Contents

Cover

Title page

Copyright page

Dedication

Preface

Chapter 1: Introduction

References

Chapter 2: Fundamental Limits of Solar Energy Conversion

2.1 Introduction
2.2 The Carnot Efficiency – A Realistic Limit for PV Conversion?
2.3 Solar Cell Absorbers – Converting Heat into Chemical Energy
2.4 No Junction Required – The IV Curve of a Uniform Absorber
2.5 Limiting Efficiency Calculations
2.6 Real Solar Cell Structures
2.7 Beyond the Shockley Queisser Limit
2.8 Summary and Conclusions
Acknowledgement
References

Chapter 3: Optical Modeling of Photovoltaic Modules with Ray Tracing Simulations

3.1 Introduction
3.2 Basics of Optical Ray Tracing Simulations
3.3 Modeling Illumination
3.4 Specific Issues for Ray Tracing of Photovoltaic Modules
3.5 From Optics to Power Output
3.6 Overview of Optical Simulation Tools for PV Devices
Acknowledgments
References

Chapter 4: Optical Modelling and Simulations of Thin-Film Silicon Solar Cells

4.1 Introduction
4.2 Approaches of Optical Modelling
4.3 Selected Methods and Approaches
4.4 Examples of Optical Modelling and Simulations
4.5 The Role of Illumination Spectrum
4.6 Conclusion
Acknowledgement
References

Chapter 5: Modelling of Organic Photovoltaics

5.1 Introduction to Organic Photovoltaics
5.2 Performance of Organic Photovoltaics
5.3 Charge Transport in Organic Semiconductors
5.4 Energetic Disorder in Organic Semiconductors
5.5 Morphology of Organic Materials
5.6 Considerations for Photovoltaics
5.7 Simulation Methods of Organic Photovoltaics
5.8 Considerations When Modelling Organic Photovoltaics
Acknowledgements
References

Chapter 6: Modeling the Device Physics of Chalcogenide Thin Film Solar Cells

6.1 Introduction
6.2 Kosyachenko’s Approach: Carrier Transport
6.3 Demtsu-Sites Approach: Double-Diode Model
6.4 Kosyachenko’s Approach: Optical Loss Modeling
6.5 Karpov’s Approach
6.6 Conclusion
Acknowledgements
References

Chapter 7: Temperature and Irradiance Dependent Efficiency Model for GaInP-GaInAs-Ge Multijunction Solar Cells

7.1 Motivation
7.2 Efficiency Model
7.3 Results and Discussion
7.4 Conclusions
7.5 Acknowledgments
References
Appendix: Shockley-Queisser-Modell Calculations

Chapter 8: Variation of Output with Environmental Factors

8.1 Conversion Efficiency and Standard Test Conditions (STC)
8.2 Variation of I-V curve with Each Environmental Factor [3]
8.3 Example of Measurement of Spectral Distribution of Solar Radiation
8.4 Irradiance
8.5 Effects on Performance of PV Modules/Cells [5]
8.6 Cell Temperature [8–11]
8.7 Results for Concentrated Photovoltaics
Acknowledgments
References

Chapter 9: Modeling of Indoor Photovoltaic Devices

9.1 Introduction
9.2 Indoor Radiation
9.3 Maximum Efficiencies
9.4 Demonstrated Efficiencies and Further Optimization
9.5 Characterization and Measured Efficiencies
9.6 Outlook
9.7 Acknowledgement
References

Chapter 10: Modelling Hysteresis in Perovskite Solar Cells

10.1 Introduction to Perovskite Solar Cells
Acknowledgements
References

Index

End User License Agreement

List of Illustrations

Chapter 1

Figure 1.1 Drawing of a model of a flying machine by Leonardo da Vinci.
Figure 1.2 Ray-tracing model of an office room. The model includes measured transmission values and other material properties [13].

Chapter 2

Figure 2.1 Current voltage characteristic of a uniform blackbody absorber with E_g = 1 eV for non-concentrated TS = 6000 K blackbody radiation. The current density is calculated as the difference between absorbed and emitted photon flux respectively. The chemical energy per extracted electron is related to the voltage that a solar cell could generate via Dm = qV. Extraction of carriers lowers Dm. At an intermediate value of the chemical energy DmMPP the extracted power is maximum. At DmOC the cell emits the same photon flux as it absorbs, resulting in zero current.
Figure 2.2 Limiting efficiency of single absorber solar cells for concentrated and non-concentrated TS = 6000 K blackbody radiation as a function of the band-gap energy E_g.

