Table of Contents
Cover
Title Page
Copyright
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-
9.7 Transient Techniques
Solutions
Appendix
Fundamental Constants
Units of Energy
Material Constants at 300 K
Standard Global AM 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 μγ = 0. The dashed line represents the Boltzmann distribution exp (−ћωkT ), a good approximation for ћω > 2kT .
Figure 2.2 Volumes of the states in momentum space.
Figure 2.3 An energy current I E V is flowing through the hole with area dA of the cavity, into the solid angle dΩ.
Figure 2.4 Solid angle dΩ2 under which the receiver area dA 2 is seen from the emitter dA 1 , and solid angle dΩ1 under which dA 1 is seen from dA 2 .
Figure 2.5 Solid angle dΩs under which the surface element dA s on the Sun is viewed from the Earth, and solid angle dΩe under which the surface element dA e on the Earth is viewed from the Sun.
Figure 2.6 Energy current from the surface element dA s on the surface of the Sun into the solid angle dΩe under which the Earth is viewed from the Sun.
Figure 2.7 Dependence of the emitted energy current dI E I E
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 AM 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 A B in the focal plane of a lens with radius r L and focal length f .
Figure 2.14 A lens projects an image of the Sun onto an absorber in a perfectly reflecting cavity.
Figure 2.15 Efficiency ηbC for the conversion of solar heat energy by a black absorber and a Carnot engine as a function of the absorber temperature T A , for maximum concentration (Ωemit = Ωabs , heavy line) and for nonconcentrated radiation (Ωemit = π, Ωabs = 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 ηL (heavy line) as a function of the absorber temperature T A compared with the efficiency ηbC (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 εΓ .
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 f (εe ) defines the probability that an electron occupies a state with energy εe .
Figure 3.4 Energy of electron states in sodium as a function of the interatomic distance a between the sodium atoms. a 0 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 εe of the electrons for a direct semiconductor as a function of their momentum p e . The minimum of the conduction band and the maximum of the valence band occur at the same momentum p e = 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 p e of the electrons.
Figure 3.8 A band with a missing electron of p e > 0 has a total momentum Σp e < 0 resulting in an electrical current j Q
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 χe .
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 1016 donors per cm3 with an energy level εD = 0.05 eV below the conduction band edge εC .
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 f C and f V .
Figure 3.15 Two compartments separated by a piston contain hydrogen H2 and oxygen O2 at different temperatures T , pressures p , 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 εe 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 G are captured by impurities with the rates R e, imp and R h, imp and they are emitted thermally with the rates G e, imp and G h, imp from the impurities back into the bands.
Figure 3.22 Difference of the Fermi energies as a function of the impurity energy εimp for a constant rate of generation G = 1017 cm−3 s−1 and for different doping levels in a material with εG = 1.12 eV and densities of states NC = NV = 1019 cm−3 . The doping concentration can be inferred from the difference between the Fermi energy in the dark i from Equation 3.78 or 3.79. The impurities have a concentration of n imp = 1014 cm−3 with equal capture cross sections for electrons and holes of σ = 10−15 cm2 , the velocity of electrons and holes is v = 105 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 εimp , 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 n A = 1012 cm−3 to n A = 1018 cm−3 . The generation rate is G = 1017 cm−3 s−1 , the impurities have a concentration of n imp = 1014 cm−3 with equal capture cross sections for electrons and holes of σ = 10−15 cm2 and the velocity of electrons and holes is v = 105 m s−1 , resulting in a minimal lifetime of τmin = 10−6 s.
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 μeh .
Figure 4.2 Average energy of absorbed photons abs AM 0 spectrum and from the 300 K background radiation, the average energy of emitted photons emit eh of a semiconductor as a function of its band gap εG for radiative recombination under open-circuit conditions, resulting from the generalized Planck radiation law. The difference between abs emit
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 dj γ, emit of emitted photons as a function of the chemical energy μeh = μe + μh of the electron–hole pairs. The dark rectangle is the current of chemical energy extracted along with the current dj eh = dj γ, abs − dj 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 μeh of the electron–hole pairs from monochromatic absorbers for different photon energies.
Figure 4.6 Monochromatic efficiency ηmono (εG ) for obtaining chemical energy μe + μh 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 AM 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 j Q
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
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
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 −εFC , holes are driven by an invisibly small gradient of εFV .
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 Vmp = 987 mV the current jmp = 34.1 mA/cm2 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 TiO2 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 ρQ
Figure 6.9 Potential distribution in an illuminated solar cell in which the diffusion voltage is e(ϕn − ϕp ) > εFC − εFV .
