17 Solar Cells

17 Solar Cells - Introduction to solar cells EE47410 Basic Operation of a Solar Cell The basic steps in the operation of a solar cell are • the

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Unformatted text preview: Introduction to solar cells EE47410 Basic Operation of a Solar Cell The basic steps in the operation of a solar cell are: • the absorption of light by the material of the solar cell • the generation of light-generated charge carriers; • the separation and collection of the light-generated charge carries to create a current; • the generation of a large voltage across the solar cell; • the dissipation of power in the load and in parasitic resistances. Quantum Nature of Light • Light is energy in the form of electromagnetic fields and is characterized by its frequency, ν , and wavelength, λ . • The Photon is the quantum of electromagnetic energy. It has an energy E = hν = hc/λ. • The energy contained in a light beam is measured by how many “photons” are impinging. • Most sources of light are made up of many photons of different frequency. The distribution of photons of different frequencies is the spectrum of the light source. • The optical power is the number of photons/sec X energy of photon. Terminology E = hυ = hω h is Plank's constant h = 6.625 x 10−34 J − s; h = 4.135 x 10−15 eV − s υ is the frequency of the electromagnetic wave h h= ; ω = 2πυ 2π h p = = hk λ p is the photon momentum; λ is the wavelength of the electromagnetic wave 2π k is the wave vector of the photon; k = λ Quantum Detectors Quantum Light Detectors have the following characteristics: Ec α (E) Ev Absorption of photon creates electron – hole pair that can be collected as current. Eg E = hν Band to band absorption has a threshold energy – Eg. • • • There is a threshold wavelength for operation, hv = Ec - Ev They have a well developed spectral response They are Power Detectors, i. e. Current = Q/t = #photons/t = P/hν Materials For Solar Cells Modern Solar Cells are constructed from solid state or molecular solid materials Most of the solid state materials have semiconducting electrical semiconducting properties. Amorphous Materials (a)– solids made up of atoms with no long or short range order. Polycrystalline Materials (b) – solids made up of small crystalline regions or grains but no long range order. Crystalline Materials (c) – atoms of solid are arranged in a regular, 3D pattern with the same periodicity in the pattern in all regions. Molecular materials (d) are comprised of layers of large molecules or of polymers that absorb light. N N N N Cu N N N N N N M N N Two-dimensional bonding Solar Cell Materials Crystal model oftructures S a crystalline solid Energy States of Electrons • Electrons in solid materials occupy certain discrete energy states whose arrangement is determined by the bonding arrangement between the atoms that make up the solid. • In atoms and molecules the electron energy states are discrete and well separated from one another. • In solids, the energy states are separated into bands of closely spaced states separated by energy gaps. Light absorption • The absorption of light occurs when a photon excites an electron from a lower energy state to a higher one. • In atoms and molecules, this process occurs between discrete spatially localized states and energy is conserved. • In solids, the energy states of the electrons are not very localized and the electron states have a specific momentum associated with them. As a result, both energy and momentum is conserved. Absorption in atoms and molecules E5 E4 E3 hν E2 E1 E5 E4 E3 E3 – E2= hν E2 E1 L ight Absorption in a Solid Electron Freed from Bonds Energy Gap, EG Missing Electron in Bonds = Hole Absorption in Solids hν hν hν = Ec – Ev hkc = hkv Conservation