Energy States of Overlapping Impurity Carriers in Semiconductors

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Abstract
An analytical solution of the Schrödinger equation for the spherically symmetrical wave function of an impurity carrier in a zero wave number state is given on the basis of the Wigner-Seitz cellular approximation. An approximate method is described for calculating the small deviations from the hydrogenic values. The variation of the lower band-edge energies with impurity concentration shows that the excited impurity bands may overlap each other strongly, but a continuous decrease of the activation energy from its hydrogenic value to zero cannot be accounted for by interaction alone.

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