Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations

Journal Article · Tue Feb 10 00:00:00 EST 2015 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.91.085202· OSTI ID:1369778

Vermeersch, Bjorn ^[1]; Carrete, Jesús ^[2]; Mingo, Natalio ^[2]; Shakouri, Ali ^[1]

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1. Purdue Univ., West Lafayette, IN (United States)
2. Commissariat a l'Energie Atomique et aux Energies Alternatives (CEA), Grenoble (France); LITEN Inst., Grenoble (France)

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 Lévy 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 ${\sigma }^2\left(t\right)~t^{\beta }(1<\beta <2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $\tau ~{\omega }^{–n}(n>3)$ and cumulative conductivity spectra ${\kappa }_{\Sigma }(\tau ;\Lambda )~{(\tau ;\Lambda )}^{\gamma }$ 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 Lévy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental $\alpha$ values for InGaAs and SiGe, determined through TR analysis with a novel Lévy heat formalism, match ab initio BTE predictions within a few percent. Finally, our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat-flow experiments.

• Research Organization: Energy Frontier Research Centers (EFRC) (United States). Center for Energy Efficient Materials (CEEM)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0001009
• OSTI ID: 1369778
• Alternate ID(s): OSTI ID: 1180790
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 91, Issue 8; Related Information: CEEM partners with the University of California, Santa Barbara (lead); Purdue University; Los Alamos National Laboratory; National Renewable Energy Laboratory; ISSN 1098-0121
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE