A continuum model for acoustic and optical phonons in heterostructures

A continuum description of dispersive acoustic and optical modes in a cubic , elastically isotropic and inhomogeneous binary crystal is given, based on a simple model for the Lagrangian density. Putting the total Hamiltonian i n the form of a sum over classical oscillators which can be quantized in th e usual way, gives rise to continuity conditions at an interface which are the standard ones for acoustic modes but which highlights the effect of the discontinuity of mass across the boundary for optical modes. Unless this d iscontinuity is very small the general boundary condition for optical modes is u = 0. (C) 2000 Published by Elsevier Science Ltd.