Chapter 2

Figure 3.1 Optical effects in a PV module: Refraction (2–9), diffraction (11), reflection (1, 3, 6, 7), absorption (2, 4, 5, 8, 9), scattering (6) and interference (10).
Figure 3.2 Definition of light rays and beams.
Figure 3.3 Refraction of light at an interface.
Figure 3.4 Typical unit cell for ray tracing simulations of solar cells: Part of the solar cell below a single surface pyramid.
Figure 3.5 Calculation of the transmittance of a plan-parallel slab with consideration of multiple internal reflections.
Figure 3.6 Visualization of the Monte-Carlo particle tracing cycle.
Figure 3.7 Definition of polar and azimuthal angles θ and φ.
Figure 3.8 Comparison of the generation of 1000 random points (x, y) by a typical pseudo-random number generator (top) and a Halton sequence (bottom). The points generated by the Halton sequence are distributed more uniformly.
Figure 3.9 Simplified visualization of the inversion method applied to discrete values. In this example, 10 discrete numbers are given. The probability distribution p(x_i) is normalized such that Σ_i p(x_i) = 1. If a random number (uniformly distributed on (0, 1)) is generated within the gray shaded range, x = 6 is returned.
Figure 3.10 Average photon emission probability per solid angle, cumulated with respect to wavelength and projected onto the horizontal plane, as determined from irradiance measurements at ISFH in the years 1992–2005.
Figure 3.11 Dimensions in PV devices: From the PV module and its surroundings (in meters) to the solar cells’ texture and metallization (in microns).
Figure 3.12 Schematic of the light rays (red) moving through and between the 3–5 domains in the multi-domain approach. The coupling of the domains is realized by photon position shifters (black lines).
Figure 3.13 Breakdown of photon termination in a PV module ray tracing simulation with 10000 photons.
Figure 3.14 Hierarchy of photon reflection severity (left) and corresponding breakdown of photon reflections (right). In this example, no photons are reflected at the glass/encapsulant interface due to the similar refractive indices.
Figure 3.15 Typical examples of spectrally resolved solar cell reflection and external quantum efficiency (EQE) measurements compared to ray tracing results.
Figure 3.16 Light distribution for a bare solar cell in air (left) and the same solar cell when encapsulated in a module (right). Absorption in the cell’s ARC is negligible in this example and thus not shown.
Figure 3.17 Optical losses in a bifacial module.
Figure 3.18 The complete calculation chain which calculates electrical module power output from ray tracing simulations (black, top) and a shortcut (blue, bottom) that can be used to analyze the impact of variations of the optical properties for a PV device whose semiconductor properties are already known.
Figure 3.19 Exemplary effective collection efficiency (λ) of two different types of solar cells.
Figure 3.20 Typical interconnection scheme for a PV module consisting of 60 solar cells connected in series which are organized in six strings. Three bypass diodes are present to bypass pairs of strings in case of failure or partial shading.
Figure 3.21 Left: Curves for calculating J_sc Absorption in the cell’s absorber A(λ), collection efficiency (λ) and spectrum in terms of potential photogeneration current J_phot. Right: Optical current losses in PV modules at standard testing conditions. As by convention, generated currents refer to the area of the solar cells and not to the area of the PV module, all currents in the right plot are divided by the fraction of module area covered by solar cells and total module area (0.93 in this example).
Figure 3.22 Current losses in PV modules under the mean annual light source (details concerning this light source see section 3.3.2).