of Momentum and Energy: oKelec - 4Khole = 4Kphot hν = Ee - Eh Kphot = 2 π/λ Kelec = π /a Kphot/Kelec = a/2λ a ~ 0.5 x 10-9 m λ ~ 620 x 10-9 m Kphot/Kelec= 1.6 x 10-3 Thus Kelec ≈ Khole Absorption andEmission on the E-K diagram. Both K and E must be conserved. (a) Direct gap material; (b) Indirect semiconductor. Conduction Band E-K diagrams for three common semiconductors. The crystallographic direction is shown on the K axis. m||* Material m*(K=0) Si GaAs Ge InP 0.077 0.067 m*|| 0.92 1.64 m* ┴ 0.197 0.082 m*ce 0.26 0.067 0.12 0.077 m*dse 1.09 0.067 0.56 0.077 The E-K diagram for the valence band in most semiconductors (h) the heavy hole band, (l) the light hole band, and (s) the split-off band. Material Si GaAs Ge InP m*lh 0.16 0.082 0.044 0.08 m*hh 0.48 0.45 0.28 0.4 m*sh 0.24 0.15 0.08 0.15 ∆ E, eV 0.044 0.34 0.29 0.11 m*ch 0.36 0.34 0.21 0.3 m*dsh 1.15 0.48 0.292 0.42 Absorption Coefficients for Si, Ge, GaAs 2500 1.0 Thin Film Spectra CuPC Pt(TPBP) Pd(TPBP) N N N N Cu N N N N Solar Energy (W/cm2/micron) 2000 1500 1000 500 0 0 1 2 Ar Ar N N Zn NN Ar OR OR Absorbance 0.5 N N M N N 0.0 300 400 500 600 700 800 Wavelength (nm) Sc(OTf)3 DDQ Ar Ar N N Zn NN Ar OR OR Wavelength (microns) Incident Photon to Current Efficiency (%) 0.5 0.4 UV-VIS EQE% i-Pr N i-Pr 15 Absorbance (a.u.) 0.3 0.2 0.1 0.0 O O 10 i-Pr N i-Pr 5 SQ1 VOC 0.74 400 JSC 5.84 FF 0.63 600 η (%) 2.7 800 0 Wavelength (nm) Solar Spectrum Solar power spectrum vs photon energy and wavelength for different conditions. Total solar insolation at mid latitudes on Earth is 1kW / m2 This is referred to as AM 1.5. Above the atmosphere the insolation is 1.3 kW / m2 AM0 Absorption of light – Beer’s Law Io (1-R) Io When light propagates into a medium with higher index of refraction, the wavelength of the light is decreased as λ medium = λ air/nmedium Some of the light is reflected at the interface thus the intensity is reduced by (1-R). Air R Io Absorber In the absorber the intensity of light is incrementally decreased by absorption events: dI = - h(E) I dx dI/I = -h(E) dx I(x) = I(0)exp{-h(E)x} I(x) = (1-R) Io exp{-h(E) x} Beer’s Law For every photon that’s absorbed an electron-hole pair is generated. What is the generation rate? Absorption of light leads to generation of carriers Number of photons lost per unit volume per unit time = Number of electrons and holes generated per unit volume and per unit time. Let N(x) be the number of photons per unit area per unit time in the solid, then N(x) = I / hν dN/dx = h I / hh (the number of photons lost per unit time per unit volume) = g(x) (the generation rate of e-h pairs) Thus, g(x) = [α Io(1-R) / hh] exp(-h x) Solar Spectrum and Absorption Average Absorption Length, Lα ~1/α Charge Collection in a Semiconductor Junction p – type n - type Absorption and Collection in a Si Solar Cell Surface Diffused Region Base Region Back Surface Field Region Charge Collection in an Organic Semiconductor Acceptor Donor hν 1 2 1) Absorption and exciton formation 2) exciton diffusion 3) Exciton dissociation 4) Charge transport 5) Carrier extraction + 34 P0 (1 sun, AM1.5) 5 h+ 4 5– e Voltage Voc Current Isc Voc and Isc vs Eg Small Eg Large Eg where Voc is the open-circuit voltage; where Isc is the short-circuit current; and where FF is the fill factor where η is the efficiency. Why is there a Maximum possible Efficiency? • When the energy gap is small a larger portion of the solar spectrum can be absorbed leading to a high short circuit current BUT the output voltage is reduced because the voltage is limited by the energy gap of the material. • In small band gap materials, high energy photons generate electrons and holes with high energy that lose their energy to heat. • When the energy gap is large, a large portion of the solar spectrum is not absorbed