Localized states in semiconductors: isocoric impurities in Si and Ge

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Abstract
A formalism is developed within the multi-valley effective mass approximation for the calculation of the groundstate energies for isocoric donor impurities in silicon and germanium taking into account the ellipsoidal shape of their energy surfaces. For the impurity potential a general screened Coulomb form is considered and its parameters are determined from the k dependent dielectric functions of Si and Ge. Variational trial wavefunctions, belonging to an irreducible representation of the tetrahedral point group Td of the Hamiltonian, are used. The groundstate energies as expressed in terms of the effective masses, the potential parameters and the location k0 of the conduction band minima, are then determined by minimization. The results for Si are in good agreement with experiments; however for Ge the predicted E(A1)-E(T2) splitting is rather too small, -0.5 to -0.7 meV compared with the observed value of -4.23 meV.