Effect of Uniaxial Stress on the Acceptor Ground State and on the Hopping Conduction in p-Type Germanium and Silicon

摘要

We constructed variational wave functions, with correct asymptotic behaviour, 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), at uniaxial stress, X, resulting from the application of a tensile or compressive force along the (001) orientation (respectively X<0 or X>0). 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 wave functions were further used for computing the stress variation of resistivity, rho(X) for hopping conduction involving single transitions between the stress-split components of the ground acceptor state, within the framework of percolation theory. Graphic representation of the critical surfaces for percolation, and their evolution with X are provided. Our calculations account adequately for rho(X) in Ge samples with low acceptor concentration for both X<0 and X>0. However, they account only qualitatively for the rho(X) data available 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 rho(X) decreases, at large X, much stronger than predicted for both Ge and Si. We attribute this discrepancy to the increase of the contribution to electron transport of multiple hopping transitions at large X values. (Atomindex citation 15:068776)