Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations

Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasiballistic behavior has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasiballistic heat conduction in semiconductor alloys is governed by Levy superdiffusion. By solving the Boltzmann transport equation (BTE) with ab initio phonon dispersions and scattering rates, we reveal a transport regime with fractal space dimension 1 < alpha < 2 and superlinear time evolution of mean-square energy displacement sigma(2)(t) similar to t(beta)(1 < beta < 2). The characteristic exponents are directly interconnected with the order n of the dominant phonon scattering mechanism tau similar to omega(-n)(n > 3) and cumulative conductivity spectra. K-Sigma(tau; Lambda) similar to (tau; Lambda)(gamma) resolved for relaxation times or mean free paths through the simple relations alpha = 3 - beta = 1 + 3/n = 2 -gamma. The quasiballistic transport inside alloys is no longer governed by Brownian motion, but instead is dominated by Levy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental a values for InGaAs and SiGe, determined through TR analysis with a novel Levy heat formalism, match ab initio BTE predictions within a few percent. Our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat-flow experiments.