and the short circuit current is reduced BUT the output voltage is high because the energy gap of the material is large. Absorption by an Optimum Cell Status of Solar Cell Technology Single Crystalline Si Muliticrystalline Si Single Crystal GaAs GaAs Multicrystalline InP Crystalline Thin Film CdTe Thin Film CIGS Amorphous Si Nanocrystalline Si Dye sensitized TiO2 Organic Tandem InGaP/InGaAs/Ge w Concentrated Sunlight a-Si /mc-Si (thin submodule) 24.7 % 20.3 % 25.3% 18.3% 21.9% 16.5% 18.4% 9.5% 10.1% 10.4% ~7% 32.3% 40.7% 11.7% EE 513 A PRIMER ON THE PN JUNCTION Forming a junction between two materials A p-n junction is formed when these two materials are joined into a common device. The shape of the energy bands vs position play a major role in the electrical properties of the resulting device. Our goal is to understand the processes that lead to the shaping of the energy bands vs position and its analytical form. Energy band diagram for the p n junction at equilibrium. is the resulting shape of the energy bands vs position when the sample is in equilibrium. e the Fermi energy does not depend on position, as expected. The conduction band e, Ec, and the valence band edge are now position dependent. So Ec is a function of x, Ec(x the 5-3 valence band is as well, Ev(x). Why are Ec and Ev functions of position? When n-type material is contacted to p-type material there are large gradients in the electron and hole concentrations because the density of electrons on the n side is large while the density of holes on the p side is large. Thus electrons in the vicinity of the junction will diffuse from the n side to the p side and holes in the vicinity of the junction will diffuse from the p side to the n side. These carriers become minority carriers when they cross the junction between the two materials and recombine within a minority carrier diffusion length, on average, on the other side of the junction. The n and p sides of the junctions were originally electrically neutral before the carriers diffused across the junction. Their loss from each side of the junction creates a charge imbalance with the n-side charged positively and the p side charged negatively. This, in turn, causes an electric field, E, to be established between the two sides and as a consequence of the field, there is an electrostatic potential difference, Vbi, as well. Vbi = − E dx . The energy bands are now altered by the presence of the electrostatic potential. Remember, the electrostatic potential and the potential energy of an electron are related by Ep(x) = - qV(x). The total energy of electrons and holes are the sum of their potential and kinetic energies. In the case of electrons or holes in their respective bands, the conduction band and the valence band edges represent their respective potential energies in a solid. ∫ The Solution to the Electrostatics Problem The variation of the energy bands as a function of position can be determined by solving for the electric field and the electrostatic potential that is created by the charge distribution in the junction region. The movement of the electrons and holes to the p and n sides of the junction, respectively, results in a region, called the depletion region, in which there are no mobile charges and the ionized impurities that are there create a imbalance of positive and negative charge. Although there are some mobile charges near the edge of the depletion region, we will make what has been called the depletion approximation, namely that there are no mobile charges anywhere in the depletion region. Then the charge distribution that results from the equilibration of the system looks like the figure below. Solution of Electrostatics Near p-n Junction The relevant Maxwell equation that is to be solved is Poisson’s