Electron–optical-phonon scattering in wurtzite crystals

Abstract

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

Optical properties of tungsten trioxide from first-principles calculations

“…However these calculations are computationally very demanding, and they are still prohibitive for a system such as WO 3 , with 256 electrons per unit cell. Therefore, following previous work on ionic crystals [63][64][65], we adopted a model Fröhlich Hamiltonian (FH)[30- 32], assuming that the interaction of electrons with optical phonons is the dominant effect contributing to e-ph interaction. We note that the CBM of WO 3 is at Γ and thus the use of a FH is a reasonably accurate approximation.…”

Photoluminescence Characterization of Cadmium Sulphide (CdS) Nanowires for Polarization Studies

“…Calculating the polarization anisotropy, ρ, using this equation for the CdS nanowires gives 0.87 (0.89) using dielectric constant ε ⊥ (ε || ) of CdS as 8.5 (9.25) from Table 1 (Lee, Kim, Dutta, & Stroscio, 1997). Therefore, to study the polarization anisotropy, PL studies were done with and without the polarization filter and PL intensity were recorded for parallel and perpendicular polarization with two orientations of the sample having light propagating parallel to the nanowire axis in one orientation and light propagating perpendicular to the nanowire axis in other orientation.…”

Phonons on Quantum Epitaxial Structures Based on Wide Band Gap Materials

“…Alternatively, for the case where the short range interatomic forces are dominant, the LO-TO splitting will be small and in this case the TO and LO mode of each symmetry group will occur in a relatively narrow band. Raman studies of quasi modes in AN have been reported by Filippidis et al [32] and Bergman et al [49]. In these studies the ^-vector direction was achieved by rotating the crystallite by an angle 6 relative to a fixed laboratory coordinate system, as depicted in Fig.…”