Combining a selective emitter with a back surface reflector (BSR) on the PV arrays is a method of spectral control that makes possible large cavity efficiency. A rare earth selective emitter provides large emittance for the range of wavelengths that are
convertible by the PV arrays. Also, in the range Xg < X < 5 pm, where Xg = —- is the wavelength corresponding to the PV bandgap energy, the emittance is small. For X > 5 pm the emittance becomes large again. However, a BSR has large reflectance for X > 5pm. As a result, the majority of these photons are not lost but are reflected back to the emitter where they are absorbed.
Consider the planar geometry system of Figure 8.1 that uses an erbium aluminum garnet, Er3Al5O12, emitter with the optical properties given in Figure 3.6. Assume the temperature gradient across the emitter and scattering can be neglected. As a result, the spectral emittance for the case where the substrate is deposited on the emitter is the following (see problem 3.7),
where Кд = K(X)d is the optical depth, K is the extinction coefficient, and d is the emitter thickness. Also Rfo is the normal reflectivity at the emitter-vacuum interference and Rfs is the normal reflectivity at the emitter-substrate interface.
R (nsR – nf )2 + П2І
(n + nf) + Пт
Here nf is the index of refraction of Er3Al5O12, and UjR is the real part of the substrate index of refraction, and nsI is the imaginary part of the substrate index of refraction. For this example assume, Rfs = 0.8, which is representative of a low spectral emittance material such as platinum on Er3Al5O12. Using the optical properties of Er3Al5O12 given in Figure 3.6 and an emitter thickness, d = 0.01cm, in equation (8.45) yields the spectral emittance shown in Figure 8.4.
of thickness d=.01cm with deposited substrate using optical properties shown in Figure 3.6 and neglecting temperature gradient across emitter. Reflectivity at substrate-garnet interface, R =.8.
The spectral emittance shown in Figure 8.4 and the same optical cavity conditions that were used in Figure 8.2 produce the results shown in Figure 8.5. These results have been obtained using the Mathematica program described in Appendix F. In order to include the large changes in Er3Al5O12 emittance with wavelength, the step size was set at AX = deltalyS = 1nm. With a gray body emitter of emittance, £e = 0.6, and no gap between the reflector and PV arrays the efficiencies were pc = 0.64, pPV = 0.31, and pTPV = 0.20 at a temperature, TE = Tb = 1251K. These results are nearly the same as those for the Er3Al5O12 selective emitter. Thus, using the selective emitter results in no improvement in performance. The most significant improvement occurs when the gap between the reflector and PV arrays is eliminated. In that case for the gray body emitter, pc increases from 0.57 to 0.64 and pTPV increases from 0.18 to 0.20.
PELc3 = 9 w
(V0c = 9.5V, Isc = .70A, FF = .67 for each of 2 arrays in Асз)
Pelc2 = 21 W
(V0c = 9.5 V, Isc = .67 A, FF = .67 for each of 5 arrays in AC2)
(Voc = 9-5 V, Isc = .67 A, FF = .67 for each of 4 arrays in Acl)
TE = Tb = 1278 K, Tcl = Tc2 = Tc3 = 300 К Cavity efficiency, T)c = .62 PV efficiency, T|py = .31 TPV efficiency, T|TPV = ilcrjpv = .19 Electrical power out, PEL = 47 W
Figure 8.5.—Performance of planar, square geometry TPV system with the same properties as used in Figure 8.2 except that the gray body emitter has been replaced by an erbium aluminum garnet selective emitter with optical properties given in Figure 3.6.