Fermi Levels under Nonequilibrium Conditions

Using Eqs. (1.46)-(1.49), we can derive the overall flow of electrons into the traps as given by 

By analogy, a similar expression can be derived for the net capture rate of holes. 

In the case of stationary illumination, the electron and hole flow must be equal (/ = / = Rp). Applying this condition to Eqs. (1.53) and (1.54),/( can be determined. Inserting the resulting equation into Eq. (1.50), one obtains 

This is the so-called Shockley-Read equation describing recombination via traps. It also plays an important role in the description of recombination processes via surface states, as discussed in Chapter 2. In the above equation one may also replace Hi and Pi by the relations 

There are various techniques for measuring the lifetime of excited carriers, which cannot be described here. Details are given by Sze [7]. 

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At pH 7 versus NHE. 3Fe(OH)2 Fe(OH)2Cl /i H2O where 3 > n > 2 (63), [Fe(II)4 Fe(III)2 (0H)i2]2+ [S04 2H20]2- (64), Single crystal. Quasi-Fermi energy level for electrons. This is the Fermi energy level under illumination (nonequilibrium conditions). For n-type semiconductors where electrons are the majority carriers, the quasi-Fermi energy level is approximately equal to the Fermi energy level (65),... 

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