Ground State of Impurity Atoms in Semiconductors Having Anisotropic Energy Surfaces

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Abstract
The nature of the ground state of a substitutional impurity atom in a crystal having an anisotropic energy-band structure is re-examined. A variational calculation has been made for the case of a band whose energy contours consist of several, symmetrically-located ellipsoids. Unlike the previous scalar, hydrogenic impurity model, this calculation at the outset uses the experimentally determined effective-mass-tensor components. Results for the impurity binding energy in germanium and silicon are on the order of thirty percent lower than those obtained directly from activation-slope measurements. Further, theoretical agreement with the experimentally determined critical impurity density for vanishing binding energy in germanium is much improved over the older model, though still not perfect.

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