Chapter 2

Figure 4.1 Example of a mesh in FEM simulations of a tandem a-Si:H/µc-Si:H solar cell with a high aspect ratio periodic texture introduced by the top superstrate. A model of non-conformal layer growth is applied to determine internal interface morphology (see section 4.4.2).
Figure 4.2 General representation of an example of the Coupled Modelling Approach (CMA) in optical modelling of PV devices. Arrows represent input-output connections between the coupled models.
Figure 4.3 (a) Coupling of ray tracing (RT) and thin-film optics represented by the transfer matrix formalism (TMF), in the CROWM model, (b) a general structure (for simplicity shown for the case of 1-D textures) which can be analyzed by 3-D simulator CROWM.
Figure 4.4 A schematic representation of the CMA approach which includes RCWA method besides ray tracing and thin-film optics. Structures including nano- and microtextures can be simulated with such a model.
Figure 4.5 Selected random textures used in simulations: (a) initial random texture (as obtained from the AFM scan of Asahi U type TCO), (b), medium-frequency (MF) filtering of the texture, (c) random texture with phase spectrum set to zero and (d) a three component texture (with periods P₁ = 300 nm, P₂ = 150 nm and P₃ = 75 nm).
Figure 4.6 (a) Height and (b) phase spectrum of the initial random texture (from Figure 4.5(a)) represented in contour plots (left) and corresponding scans in y-direction (right). Denotations LF, MF and HF correspond to low-, medium- and high-frequency regions of the spectrum.
Figure 4.7 Structure of the simulated single-junction a-Si:H silicon solar cell in substrate configuration.
Figure 4.8 Simulated relative increases in J_SC (%) of the analyzed single-junction a-Si:H cell in substrate configuration. The increases relate to the change of the substrate morphology by the top-down approach). LF, MF, HF and MF+HF labels correspond to the random textures with low-, middle-, high- and high+middle- frequency components present in the modified random texture, respectively. Labels 1-comp and 3-comp correspond to the texture with only one and with three frequency components, respectively. The label PH0 indicates that phase spectrum of the texture was set to zero.
Figure 4.9 A schematic representation of the combined model of non-conformal growth (top). Below are vertical cross-sections of a thin-film layer grown on a substrate as calculated by the model considering: a) fully conformal (g = 0), b) fully isotropic (g = 1) and c) combined growth type (g = 0.3). The dashed lines on the top surfaces in b) and c) indicate the reference texture obtained by conformal growth type.
Figure 4.10 Example of a V-shape valley formed after the growth of a layer (example of Ag layer, simulation). The valley is characterized by the opening angle φ. Note that the valley is not present at the initial substrate surface but is a consequence of the layer growth.
Figure 4.11 The gradual change in surface morphology for g = 0.4 as a function of the layer thickness (0 nm – no layer, 200 nm, 500 nm and 1000 nm). The top figures a) to d) are 3-D AFM-like images of the modelled surfaces. The cross-sections denoted with the white lines in the top images are enlarged and shown in the figure below. (a) corresponds to AFM scan of the surface, whereas (b), (c) and (d) are results of calculations with the developed model.
Figure 4.12 (a) Cross-sectional SEM image of µc -Si:H pin solar cell with introduced periodic sinusoidal texture, (b) growth as predicted by the combined model with g = 0.2/0.3 for Ag and ZnO / µc -Si:H stack (white lines).
Figure 4.13 (a) Cross-sectional SEM image of a-Si:H solar cell grown on variable sinusoidal texture, (b) prediction of subsequent interface morphology as obtained with the model, depending on the considered growth type, are shown in dotted, dashed and full lines for conformal, isotropic and combined growth type (with g = 0.2 for Ag and ZnO and g = 0.3 for a-Si:H layers).
Figure 4.14 (a) Cross-sectional SEM image of mc -Si:H solar cell deposited on a randomly textured substrate, (b) first step of modelling of growth – calculation of direction vectors with the corresponding final points, (c) generation of lines from the final points, (d) the highest points selection / elimination of the loops underneath. Figures (b), (c), and (d) are results calculated by the model.
Figure 4.15 Example of a sample with an embossed periodic texture with the parabolic shape and lateral period P = 0.8 mm and the peak-to-valley height h = 0.12 mm: (a) schematics of the vertical cross-section, (b) SEM picture of the IOH surface – top view, and (c) the AFM image.
Figure 4.16 Cross-sectional SEM image of the a-Si:H/µc -Si:H cell [83] obtained by focused ion beam (FIB) cutting (left) and the model of the structure (in case of applying symmetrical boundary conditions, the simulation domain can be laterally reduced to P/2 x P/2). Internal interfaces were obtained by the non-conformal layer growth model.
Figure 4.17 Verification results of optical simulations: (a) short-circuit current density of the top a-Si:H cell and (b) short-circuit current density of the bottom µc-Si:H cell, both as a function of the texture period. The values of structures with random textures are presented by horizontal lines. (c) external quantum efficiencies of the top and bottom cell and one minus total reflectance curve for the structure with LP-CVD ZnO:B front TCO with native random texture with σ_rms = 100 nm.
Figure 4.18 Vertical cross-section of the periodic texture with semi-ellipsoidal shapes corresponding to three different values of h. Top view of the texture (h = 0.6 mm) is shown as the insert.
Figure 4.19 Modelled interface texture development (applying g = 0.3) during the layer growth and defective region positions (critical positions p_cs indicate the starting point of the defective region formation): (a) LP-CVD ZnO:B random texture, (b) parabolic texture, (c) and (d) semi- ellipsoidal textures.
Figure 4.20 Calculated critical positions p_cs as a function of the period of the semi-ellipsoidal texture for three different heights. The growth parameter g = 0.3 was considered in the model.
Figure 4.21 Simulated short-circuit current densities of the top (a) and the bottom (b) cell in the a-Si:H/µc-Si:H structure in a superstrate configuration with the semi-ellipsoidal superstrate texture. The random reference corresponds to the LP-CVD ZnO:B texture embossed in the lacquer layer.
Figure 4.22 Solar spectrum compared to an example of warm white LED spectrum. Both spectra are normalized.
Figure 4.23 Simulated external quantum efficiencies of two a-Si.H cells in superstrate configuration with different values of the interface roughness. In addition the LED spectrum as presented in Figure 4.22 is shown in the background.

