Phonon conduction in superlattices

• Lattice thermal conductivity of superlattices are computed.
• Relaxation times of various scattering processes are observed in terms of phonon line widths.
• The internal boundary scattering is found reasonably applicable in superlattices.
• Phonon life time’s removes all the inadequacies of the Callaway model.
• Thermal conductivity of superlattices is much less than that of bulk sample.

The lattice thermal conductivity of InAs/AlSb superlattices is investigated on the basis of modified Callaway model, which successfully explains the inadequacies of Matthiessen’s rule. In the new formulation, the relaxation times of various contributing processes have been observed in terms of line widths. The evaluation of line widths is carried out by double time temperature dependent Green’s function theory, using a comprehensive Hamiltonian which includes the contribution due to electrons, phonons, impurities, anharmonicities and interactions thereof. The frequency line widths are observed as an extremely sensitive quantity in the transport phenomena of superlattices, as it depends on large number of scattering events, namely; combined boundary, impurity, phonon–phonon and interference scattering processes. It is observed in the present work that the lattice thermal conductivity of superlattices is much less than that of a bulk sample. This can be attributed due to the reduction of phonon group velocity and strong phonon–phonon interactions, which in turn causes the decrease in relaxation times and phonon conductivity. Also, it is remarkable to note that the present theoretical model is equally application to all quantum well structures.