Isotope scattering of large-wave-vector phonons in GaAs and InSb: Deformation-dipole and overlap-shell models

Abstract

Scatterings of near-zone-boundary phonons by isotopic disorder in diatomic GaAs and InSb crystals are studied theoretically. In multiatomic lattices the scattering rate depends importantly on the vibrational amplitudes of constituent atoms. We find that the wave-vector dependences of these amplitudes, which are predicted by sortle lattice models, show quite dissimilar behaviors as compared to others. The typical examples investigated in this paper are the deformation-dipole model and the overlap-shell model. With the use of these models the frequency dependence of the relaxation time of phonons is calculated. Both models, however, predict the relaxation time of about 0.1 J1-sec for 1-THz T A phonons in GaAs, which is at least 1 order of magnitude shorter than the lifetime reported by Ulbrich et al.

Anharmonic properties inMg2X(X=C,SiChernatynskiy1, Phillpot2 2015Phys. Rev. B17280View full textAdd to dashboardCite

“…The presence of the point defects introduces two distinct effects: mass disorder scattering and alteration of the local interatomic constants around the defect. For a low concentration of the defects, perturbation theory can be expected to apply: it adds an additional term in the BTE 17,57 linearly proportional to the scattering parameters, Γ, which are simple sum of contributions from mass and elastic disorder. The mass disorder term permits rigorous calculation, 24 including the contribution from different sublattices 57 ; however, the effect of altered interatomic interactions is much less well understood.…”

Keeping it Cool

“…BAs has a large mixture of B isotopes, however, it has relatively small contributions from isotopic scattering, smaller even than cubic BN, BSb, and diamond (Table I). The reason for this is that for BAs, the large As to B mass ratio causes the atomic motion of the short wavelength acoustic phonons, which give the largest contributions to , to be dominated by the heavier As mass [21,35], and As happens to be isotopically pure. As a result, both the RT pure and nat for BAs are similar to that of diamond (Table I).…”

“…Scattering of phonons by isotopes can also play an important role in reducing in some materials and is included using a standard perturbation theory approach [21,22] to determine for naturally occurring isotope concentrations, nat . Expressions for the intrinsic phonon-phonon scattering rates and phonon-isotope scattering rates have been given previously [7,12,21]. In real materials, sample-specific thermal resistance from extrinsic defects, grain boundaries, and other impurities can lower from the values given here.…”

“…In high quality bulk materials around RT, the dominant thermal resistance for acoustic (a) and optic (o) phonons arises from this threephonon scattering, with the most important scattering channels involving three acoustic phonons (aaa) and two acoustic phonons combining with one optic phonon (aao) [20]. Scattering of phonons by isotopes can also play an important role in reducing in some materials and is included using a standard perturbation theory approach [21,22] to determine for naturally occurring isotope concentrations, nat . Expressions for the intrinsic phonon-phonon scattering rates and phonon-isotope scattering rates have been given previously [7,12,21].…”

High-Resolution Raman and Luminescence Spectroscopy of Isotope-Pure ²⁸Si¹²C, Natural and ¹³C – Enriched 4H-SiC

“…SiC [3]. The main mechanism of line broadening is elastic scattering of the phonons induced by mass defects [4]; according to the theory [8] the magnitude of the broadening  of a mode with frequency  is proportional to  2 g|e| 4 (), where () is the phonon density of states, e is the relevant phonon eigenvector and g is the relative mass variance. In the case of FLA and FTA modes the weight of the Si eigenvector dominates in e and the relative mass variance is much smaller for Si than for C. In addition, the factor  2 contributes another order of magnitude in diminishing  for the low-energy modes in comparison to the optical modes, which explains why the isotope-induced broadening is not observed with our experimental resolution (about 0.8 cm -1 ).…”