Phonon Transmission Rates in Randomly Stacked Superlattices

我用数值和解析方法研究了半导体材料随机堆叠超晶格中的声子传输率（AlAs和GaAs）的透射率，数值计算得到的透射率随频率的变化呈现出尖峰和低谷，其模式是随机超晶格组成层的结构所特有的，在无规超晶格中，在许多可能的结构上，平均透射率与无规超晶格的绝对结构因子的平方具有相似的频率依赖性，而在无规超晶格的界面处没有多重散射。利用绿色函数计算了随机超晶格样品的平均透射率，证明了与声子局域化长度成反比的Lyapunov指数与随机超晶格绝对结构因子的平方成正比，并证明了平均透射率以及与之相关的普适透射率涨落可以用系统长度与局域化长度之比来描述.

I have numerically and analytically investigated phonon transmission rates in randomly stacked superlattices fabricated of semiconducting materials (AlAs and GaAs), using the transfer matrix method and Green's functions.The transmission rates which are numerically obtained show sharp peaks and dips with respect to frequency, whose pattern is peculiar to configuration of constituent layrs of random superlattices, resulting in a finger print of random superlattices.The average transmission rates over a number of possible configurations of constituent layrs exhibit similar frequency dependence to that of squared absolute structure factor of the random superlattices without multiple scattering at the interfaces between the constituent layrs.I have analytically derived the averaged transmission rates over the sample of random superlattices by means of Green's functions.I exhibit that the Lyapunovexponent, which is inverse of the localization length of phonons, is proportional to the squared absolute structure factor of the random superlattices and that the averaged transmission rates and related quantities such as universal transmission fluctuations can be described in terms of the ratio of system length to localization length.