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Herausgeber: Wiley-VCH
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch

Beschreibung

The new edition of this highly regarded textbook provides a detailed overview of the most important characterization techniques for solar cells and a discussion of their advantages and disadvantages.
It describes in detail all aspects of solar cell function, the physics behind every single step, as well as all the issues to be considered when improving solar cells and their efficiency. The text is now complete with examples of how the appropriate characterization techniques enable the distinction between several potential limitation factors, describing how quantities that have been introduced theoretically in earlier chapters become experimentally accessible.
With exercises after each chapter to reinforce the newly acquired knowledge and requiring no more than standard physics knowledge, this book enables students and professionals to understand the factors driving conversion efficiency and to apply this to their own solar cell development.

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Leseprobe

Cover

Title Page

List of Symbols

Preface

Chapter 1: Problems of the Energy Economy

1.1 Energy Economy

1.2 Estimate of the Maximum Reserves of Fossil Energy

1.3 The Greenhouse Effect

1.4 Problems

Chapter 2: Photons

2.1 Black-body Radiation

2.2 Kirchhoff's Law of Radiation for Nonblack Bodies

2.3 The Solar Spectrum

2.4 Concentration of the Solar Radiation

2.5 Maximum Efficiency of Solar Energy Conversion

2.6 Problems

Chapter 3: Semiconductors

3.1 Electrons in Semiconductors

3.2 Holes

3.3 Doping

3.4 Quasi-Fermi Distributions

3.5 Generation of Electrons and Holes

3.6 Recombination of Electrons and Holes

3.7 Light Emission by Semiconductors

3.8 Problems

Chapter 4: Conversion of Thermal Radiation into Chemical Energy

4.1 Maximum Efficiency for the Production of Chemical Energy

4.2 Shockley–Queisser Limit

4.3 Problems

Chapter 5: Conversion of Chemical Energy into Electrical Energy

5.1 Transport of Electrons and Holes

5.2 Separation of Electrons and Holes

5.3 Diffusion Length of Minority Carriers

5.4 Dielectric Relaxation

5.5 Ambipolar Diffusion

5.6 Dember Effect

5.7 Mathematical Description

5.8 Problems

Chapter 6: Basic Structure of Solar Cells

6.1 A Chemical Solar Cell

6.2 Basic Mechanisms in Solar Cells

6.3 Dye Solar Cell

6.4 The pn-Junction

6.5 pn-Junction with Impurity Recombination, Two-Diode Model

6.6 Heterojunctions

6.7 Semiconductor–Metal Contact

6.8 The Role of the Electric Field in Solar Cells

6.9 Organic Solar Cells

6.10 Light Emitting Diodes (LED)

6.11 Problems

Chapter 7: Limitations on Energy Conversion in Solar Cells

7.1 Maximum Efficiency of Solar Cells

7.2 Efficiency of Solar Cells as a Function of Their Energy Gap

7.3 The Optimal Silicon Solar Cell

7.4 Thin-film Solar Cells

7.5 Equivalent Circuit

7.6 Temperature Dependence of the Open-circuit Voltage

7.7 Intensity Dependence of the Efficiency

7.8 Efficiencies of the Individual Energy Conversion Processes

7.9 Problems

Chapter 8: Concepts for Improving the Efficiency of Solar Cells

8.1 Tandem Cells

8.2 Concentrator Cells

8.3 Thermophotovoltaic Energy Conversion

8.4 Impact Ionization

8.5 Two-step Excitation in Three-level Systems

8.6 Problems

Chapter 9: Characterization of Solar Cells

9.1 Spectral Response and Quantum Efficiency

9.2 Quasi-Steady-State Photoconductance

9.3 Luminescence

9.4 Thermography

9.5 Light-Beam-Induced Current (LBIC)

9.6 The Suns- Method

9.7 Transient Techniques

Solutions

Appendix

Fundamental Constants

Units of Energy

Material Constants at 300 K

Standard Global

1.5 Spectrum

References

Index

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Chapter 1: Problems of the Energy Economy

Figure 1.1 Annual consumption of oil. The area under the curve gives the estimated total oil reserves.

