These alternatives will become increasingly feasible with the likely evolution of materials technology over the decades to 2020. This book discusses a range of these options systematically as well as paths to practical implementation. By clearly defining these options and identifying their strengths, weaknesses and areas where further work is required, their development may be accelerated.

1.2 The Three Generations

Most solar cells sold in 2003 were based on silicon wafers, so-called “first generation” technology (Fig. 1.1). As this technology has matured, its economics have become dominated increasingly by the costs of starting materials already

1.2 The Three Generations 3

cover sheet and other encapsulants (Woodcock et al. 1997). There will be a lower limit on such costs that, when combined with likely attainable cell efficiency (15% or 150 peak watts/m^2 ), determines the lower limit on photovoltaic module and, hence, electricity generation costs. One approach to progress further is to increase conversion efficiency substantially. In principle, sunlight can be converted to electricity at an efficiency close to the Carnot limit of 95% for the sun modelled as a black-body at 6000 K and a 300 K cell (Chap. 2). This is in contrast to the upper limit, 31% on the same basis, upon the conversion efficiency of a single junction solar cell, as would limit silicon wafer and most present thin-film devices. This suggests the performance of solar cells could be improved 2-3 times if fundamentally different underlying concepts were used in their design, ultimately to produce a “third generation” of high performance, low-cost photovoltaic product. There would be an enormous impact on economics if these new concepts could be implemented in thin-film form, making photovoltaics one of the cheapest known options for future energy production. Figure 1.2 shows this more graphically by showing possible production costs per unit area together with energy conversion efficiency ranges for the three generations of technology mentioned above. “First generation” wafer technology has high areal production costs and moderate efficiency, with few prospects for reducing the former below

I

US$0.50/W

Thermodynamic limit

US$1.00/W

US$3.50/W

Cost, US$/m^2

US$0.10/W US$0.20/W

Efficiency,% Present limit

I I

I I I

Fig. 1.2: Efficiency-cost trade-off for the three generations of solar cell technology; wafers, thin-films and advanced thin-films (year 2003 dollars).

4 1 Introduction

about US$150/m^2 or the latter much above 20% (all dollar values in this book are year 2003 dollars). “Second generation” thin-film technology offers lower areal production costs, perhaps as low as US$30/m^2 , but even more modest efficiency (presently in the 5-10% range). If the efficiency can be increased substantially using advanced “third generation” technology, much lower overall costs are possible even if there is a moderate increase in areal processing costs, relative to the second generation approaches.

1.3 Outline of Options

What are the prospects for developing thin-film cells based on new concepts capable of “third generation” performance? Fortunately, with the likely evolution of new materials technology over the coming decades, these appear quite good! Apart from tandem cells (Chap. 5), where efficiency can be increased progressively merely by stacking more cells on top of one another, a number of better-integrated “parallel” conversion approaches have also been suggested capable of similar efficiency, as previously mentioned. One general class of approach that includes tandem cells is based on having multiple energy threshold processes available in the one device (Chap. 8). Other examples of this approach include multiple quantum well solar cells (Barnham and Duggan 1990) and devices based on the impurity photovoltaic effect (Green 1995). Recent work has clarified the limits on the efficiency of such devices by examining a general “three band” case (Luque and Marti 1997). In this case, excitation and recombination are allowed not only between the valence and conduction band, as in standard solar cells, but also between these bands and a third impurity band. Generalisation of this approach to more than three bands is possible, in principle, leading to energy cascade cells with potentially greatly improved performance. A second class of approach is based on making fuller use of the energy of the high energy photons in sunlight such as by creating multiple electron-hole pairs per incident photon, as many as allowed by energy conservation (Chap. 7). Other quantum multiplication approaches are to create two lower energy photons from a single high energy photon, or an electron plus a lower energy photon. A third class of approach is based on hot carrier effects (Chap. 6). Here, the sun’s energy is stored in the vigorous motion of photoexcited carriers. To improve efficiency, these carriers must be collected before they get the chance to cool down to ambient temperature. Another group of approaches is based on using sunlight to heat an absorber, with energy extracted from the heated absorber then being converted to electricity. Well known techniques of this type are the normal solar thermal electric approach, where heat from the absorber drives a heat engine, as well as thermionics and thermoelectrics. Another thermal approach is thermo-

6 1 Introduction

Bruton TM, Luthardt, G, Rasch K-D, Roy K, Dorrity IA, Garrard B, Teale L, Alonso J, Ugalde U, Declerq K, Nijs J, Szlufcik J, Rauber A, Wettling W and Vallera A (1997), A study of the manufacture at 500 MWp p.a. of crystalline silicon photovoltaic modules, Conf. Record, 14th^ European Photovoltaic Solar Energy Conference, Barcelona, June/July, pp. 11-16. Coutts TJ and Fitzgerald MC (1998), Thermophotovoltaics, Scientific American, 68-73, September. Green MA (1995), Silicon Solar Cells: Advanced Principles and Practice, (Bridge Printery, Sydney). Luque A and Marti A (1997), Increasing the efficiency of ideal solar cells by photon induced transitions at intermediate levels, Physical Review Letters 78;

Woodcock JM, Schade H, Maurus H, Dimmler B, Springer J and Ricaud A, (1997) A study of the upscaling of thin-film solar cell manufacture to w ards 500 MWp per annum, Conf. Record, 14 th^ European Photovoltaic Solar Energy Conference, Barcelona, June/July, pp. 857-860.