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 R imp as a function of the mean value of the Fermi energies (εFC + εFV )/2 relative to the edge of the valence band εV in a semiconductor with an energy gap of εG = 1.12 eV calculated for an applied voltage of V = 0.4 V.
Figure 6.13 Potential distribution in a pn-junction with impurities at εi 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 Vmp = 730,1 mV the current jmp = 17,1 mA/cm2 and the efficiency η = 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 χe (x ) = −μe, 0 (x ) compensates the concentration-dependent part kT In[n e (x )/N C ] 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 108 cm2 /(Vs) and a hole mobility of 10−8 cm2 /(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 εC . 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 χe,2 than material 1 on the left. As a result, the energy of a free electron εe ≥ εC,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 εF, 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 εF, 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 AM 1.5 spectrum.
Figure 7.3 Cross-section of a silicon pn solar cell.
Figure 7.4 Charge current j Q V for a Si solar cell with a thickness of 400 μm illuminated by the AM 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 a 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 r = 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 L 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 D1 with direct recombination, diodes D2 with impurity recombination, current source
Figure 7.10 Current–voltage characteristic of a 100 cm2 solar cell with (2)
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 εG of its absorber for a black-body spectrum with
Figure 8.2 Current–voltage characteristics of two solar cells with energy gaps εG1 = 1.8 eV and εG2 = 0.98 eV.
Figure 8.3 Efficiency for two solar cells in tandem operation, with energy gaps εG 1G 2AM 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 j Q V 1 and V 2 are added to give the total voltage V .
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 T 0 , and in membranes through which electrons and holes flow outward and where they are in temperature equilibrium with the environment at T = T 0 .
Figure 8.10 Efficiency for a hot-carrier cell with impact ionization for nonconcentrated incident solar radiation with Ω = ΩS and for maximum concentration with Ω = π.
Figure 8.11 In addition to radiative band–band transitions with the rates
Figure 8.12 Efficiency as a function of the energy gap εC − εV for radiative band–band transitions and radiative transitions between the bands and an impurity level at εimp . 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 ≥ εG 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 εG operating with directly absorbed and with up-converted photons from a 6000 K black-body spectrum, from a solid angle ΩS = 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 εG 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 j SC and the different loss contributions, see text for details.
Figure 9.3 IQE curves of three silicon solar cells (all with a thickness of d = 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 y -axis shows the intensity in multiples of 1 sun (solid line), and the right y -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 L e . Three curves for each combination show the influence of the rear surface recombination velocity S r .
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 A and B . The series resistance of the solar cell leads to an increase of the voltage by ΔV due to an increase of the current density by Δj Q .
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
Figure 9.13 Normal j Q (V ) curve (solid line) and pseudo j Q (V ) curve obtained from the Suns-
Figure 9.14 Visualization of the ground-state bleach. As the pump beam excites electrons from ε1 to ε2 , fewer electrons are available in ε1 (and holes in ε2 ) for subsequent excitations of the same type by the probe beam.
Figure 9.15 Photoinduced absorption. First, electrons are excited from ε1 to ε2 by the pump beam. Then they can be excited from ε2 to higher states ε2b 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 V 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 F * as a function of the electron (hole) concentration n e,h as a result of the Sackur–Tetrode equation (3.35). (b) F * (solid line) and n e (dotted line) as the sum of the contributions of all states with energies εe ≤ εe, l as a function of εe, l . In graph (a), effective densities of states N C = 3 × 1019 cm−3 and N V = 1 × 1019 cm−3 were assumed and in graph (b) the corresponding effective masses T = 300 K.
Figure S.2 Recombination rates R imp from impurity states as a function of their energetic position for T = 300 K (solid line) and T = 400 K (triangles). The vertical solid line indicates the position of the intrinsic Fermi level with respect to the valence band maximum εi − εV for T = 300 K, whereas the vertical dotted line represents εi − εV for T = 400 K. The difference in εi for the two temperatures is rather small: εi (300 K) − εV = 0.5458 eV; εi (400 K) − εV = 0.5411 eV.
Figure S.3 Separation of the quasi-Fermi energies εFC − εFV in Si as a function of the impurity level εimp for three different doping concentrations. (a) With a generation rate G = 1018 cm−3 s−1 . (b) With G = 5 × 1020 cm−3 s−1 .