Figure 1.2 Balance of the absorbed and emitted energy currents on the surface of the Earth.

Chapter 2: Photons

Figure 2.1 Bose–Einstein distribution function for μ

= 0. The dashed line represents the Boltzmann distribution exp (−ћω

), a good approximation for ћω > 2

Figure 2.2 Volumes of the states in momentum space.

Figure 2.3 An energy current

originating from the volume element d

is flowing through the hole with area d

of the cavity, into the solid angle dΩ.

Figure 2.4 Solid angle dΩ

under which the receiver area d

is seen from the emitter d

, and solid angle dΩ

under which d

is seen from d

Figure 2.5 Solid angle dΩ

under which the surface element d

on the Sun is viewed from the Earth, and solid angle dΩ

under which the surface element d

on the Earth is viewed from the Sun.

Figure 2.6 Energy current from the surface element d

on the surface of the Sun into the solid angle dΩ

under which the Earth is viewed from the Sun.

Figure 2.7 Dependence of the emitted energy current d

on the angle ϑ relative to the normal to the surface. The length of the arrow on the right is a measure of the magnitude of d

Figure 2.8 Exchange of radiation between two plates in a cavity with a filter in between, transmitting only photons with energy ћω.

Figure 2.9 Energy current density per photon energy from the Sun as a function of the photon energy just outside the Earth's atmosphere (heavy line) compared with a black-body at a temperature of 5800 K (thin line).

Figure 2.10 Energy current density per wavelength from the Sun as a function of the wavelength outside the Earth's atmosphere (heavy line) compared with a black body at a temperature of 5800 K (thin line).

Figure 2.11 The

1.5 spectrum (heavy line) compared with a black body at a temperature of 5800 K (thin line).

Figure 2.12 An imaging system projecting two area elements onto each other by redirecting their thermally emitted radiation must not disturb the thermal equilibrium between them.

Figure 2.13 Image of the Sun with an area

in the focal plane of a lens with radius

and focal length

Figure 2.14 A lens projects an image of the Sun onto an absorber in a perfectly reflecting cavity.

Figure 2.15 Efficiency η

for the conversion of solar heat energy by a black absorber and a Carnot engine as a function of the absorber temperature

, for maximum concentration (Ω

emit

= Ω

abs

, heavy line) and for nonconcentrated radiation (Ω

emit

= π, Ω

abs

= 6.8 × 10

−5

, broken line).

Figure 2.16 Net absorbed photon current of 1.5 eV photons as a function of the free energy per photon produced by a Carnot engine. The hatched rectangle, the largest rectangle for any point on the photon current curve, belongs to the point of maximum power, which also follows from the maximum of the energy current curve.

Figure 2.17 Efficiency of monochromatically absorbing Carnot engines as a function of the photon energy for fully concentrated black-body radiation of 5800 K.

Figure 2.18 Balance of absorbed and emitted energy and entropy currents for a reversible heat engine working with radiation.

Figure 2.19 Landsberg efficiency η

(heavy line) as a function of the absorber temperature

compared with the efficiency η

(thin line) of a solar heat engine with a single black absorber.

Chapter 3: Semiconductors

Figure 3.1 Excitation of an electron in the conduction band of a metal by the absorption of a photon with energy ћω and the subsequent loss of the excitation energy by the generation of single phonons with energy ε

Figure 3.2 Excitation of an electron from the valence band to the conduction band of a semiconductor by the absorption of a photon with energy ћω.

Figure 3.3 The Fermi distribution function

(ε

) defines the probability that an electron occupies a state with energy ε

Figure 3.4 Energy of electron states in sodium as a function of the interatomic distance

between the sodium atoms.

is the interatomic distance in solid sodium. States in the shaded energy ranges are occupied by electrons.

Figure 3.5 Density of states for electrons in the conduction and valence bands of the semiconductor germanium.

Figure 3.6 Energy ε

of the electrons for a direct semiconductor as a function of their momentum

. The minimum of the conduction band and the maximum of the valence band occur at the same momentum

= 0.

Figure 3.7 Energy of the electrons for an indirect semiconductor as a function of their momentum. The minimum of the conduction band and the maximum of the valence band occur at different values of the momentum

of the electrons.

