The criteria of diffusionless solution validity in the theory of exclusion in “super-pure” semiconductors

The criteria of validity of the diffusionless solution previously obtained in the theory of the exclusion effect in “pure” semiconductors with non-injecting contacts are determined and the conditions discussed of their realization. With this in view, a more general solution to the bipolar continuity equation is obtained for various relations between the residual impurity and intrinsic conductivities of a crystal. The distributions of current carrier concentration and field, the length of high-level carrier depletion layer, and the characteristic length of exponential drop in the carrier concentration deficit are also found. It is shown that, despite of the considerable carrier concentration gradient in “super-pure” semiconductors caused by exclusion, the neglect of carrier diffusion is practically justified in the whole base of the structure except a very thin layer near the depletion region boundary. It ascertains the existence of a minimum residual impurity concentration corresponding to the limit of satisfication of the quasi-neutrality condition on which the theory is based, and determines its dependence on the material parameters and external excitation. The condition of equality of electron and hole lifetimes is also obtained. It is shown that the criteria found and valid in the case of “super-pure” germanium. [Russian Text Ignored].

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