Abstract
The standard impurity resistivity formula ρ=m/〈τ〉 in the absence of phonons and electron-electron interactions is clearly understood to be derived under adiabatic conditions. Considering coupling to a heat bath of phonons, a charged carrier can interact with other carriers via the electron-phonon interaction and thus acquires a momentum-conserving inelastic scattering time . The attendant phonon-mediated electron-electron interaction promotes a tendency toward thermalization of the drifted system. On the basis of the force-balance-equation approach, we demonstrate that under isothermal conditions the impurity resistivity is devoid of the divergencies of van Hove’s ‘‘t’’ series expansion. Electron-electron interactions will yield similar results. In the limit of (the impurity scattering time), the impurity resistivity reduces to the expression given by the lowest-order term in the force balance equation, ρ=(m/)〈1/τ〉. We also show that this conclusion is consistent with results based upon the Boltzmann equation in a relaxation-time approximation.
- Received 25 January 1989
DOI:https://doi.org/10.1103/PhysRevB.40.3756
©1989 American Physical Society