Dr Paul Kinsler. [Acknowledgements & Feedback]
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<> (40) TI: MICROSCOPIC BASIS FOR A SUM-RULE FOR POLAR-OPTICAL-PHONON <> SCATTERING OF CARRIERS IN HETEROSTRUCTURES <> AU: REGISTER_LF <> NA: UNIV ILLINOIS,BECKMAN INST,URBANA,IL,61801 <> UNIV ILLINOIS,COORDINATED SCI LAB,URBANA,IL,61801 <> JN: PHYSICAL REVIEW B-CONDENSED MATTER, 1992, Vol.45, No.15, <> pp.8756-8759 <> IS: 0163-1829 <> DT: Note <> AB: 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. <> KP: ELECTRON
This is a generalisation of the Mori and Ando (Mori-A-1989) sum-rule.
This is for a system of harmonically coupled ions with phonon modes of uniform energy. As a result it ignores the practical issue of momentum and (kind of) energy conservation, as any scattering event is equally likely to produce any phonon -- hence the phonon overlap integrals decouple from the electronic ones and the sum-rule holds (as the phonon modes are orthonormal and complete).
So does it not hold in general, but it will near the zone-centre of a single LO-phonon branch (see Babiker-Z-1998) -- or a hybrid-phonon branch that is mostly LO-phonon (ie is weakly hybridised).
OLD: I suspected the validity of the sum-rule, on the basis that hybrid-phonon solutions would span a subset of the wave-function space spanned by all the individual phonon basis modes (implicit assumption, based off Ridley-1993). However, these Ridley hybrid-phonons have quite 'tight' boundary conditions, and in a thick multilayer heterostructure the boundary-conditions might be effectively less restrictive -- in the same way a wide quantum-well has more closely spaces and 'continuum-like' wavefunctions than a narrow quantum-well. So for a very thick, not very heterogeneous structure (which could be assumed to minimse phonon confinement in one layer), the space spanned by the hybrid-phonons might well be 'most-of' that spanned by all the individual phonon basis modes. However, see above for Babiker-Z-1998s zone center explanation -- these do not seem equivalent. So?
XINDEX: sum-rule, log-file, hybrid-phonon, Babiker-Z-1998, index-file, log-file.
19971212
Email Feedback: Dr.Paul.Kinsler@physics.org
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