Thornber–Feynman carrier-optical-phonon scattering rates in wurtzite crystals

Abstract

It is well known that the carrier-optical-phonon scattering rates dominate the carrier-acoustic-phonon scattering rates in many polar materials of interest in electronic and optoelectronic applications. Furthermore, it is known that the Fröhlich coupling constants for carrier-optical-phonon in many materials is close to or great than unity, calling into question the validity of scattering rates based on the Fermi golden rule. In a celebrated paper by Thornber and Feynman it was shown that that the large Fröhlich coupling constant in polar materials does indeed lead to substantial corrections to the Fermi golden rule scattering rates. These large corrections are due to the fact that for strong coupling constants, the first-order perturbative approach underlying the Fermi golden rule does not take into account the presence of many phonons interacting simultaneous with the carrier. In this paper, the Thornber–Feymnan scattering rates for carrier-optical-phonon interactions are derived for several technologically important wurtzite semiconductors—BN, ZnO, CdS, CdSe, ZnS, InN, and SiC- and it is shown that the commonly used Fermi golden rule scattering rates must be corrected by factors ranging up to an order-of-magnitude. The corrections to the Fermi golden rule reported herein have widespread impact on carrier transport for materials with large Fröhlich coupling constants.

Electric field – velocity relation for strongly coupled Fröhlich polaron in emerging 2D materials

“…Thus, the phonon absorption rate cannot be neglected here at room temperature and have been duly accounted for in equation ( 14) to model energy loss per unit distance. From figure 2 and table 1, we see that the mean time between the emission ranges from∼0.9×10 −14 -1.7× 10 -14 sec whereas, the FGR is valid only when the electron phonon interaction time scale w  t 2 LO [9,12] which lies in the range∼3.9×10 -14 -6.9×10 -14 sec. It is evident that the mean time between phonon emissions is even smaller than the minimum interaction time required for the validity of the FGR.…”

“…As an example, it was first noted in the context of 3D materials [11] that, for the materials with LO phonon energy in the range 50-100 meV the mean free time between collisions (based on perturbative treatment) becomes as small as 2 x -10 15 sec which is further reduced at high temperatures where phonon absorption becomes significant. Consequently, in our previous work on 3D wurtzite [12] and cubic materials [13] we investigated the energy loss per unit distance (electric field ) versus electron velocity in high alpha materials in the purview of nonperturbative path integral formalism by Thornber and Feynman (TF) [11] and the FGR model and found that the FGR model underestimates the energy lost by the electron as a result of the Fröhlich interaction, as it neglects the situation of many phonons interacting with the electron simultaneously and the quantum interferences between the emitted phonons in successive collisions; in such situations the scattering events cannot be separated in time. The correction factors for the energy loss for the FGR was about an order of magnitude and higher for materials with a in the range 0.21-0.93 for wurtzite and 0.1-0.7 for cubic materials.…”

Electron–optical-phonon scattering rates in cubic group III-nitride crystals: path-integral corrections to Fermi golden rule matrix elements

“…The minimization of polaron energy as represented by the above equation yields the ground state energy, G, for a specific value of variational parameters v 0 and w 0 . This approach has been shown to yield moderate corrections to the Fermi golden rule for GaAs and AlAs and significant corrections for wurtzite III-nitrides [16][17][18] but to our knowledge these techniques have not been applied previously to model corrections to the Fermi golden rule for the technologically important cubic III-nitrides, the subject of this paper.…”