Electron-Phonon Interaction in Ionized Impurity-Pairs in Silicon

Abstract

A microscopic theory is developed to treat the adiabatic as well as the non-adiabatic interaction of a carrier trapped by a pair of impurities in Si with the lattice vibrations. Two complementary methods, which are called the electron (the adiabatic) and the polaron (the non-adiabatic) approaches, are proposed and formulated with the use of the canonical transformations known in the theories of small polarons. The Hamiltonian is rewritten in terms of the quasi-particle ( i. e. , “electron” and “polaron”) operators to obtain the zeroth-order energies. The residual interactions are treated as perturbations which shift and broaden the levels with the use of the thermal Green's functions. Approximate “single-phonon” Hamiltonians are derived from the exact “multi-phonon” Hamiltonians to clarify the physical natures of the problems involved since multi-phonon processes are not important in pairs in Si. The adiabatic criterion is discussed with the use of these single-phonon Hamiltonians. Completely homopolar pairs and extremely polar ones are investigated in detail; the former is important in the microwave experiment of photon-assisted hopping (Tanaka et al. ) and the latter in the dc and ac experiments of phonon-assisted hopping and in the far-infrared experiment of photon-assisted hopping.