Figure 3.8 A band with a missing electron of

> 0 has a total momentum Σ

< 0 resulting in an electrical current

> 0.

Figure 3.9 Creation of an electron–hole pair by the absorption of a photon.

Figure 3.10 Energy scale for electrons and holes in a semiconductor. The binding energy of an electron in a state at the lower boundary of the conduction band is referred to as the

electron affinity

Figure 3.11 By doping lattice atoms are replaced by impurity atoms having a higher (D) or lower (A) valency.

Figure 3.12 Temperature dependence of electron and hole concentrations in an n-type semiconductor with a band gap of 1 eV, containing 10

donors per cm

with an energy level ε

= 0.05 eV below the conduction band edge ε

Figure 3.13 The broad energy distribution of electrons and holes, right after their generation by solar radiation, reflects the broad energy spectrum of the photons. After about 10

−12

s, electrons and holes are thermalized into a narrow room temperature distribution.

Figure 3.14 In an illuminated semiconductor, the occupations of the conduction band and the valence band are described by different Fermi distributions

and

Figure 3.15 Two compartments separated by a piston contain hydrogen H

and oxygen O

at different temperatures

, pressures

, and chemical potentials μ.

Figure 3.16 The energy forms of electrons and holes.

Figure 3.17 Absorption coefficient α of the “direct” semiconductor gallium arsenide and the “indirect” semiconductor silicon.

Figure 3.18 Energy ε

of electron states in the conduction and valence bands between which transitions are possible with the absorption of a photon γ and the simultaneous absorption or emission of a phonon Γ.

Figure 3.19 In accordance with the law of refraction at the interface between two media, only photons from a smaller solid angle in the medium with the larger refractive index are exchanged with the other medium. Photons for which the momentum lies in the solid angle range inaccessible from outside undergo total internal reflection (dashed light path).

Figure 3.20 In Auger recombination, the energy set free by recombination of an electron–hole pair is absorbed by a free carrier (an electron in this figure) and is subsequently dissipated by generating phonons in collisions with the lattice.

Figure 3.21 Electrons and holes produced by the absorption of photons with the generation rate

are captured by impurities with the rates

e, imp

and

h, imp

and they are emitted thermally with the rates

e, imp

and

h, imp

from the impurities back into the bands.

Figure 3.22 Difference of the Fermi energies as a function of the impurity energy ε

imp

for a constant rate of generation

= 10

−3

−1

and for different doping levels in a material with ε

= 1.12 eV and densities of states N

= N

= 10

−3

. The doping concentration can be inferred from the difference between the Fermi energy in the dark and the intrinsic Fermi energy ε

from Equation 3.78 or 3.79. The impurities have a concentration of

imp

= 10

−3

with equal capture cross sections for electrons and holes of σ = 10

−15

, the velocity of electrons and holes is

= 10

m s

−1

, resulting in a minimal lifetime of τ = 10

−6

s. The asymmetry is caused by the acceptor character of the impurities.

Figure 3.23 Lifetime τ of electrons and holes in p-doped silicon limited by impurity recombination as a function of the impurity energy ε

imp

, measured from the upper edge of the valence band. With each curve from the inside toward the outside, the acceptor density increases by a factor of 100 from

= 10

−3

= 10

−3

. The generation rate is

= 10

−3

−1

, the impurities have a concentration of

imp

= 10

−3

with equal capture cross sections for electrons and holes of σ = 10

−15

and the velocity of electrons and holes is

= 10

m s

−1

, resulting in a minimal lifetime of τ

min

= 10

−6

Figure 3.24 Recombination via surface states continuously distributed over energy in the energy gap of a semiconductor.

Figure 3.25 The continuous distribution of a high density of states around the Fermi energy in a metal results in a high interface recombination velocity at a semiconductor–metal contact.

Chapter 4: Conversion of Thermal Radiation into Chemical Energy

Figure 4.1 Electrons and holes generated by photons with energy ћω lose energy by thermalization, which produces chemical energy per electron–hole pair μ

Figure 4.2 Average energy of absorbed photons ћω

abs

from a nonconcentrated

0 spectrum and from the 300 K background radiation, the average energy of emitted photons ћω

emit

and the chemical potential of electron–hole pairs μ

of a semiconductor as a function of its band gap ε

for radiative recombination under open-circuit conditions, resulting from the generalized Planck radiation law. The difference between ћω

abs

and ћω

emit

is lost by thermalization of the electron–hole pairs.

