Photo-ionization of deep impurity levels in semiconductors with non-parabolic bands

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Abstract
Theoretical expressions for the photo-ionization cross section of deep impurity levels are developed. With the approximations of a delta-function potential for the impurity atom and a free-electron-like mass for the donor electron it is shown that good agreement with data for oxygen-doped GaAs is obtained. The expressions are then further generalized so as to be valid for both non-spherical and non-parabolic bands and are applied to recently published photo-ionization cross sections for Si:Au and Si:Zn. For all the cases studied, the authors find effective field ratios close to unity. The optical threshold energies for Si:Zn are reevaluated and agreement with the thermal ionization energies for both acceptor levels is found. The bands in the 110 direction as determined by the kp method do not influence the cross section in the manner expected.