Phonon tunneling through a double barrier system

The tunneling of optical and acoustic phonons at normal incidence on a double-barrier is studied in this paper. Transmission coefficients and resonance conditions are derived theoretically under the assumption that the long-wavelength approximation is valid. It is shown that the behavior of the transmission coefficients for the symmetric double barrier has a Lorentzian form close to resonant frequencies and that Breit–Wigner's formula have a general validity in one-dimensional phonon tunneling. Authors also study the so-called generalized Hartman effect in the tunneling of long-wavelength phonons and show that this effect is a numerical artifact resulting from taking the opaque limit before exploring the variation with a finite barrier width. This study could be useful for the design of acoustic devices.