Figure 4.3 Electrons and holes generated in narrow energy ranges by monochromatic radiation have the same energy distribution after thermalization as before.

Figure 4.4 Current d

γ, emit

of emitted photons as a function of the chemical energy μ

= μ

+ μ

of the electron–hole pairs. The dark rectangle is the current of chemical energy extracted along with the current d

= d

γ, abs

− d

γ, emit

of extracted electron–hole pairs. It is produced from the current of absorbed energy represented by the grey rectangle.

Figure 4.5 Efficiency η with which chemical energy is extracted as a function of the chemical potential μ

of the electron–hole pairs from monochromatic absorbers for different photon energies.

Figure 4.6 Monochromatic efficiency η

mono

(ε

) for obtaining chemical energy μ

+ μ

as a function of the photon energy ћω of fully concentrated (full line) and nonconcentrated (broken line) monochromatic solar radiation.

Figure 4.7 Efficiency of solar cells with radiative recombination only as a function of their energy gap for the

0 spectrum, non-concentrated (solid line) and for full concentration (dashed line).

Chapter 5: Conversion of Chemical Energy into Electrical Energy

Figure 5.1 Electrons in the conduction band and holes in the valence band have to move in different directions to produce an electrical charge current

Figure 5.2 Electron energies in an electric field for uniform electron and hole concentrations.

Figure 5.3 Electron energies for a position-dependent electron concentration in the absence of an electric field.

Figure 5.4 Constant Fermi energy in a semiconductor in which both an electric field and a concentration gradient exist.

Figure 5.5 Distribution of the Fermi energies of a homogeneously illuminated n-type semiconductor with strong surface recombination on the left and on the right.

Figure 5.6 Distribution of the Fermi energies in a homogeneously illuminated pn-structure.

Figure 5.7 Distribution of electrons injected as minority charge carriers into a p-conductor.

Figure 5.8 Distribution of potentials in the (a) dark state and (b) on illumination of the free left surface of a semiconductor in which only electrons are mobile.

Figure 5.9 Distribution of potentials in a semiconductor with metal contacts in which only electrons are mobile, (a) in the dark state and (b) with the left surface exposed to light.

Chapter 6: Basic Structure of Solar Cells

Figure 6.1 Hypothetical chemical solar cell in which water is decomposed into hydrogen and oxygen by the absorption of photons. Hydrogen and oxygen can be separately removed through membranes that selectively pass hydrogen on the left and oxygen on the right.

Figure 6.2 The conductivities for hydrogen in the hydrogen membrane on the left and for oxygen in the oxygen membrane on the right, are assumed to be large. The gradients of the partial pressures required to drive the currents are therefore small and do not show up in the spatial distribution of the pressures.

Figure 6.3 Current of hydrogen, positive if flowing from the hydrogen bottle in Figure 6.1 into the cell as a function of the hydrogen partial pressure, without illumination (broken line) and with additional generation by illumination (solid line). The oxygen pressure is kept constant.

Figure 6.4 Current of hydrogen, positive if flowing from the hydrogen bottle in Figure 6.2 into the cell as a function of the deviation of the chemical potentials of hydrogen and oxygen from their equilibrium values, without illumination (broken line) and with additional generation by illumination (solid line). The chemical potential of water is not changed by illumination. A smaller and more realistic equilibrium generation rate than in Figure 6.3 is assumed. The shaded rectangle is the largest current of chemical energy delivered by the cell.

Figure 6.5 A n-type electron membrane on the left allows electrons generated in the absorber by illumination, to flow to the left, while blocking the holes. A p-type hole membrane on the right allows holes to flow to the right, blocking the electrons. Electrons are driven by an invisibly small gradient of −ε

, holes are driven by an invisibly small gradient of ε

Figure 6.6 Energy diagram for the hetero-structure solar cell in Figure 6.5 under AM1.5 illumination and at maximum power. The bandgap is 1.34 eV, the voltage V

= 987 mV the current j

= 34.1 mA/cm

and the efficiency η = 33.7 %.