Chapter 2

Figure 5.1 A diagram of a perovskite organic-inorganic hybrid solar cell. Metallic atoms surrounded by halide anions, arranged in octahedra, form an inorganic crystal, within the crystal are captive organic cations. The halide anions can move around the crystal through defect hopping and the organic molecules can diffuse through the crystal, an applied electric field can cause the ions to separate.
Figure 5.2 A figure showing the energetic landscape of an electron transfer event. Here the electronic coupling term is small compared to λ_ΑΒ and the overall transfer reaction is non-adiabatic. For the system to translate from state A to B there needs to a thermal excitation from the energetic minimum of state A. In this figure we have described all parameters in terms of the two states.
Figure 5.3 A diagram showing the change in the electronic orbital when a heavy atom is present in a molecule. The presence of an atom with a large electronegativity value distorts the charge distribution of the molecule and creates a highly localized electronic wave function. With respect to electron transport this means we can consider the heavy atom as the focus of hopping to and from the molecule.
Figure 5.4 A diagram showing the effect of a bond rotation in a polymer chain. (a) A conjugated polymer where the dihedral angles are close to zero. The electronic orbitals of each monomer closely overlap and form a single continuous region where charge density is delocalized and transport occurs most efficiently. (b) By twisting the polymer and introducing a large dihedral rotation, the region of charge delocalization is broken. Charge transport between the two conjugated sections is a slower process than within each region, described by a hopping process.
Figure 5.5 A figure showing possible arrangements for inter-polymer charge transport, here the polymers are shown as ribbons with the top and bottom representing the conjugation plane. (a) Totally unaligned polymers will have poor inter-polymer transport, there are few areas where conjugated polymer sections are close and co-planar. (b) The polymers are close but they are not co-planar, this intermediate case will possess intermediate inter-polymer transport. The transport that occur will be heavily focussed around the most co-planar segments creating charge transport bottlenecks. (c) Polymers that are close and co-planar possess the best inter-polymer coupling. Creating polymers in this arrangement is difficult, but can be achieved. The more crystalline the arrangement of polymers the more efficient inter-polymer charge transport is.
Figure 5.6 A diagram showing a system with aligned molecular dipoles for molecules with two localization sites as well as the corresponding electron distributions around each molecule. As the structure is ordered all molecules experience the same local environment and there is little energetic disorder across the different localization sites. Sites at the negative end of the dipole are more electronegative than the positive end, thus they have a slightly reduced LUMO energy.
Figure 5.7 A diagram showing frustration in molecules with two localization sites as well as the corresponding electron distributions around each molecule. Consider the central molecule, the dipoles below are aligned in a locally crystalline order, however the neighbouring molecules above are aligned in a second crystallite that directly opposes the order of the first. This means that the central row of molecules is trapped in an interface between locally oriented dipole domains. The precise orientation of the central molecules depends largely on the history of the system and how it was prepared, a common feature of glassy and frustrated systems.
Figure 5.8 An energy diagram showing the typical mechanisms for exciton dissociation in organic semiconductors. (a) A bound pair exists in the p-type side of the interface, if the pair can dissociate with the electron hopping to the n-type material then the total energy of the resultant state is lower than for a pair of free carriers in the p-type material. The symmetric mechanism can occur starting in the n-type material where the hole hops to the p-type after dissociating. (b) Shows the prevention of dissociation by energy levels. For the bound pair to dissociate, one of the carriers would need to perform an energetically unfavourable hop to the other material.
Figure 5.9 A diagram showing the processes involved in Förster resonance energy transfer of a singlet state. The excited chromophore state relaxes and emits a virtual photon with equivalent energy. A second acceptor chromophore absorbs the virtual photon and excites the molecule into the excited state. This is equivalent to one singlet state moving between the two chromophores.
Figure 5.10 A diagram showing the processes involved in Dexter energy transfer of excitons. (a) The transfer mechanism of a singlet state, note there is no radiative energy loss or virtual exchange. (b) The transfer mechanism of a triplet state, triplets cannot perform FRET due to Wigner spin restrictions. In both cases the two molecules bilaterally exchange electrons with the spin conserved during the transfer. This is equivalent to an exciton moving between the two molecules.
Figure 5.11 A diagram showing the process of TTA, first there is a regular electron exchange process leaving a ground state molecule and a highly unstable molecule which quickly relaxes into a singlet. This is equivalent to two triplets annihilating one another and a singlet being created.
Figure 5.12 An illustration of how to select an event from the resident-time algorithm, μ ∈ [0, k_tot] is a uniform random number. All of the events are placed on a number line according to the cumulative sum of previous event rates. In the illustrated example we have chosen to perform event 3.

