Existence of a giant hypersonic elastic mirror in porous silicon superlattices

Abstract

In this work, we theoretically predict the possibility to obtain a giant hypersonic elastic mirror in porous silicon superlattices by using a phononic heterostructure. The heterostructure is composed of a tandem of multiple phononic crystal lattices with periods in the range 37–167 nm, which recently have been experimentally reported [L. C. Parsons and G. T. Andrews, Appl. Phys. Lett. 95, 241909 (2009)]. Considering the scalability of the eigenvalues of the elastic wave equation, the lattices are chosen such that each stop band can be superposed to obtain a larger overall stop band. Theoretical evidence of a giant hypersonic phononic mirror for longitudinal and transverse vibrations is found in the gigahertz range.

Cavity-type hypersonic phononic crystals

“…Progress in phononic crystals, supported by recent advances in nanofabrication techniques, led to functional hypersonic (GHz range) phononic structures [7,[18][19][20][21][22][23][24][25][26]. Recent years have witnessed a growing interest in hypersonic phononics due to new ways of manipulation of the phonon propagation in periodic structures and potential technological applications such as dual bandgap structures [27], acousto-optical devices [28,29] with phonon-photon interaction in a cavity, heat management [1,30] and elastic mirrors [31]. However, a detailed understanding of phonon propagation in the hypersonic regime remains a key issue for phonon band structure engineering at high frequencies.…”

Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance

“…Recent ultrasonic measurements along the modulation direction of films with square-wave, 4,7 sinusoidal, 5 and linearly graded modulation 10 variations in the porosity have reported the existence of one-dimensional phononic band gaps in the bulk longitudinal acoustic phonon band structure; these band gaps were centered at frequencies on the order of 1 GHz. Additionally, theoretical and experimental studies of stacked phononic crystal mirrors 6,9 have shown the existence of giant phononic band gaps in the MHz frequency range of these structures. As well, Brillouin light scattering studies on binary periodic porous silicon (p-Si) superlattices (SLs) showed a complex bulk longitudinal acoustic band structure, 3,8 with a second longitudinal mode branch observed for phonons directed along the superlattice modulation axis.…”

“…Multilayered mesoporous silicon films with a spatial modulation in the porosity, and hence in the elastic impedance, exhibit rich acoustic phonon band structures. [1][2][3][4][5][6][7][8][9][10] The resulting bulk acoustic dispersion curves contain multiple zone-folded branches which may be accompanied by the appearance of forbidden phonon frequency bands, or in analogy to photonic crystals, phononic band gaps. Recent ultrasonic measurements along the modulation direction of films with square-wave, 4,7 sinusoidal, 5 and linearly graded modulation 10 variations in the porosity have reported the existence of one-dimensional phononic band gaps in the bulk longitudinal acoustic phonon band structure; these band gaps were centered at frequencies on the order of 1 GHz.…”

Thermal tuning of omnidirectional reflection bands in one-dimensional finite phononic crystals

“…3,4 In recent years, it has been shown theoretically and experimentally that, under some conditions, 1D PnCs can exhibit omnidirectional reflection (ODR), which means that in some frequency ranges incident elastic waves coming from a substrate undergo total reflection independent of polarization and incidence angle. [5][6][7][8] That is, 1D PnCs exhibit an absolute band gap similar to either to the 2D or 3D phononic band gap. The advantage of achieving ODR bands using 1D PnCs lies in the fact that their design is more practical and their analysis requires only relatively simple analytical and numerical calculations.…”