Figure 6.7 Dye solar cell in which the electron–hole pairs are produced in a ruthenium bipyridine dye. The electrons flow outward toward the left through the n-conductor TiO

and the holes toward the right through the triiodide ions with which the acetonitrile electrolyte is doped.

Figure 6.8 Distribution of the space charge density ρ

and of the electrical energy −eϕ per electron in a pn-junction.

Figure 6.9 Potential distribution in an illuminated solar cell in which the diffusion voltage is e(ϕ

− ϕ

) > ε

− ε

Figure 6.10 Electron and hole currents in a pn-junction. (a) For a negative polarity of the n-region with respect to the p-region, i.e. in the forward direction, electrons and holes flow toward the pn-junction, where they recombine. (b) In the reverse direction, for a positive polarity of the n-region, electrons and holes flow away from the pn-junction where they are produced.

Figure 6.11 Charge current of the pn-junction in the dark (dashed line) and with illumination (solid line) as a function of the voltage. The sign of the voltage corresponds to the polarity of the p-region. The shaded rectangle represents the maximum power delivered by the illuminated pn-junction.

Figure 6.12 Impurity recombination rate

imp

as a function of the mean value of the Fermi energies (ε

+ ε

)/2 relative to the edge of the valence band ε

in a semiconductor with an energy gap of ε

= 1.12 eV calculated for an applied voltage of

= 0.4 V.

Figure 6.13 Potential distribution in a pn-junction with impurities at ε

in the middle of the forbidden zone.

Figure 6.14 Energy diagram of a symmetrical pn-junction under AM1.5 illumination and at maximum power. The bandgap is 1.34 eV, the voltage V

= 730,1 mV the current j

= 17,1 mA/cm

and the efficiency

= 12.5 %.

Figure 6.15 Two different semiconductors prior to making contact.

Figure 6.16 The two different semiconductors of Figure 6.16 in contact.

Figure 6.17 Schematic energy diagram of a semiconductor and a metal (a) before making contact and (b) in contact.

Figure 6.18 Holes from the valence band can tunnel through a thin potential barrier of a strongly p-doped depletion layer into the metal.

Figure 6.19 A metal with a small work function (left) forms a Schottky contact on a p-conductor with a larger work function. On the right side, a metal with a large work function forms an ohmic contact.

Figure 6.20 In a metal-insulator-silicon (MIS) structure, a very thin oxide layer between the metal and the silicon prevents surface recombination. The depletion of holes in the p-conductor is the result of a positive charge trapped in the oxide near the silicon.

Figure 6.21 Water in a closed pipe does not flow, although the gradient of the gravitational potential Φ drives it downwards.

Figure 6.22 The distribution of the electrical potential ϕ in a pn-junction with metal contacts shows that a charge cannot gain energy from moving around a closed circuit.

Figure 6.23 Potential distribution in a pn-junction, where the electron affinity χ

(

) = −μ

e, 0

(

) compensates the concentration-dependent part

In[

(

] of the chemical potential. (a) In the dark and in electrochemical equilibrium.(b) Illuminated and at open-circuit.

Figure 6.24 A 10 µm thick intrinsic absorber with a bandgap of 1.34 eV is sandwiched between two intrinsic transport layers of the same bandgap with a thickness of 100 nm. Selective conductivities of the transport layers are achieved by different mobilities. The electron transport layer has an electron mobility of 10

/(Vs) and a hole mobility of 10

−8

/(Vs). Opposite values are assumed for the hole transport layer. The energy diagram shows the situation at maximum power, where the efficiency is 33.7 %. Absorption in the transport layers is neglected.

Figure 6.25 The exciton can be represented in two different ways. On the left, the electron is shown in the electric field of the hole and its energy (in the ground state of the exciton) is given relative to the energy of a free hole. The exciton binding energy is the energy difference from the ground state of the electron in the exciton to the conduction band edge ε

. On the right everything is reversed as from the perspective of the hole in the field of the electron and its energy is relative to that of a free electron.