Chapter 2

Figure 6.1 Band diagram of a CdS/CdTe thin film solar cell with trap level, E_t, at around the mid gap in the depletion width and the recombination paths [11].
Figure 6.2 Modeling of JV characteristics of ultrathin film solar cells with d_CdTe = 1.1, 0.7, and 0.5 µm using Sah–Noyce–Shockley theory. The inset shows the impact of various recombination lifetimes within SCR d_CdTe = 0.8 µm [11].
Figure 6.3 Band diagram of the CdS/CdTe/metal structure. The back barrier height indicated as the non-aligned valence band (of CdTe layer) and the metal’s work function (Φ₀) [4].
Figure 6.4 Double diode model of the CdS/CdTe thin film solar cells. Two opposite polarity diode are accounted for front and back junctions separately [4].
Figure 6.5 I-V characteristics of a CdS/CdTe/metal solar cell modelled with double-diode approach given by Demstsu-Sites [4].
Figure 6.6 Reflection rates at the interfaces of a typical CdS/CdTe thin film solar cell [18].
Figure 6.7 J_sc and ΔJ_sc obtained using the Kosyachenko’s optical model [18].
Figure 6.8 Ultrathin photovoltaics modelled with capacitance approach. Karpov et al. [7].
Figure 6.9 (a) Shunting pathways containing different numbers of defects can have either 1. high, 2. moderate, or 3. low resistances. (b) Ideal diode and shunt connected in parallel dashed I-V curves give a I-V characteristics with lower V_oc [7].

Chapter 2

Figure 7.1 Packaging of the CPVT demonstrator of IBM Research. A high efficiency PV cell is soldered to a silicon microchannel cooler with a thermal interface (TIM).
Figure 7.2 Solar simulator with a maximum concentration of 4930 suns at the Paul Scherer Institute (PSI), Switzerland.
Figure 7.3 Outdoor setup of the CPVT-testing system with a mirror array (a) and the 6x6 triple junction cell arrays on the receiver module (b) that were built for the 40 m² “Sunflower” CPVT system (c). Six receiver modules (b) are integrated in the receiver of the large “Sunflower” system in six separate focal points (c).
Figure 7.4 Maximum absorption of a triple junction solar cell at 25 °C for an AM 1.5 global spectrum and the Shockley Queisser model.
Figure 7.5 Maximum absorption of a triple junction solar cell at 65 °C for an AM 1.5 direct spectrum, C = 2500, and the Shockley Queisser model.
Figure 7.6 Calculated efficiencies following the real cell model described in this chapter and the Shockley Queisser model.

Chapter 2

Figure 8.1 Spectral distribution of reference sunlight [1, 2].
Figure 8.2 Equivalent circuit of a solar cell.
Figure 8.3 Variation of I-V characteristic and conversion efficiency with irradiance.
Figure 8.4 Variations of I-V characteristic and conversion efficiency with cell temperature.
Figure 8.5 Spectral response as a function of wavelength.
Figure 8.6 Spectral response of various types of photovoltaic cell.
Figure 8.7 Spectral distributions of solar radiation for different weather.
Figure 8.8 Spectral rate of change with wavelength for each month.
Figure 8.9 Effect of spectral radiation for each month effected by spectral response.
Figure 8.10 Cumulative irradiation per day during the year with an angle of inclination. (azimuth: due south, location: Suwa, Nagano prefecture, Japan)
Figure 8.11 Annual accumulated irradiation varies with azimuth angle and inclined angle. (location: Suwa, Nagano prefecture in Japan)
Figure 8.12 Testing site [5].
Figure 8.13 Photovoltaic energy conversion loss analysis model of PV systems [8.12].
Figure 8.14 Performance ratios of seven different PV systems [5].
Figure 8.15 Monthly effective array peak powers (lines) of the seven different systems and normalized indoor STC measurement results (symbols) of the four different types of PV modules [5].
Figure 8.16 Relationship between the PV module temperature and the normalized maximum power when the temperature coefficient a is –0.44, –0.31 and –0.29 %/°C.
Figure 8.17 Normalized output energy of the PV module and the module temperature when ΔT is 18.4V.
Figure 8.18 Daily mean efficiency and FF.
Figure 8.19 Daily V_OC and I_SC.
Figure 8.20 I_SC decreasing measured in the field test and estimated on accelerated thermal aging test.
Figure 8.21 Current ratio α and voltage ratio β.
Figure 8.22 Measured FF and FF_s which was calculated except the influence of decreasing I_SC.
Figure 8.23 Current coefficient g.
Figure 8.24 Influence of decreasing I_SC in generation efficiency.

Chapter 2

Figures 9.1-9.5 Simulated test room with Radiance and in reality [13, 14]. The models were built with increasing level of detail. Radiometric validation measurements showed, that including the main furniture as in Figure 9.2 is sufficient for IPV applications [18,19].
Figure 9.6 Maximum photon yield for different radiation sources and varying band gap [9, 13].
Figure 9.7 Maximum photovoltaic efficiencies for different radiation sources and varying band gap [9, 13].
Figures 9.8 Effect of the resistance design on the efficiency [9, 13].
Figures 9.9 and 9.10 Demonstrated and theoretical current density versus voltage curves of a 1-mm2 GaAs cell under (a) AM1.5 illumination and (b) white LED illumination. Corresponding power conversion efficiencies are labeled for the maximum power point [29].

