Page 61 - Applied Photovoltaics

Figure 3.6. The creation of electron-hole pairs and dissipation of energy in excess
of E g.

The quantum efficiency (QE) of a solar cell is defined as the number of electrons
moving from the valence band to the conduction band per incident photon. The
longest wavelength for which this is finite is limited by its bandgap. Maximum use
can only be made of incoming sunlight if the bandgap is in the range 1.0–1.6 eV. This
effect alone acts to limit the maximum achievable efficiency of solar cells to 44%
(Shockley & Queisser, 1961). The bandgap of silicon, at 1.1 eV, is close to optimum,
while that of gallium arsenide, at 1.4 eV, is even better, in principle. Fig. 3.7
illustrates the dependence of ideal quantum efficiency on bandgap.

Also of interest is the spectral responsivity of a solar cell, given by the amperes
generated per watt of incident light (Fig. 3.8). Ideally, this increases with wavelength.
However, at short wavelengths, cells cannot use all the energy in the photons,
whereas at long wavelengths, the weak absorption of light means that most photons
are absorbed a long way from the collecting junction and the finite diffusion length in
the cell material limits the cell’s response.
Spectral responsivity (SR) can be calculated as follows:

I qu n Ȝ q
SR sc e EQE (3.9)
P Ȝ hc hc
in u n ph
Ȝ
where n e is the flux of electrons, per unit time, flowing in an external circuit at short
circuit conditions and I sc is the short circuit current, n ph is the flux of photons of
wavelength Ȝ incident on the cell per unit time, P in is the incident light power and
EQE = (1 – R) × IQE is the external efficiency, which differs from the internal
quantum efficiency (IQE) in that the latter excludes the fraction, R, of light reflected
from the top surface. SR ĺ 0 as Ȝ ĺ 0, since there are fewer photons in each watt of
incident light.

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