This book focuses on the theory of phonon interactions in nanoscale structures with particular emphasis on modern electronic and optoelectronic devices. The continuing progress in the fabrication of semiconductor nanostructures with lower dimensional features has led to devices with enhanced functionality and even novel devices with new operating principles. The critical role of phonon effects in such semiconductor devices is well known. There is therefore a great need for a greater awareness and understanding of confined phonon effects. A key goal of this book is to describe tractable models of confined phonons and how these are applied to calculations of basic properties and phenomena of semiconductor heterostructures. The level of presentation is appropriate for undergraduate and graduate students in physics and engineering with some background in quantum mechanics and solid state physics or devices. A basic understanding of electromagnetism and classical acoustics is assumed.

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The con6ned acoustic phonons in free-standing quantum wells are considered in detail. She Hamiltonian describing interactions of the confined acoustic phonons with electrons in the approximation of the deformation potential and the corresponding electron transition probability density are derived. They are used to analyze the electron scattering times (inverse scattering rate, momentum relaxation time, and the energy relaxation time) in the test-particle approximation as well as in the kinetic approximation. It is shown that the first dilatational mode makes the main contribution to electron scattering in the lowest electron subband. The contribution of the zeroth mode and the second mode are also essential while the modes of higher order are insignificant. Our analysis is performed for both nondegenerate and degenerate electron gases. It is shown that electron scattering by con6ned acoustic phonons interacting through the deformation potential is substantially suppressed up to the electron energies corresponding to the energy of the first dilatational mode.

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We present Fröhlich-like electron-optical-phonon interaction Hamiltonian for wurtzite crystals in the longwavelength limit based on the macroscopic dielectric continuum model and the uniaxial model. In general, the optical-phonon branches support mixed longitudinal and transverse modes due to the anisotropy. We calculate electron scattering rate due to the optical phonons in the bulk wurtzite GaN and demonstrate that the scattering rate due to transverselike phonon processes can be strongly enhanced over a range of angles with respect to the c axis. For the case of longitudinal-like modes, the anisotropy is small and the result is almost the same as that obtained with the cubic Fröhlich Hamiltonian. ͓S0163-1829͑97͒05428-3͔Recent advances in semiconductor optoelectronics 1 and electronics 2 based on wide band-gap nitride materials have resulted in substantial interest in the basic properties of wurtzite crystals. Particularly, a complete understanding of carrier-phonon interaction mechanisms and rates is essential to further progress in these fields. Since the wurtzite crystals have a different unit-cell structure ͑i.e., four atoms per unit cell͒ as well as lower symmetry compared to zinc-blende counterparts, phonon dynamics and carrier-phonon interactions in this material system may be substantially different from those with cubic symmetry. Clearly, there are many more distinct phonon branches ͑nine optical and three acoustic modes͒ in wurtzite materials. At the same time, the phonon modes may not be purely longitudinal nor transverse ͑the ͓0001͔ direction excepted͒. Current understanding of phonon dynamics and their interaction with carriers in wurtzite semiconductors is very primitive. In this paper, the macroscopic dielectric continuum model and the uniaxial model of Loudon 3 are applied to derive the Fröhlich Hamiltonian and the corresponding scattering rates for wurtzite materials.We consider a uniaxial crystal in which only one group of three optical-phonon branches is infrared active. The wurtzite structure is a case in point since at the ⌫ point, only the A 1 (Z) and E 1 (X,Y ) modes are infrared active among the nine optical-phonon modes. Our model can be extended to other uniaxial crystals which have larger numbers of polar modes since the method is the same. We take the c axis along the z direction and denote the perpendicular direction as Ќ. Within the dielectric continuum approach, the opticalphonon modes in the no-retardation limit satisfy the classical electrostatic equations, i.e., E͑r͒ϭϪ"⌽͑r͒, ͑1͒D͑r͒ϭE͑r͒ϩ4P͑r͒ϭ⑀ Ќ ͑͒E Ќ ͑r͒ ϩ⑀ z ͑͒E z ͑r͒ẑ, ͑2͒where ⌽͑r͒ is the electrostatic potential due to the opticalphonon mode, E is the electric field, D is the displacement, P is the polarization field, and ẑ ( ) denotes the unit vector along the z ͑Ќ͒ direction. The direction-dependent dielectric functions ⑀ Ќ () and ⑀ z () are given by