Dispersion considerations affecting phonon-mass impurity scattering rates

Abstract

This work presents a derivation of phonon-mass impurity scattering rates applicable to dispersive phonon systems. This form of mass impurity scattering is compared with the previously accepted form assuming a nondispersive crystal by calculating the thermal conductivity of Si. The mass impurity scattering rate determined from this approach considering dispersion is in excellent agreement with theoretical calculations, where the scattering rates determined from the dispersionless model under predict the role of phonon-mass impurity scattering in thermal transport by over an order of magnitude

Analytical Models of Phonon–Point-Defect Scattering

“…The following section reviews the full derivation of the Callaway/Klemens model to generalize beyond mass difference scattering alone, clarify assumptions made in the derivation, and discuss the model's dependence on phonon dispersion, a topic garnering recent interest 16,44 .…”

“…Previous studies have explicitly compared the κ L predictions of the Klemens model using various approximations of the phonon dispersion relation, ranging from the Debye model to polynomial or trigonometric fits of the dispersion 16,44 . For example, in a study of two Half-Heusler systems, three different approximations were used to describe the phonon structure of the two materials-the Debye model, a truncated Debye model, and a cubic polynomial fit of the full dispersion relation.…”

A quasi-continuum thermomechanical model for phonon damping analysis of single crystal silicon nano-resonators

“…3. (τ −1 nn ) avg for Si isotope impurity scattering can be approximated based on the scattering rates on point defects as [29] (…”

“…The stored strain energy E st is taken as the same value calculated from Eq. (29) in the theoretical model. The equivalence of E st in both MD and our model is described in Appendix A.…”

Raman Measurements of Optical Phonon Scattering in Sub-Micron Si_(1-x)Ge_x Films

“…The dependence can be rewritten as ω 2 /λ 2 using the linear dispersion relationship and q = 2π/λ where λ is the phonon wavelength, which shows that the scattering rate is equally dependent on both frequency and wavelength. Additionally, several other works have highlighted the importance of correctly describing the dispersion in phonon transport [57][58][59].…”