Figure 6.26 An exciton is shown in a material 1, the absorber, on the left as an electron bound to a free hole. The Coulomb potential well of the hole extends into material 2 on the right. This material has a larger electron affinity χ

e,2

than material 1 on the left. As a result, the energy of a free electron ε

≥ ε

C,2

is smaller in material 2 than the energy of the electron bound to a free hole in material 1, even if it is far away from the hole.

Figure 6.27 An exciton in the absorber in the middle dissociates into a free electron at the interface with the electron membrane on the right, which is then free to move to the metal contact on the right, represented by its Fermi energy ε

F, e

. The free hole that remains in the valence band of the absorber after exciton dissociation can only leave the absorber through a hole membrane on the left and further on to a metal contact represented by ε

F, h

Figure 6.28 An exciton in the absorber in the middle may dissociate into a free electron at the interface with the electron membrane on the right or into a free hole at the interface with the hole membrane on the left. The absorber must support transport of the remaining holes from right to left and electrons from left to right.

Figure 6.29 (a) In a planar configuration an organic absorber (black) is placed between a hole-conducting membrane (gray) and an electron-conducting membrane (white). Its thickness is less than the exciton diffusion length and therefore insufficient to absorb the absorbable light. (b) By folding the layer stack from (a), the absorption is increased without increasing the distance, the excitons have to diffuse. Contacts are added to the front and rear side of the folded layer stack. The front contact as well as the electron and hole collecting layers have to be transparent, of course.

Chapter 7: Limitations on Energy Conversion in Solar Cells

Figure 7.1 Geometrical construction of the maximum power point.

Figure 7.2 Efficiency of solar cells with radiative recombination only as a function of the energy gap for the

1.5 spectrum.

Figure 7.3 Cross-section of a silicon pn solar cell.

Figure 7.4 Charge current

as a function of the voltage

for a Si solar cell with a thickness of 400 μm illuminated by the

1.5 spectrum. The maximum power given by the rectangle corresponds to an efficiency of 25%.

Figure 7.5 Surface texture for reducing reflection and increasing the length of the light path.

Figure 7.6 Absorptance

as a function of the photon energy ћω for 20 μm thick silicon with light trapping (heavy line) and for 400 μm thick silicon without light trapping (thin line), assuming a reflectance of

= 0.1 in both cases.

Figure 7.7 Structure of the best silicon solar cell manufactured to date with an efficiency of 24.4%, developed by M.A. Green's group at UNSW. (Courtesy of M.A. Green).

Figure 7.8 (a) In the plane arrangement of an absorber between electron and hole membranes, the diffusion lengths

e, h

must be larger than the thickness of the absorber and the thickness must be larger than the penetration depth 1/α of the photons. (b) Many absorbing layers in a meander-like structure combine good absorption with a small distance between the membranes.

Figure 7.9 Equivalent circuit for a solar cell consisting of (from left) diode D

with direct recombination, diodes D

with impurity recombination, current source , parallel resistance and series resistance .

Figure 7.10 Current–voltage characteristic of a 100 cm

solar cell with (2) = 0 Ω, = 0.5 Ω; and (3) = 0.05 Ω, = ∞, compared with (1) = 0 Ω and = ∞.

Figure 7.11 Individual processes in a solar cell.

Chapter 8: Concepts for Improving the Efficiency of Solar Cells

Figure 8.1 Short-circuit current of a solar cell as a function of the energy gap ε

of its absorber for a black-body spectrum with = 5800 K.

Figure 8.2 Current–voltage characteristics of two solar cells with energy gaps ε

= 1.8 eV and ε

= 0.98 eV.

Figure 8.3 Efficiency for two solar cells in tandem operation, with energy gaps ε

and ε

for the

0 spectrum when their energy currents are added.

Figure 8.4 Electrical series connection of two solar cells by a tunnel junction provides efficient recombination of electrons and holes without requiring a difference of their Fermi energies.

Figure 8.5 Current–voltage characteristic for the series connection of two solar cells with different short-circuit currents and open-circuit voltages. For each value of the current

the voltages

and

are added to give the total voltage

Figure 8.6 The p- and n-type membranes for holes and electrons and the metal contacts of the point-contact cell for concentrated radiation are both placed on the back side of the cell.