2 Black-Bodies, White Suns

2.1 Introduction

A black-body is simply a body or object that is a perfect absorber of light and therefore, by a fundamental reciprocal relation, a perfect emitter. Although the perfect black-body represents a mathematical ideal, physical objects and devices can approach black-body properties reasonably closely. Even though defined so simply, black-bodies have played a surprisingly large role in the evolution of physics. Attempts to understand the spectral distribution of light emitted by heated black-bodies led directly to the development of quantum mechanics (Duck 2000). One particular approximation to a black-body, the paradoxically white and bright sun, has had an even more significant impact on human culture, being indispensable to human life itself. Black-bodies feature prominently in the theory of the limiting performance of solar cells. Not only is the radiation emitted by the sun a good approximation to that from a very hot black-body, but an ideal solar cell would be expected to be a good absorber of light and hence be related to a black-body in some way. The details of this relationship forms the focus of many of the following chapters. An additional reason for the interest in black-bodies in solar cell theory is that, given their prominence in the development of physics, their thermodynamics have been thoroughly explored. This is particularly helpful when seeking to evaluate limiting solar cell performance.

2.2 Black-Body Radiation

A simple way to make a black-body is to put a small hole in an otherwise fully enclosed cavity (Fig. 2.1). Any ray entering the cavity via this hole will have great difficulty escaping, particularly if the cavity walls have moderately good absorption properties. The cavity therefore acts as an excellent absorber of radiation entering the hole. As a result, the area of the hole acts like an almost ideal black-body radiator for the inverse emission process. From experimental data for such cavities, Max Planck first guessed the correct expression for the spectral variation of black-body radiation in 1900 and then attempted to derive this expression theoretically (Duck 2000; Bailyn 1994). Simply stated, he had to stretch both statistics and physics to achieve his goal! In

2.2 Black-Body Radiation 9

k^2 k^2 k^2 h^2 f^2 /c^2 x +^ y + z = (2.1) Using a forerunner of Heisenberg’s Uncertainty Principle of 1926 ( ∆ x ∆ k (^) x ≥ h) , Bose imagined a 6-dimensional xyzk (^) xk (^) y kz phase space with the phase space volume divided into a mosaic of cells each corresponding to a separate state and each of volume:

h ==== dxdydzdkx dkydk z

At fixed x, y, and z, the three dimensional k (^) x k (^) y kz sub-space is of interest. A spherical cell in the k (^) x k (^) y kz sub-space between radius k and k + dk contains photons with approximately the same frequency, f = ck/h. The total phase volume d Ω associated with these photons is:

d Ω = k dk ∫∫∫ dxdydz = V(hf/c) d(hf/c) 4 π 2 4 π^2 (2.3)

where V is the physical volume of the cavity being considered. The number of states enclosed is:

ρ (^) fdf = (g/h^3 )d Ω= g( 4 π V/c^3 )f^2 df (2.4)

where the degeneracy factor, g equals 2. This is because light, considered as a planar transverse wave, needs two parameters to specify how it is orientated (i.e., has two possible polarisation states for each value of f ) or has two possible spins, if considered as a particle. Most readers, as for the author, probably find it easier to think in 3- dimensional rather than 6-dimensional space. Some feeling for the previous mathematics can be gained by thinking in the 3-dimensional xk (^) x k (^) y space of Fig. 2.2, as might be important for fixed y, z and kz. The k (^) xk (^) y plane is the analogue of the 3-dimensional k (^) xk (^) y kz space, in this example. The analogue of the spherical shell is the annular ring shown for three such planes in Fig. 2.2. The volume corresponding to k (^) x and k (^) y values within this ring within the 3-dimensional space is just the area of the ring multiplied by the extent of the region in the x-direction, for the fixed values of y and z. This corresponds to the tubular volume shown. The calculation is simplified since the geometry in the k (^) x k (^) y plane is independent of x - value. For the 6-dimensional case, the volume of the shell in the k (^) x k (^) y k (^) z sub-space is independent of x,y and z co-ordinates. The volume in the 6-dimensional space is found for an incremental physical volume around any particular x, y, z co-ordinate and integrated over the entire physical volume. The latter converts to a multiplication due to the non-dependence upon spatial co-ordinates. Bose then calculated the most probable distribution of photons amongst his mosaic of cells within phase space. He was able to show that the average number of particles is given by the function that now bears his name (together with

10 2 Black-Bodies, White Suns

ky

kx

x

dk

planes of constant x

k

Fig. 2.2: 3-dimensional xk (^) xk (^) y space analogue of the calculation conducted in 6-dimensional xyzk (^) xk (^) yk (^) z space in text.

Einstein’s who was quick to realise the significance of Bose’s work and to develop it). The Bose-Einstein distribution function is given by:

f (^) BE = 1 /( ehf/kT − 1 ) (2.5)

The total photon energy per unit volume in the cavity in the frequency range df is therefore given by:

e 1

u df^8 (hf/c)df hf/kT

3 3 V −

= π^ (2.6)

2.3 Black-Body in a Cavity

If a black-body is inserted in the cavity of Fig. 2.1, as in Fig. 2.3, several properties of the black-body can be deduced (Siegal and Howell 1992). A black-body must be a perfect emitter of light as well as a perfect absorber. This follows since the black-body absorbs all incident radiation from the cavity. After a period of time, the black-body and the cavity will reach a common equilibrium temperature. Since there can be no net energy transfer when at a common temperature, the black-body must be emitting the maximum amount of radiation. This must follow because anything less than a perfect absorber would have to emit less to remain in equilibrium.