Dynamical thermal conductivity of bulk semiconductor crystals

作者：Ezzahri Younes^*; Joulain Karl

来源：Journal of Applied Physics, 2012, 112(8): 083515.

DOI：10.1063/1.4759366

The paper discusses the behavior of the dynamical lattice thermal conductivity kappa(Omega) of bulk semiconductor crystals. The calculation approach is based on solving Boltzmann-Peierls phonon transport equation in the frequency domain after excitation by a dynamical temperature gradient, within the framework of the single relaxation time approximation and using modified Debye-Callaway model. Our model allows us to obtain a compact expression for kappa(Omega) that captures the leading behavior of the dynamical thermal conduction by phonons. This expression fulfils the causality requirement and leads to a convolution type relationship between the heat flux density current and the temperature gradient in the real space-time domain in agreement with Gurtin-Pipkin theory. The dynamical behavior of kappa(Omega) is studied by changing temperature as well as different intrinsic and extrinsic parameters. Our calculations show the cut-off frequency of kappa(Omega) to be sensitive to the changes of some of these parameters. The paper investigates also the applicability of Shastry%26apos;s sum rule (SSR) in the frame work of Boltzmann theory. It is shown that within the frame work of Callaway approximated form of the collision operator and time independent Callaway parameter, the SSR breaks down and is only valid when resistive processes dominate normal processes, for which case, we derive an alternative expression to the classical limit of the expectation of the thermal operator introduced in Shastry%26apos;s formalism.

• 出版日期2012-10-15