Effect of uniaxial stress on the acceptor ground state and on hopping conduction in p-type germanium and silicon

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Abstract
Variational wavefunctions which show the correct asymptotic behaviour are constructed for the ground state of shallow acceptors in Ge and Si, utilizing the spherical tensor representation of the effective-mass Hamiltonian of Baldereschi and Lipari (1973), under a uniaxial stress X resulting from the application of a tensile or compressive force along the [001] orientation (respectively X < 0 or X > 0). The energies of the components of the ground state, computed variationally, account very well for the X-induced displacements of the binding energies and the stress splitting of shallow acceptors in both Ge and Si (at X > 0; no data for X < 0 are available). The wavefunctions were also used to compute the stress variation of resistivity ρ (X) for hopping conduction involving single transitions between the stress-split components of the ground acceptor state, within the framework of percolation theory. Graphic representations of the critical surfaces for percolation, and their evolution with X, are given. The calculations account adequately for ρ(X) in Ge samples with a low acceptor concentration for both X < 0 and X > 0. However, they account only qualitatively for the available ρ(X) data for Si (X > 0 only), probably because of a larger chemical shift of the acceptor ground state in Si and its possible variation with X. At larger acceptor concentrations ρ(X) decreases, at large X, much more strongly than predicted for either Ge or Si. This discrepancy is attributed to an increase in the contribution to electron transport of multiple-hopping transitions at large X values.