Design of phonon optics devices based on multilayred semiconductor heterostructures of nanometer dimension

合成半导体异质结构或超晶格不仅可以应用于纳米尺寸的电子器件，而且可以用于设计各种声子光学器件，如声子镜、声子反射器、声子谐振器等。在制造这些器件的想法的刺激下，我们提出了基于多个超晶格结构的声子系统。关键思想是利用这样一个事实，即在周期超晶格中，长波长声子会发生布拉格反射，或者超晶格在由超晶格的周期性引起的频率间隙内充当声子的不透明屏障。如果超晶格的周期为30 a或更长，则声子的最低频率间隙在亚太赫兹范围内产生。1太赫兹声子的波长通常为30-50 A，它们在纯固体中的平均自由程在低温下约为1毫米或更长。因此，这些高频声子在纳米范围内的线性系统中以弹道方式传播。在本项目中，我们研究了声子在超晶格中传播的动力学性质，这是以前没有讨论过的。通过数值模拟研究了声子包入射到半导体超晶格声子单势垒和双势垒结构上的时间演化。在远离障碍物的渐近区域，可以观察到传输包和反射包的时延和时延。为了解释这些模拟结果，我们在本项目中开发了声子与由周期超晶格组成的一维弹性势垒相互作用相关的传输和反射时间的分析计算。推导出了精确而有用的相位时间近似表达式，它能很好地描述波矢量空间中狭窄声子包的延迟时间。这些结果提供了声子通过超晶格传输的动力学方面的重要信息，因此对设计声子光学器件是有用的。少

Synthetic semiconsuctor heterostructures or superlattices are useful not only for the application to electronic devices of nanometer dimensions but also for the design of various phonon optics devices such as the phonon mirror, the phonon reflector, the phonon resonator, and so on. Stimulated by the idea for fabricating the these devices, we have proposed systems for phonons based on multiple superlattice structures. The key idea is to utilize the fact that in perioid superlattices Bragg reflections occur for long wavelength phonons, or the superlattices act as opaque barriers for phonons within the frequency gaps induced by the periodicity of a superlattice. If a periodicity of a superlattice is 30 A or longer, the lowest frequency gap of phonons is produced in the sub-THz range. The wavelength of 1-THz phonons is typically 30-50 A and their mean free path in pure solids is about 1 mm or longer at low temperatures. Therefore, these high-frequency phonons propagate ballilstically throu … More gh the systems with linear dimensions in the nanometer range.In the present project, we studied the dynamical properties of phonons propagating in superlattices, which had not been discussed before. Explicitly, we studied by numerical simulations the time evolutions of phonon packets incident on the single and double-barrier structures for phonons realized by semiconductor superlattices. In the asymptotic regions far from the barriers both the time delay and advance are observed for the transmitted and reflected packets. To explain these results of the simulations, we developed in the present project, the analytical calculations for the transmission and reflection times associated with the interaction of phonons with one-dimensional elastic barriers composed of periodic superlattices. The exact and useful approximate expressions for the phase times which well describe the delay times for phonon packets narrow in the wave-vectors space were derived. These results provide important information on the dynamical aspect of phonon transmission through superlattices and hence are useful for designing phonon optics devices. Less