Chapter 2

Figure 10.1 Perovskite structure for FAPbI₃, widely used in PSCs. The spheres represent atoms or ions. The pink spheres are iodide ions and the darker olive spheres are lead ions. The organic molecule in the centre is formamidium, FA, consisting of carbon (cyan), nitrogen (dark blue) and hydrogen (white).
Figure 10.2 Perovskite Solar Cell Power Conversion Efficiencies, PCEs, vs time since 2009. Liquid state perovskite cells, studied 2009-2012, were superseded by solid state perovskite cells from 2012.
Figure 10.3 (a) Simulated JV curves and (b) bulk electric field for a perovskite solar cell, with (red) and without (blue) mobile ions. The latter show higher short circuit current densities.The reverse scan where the voltage decreases with time is denoted by the thin solid lines and forward scan (voltage increasing with time) by thick dashed lines. A positive electric field points from the ETL to the HTL, such that a positive field drives carriers toward their corresponding contacts.

List of Tables

Chapter 3

Table 3.1 Typical dimensions of components in the simulation scene.
Table 3.2 Fraction of lost potential photogeneration current for both STC and the mean annual light source.
Table 3.3 Optical simulators for solar cells and wafers.
Table 3.4 Optical simulators for PV modules and their surrounding.

Chapter 4

Table 4.1 Simulated short-circuit current densities of the a-Si:H solar cells with two different surface roughnesses and applying two different illumination spectra.

Chapter 7

Table 7.1 Power Distribution of a Photovoltaic System for Standard Terrestrial Applications (Table adapted from [3]).
Table 7.2 Power Distribution of a Photovoltaic-Thermal System for Ultra-High-Concentration and a Desalination System as Thermal Load (Table adapted from [3]).
Table 7.3 Assumed layer thicknesses and surface velocities of the GaInP top cell.
Table 7.4 Assumed layer thicknesses and surface velocities of the GaInAs middle cell.
Table 7.5 Assumed layer thicknesses and surface velocities of the Ge bottom cell.
Table 7.6 Temperature dependent mobility of the GaInP top cell.
Table 7.7 Temperature dependent mobility the GaInAs middle cell.
Table 7.8 Temperature dependent mobility of the Ge bottom cell.
Table 7.9 Carrier lifetimes and effectives masses of the GaInP top cell.
Table 7.10 Carrier lifetimes and effectives masses of the GaInAs middle cell.
Table 7.11 Carrier lifetimes and effectives masses of the Ge bottom cell.
Table 7.12 Temperature dependent densities of states and doping concentrations for GaInP.
Table 7.13 Temperature dependent densities of states and doping concentrations for GaInAs.
Table 7.14 Temperature dependent densities of states and doping concentrations for Ge.
Table 7.15 Material dependent permittivities.
Table 7.16 Assumed radiative coefficient of the GaInP top cell.
Table 7.17 Assumed radiative coefficient of the GaInAs middle cell.
Table 7.18 Assumed Auger coeffients of the Ge bottom cell.
Table 7.19 Efficiencies of a GaInP-GaInAs-Ge cell for AM 1.5 AST G173–03 global spectrum at 25 °C (1003 Wm^-2).
Table 7.20

Chapter 8

Table 8.1 Cumulative irradiation during one year for different angles of inclination (azimuth: due south, location: Suwa, Nagano prefecture, Japan)
Table 8.2 Annual degradation rate.

This edition first published 2018 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA
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Library of Congress Cataloging-in-Publication Data

Names: Freunek Muller, Monika, editor.
Title: Photovoltaic modeling handbook / edited by Monika Freunek M?uller.
Description: Hoboken, NJ : Wiley-Scrivener, [2018] | Includes bibliographical references and index. |
Identifiers: LCCN 2018028384 (print) | LCCN 2018028620 (ebook) | ISBN 9781119364207 (ePub) | ISBN 9781119364191 (Adobe PDF) | ISBN 9781119363521 (hardcover : alk. paper)
Subjects: LCSH: Photovoltaic power generation–Mathematical models.
Classification: LCC TK1087 (ebook) | LCC TK1087 .P4657 2018 (print) | DDC 621.31/244–dc23
LC record available at https://lccn.loc.gov/2018028384

Preface

This book provides the reader with a solid understanding of the modeling of photovoltaic devices. To that aim, it covers different modeling approaches, from very fundamental theoretic investigations to numerical simulations based on ray tracing and experimental values. The book covers both standard applications and models and new approaches and fields of research such as perovskite materials. Recognized experts in their fields have written each chapter. Wherever available, the chapters refer to simulation software and the basic literature of the field. In the end, you, the reader, can proceed to your specific application with solid background information in hand, and judge which materials could be appropriate. You will be provided with hints as to where to search further so as to have realistic expectations for the performance achievable by your devices. The chapters of this book can therefore also be used as a source of literature tailored to the interests of the readers.

The introduction to the book provides a short overview of the developmental history of photovoltaics, including some of the fundamental literature in the field of photovoltaics and scientific publications covering important milestones.

Then, in Chapter 2, you will be introduced to the physics of photovoltaics and the material independent efficiency limits of photovoltaic devices.