equation: ur ur u r ρ qND xn xo xp ∇ • D = ρ where D = εE. In one dimension this equation becomes d (ε sE ) dE ρ = ρ or = in a homogeneous material dx dx ε 0 for x < x n ' qN D + for x n ≤ x ≤ x o εs dE = ' dx qN A − for x o ≤ x ≤ x p x εs 0 for x > x p -qNA The Solution to the Electrostatics Problem (cont.) 0 for x < x n ' qN D x + A for xn ≤ x ≤ x0 εs E = where A and B are to be determined ' − qN A x + B for x ≤ x ≤ x o p εs 0 for x > x p by the boundary conditions which are: E = 0 in neutral regions and E is continuous everywhere. By applying the continuity of E at x n and x p , we then find that A = - qN 'D xn / ε s , B = qN 'A x p /ε s , ' and N D ( xo − xn ) = N 'A ( x p − xo ). - an expression of charge balance . Then: 0 ' qN D ( x − xn ) εs E = ' qN A ( x p − x) εs 0 E xn xo xp x The Solution to the Electrostatics Problem (cont.) Please note: The electrostatic potential, V , which us related to E by The electrostatic potential is dV denoted by φ (x) in Neamen. E =can be found by integration: dx Many books, however, use 0 V(x) as I have done here. ' qN D 2 − ( x − xn ) + C 2ε s V = . Where we have applied the following boundary conditions: ' qN A ( x − x) 2 + D 2ε s p −V j V ( x < xn ) = 0 (by our choice of the zero) and V ( x > x p ) = −V j = −(Vbi − Va ). If we also apply the conditions that V is continuous and the charge balance condition, then 0 ' qN D − ( x − xn ) 2 2ε s V = ' qN A 2 ( x p − x) − V j 2ε s −V j xn xo xp Vbi x V(x) Energy Bands The conduction band and valence band energies as a function of position can then be calculated by modifying Ec(x) and Ev(x) by adding the variation owing to the electrostatic potential variation. That is Ec(x) = Ec(xn) – qV(x), etc. Ec Ef,n n – type Ev V Vbi x p - type Ef,p Before Equilibration Ec(x) Ef n – type Ev(x) p - type Built-in Voltage qVbi = Eg − (δ n − δ p ) N N N N δ n = Ec − EF ,n = kT ln c ≈ kT ln 'c and δ p = EF , p − Ev = kT ln v ≈ kT ln v ' p po ND NA nno If either the n-side or the p-side is degenerate then δ n = 0 or δ p = 0, respectively. N N qVbi = Eg − kT ln 'c + ln v ' NA ND but for n + p or p + n junctions the expressions reduce to N qVbi = Eg − kT ln c for n + p junctions and ' NA N qVbi = Eg − kT ln 'v for p + n junctions, respectively. ND N N Now, we have shown that Eg = kT ln c 2 v from the expression for ni2 , ni ' ' ND N A therefore qVbi = kT ln ni2 ' ' N D NV Nc N A + + OR ( = kT ln for p n junction) OR ( = kT ln 2 for a n p junction.) 2 ni ni Built-in Voltage We can also calculate Vbi by introducing two new symbols that will be used extensively in discussions of MOSFETs. These symbols are φ Fp and φ Fn, the energy differences between the Fermi energy of the sample and the intrinsic Fermi energies on the p and n sides of the junction, respectively. Thus, we can write: where EFi,n is the intrinsic no = ni exp[( EF − EFi ,n ) / kT ] Fermi level for the n type material. n N EF − EFi ,n = qφFn = kT ln o ≈ kT ln D ni ni p N qφFp = kT ln o ≈ kT ln A ni ni ND N A = kT ln ni2 A similar consideration for the P side of the junction. Vbi is the sum of |φ Fn| and |φ Fp|. qVbi = qφFp + qφFn Current Voltage Characteristics of PN Junction I (V ) = I s (e qVa / kT − 1) I s is the reverse saturation current of the diode. J s = I s / Adiode = q (n po ni2 n po ≈ NA Dp Lp Dn Ln + pno ) = q (n po + pno ) Lp Ln τp τn ni2 pno ≈ ND Carrier Distributions and Potential Barriers Diffusive Carrier Motion = Drift Carrier Motion V=0 Diffusive Carrier Motion >> Drift Carrier Motion V=+Va Reverse Biased Diode Diffusive Carrier Motion << Drift Carrier Motion VR VR Va = -VR Forward Biased pn Junction Va > 0| qVa •Majority carrier flow to opposite side of junction. i.e. majority becomes minority •Number limited by energy distributions •Current limited by diffusion of the minority