A recently developed long-wavelength continuum phenomenological model is employed to study phonon tunneling for an arbitrary incidence angle, and to estimate the contribution of optical phonons to the perpendicular thermal conductivity in simple and multisuperlattice nonpolar semiconductor heterostructures. Phonon tunneling is a multicomponent problem with different tunneling channels. We rigorously define the transmission and reflection coefficients from the energy density balance equation. Simple general rules are presented for the relationship between (a) the key features of the transmission and reflection rates, and (b) the vibrational properties. The range of applicability of the model is increased by simultaneously considering both acoustic and optical phonons. The defined coefficients are employed to test the interrelationship between the coupled modes. Interesting oscillation effects in the relative contribution of different coefficients as a function of the incidence angle are found. We report numerical results for isotopic Ge superlattices to illustrate the model considered. Approximate analytical expressions for the dispersion relation are derived for this system. The contribution of optical phonons to the thermal conductivity is elucidated with the help of these expressions.
- Received 11 July 2000
©2001 American Physical Society