CONSTRAINTS ON THE POLAR-OPTICAL-PHONON INFLUENCE FUNCTIONAL IN HETEROSTRUCTURES

The Feynman influence functional for the polar coupling of carriers to confined phonon modes in heterostructures is considered. It is found that the partial contributions to the total influence functional from the individual branches of the optical-phonon energy spectrum are related and constrained by conservation relations. The derivation of these conservation relations requires no specific functional form for the phonon modes; rather it employs only the inherent orthogonality and mathematical completeness of the classical vibrational modes over the crystal-lattice degrees of freedom. In the bulk-crystal limit these conservation relations lead to the familiar results of Feynman; for arbitrary heterostructures, these conservation relations provide a basis for an estimation of the influence functional from limited knowledge of the spatial confinement of the individual phonon branches.