carriers •Minority carrier flow to opposite side of junction. i.e. minority becomes majority •Number limited by thermal generation. •Current limited by drift of carriers. Forming Junctions Between Dissimilar Materials Junctions between n and p type material of the same semiconductor have been discussed in the previous material. In many applications, it is desirable and necessary to fabricate junctions between dissimilar materials such as metals and semiconductors or between two different semiconductors. The general principle that the Fermi energy will be a constant of the device at equilibrium also holds true. But we are left with the problem of deciding how the energy states of the dissimilar materials line up before charge redistributes. Consider two semiconductors, A and B, with different energy gaps and other physical characteristics: EcA EcB EFB EvB A B EFA EvA Energy Band Alignment The question is: what is the absolute energy position of the energy states? To determine this we must know the energy of the bands wrt to a known standard. We want to choose some energy that the various bands can be measured with respect to. We take that to be the energy of an electron at rest outside the material. This is called the vacuum level. Techniques exist for measuring the energy of the Fermi level wrt the vacuum level. This energy difference is called the Work Function -- φ s. Prior to the contact between materials and the redistribution of mobile charges, the vacuum level is the same for both material: Vacuum Level φA φB EcB EFB EvB A B EcA EFA EvA Energy Band Alignment After contact and electron and hole redistribution, the bands are bent by the presence of an electric field and a potential difference between the materials. The discontinuities in the band edges remain but the Fermi energy is a constant of the problem. Vacuum Level qVbi φB EcB EFB A B The spatial variation of the Vacuum level is a reflection of the fact that the internal field generates a potential difference between the two sides of the junction. EvB φA EcA EFA EvA Lifetime of measure of how long a carrier is likely to stay The minority carrier lifetime is aMinority Carriers around for before recombining. It is often just referred to as the "lifetime". Stating that "a silicon wafer has a long lifetime" usually means minority carriers generated in the bulk of the wafer by light or other means will persist for a long lifetime before recombining. Depending on the structure, solar cells made from wafers with long minority carrier lifetimes will usually be more efficient than cells made from wafers with short minority carrier lifetimes. The terms "long lifetime" and "high lifetime" are used interchangably.The low level injected material (where the number of minority carriers is less than the doping) the lifetime is related to the recombination rate by: δn , τ= where τ is the minority carrier lifetime, Δn is the excess minority carriers R concentration and R is the recombinaton rate. 1 τ total τ of carrrier τ SRH The auger lifetime is a functionbandthe τ Auger concentration and is given by: Where the auger coefficienct C is typically given as: 1.66 × 10-30cm6/s (Sinton, Altermatt ) = 1 + 1 + 1 Lifetimes of Si Lifetimes of GaAs Lifetime and Diffusion Length If the number of minority carriers is increased above that at equilibrium by some transient external excitation, the excess minority carrier will decay back to the equilibrium carrier contraction due to recombination processes. A critical parameter in a solar cell is the rate at which recombination occurs. Such a process, known as the "recombination rate" depends on the number of excess minority carriers. If for example, there are no excess minority carriers, then the recombination rate must be zero. The "minority