Abstract
A theory is developed for the combined effects of electron-phonon scattering and elastic reflection of electrons on electrical current through a nanostructure. We use a time-dependent quantum-linear-response theory, then take the limit of zero frequency. In addition we develop a parallel theory that is semiclassical. The results obtained by the two methods are the same. The effect of phonons on the current flow is small because in this effect final as well as initial electron states in the electron-phonon scattering must have nonzero transmission through the nanostructure.
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