Theory of Space-Charge Layers

We review briefly the expressions and concepts needed to describe the electronic phenomena of surfaces and space charges. We refer the reader to the extensive literature on crystalline semiconductors (Many et al., 1965 Sze, 1969 Many, 1974 Goetzberger et al, 1976). It will be shown that the continuous distribution of gap states in amorphous semiconductors requires some changes in the expressions for the conduction and potential distribution in the space-charge region and that the quasi-two-dimensional conduction in a narrow potential well of a space-charge layer introduces some new and as yet unresolved problems. 

The substrate interface looks similar to Fig. 4a. The average energy to remove an electron from the semiconductor to the conduction band of the insulating substrate in this case will be represented by an internal work 

One realizes that the equilibrium depicted in Figs. 4a and b can be disturbed by various experimental parameters. The simple picture of chemisorption may be disturbed by gases such as water or oxygen diffusing into the oxide, introducing new states, and reacting with the silicon interface. Moreover, as discussed in Part 11 the density of surface states may depend on the thermal history and exhibit relaxation efiects (Street and Knights, 1981). 

In addition, the strong fields at the surface and interface at elevated temperatures may lead to field-assisted diffusion of mobile ion species such as protons and alkali ions, and strong illumination will require a new quasistatic equilibration, accompanied possibly by photodesorption (or adsorption), which might require long-time relaxation back to the dark equilibrium. 

Many of these effects, once identified, can be used as diagnostic tools for characterizing the surface condition. One obviously needs the guidance of experiments to sort out the various chemical and electronic processes that yield a specific surface condition. 

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