The third chapter provides both a detailed model of a silicon-based photovoltaic module and a profound introduction to ray-tracing methods for optical numerical models.

Amorphous silicon is one of the most important photovoltaic materials. Due to its physical properties, its modeling is more complex, by far, than the modeling of direct semiconductor materials. Numerical modeling methods and results are explained in Chapter 4.

The modeling of organic semiconductors is discussed in Chapter 5. The differences between organic and inorganic charge transport and exciton behavior are explained. The chapter also gives an introduction to kinetic Monte Carlo methods to simulate the dynamics in organic semiconductor devices.

Chapter 6 reviews a few theories on modeling the device physics of chalcogenide thin-film solar cells such as CdTe and Cu(In,Ga)(Se,S)₂ (or CIGS) devices. Several approaches are discussed, each varying in some basic assumptions related to device structure and carrier transport.

Chapter 7 shows the modeling of stacked multi-material solar cells for ultra-high irradiance applications. The chapter covers some of the fundamental models in semiconductor photovoltaics for III-V materials, including the effects of variance in intensity and temperature.

The influence of spectral variations is shown in Chapter 8 both theoretically and experimentally, with a special focus on outdoor applications. Chapter 9 discusses this effect for indoor applications and shows the resulting ideal choice of materials and the enhanced indoor efficiencies.

The book closes with an outlook on one of the newest fields in PV, the perovskite materials.

Researchers of high reputation from all over the world have made this book possible, yielding a book of both high scientific quality and good readability. The editor sincerely thanks all contributing authors and coauthors for their great efforts, and the publisher for his always very helpful assistance.

Monika Freunek (Müller)
Bern, Switzerland
June 2018

Chapter 1
Introduction

Monika Freunek Müller

BKW AG, Bern, Switzerland

Corresponding author: monika.freunek@gmx.de

Abstract

The introduction gives a brief overview of the history of modelingand its use in photovoltaics. Important milestones in the research and development of photovoltaic devices are explained. The references of this chapter can serve to the the reader as a summary of the most fundamental literature in the field of photovoltaics.

keywords: History of photovoltaic modeling, modeling and simulation, solar cell, analytical model, numerical model, photovoltaic applications

Although models are rarely visible in a final invention or technical system, they are essential to their existence. Models are a core component of each innovative process. First models often consist of an abstract understanding of a system itself and its possible improvements. These models might be explained easily, and paper and pencil could suffice as tools for their further development. They can be extended in detail using more complex models, such as scientific calculations. The next steps often include prototype models using building materials such as clay, paper or three-dimensional printing technologies. Among the most famous models are the drawings and model buildings of Leonardo da Vinci. Although not all of them proved to be fully functional designs, they still are a source of inspiration to many people today with respect to their high scientific and artistic quality. Figure 1.1 shows a drawing of a model of a flying machine by Leonardo da Vinci.

**Figure 1.1** Drawing of a model of a flying machine by Leonardo da Vinci.

However, for a long time any mistakes and changing assumptions—both being characteristics of an innovation process—have led to an elaborative effort in adapting the model. The invention of computers has brought a radical change to the field of modeling. Steadily increasing computing power has enabled scientists, engineers, and architects to increase the level of detail and variation in their models. Analytical models, which had to be simplified before or were too laborious for use in research, development and field applications, can now be calculated. A new type of model has even evolved: Numerical models using mathematical models based on often iterative computational algorithms. The current level of maturity in photovoltaic research and development has been significantly enabled through the use of numerical models, while the findings of quantum and semiconductor physics have enabled photovoltaics (PV) at all.

Today, there are more than 150 years of research on photovoltaic modeling. Beginning with the observations of Edmond A. Becquerel in 1839 [1], the first patent of a solar cell was filed in 1888 [2]. Ultimately, the first solar cell was demonstrated by Bell Laboratories in 1954 [3]. The fundamental theoretical work in semiconductor physics, such as the work of William Shockley and Hans J. Queisser [4, 5], laid the foundation for the photovoltaic prototypes built in the middle of the last century. Based on the study of Shockley and Queisser [4], research has mainly focused on silicon for terrestrial outdoor applications and III-V devices for space.

In the following years, research has become more application-oriented, addressing the fundamental questions of 1) how to obtain an acceptable performance at acceptable cost and 2) how to build and process photovoltaic devices industrial scale. With the work of Harold Hovel [6], and later on, Martin A. Green [7] and Jenny Nelson [8], photovoltaic devices were modeled in detail, both in theory and in practical aspects. Most of the fundamental literature on modeling focused on semiconductor materials, especially Si and III-V materials. The optimal use of both extraterrestrial and terrestrial radiation led to the invention of multijunction solar cells. Additionally, modeling approaches included research on the thermodynamic limits of photochemical conversion [9, 10].

