Energy Levels of Electrons in Semiconductors

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

In the hopping model the electrochemical potential, p, of electrons is expressed conventionally in the same way as that of ions as shown in Eqn. 2-26  

We now consider the relationship which connects the electrochemical potential of electrons in the hopping model with that in the band model. The total concentration, N, of electron sites for the hopping model may be replaced by the effective state density, JVc, for the band model. For the two models thereby we obtain from Eqn. 2-27 the following equation  

The concentration of electrons that occupy a part of the total concentration, N, of the energy states available for electrons is obtained by integrating the product of the state density. Die), and the Fermi function, fie), as shown in Eqn. 2-30  

Compeuing Eqn. 2-30 with Eqn. 2-31, we consequently obtain the activity coefficient, y, as shown in Eqn. 2-32  

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