Solar Cell Efficiency

In view of the central importance of efficiency for energy conversion, this issue is addressed here in some detail. The main concern in this regard is not so much the performance figures that have been registered by commercial PV systems, but rather the boundaries that are derived from physics. This section concludes with observations concerning the possibility of exceeding these boundaries.

2.3.2 Spectral Efficiency zs (of Solar Cells with a Single Junction)

The spectral composition of sunlight is discussed in Section 2.7 and the internal photoelectric effect is discussed in Section 3.1. Figure 3.19 shows the sunlight spectrum (AM 1.5). Only those photons whose energy, E = h ■ n, exceeds the band gap energy EG of the semiconductor material being used can generate an electron-hole pair. Hence only a portion of this energy can be used.

Equation 2.33 allows for the following determination, based on the intensity distribution of spectral irradiance (see Figure 2.42), the number of photons dnPh per m[1] and the number of seconds per wavelength interval dl:

By integrating a range from 0 to lmax, the number of sufficiently energized photons incident on the solar cell per area unit and per second is obtained. Assuming that an ideal solar cell material is available that can separate each of these electron-hole pairs, the maximum possible current density

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Jmax — JScmax can be determined for such an ideal solar cell, based on the number of photons per area unit:

where:

Jmax — JSCmax — /scmax/Az — maximum possible short-circuit current/cell area

/(1) — spectral intensity distribution as in Figures 2.42 and 3.19 (AM1.5)

1max — h ■ c/EG, i. e. the maximum wavelength that is sufficient to separate an electron-hole pair in the presence of a given band gap energy EG

This method allows for the determination of Jmax as a function of EG. [Gre86] contains a graph for Jmax for AM0 up to 60 mA/cm2. [Gre95] contains a table indicating the Jmax values as a function of EG for the (increased) AM1.5 spectrum with 1kW/m2. Figure 3.20, which shows Jmax as a function of EG, was elaborated using these figures.

Whereas in the AM0 spectrum current density rises relatively steadily as band gap energy EG decreases, this increase in the AM1.5 spectrum is less regular. As Figures 3.19 and 2.42 show, radiation intensity is extremely low in certain wavelength ranges of the AM1.5 spectrum (according to the photon energy range), as a result of greater light absorption by atmospheric water and carbon dioxide. Consequently, current can increase only slightly.

If we presume that all of the energy EG obtained from this ideal solar cell can be output to the external electric circuit, then spectral conversion efficiency zs can be calculated as a function of band gap energy EG.

 The voltage for this ideal solar cell is determined as follows (e = elementary charge): Theoretical photovoltage VPh = -Eg e (3.16) The following applies to area-specific power P/AZ of this ideal solar cell (area AZ): Area-specific power of an ideal solar cell P -T = Vph Az ■ Jmax (3.17) The following then applies to spectral efficiency Zs: Spectral efficiency of an ideal solar cell : zs = P G ■ Az ~ VPh ■ Jmax G (3.18)

Here, G is the irradiance on the solar cell.

Figure 3.21 shows this spectral efficiency zs as a function of EG for the AM0 and AM1.5 spectra with 1 kW/m2, which is generally used to determine the efficiency of terrestrial solar cells.

If Eg is low, then virtually all photons will generate electrons and current density Jmax will be high. However, the energy released per electron EG will be low, and thus VPh will likewise be low. It therefore follows that spectral efficiency in the ideal solar cell will be low. In the presence of elevated EG values, only a minute proportion of the photons will be able to generate an electron, and thus current density Jmax will decrease to a low value. As EG is high, also VPh is high. Therefore spectral efficiency in the presence of high EG values is likewise low owing to the low current density. The optimum lies somewhere in between.

For the AM1.5 spectrum, which is important for terrestrial applications, efficiency zs for mean EG values is several per cent higher, by virtue of the fact that, irradiance G being equal, the infrared portion

 Spectral Efficiency of an Ideal Solar Cell in the AM0- and AM1.5-Spectrum Figure 3.21 Spectral efficiency Zs of an ideal solar cell as a function of semiconductor material band gap energy EG

Energy used to generate electron/hole pairs

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Figure 3.22 Spectral energy absorption in a crystalline silicon solar cell. Photons with unduly low energy, h ■ n < EG (l > 1.11 pm), are not absorbed by the semiconductor material, and thus their energy is unusable. In photons where h ■ n > Eg, the difference, h ■ n — EG, is likewise unusable and is converted into heat in the semiconductor material. In this ideal solar cell, only the energy represented by the vertically hatched area can be converted into electrical energy of this spectrum contains somewhat less energy that is usable for a solar cell, relative to the AM0 spectrum. Forthe same reasons as for Jmax, the цs curve for the AM1.5 spectrum is more irregular than for the AM0 spectrum.

The curves inFigures 3.20 and 3.21 apply solelytothe aforementioned ideal solarcells and nottoreal – world solar cells. Figure 3.22 shows the relationships that apply in such an ideal silicon solar cell (according to the suppositions made in the present section).

Updated: August 3, 2015 — 10:08 pm