carrier lifetime" of a material, denoted by τ n or τ p, is the average time which a carrier can spend in an excited state after electron-hole generation before it recombines. A related parameter, the "minority carrier diffusion length" is the average distance a carrier can move from point of generation until it recombines. The diffusion length is related to the carrier lifetime by the diffusivity according to the following formula: L = Dτ where L is the diffusion length in meters, D is the diffusivity in m²/s and τ is the lifetime in seconds. Charge Collection Consider a reverse biased p-n junction illuminated to produce a uniform generation rate, go. p diffusion sc wsc n dr ift n p dr ift diffusion Surface Recombination Any defects or impurities within or at the surface of the semiconductor promote recombination. Since the surface of the solar cell represents a severe disruption of the crystal lattice, the surfaces of the solar cell are a site of particularly high recombination. The high recombination rate in the vicinity of a surface depletes this region of minority carriers. A localised region of low carrier concentration causes carriers to flow into this region from the surrounding, higher concentration regions. Therefore, the surface recombination rate is limited by the rate at which minority carriers move towards the surface. A parameter called the "surface recombination velocity", in units of cm/sec, is used to specify the recombination at a surface. In a surface with no recombination, the movement of carriers towards the surface is zero, and hence the surface recombination velocity is zero. In a surface with infinitely fast recombination, the movement of carriers towards this surface is limited by the maximum velocity they can attain, and for most semiconductors in on the order of 1 x 107 cm/sec. The motion of the carriers toward the surface is diffusive. The current density toward the surface is characterized by the surface recombination velocity as: qDp ∂δ p ∂x = −qSpδ p(0) x =0 Charge Collection (continued) In the neutral regions: n side (0 < x < ∞ ) d 2δ p δ p Dp − + go = 0 dx 2 τp → δ p = A + Be x − Lp Ln np Lp δ n = g oτ n -W 0 δ p = goτ p pn + Ce x Lp where L2 = Dpτ p p A = goτ p by sub into Diff. Eq. at x=0 pn = 0 = goτ p + C + B but C=0 → B = − goτ p → δ p = goτ p (1 − e −x Lp Dp dδ p J p ( x = 0) = −qDp = −q g oτ p dx x =0 Lp J p (0) = −qLp g o ) Charge Collection (cont.) p side (-W >x> -∞ ) d 2δ n δ n Dn − + go = 0 2 dx τn → δ n = A + Be x − Ln Ln δ n = goτ n Lp -W 0 np δ p = goτ p pn + Ce x Ln Jn = qDn dδ n dx = −qDnτ n g o / Ln x =−W where L2 = Dnτ n n A = g oτ n by sub into Diff. Eq. B=0; at x = -w; δ n = 0 = g oτ n + Ce → C = −g oτ n e W Ln ( x +W ) −W Ln Jn = −qLn g o In the space charge region (0> x > -W): High electric field → Drift of carriers All carriers collected: Jsc = −qg oW ∴ J photo = Jn + J p + Jsc J photo = −qg o (Ln + Lp + W ) ) → δ n = g oτ n (1 − e Ln Detector of Light The current that flows in the device as a result of the optical illumination is Iphoto = JphotoA = -qgo(Ln+Lp+W)A The total current that flows is the sum of the current due to biasing the diode and the photocurrent: I (amps) Dark Itotal = Is (eqV/kT - 1) + Iphoto Light Iphoto V (volts) Photocurrent derives from the e-h generated in the semiconductor that are separated by the electric field in the junction region. Carriers generated in the neutral n and p regions must diffuse to the region of high electric field (space charge region) to be collected. Therefore, carriers are collected from ~ 1 diffusion length away from depletion region boundary. Of course all carriers generated in the space charge region itself will be directly collected. Solar Cell + Iphoto + RL -IL Voc V I m , Vm Isc Since the diode generates current, it is