Figure S.4 Current–voltage characteristics of an ideal pn-junction with
Figure S.5 The total recombination rate (solid line) as a function of the minority carrier concentration n h and the different contributions from radiative (
Figure S.6 Difference of the quasi-Fermi energies εFC − εFV under open-circuit conditions as a function of the generation rate G . The recombination mechanism taken into account is either radiative (
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
From Basic Principles to Advanced Concepts
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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Cover Design Formgeber, Mannheim, Germany
h , ћ = h /(2π)eVs
ћω
photon energy
eV
a (ћω)absorptance
r (ћω)reflectance
t (ћω)transmittance
ε(ћω) = a (ћω)
emittance
α(ћω)
absorption coefficient
cm−1
k Boltzmann's constant
eV K−1
σ
Stefan–Boltzmann constant
W m−2 K−4
T temperature
K
n j concentration of particle type j
cm−3
e
electron
h
hole
γ
photon
Γ
phonon
n e , n h concentration of electrons, holes
cm−3
n i intrinsic concentration of electrons and holes
cm−3
N C , N V effective density of states in conduction band, valence band
cm−3
εe , εh
energy of an electron, hole
eV
εC
energy of an electron at the conduction band minimum
eV
εV
energy of an electron at the valence band maximum
eV
μj
chemical potential of particle type j
eV
ηj
electrochemical potential of particle type j
eV
χe
electron affinity
eV
ϕ
electrical potential
V
e
elementary charge
As
ε0
dielectric permittivity of free space
As (V m)−1
ε
relative dielectric permittivity
V voltage = [ηe (x 1 ) − ηe (x 2 )]/e
V
εFC
eV
εFV
Fermi energy for electron distribution in valence band
eV
effective mass of electrons, holes
g
b e , b h mobility of electrons, holes
cm2 (Vs)−1
D e , D h diffusion coefficient of electrons, holes
cm2 s−1
τe , τh
recombination life time of electrons, holes
s
R e , R h recombination rate of electrons, holes
cm−3 s−1
G e , G h generation rate of electrons, holes
cm−3 s−1
σe , σh
cross-section for the capture of an electron, hole by an impurity
cm2
j j current density of particles of type j
(cm2 s)−1
j Q charge current density
A cm−2
Mankind
This book provides a fundamental understanding of the functioning of solar cells. The discussion of the principles is as general as possible to provide the basis for present technology and future developments as well. Energy conversion in solar cells is shown to consist of two steps. The first is the absorption of solar radiation and the production of chemical energy. This process takes place in every semiconductor. The second step is the transformation into electrical energy by generating current and voltage. This requires structures and forces to drive the electrons and holes, produced by the incident light, through the solar cell as an electric current. These forces and the structures which enable a directional charge transport are derived in detail. In the process it is shown that the electric field present in a pn junction in the dark, usually considered a prerequisite for the operation of a solar cell, is in fact more an accompanying phenomenon of a structure required for other reasons and not an essential property of a solar cell. The structure of a solar cell is much better represented by a semiconducting absorber in which the conversion of solar heat into chemical energy takes place and by two semi-permeable membranes which at one terminal transmit electrons and block holes and at the second terminal transmit holes and block electrons. The book attempts to develop the physical principles underlying the function of a solar cell as understandably and at the same time as completely as possible. With very few exceptions, all physical relationships are derived and explained in examples. This will provide the nonphysicists particularly with the background for a thorough understanding.
Emphasis1
In some respects this book is more rigorous than is customary in semiconductor device physics and in solar cell physics in particular. The most obvious is that identical physical quantities will be represented by identical symbols. Current densities will be represented by j and the quantity that is transported by the current is defined by its index, as in j Q j e for the density of a current of electrons. In adhering to this principle, all particle concentrations are given the symbol n , with n e representing the concentration of electrons, n h the concentration of holes and n γ the concentration of photons. I hope that those who are used to n and p for electron and hole concentrations do not find it too difficult to adapt to a more logical notation.
The driving force for a transition from exhausting energy reserves, as we presently do, to using renewable energies, is not the exhaustion of the reserves themselves, although oil and gas reserves will not last for more than one hundred years. The exhaustion does not bother most of us, since it will occur well beyond our own lifetime. We would certainly care a lot more, if we were to live for 500 years and would have to face the consequences of our present energy use ourselves. The driving force for the transition to renewable energies is rather the harmful effect which the byproducts of using fossil and nuclear energy have on our environment. Since this is the most effective incentive for using solar energy, we start by discussing the consequences of our present energy economy and its effect on the climate. The potential of a solar energy economy to eliminate these problems fully justifies the most intensive efforts to develop and improve the photovoltaic technology for which this book tries to provide the foundation.
Peter Würfel and Uli Würfel
1 W. Shockley, H. J. Queisser, J. Appl. Phys . 32 , (1961), 510.
