Microscopic basis for a sum rule for polar-optical-phonon scattering of carriers in heterostructures

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Abstract
A fully microscopic model of the carrier-phonon interaction is employed to obtain a sum rule for polar-optical-phonon scattering of carriers in semiconductor heterostructures. In 1989, Mori and Ando, considering diatomic polar semiconductors and using a dielectric continuum model to derive the phonon modes, derived a sum rule for the carrier–polar-optical-phonon interaction in single and double planar heterostructures that related and constrained the partial contribution from each branch of the optical-phonon spectrum to the total interaction. Here again such a sum rule is derived, but this work differs in two important ways: (1) Fully microscopic models of the phonons and the carrier-phonon interaction are employed, and (2) the results are valid for any semiconductor heterostructure regardless of geometry or materials, including alloy and nonpolar constituents. It is demonstrated that this sum rule reproduces the usual scattering-rate result in the bulk-crystal limit. The derivation of this sum rule requires no assumptions about the functional form of 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, relationships valid for any harmonically coupled system of particles. Thus this work provides independent theoretical support for the sum rule of Mori and Ando and extends the sum rule to arbitrary heterostructure geometries and nonmetallic materials.