Fermi Levels under Non-Equilibrium Conditions

At equilibrium, the Fermi level, i.e. the electrochemical potential is constant throughout the semiconductor sample (Fig. 1.17a). In addition, the density of electrons and holes can be calculated simultaneously from Eqs. (1.28) and (1.30) if the position of the Fermi level within the bandgap is known. If the thermal equilibrium is disturbed, for instance by light excitation, then the electron and hole densities are increased to above their equilibrium value and we have np n], Accordingly, the electron and hole density are not determined by the same Fermi level. It is useful to define quasi-Fermi levels, p and one for electrons and another for holes, as given by 

Let us consider a light excitation of electrons and holes (An = Ap) within a doped n-type semiconductor so that Am no and A/ p(). Then the Fermi level of electrons, fipn, remains unchanged with respect to the equilibrium case, whereas that of holes, Epp, is shifted considerably downwards, as illustrated in Fig. 1.17b. In many cases, however, the excitation of electron-hole pairs occurs locally near the sample surface because the penetration of light is small. Then the splitting of the quasi-Fermi levels is 

Tire quasi-Fermi levels play an important role in processes at the semiconductor-liquid interface, because the relative position of the quasi-Fermi level with respect to that in solution yields the thermodynamic force which drives an electrochemical reaction (see Section 7.4). 

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