Energy States of Overlapping Impurity Carriers in Semiconductors
Physical Review1952Vol. 88(4), pp. 893–894
Abstract
An analytical solution of the Schr\"odinger 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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