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

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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