In the meantime, organic materials evolved and chalcocites continuously kept a small, but distinct, proportion of PV appliances. Cost issues enforced the development of low-cost silicon materials such as amorphous, polycrystalline and “dirty” silicon. In order to enhance their performance, light trapping and advanced doping methodologies were developed.

Today, we are closer than ever before to realizing a broad range of PV applications covering almost every area where human beings use technology. Many countries have decided to make PV a part of their national energy supply, and PV materials are a standard solution for space applications and distinct places. Some mobile applications, such as electric fences or mobile charging stations, are powered with PV. Furthermore, new applications arise. For example, low power electronic devices and the internet of things with its many distributed wireless sensor nodes can use PV as their power source.

There are as many applications as materials, and each material will behave very differently for a specific application. In most cases, the influence of the incoming radiation in its spectral variation and intensity will dominate. However, as is the case for space applications or concentrated photovoltaics, the influence of temperature on the devices will affect the performance for most materials, and this effect will vary from material to material.

Most materials are tested and modeled to the solar standard spectrum AM1.5 and a device temperature of 25 °C. This standard is very important in order to have reproducible reference conditions in order to mark progress, and the current best performers are updated twice a year in Green’s Table [11]. However, these conditions will never occur in nature and might not reveal the best performer for low irradiance or indoor applications or concentrated PV. Already under realistic outdoor operation, the performance might differ significantly from STC. Knowledge of the incoming spectral irradiance is therefore as important as knowledge of the material used. Ray-tracing programs combined with meteorological and building models, such as DAYSIM [12], can assist in obtaining realistic conditions for an application. Figure 1.2 shows a ray-tracing model of an office room simulated with Radiance.

**Figure 1.2** Ray-tracing model of an office room. The model includes measured transmission values and other material properties [13].

The recent introduction of cloud computational power, providing easy access to large and distributed computational resources at reasonable cost, might also open up a new world in the research and development of photovoltaics for two reasons. First, numerical models are by their nature deeply coupled to the available computing power. Thus, cloud computing enables more complexity in the applied models. Second, cloud computing also provides easy access to parallel computing, which leads to significant reduction in the computing time for each model. This will be a major step for all ray-tracing models, but will also ease the use of quantum mechanical models, as they are required for the detailed calculation of many material parameters in photovoltaics. These calculations could also reduce the required amount of measurements, thus reducing the research cost.

The increasing availability of various data, such as local weather data or geographical information, is also known as Big Data. While at first glance this might not be of interest from a research point of view, Big Data might become a powerful tool in the development of prototypes and application-shaped products. The use of machine learning and artificial intelligence in data science can also assist in developing models. For example, patterns could be found in characterization measurements while using material components as a feature. Thus, the modeling of photovoltaic devices promises to become even more interesting in the coming years.

This book covers the current most important analytical, numerical and experimental models for the main photovoltaic materials and applications and invites you, the reader, to participate in this interesting and important field of science and engineering.

References

1. Becquerel, E., On Electron Effects under the Influence of Solar Radiation. C. R. Acad. Sci., 9, 561, 1839.

2. Weston, E., Art of utilizing solar radiant energy, US Patent 389125 A, 1888.

3. Chapin, D. M., Fuller D. M. and Pearson, G. L., A New Silicon p-n Junction Photocell for Converting Solar Radiation into Electrical Power. J. Appl. Phys. 25(5), 676–677, 1954.

4. Shockley, W. and Queisser, H. J., Detailed Balance Limit of Efficiency of p-n Junction Solar Cells. J. Appl. Phys. 32, 510-529, 1961.

5. Sze, S. M. and Ng, K. K., Photodectectors and Solar Cells, in: Physics of Semiconductor Devices, John Wiley & Sons, New Jersey, 2007.

6. Hovel, H. J., Semiconductors and Semimetals, Volume II: Solar Cells, Willardson, R.K. and Beer, A. C. (Eds.), Academic Press, New York, 1975.

7. Green, M. A., Solar Cells: Operating Principles, Technology, and System Applications, University of New South Wales, 1982.

8. Nelson, Jenny, The Physics of Solar Cells. World Scientific Publishing Co Inc, 2003.

9. Würfel, P. and Würfel, U., Physics of Solar Cells: From Basic Principles to Advanced Concepts. John Wiley & Sons, New Jersey, 2016.

10. Marti, A. and Gerardo L. A., Limiting efficiencies for photovoltaic energy conversion in multigap systems. Sol. Energ. Mat. Sol. Cells 43(2), 203-222, 1996.

11. Green, M. A., et al., Solar cell efficiency tables [version 50], Progr. Photovolt: Res. Appl. 25(7), 668-676, 2017.

12. Reinhart, C.F., Walkenhorst, O., Validation of dynamic RADIANCE-based daylight simulations for a test office with external blinds. Energ. Buildings 33(7), 683-697, 2001.

13. Müller, M., Energieautarke Mikrosysteme am Beispiel von Photovoltaik in Gebäuden, Der Andere Verlag, Osnabrueck, Germany, 2010.