Figure 8.7 In the thermophotovoltaic converter, the intermediate absorber is surrounded in an evacuated cavity by solar cells illuminated by its thermal radiation.

Figure 8.8 Transition of an electron from a higher band to the minimum of the conduction band by impact ionization in an indirect semiconductor, resulting in the additional generation of an electron and a hole at the band edges.

Figure 8.9 Energies of electrons and holes in the absorber, in which impact ionization and Auger recombination are in equilibrium at >

, and in membranes through which electrons and holes flow outward and where they are in temperature equilibrium with the environment at

Figure 8.10 Efficiency for a hot-carrier cell with impact ionization for nonconcentrated incident solar radiation with Ω = Ω

and for maximum concentration with Ω = π.

Figure 8.11 In addition to radiative band–band transitions with the rates and , radiative transitions between the bands and the impurity are taken into account. Nonradiative transitions are excluded.

Figure 8.12 Efficiency as a function of the energy gap ε

− ε

for radiative band–band transitions and radiative transitions between the bands and an impurity level at ε

imp

. Nonradiative transitions are excluded. The numbers at the curve give the optimal position of the impurity level with regard to the valence band for selected band gaps.

Figure 8.13 Equivalent circuit for a solar cell with an impurity level between valence and conduction bands as shown in Figure 8.11.

Figure 8.14 Two solar cells with small band gaps drive an LED with a large band gap, to emit photons useful for a large band gap solar cell, thereby up-converting two small-energy photons into one higher-energy photon.

Figure 8.15 An up-converter behind a solar cell absorbs small-energy photons, transmitted by the solar cell, in a two-step excitation process. Higher-energy photons with ћω ≥ ε

emitted by the up-converter generate additional electron–hole pairs in the solar cell.

Figure 8.16 Efficiency of a solar cell as a function of its band gap ε

operating with directly absorbed and with up-converted photons from a 6000 K black-body spectrum, from a solid angle Ω

= 6.8 × 10

−5

(thick line) and with maximum concentration from Ω = π (thin line).

Figure 8.17 Efficiency of a solar cell as a function of its band gap ε

operating with directly absorbed and with down-converted photons from a nonconcentrated 6000 K black-body spectrum for a down-converter placed on the rear side of the solar cell (thin line). The efficiency for operation only with photons from the down-converter when it is placed on the front side is smaller (thick line).

Chapter 9: Characterization of Solar Cells

Figure 9.1 Measurement setup to determine the spectral response of a solar cell.

Figure 9.2 EQE and (in %) of an a-Si/c-Si heterojunction solar cell with a power conversion efficiency of 21.3%. Shown are the

and the different loss contributions, see text for details.

Figure 9.3 IQE curves of three silicon solar cells (all with a thickness of

= 250 µm) with different electron diffusion lengths in their p-doped base. Courtesy: Stefan Glunz, Fraunhofer ISE.

Figure 9.4 QSSPC data from a high-efficiency crystalline silicon solar cell without applied metal contacts [37]. The left

-axis shows the intensity in multiples of 1 sun (solid line), and the right

-axis the transient photoconductance (dashed line). As the lifetime is derived from the decay of the photoconductance, the data analysis is carried out starting from the point marked with the black dot.

Figure 9.5 Lifetime versus excess carrier density derived from the QSSPC measurement shown in Figure 9.4 of a high-efficiency crystalline silicon solar cell without metal contacts.

Figure 9.6 Electroluminescence intensity distribution from a multicrystalline silicon solar cell. In this cell design, the horizontal gridfingers in the left and right half of the cell are separately connected to the left and right bus bars and not connected in the middle. The lower intensity of the right half is probably due to a lower voltage caused by a larger series resistance.

Figure 9.7 Theoretical intensity ratio of luminescence for several combinations of short-pass filters as a function of the diffusion length

. Three curves for each combination show the influence of the rear surface recombination velocity

Figure 9.8 Diffusion length distribution for electrons obtained from the ratio of two luminescence images taken with 1000 and 900 nm short-pass filters.

