arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1406.7341cond-mat.mtrl-sci
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半导体合金中的超扩散热传导I.理论基础

Superdiffusive heat conduction in semiconductor alloys -- I. Theoretical foundations

Bjorn Vermeersch, Jesus Carrete, Natalio Mingo, Ali Shakouri

摘要:

半导体合金的有效热导率对测量频率有很强的依赖性。到目前为止,这种准弹道行为只被解释为现象学,提供有限的洞察到底层的热输运动力学。在这里,我们表明,半导体合金中的准弹道热传导是由Lévy超扩散。通过求解具有从头算声子色散和散射率的玻尔兹曼输运方程,揭示了具有分形空间维数$1 < α< 2$和均方能量位移超线性时间演化$σ^2(t) \sim t^β (1 < β< 2)$的输运机制.的特征指数直接互连的顺序$n$的主要声子散射机制$τ\sim ω^{-n} (n>3)$和累积电导率谱$κ_Σ(τ;Λ)\sim (τ;Λ)^γ$解决松弛时间或平均自由程通过简单的关系$α= 3-β= 1 + 3/n = 2 - γ$。合金内部的准弹道输运不再受布朗运动控制,而是受Lévy动力学控制。这对用改进的傅里叶理论解释热反射(TR)测量具有重要意义。InGaAs和SiGe的实验$α$值,确定通过TR分析与一种新的Lévy热形式主义,符合从头算BTE预测的百分之几。我们的研究结果导致更深入,更准确的定量理解的物理纳米热流实验。

英文摘要:

Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasi-ballistic behaviour has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasi-ballistic 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 $1 < α< 2$ and superlinear time evolution of mean square energy displacement $σ^2(t) \sim t^β (1 < β< 2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $τ\sim ω^{-n} (n>3)$ and cumulative conductivity spectra $κ_Σ(τ;Λ)\sim (τ;Λ)^γ$ resolved for relaxation times or mean free paths through simple relations $α= 3-β= 1 + 3/n = 2 - γ$. The quasi-ballistic transport inside alloys is no longer governed by Brownian motion, but instead dominated by Lévy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental $α$ values for InGaAs and SiGe, determined through TR analysis with a novel Lévy 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.

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