Spectral Effects

The amount of light distributed to each subcell, and thus, the photocurrents generated by each subcell, is determined by the spectrum of the incident light. (See Chapter 17 for more complete

Figure 8.10 Efficiency vs subcell bandgaps for a series-connected two-terminal thickness – optimized three-junction cell under the low-AOD direct spectrum at 500-suns concentration and 300K temperature. 52 and 51% isoefficiency surfaces are shown, as indicated by their pro­jections onto the two-dimensional contours. Bandgap combinations of actual champion devices discussed in the text are also shown with markers of various shapes: {1.86, 1.39, 0.67} eV cylinder; {1.80, 1.29, 0.67} eV, cone; and {1.83, 1.34, 0.89} eV, sphere. Adapted from reference [14]

discussion of spectra and absorption...

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Three-junction cells

The concepts and approach used above for two-junction cells can be applied to cells with any number of junctions. Figure 8.10 shows the calculated efficiency of a three-junction cell as a function of the three subcell bandgaps. The bottom subcell is taken to be optically thick, and the two subcells above it are optically thinned to optimize the efficiency. The figure is calculated at 500-suns concentration using the low-aerosol-optical-depth (AOD) AM1.5 direct spectrum. Under these conditions, a maximum efficiency of almost 53% is obtained at a bandgap combination of {1.86, 1.34, 0.93 eV}; there is also a local maximum at {1.75, 1.18, 0.70 eV} with comparable effi­ciency. Several bandgap combinations of particular interest are indicated. The bandgap combination {1.86, 1.39, 0...

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Efficiency vs Bandgap Two-junction cells

To obtain concrete, numerical values for the cell performance from the concepts described above, we need to choose numbers for the relevant materials properties to determine J0 for each junction. Reference [7] provides a reasonable model of a two-junction n/p cell, in which the bottom junction has the properties of GaAs, except that the bandgap is allowed to vary. The absorption coefficient

Figure 8.8 Effect of base thickness xb and surface-recombination velocity Sb on VOC for a GalnP top cell with JSC = 14 mA/cm2. The base is characterized by a bulk recombination velocity Db/Lb = 2.8 x 104 cm/s. Note that when the bulk and surface recombination velocities are equal, VOC is independent of base thickness. Photon recycling is neglected

is shifted rigidly with...

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Current-matching Effect on Fill Factor and Voc

The fill factor (FF) of the tandem cell depends on the top – and bottom-subcell photocurrents. Figure 8.7c, e show the fill factor as a function of top-cell thickness, and thus effectively as a function of JSCt/JSCb, for the device of Figure 8.7b. The fill factor is a minimum at the current – matched condition, an effect that holds in general for reasonably ideal (non-leaky) subcells. This effect slightly undermines the efficiency gains that accrue from the increase in JSC at the current – matched condition; however, the decrease in fill factor at current-matching is roughly half the increase in JSC...

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Current Matching and Top-cell Thinning

The relative magnitudes of the top – and bottom-subcell short-circuit current densities JSCt and JSCb depend on the bandgaps of the subcells, as Equation (8.10) shows explicitly for the case of optically thick subcells. For this case, Figure 8.7a shows JSCt and JSCb as a function of Egt for Egb = 1.42 eV for the AM1.5 global spectrum. The figure shows that as Egt decreases, JSCt increases and JSCb decreases, becoming less than JSCt for Egt < 1.95 eV. The JSC for the series – connected combination of these two cells will be the lesser of JSCt and JSCb. This quantity is a maximum at the current-matched bandgap Egt = 1.95 eV, and falls off rapidly as Egt is decreased below 1.95 eV.

Because the absorption coefficient a(hv) for solar-cell materials is not infinite, a cell of finite thickness (i...

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Multijunction J-V Curves

For any set of m series-connected subcells (or, indeed, any sort of two-terminal element or device) whose individual current-voltage (J – V) curves are described by Vi(J) for the 1th device, the J – V curve for the series-connected set is simply


V(J) = E Vi(J); (8.ii)


i. e., the voltage at a given current is equal to the sum of the subcell voltages at that current. Each individual subcell will have its own maximum-power point {Vmp i, Jmp i} which maximizes J x Vi (J). However, in the series-connected multijunction connection of these subcells, the currents through each of the subcells are constrained to have the same value, and therefore each subcell will be able to operate at its maximum-power point only if J mpj is the same for all the subcells, i. e. Jmp1 = Jmp 2 = … = Jmp, m...

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Top and Bottom Subcell QE and Jsc

The short-circuit current density (Jsc) of each subcell is determined by the quantum efficiency of the subcell, QE(A), and by the spectrum of light incident on that cell $inc(A) in the usual way:


Jsc = e j QE(k)i$incWdk.


The QE for an ideal cell of finite base thickness xb, emitter thickness xe, and depletion width W (for a total thickness x = xe + W + xb,) is given by the standard equations

QE = QEemitter + QEdepl + exp[-a(xe + W)] QEtase, (8.2)


The photon wavelength dependence is not explicit in these equations, but enters through the wavelength dependence of the absorption coefficient a(X)...

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8.1.4 Overview

This section discusses the quantitative modeling of the performance of series-connected, two-terminal, multijunction devices, as well as the quantitative design of these devices. Emphasis is placed on selecting bandgap pairs, and predicting the efficiency of the resulting structures. This modeling also lays the groundwork for the analysis of the dependence of the device performance on spectrum, concentration, and temperature...

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