Figure 9.9 characteristics of a solar cell for two different illumination intensities. The luminescence intensity emitted by the solar cell is identical in points

and

. The series resistance of the solar cell leads to an increase of the voltage by Δ

due to an increase of the current density by Δ

Figure 9.10 Scheme of an LBIC measurement setup with five different wavelengths (exemplarily).

Figure 9.11 Spatially resolved EQE map derived from an LBIC measurement of a 156 mm × 156 mm multicrystalline Si solar cell detected at .

Figure 9.12 curves of two subcells with different values of their parallel resistance (a). Difference of the absolute values of the current densities: as a function of applied voltage (b).

Figure 9.13 Normal

(

) curve (solid line) and pseudo

(

) curve obtained from the Suns- method (dashed line) of a high-efficiency crystalline silicon solar cell [37].

Figure 9.14 Visualization of the ground-state bleach. As the pump beam excites electrons from ε

to ε

, fewer electrons are available in ε

(and holes in ε

) for subsequent excitations of the same type by the probe beam.

Figure 9.15 Photoinduced absorption. First, electrons are excited from ε

to ε

by the pump beam. Then they can be excited from ε

to higher states ε

within the conduction band (inorganic semiconductor) or to either higher vibronic states within the same electronic state or to a higher electronic state (molecules).

Figure 9.16 Stimulated emission. The incident probe beam can induce the emission of photons with the same phase, wavelength, polarization, and direction.

Figure 9.17 Scheme of a CELIV measurement. (a) The pre-bias

pre

and the subsequent voltage ramp in reverse direction. (b) The current response of the device.

Solutions

Figure S.1 (a) Free energy per volume

* as a function of the electron (hole) concentration

e,h

as a result of the Sackur–Tetrode equation (3.35). (b)

* (solid line) and

(dotted line) as the sum of the contributions of all states with energies ε

≤ ε

as a function of ε

. In graph (a), effective densities of states

= 3 × 10

−3

and

= 1 × 10

−3

were assumed and in graph (b) the corresponding effective masses and . For both, the temperature is

= 300 K.

Figure S.2 Recombination rates

imp

from impurity states as a function of their energetic position for

= 300 K (solid line) and

= 400 K (triangles). The vertical solid line indicates the position of the intrinsic Fermi level with respect to the valence band maximum ε

− ε

for

= 300 K, whereas the vertical dotted line represents ε

− ε

for

= 400 K. The difference in ε

for the two temperatures is rather small: ε

(300 K) − ε

= 0.5458 eV; ε

(400 K) − ε

= 0.5411 eV.

Figure S.3 Separation of the quasi-Fermi energies ε

− ε

in Si as a function of the impurity level ε

imp

for three different doping concentrations. (a) With a generation rate

= 10

−3

−1

. (b) With

= 5 × 10

−3

−1

Figure S.4 Current–voltage characteristics of an ideal pn-junction with (dotted line), one with (broken line) and one with (solid line).

Figure S.5 The total recombination rate (solid line) as a function of the minority carrier concentration

and the different contributions from radiative (), Auger (), and impurity recombination ().

Figure S.6 Difference of the quasi-Fermi energies ε

− ε

under open-circuit conditions as a function of the generation rate

. The recombination mechanism taken into account is either radiative (), Auger (), or impurity recombination () or a combination of all three types of recombination (solid line).

List of Tables

Chapter 1: Problems of the Energy Economy

Table 1.1 Primary Energy Consumption in Germany in 2002

Table 1.2 World Primary Energy Consumption in 2002

Table 1.3 The World's Remaining Energy Reserves

Chapter 3: Semiconductors

Table 3.1 Electron and Hole Densities In n-type and p-type Secmiconductors

Chapter 6: Basic Structure of Solar Cells

Table 6.1 Work Functions and Electron Affinities of Common Semiconductors and Metals

Peter Würfel and Uli Würfel

Physics of Solar Cells

From Basic Principles to Advanced Concepts

3rd Edition

Authors

Peter Würfel

Karlsruhe Institute of Technology (KIT)

Facultyt of Physics

Engesserstr. 7

76131 Karlsruhe

Germany

Uli Würfel

Fraunhofer ISE

Heidenhofstr. 2

79110 Freiburg

Germany

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