a power source that can drive a load. When V = 0, I = -Iphoto = Isc Short Circuit Current When I = 0, 0 = Io(eqV/kT-1) – Iphoto Open Circuit Then Voc = kT/q ln (1+Iphoto/Io) Open Circuit Voltage Power Efficiency of the device is hconv = Pm/Psolar = ImVm/Psolar The maximum power output of the device is usually expressed in terms of the short circuit current and the open circuit voltage as Pm = IscVocF where F is the fill factor and is the ratio of the max power to the product of IscVoc. Solar Cell Characteristics I (amps) Dark Light Iphoto V (volts) Itotal = Is (eqV/kT - 1) + Iphoto where Iphoto = JphotoA = -qgo(Ln+Lp+W)A This is calculated for the case of uniform generation rate. If the same boundary conditions were used but we assumed the generation were due to monochromatic light incident on the front surface, the details of the calculation would be altered. Consider the following geometry: The light intensity decreases as e-αx in the material owing to absorption of light and generation of e-h pairs. Thus, g(x, E) = α (E)Io(1-R(E)) e-α(E)x / hν g(x,E) = g(E) e-α(E)x where g(E) = α (E)Io(1-R(E)) /hν H I(x) ~ g(x) 0 xn xp Solution In the neutral n region: n side (0 < x < ∞ ) d 2δ p δ p Dp − + g (E )e −α ( E ) x = 0 dx 2 τ p → δ p = Ae −α ( E ) x + Be where L = Dpτ p 2 p − x Lp + Ce x Lp Boundary Conditions At the surface of the semiconductor, the boundary condition on the excess hole concentration is governed by the resultant surface recombination that occurs there. This is characterized by a surface recombination velocity, Sp, as follows: Dp ∂δ p ∂x = −Spδ p(0) x =0 A = g (E )τ p by sub into Diff. Eq. At x= 0 the BC on δ p is The flux of holes toward the surface is proportional to the hole concentration there and the surface recombination velocity there. At the edge of the space charge region at xn, the excess hole concentration is zero, that is, δ p(xn) = 0. Dp ∂δ p ∂x = −Spδ p(0) x =0 At x = xn, the BC on δ p is δ p(xn) = 0 Solution (cont.) The solution for the hole concentration in the n layer is given by (after a great deal of manipulation): SpLp xn − x x x −α ( E ) xn Sp Lp + α (E )Lp sinh +e sinh + cosh L D L L α (E )F (1 − R )τ p Dp p p p p δp = α 2L2 − 1 xn xn Sp Lp p sinh + cosh L L Dp p p This results in a current at the Junction , xn , given by: S L S L x x p p + α (E )Lp − e −α ( E ) xn p p cosh n + sinh n L L Dp α (E )F (1 − R )τ p Dp p p Jp = α 2L2 − 1 xn xn Sp Lp p sinh + cosh L L Dp p p − α (E )Lp e −α ( E ) xn Solution (cont.) The solution for the electron concentration on the p side is given by: BC ' s : δ n( x p ) = 0 and Snδ n(H ) = −Dn dδ n dx x =H α F (1 − R )τ n −α ( E )( xp ) δn = e 22 α Ln − 1 (H − x p ) (H − x p ) Sn Ln −α ( E )( H − x p ) −α ( E )( H − x p ) −e + α (E )Ln e cosh + sinh Ln Ln x − xp cosh x − x p − e −α ( E )( x − xp ) − Dn X sinh (H − x p ) (H − x p ) Sn Ln Ln Ln + cosh sinh Dn Ln Ln (H − x p ) (H − x p ) Sn Ln −α ( E )( H − x p ) −α ( E )( H − x p ) −e + α (E )Ln e cosh + sinh Ln Ln qα Ln F (1 − R ) −α ( E )( xp ) Dn Jn = α (E )Ln − e 22 (H − x p ) (H − x p ) Sn Ln α Ln − 1 sinh + cosh Dn Ln Ln The current from the space charge region is given , xn < x < xp, by: −α ( E )( x p − xn ) JSC = qF (1 − R )e −α ( E ) xn 1 − e Silicon Solar Cell Response Front Surface Recombination Solar Electricity Production Potential for Inorganic Materials H ome I nstallations of Flat Panel Arrays Require H igher Efficiencies and Lower Costs 3.5 KW Installation Generates 6400 kWhr/year 40 ft $5 - $6 per peak W $0.14 / kWhr Subsidized $0.23 /kWhr Unsubsidized Over 20 year life ...
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This note was uploaded on 02/23/2011 for the course EE 474 taught by Professor Lingo during the Spring '11 term at USC.

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