One-dimensional phonon-coupled electron tunneling: a realistic model

The transition probability for a one-dimensional tunneling electron coupled to acoustical phonons is calculated, with the Feynman path-integral method. We considered a realistic electron-phonon interaction (deformation potential, piezoelectric), making use of slowness of the phonon system compared to electron tunneling. We show that the problem of the complex nonlinear coupling of a tunneling electron to the zero-point fluctuations of a phonon field is equivalent to that of an electron tunneling through a slow fluctuating spatially uniform barrier, thus resulting in an increase of the tunneling probability due to electron coupling with zero-point phonon oscillations. We calculated also the energy change of the tunneling electron due to phonon emission.