**3.4. Detailed balance efficiency limit**

The detailed balance limit efficiency for an ideal solar cell, consisting of single semiconducting absorber with energy band-gap *Eg*, has been first calculated by Shockley and Queisser (SQ) [6]. The illumination of a *pn* junction solar cell creates electron-hole pairs by electronic transition due to the fundamental absorption of photons with *hν* > *Eg*, which is basically a quantum process. The photogenerated pairs either recombine locally or circulate in an external circuit and can transfer their energy. Their approach reposes on the following main assumptions; the probability that a photon with energy *hν* > *Eg* incident on the surface of the cell will produce a hole-electron pair is equal to unity, while photons of lower energy will produce no effect, all photogenerated electrons and holes thermalize to the band edges (photons with energy greater than *Eg* produce the same effect), all the photogenerated charge carriers are collected at short-

**Figure 10.** The ultimate efficiency against the energy band-gap of the solar cell, using the AM1.5G spectrum with the blackbody spectrum at *Ts*=6000°*K*.

circuit condition and the upper detailed balance efficiency limit is obtained if radiative recombination is the only allowed recombination mechanism.

The model initially introduced by SQ [6] has been improved by a number of researchers, by first introducing a more exact form of radiative recombination. The radiative recombination rate is described using the generalised Planck radiation law introduced by Würfel [7], where the energy carried by emitted photons turn out to be the difference of electron-hole quasi Fermi levels. While for non-radiative recombination the released energy is recovered by other electrons, holes or phonons.

In the following sub-section the maximum achievable conversion efficiency of a single bandgap absorber material is determined.
