Foundations of the EnvelopeFunction Theory for Electrons and Phonons in Semiconductor Heterostructures.
Abstract
Envelopefunction models form a valuable tool for the analysis of electrons and phonons in semiconductor heterostructures because they provide a high degree of physical insight at a low computational cost. This dissertation investigates the fundamental physical principles underlying the envelopefunction approach to heterostructures through the direct derivation of longwavelength envelopefunction models from basic microscopic theory. The derivation starts with the establishment of an exact envelopefunction formalism for electrons and phonons, following the work of Burt and Kunin, and proceeds through a series of approximations to reduce the exact equations of motion to simple, second order differential equations with spatially varying coefficients. This provides the first direct proof of the validity of second order differential equations at an abrupt heterojunction and resolves a longstanding controversy in the literature. The effectivemass theory for electrons derived here gives a straightforward analytical justification for the approximations used by Burt in his treatment of the problem (J. Phys. Condens. Matter, 6651 (1992)). Burt showed that by assuming the envelope functions are slowly varying, one can derive an effectivemass theory which reproduces very accurately the properties of the solutions to the exact theory; however, he offered no analytical justification for why such an approximation should be valid at an abrupt junction. The present work provides this justification, showing that the envelopes can be treated as slowly varying so long as any rapid interface fluctuations are confined to a region small on the macroscopic scale. The longwavelength theory of phonons derived here reproduces the boundary conditions of classical elasticity for acoustic vibrations, but it also shows that these boundary conditions are not adequate to describe optical modes. In general, the change in vibrational properties at the interface leads to the appearance of deltafunction terms in the reduced mass and zonecenter force constant, which tend to dominate the optical boundary conditions. Thus the phenomenological models currently used for optical phonons in GaAs/AlAs heterostructures must be modified if they are to describe the strong interface effects that exist in InAs/GaSb structures.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........53F
 Keywords:

 Physics: Condensed Matter; Engineering: Electronics and Electrical