Observation of hypersonic phononic crystal effects in porous silicon superlattices

Abstract

Brillouin light scattering experiments were carried out on porous silicon superlattices with modulation wavelengths in the range 37-167 nm. Phonon frequencies deduced from the Brillouin spectra show good agreement with those obtained from an elastic continuum model for a system with one-dimensional periodicity. Evidence for the existence of a hypersonic phononic bandgap and zone-folded longitudinal acoustic phonons is reported. © 2009 American Institute of Physics. ͓doi:10.1063/1.3275742͔It is well known that the introduction of artificial spatial periodicity in the elastic properties of a materials system results in Brillouin zone-folding. Such folding is often accompanied by the appearance of bandgaps in the phonon frequency spectrum and thus materials systems that exhibit this phenomenon are promising candidates for phononic crystals. Porous silicon ͑-Si͒ is especially interesting in this regard since its elastic properties can be varied over nanometer length scales and because it can be readily integrated into existing silicon technologies.In this letter, the results of Brillouin scattering experiments on -Si superlattices ͑SLs͒ are reported. Good agreement is obtained between measured phonon frequencies and those calculated from a one-dimensional elastic continuum model. Clear evidence for the existence of an acoustic bandgap and for zone-folding of longitudinal acoustic phonons is presented.Two sets of -Si SLs and associated single layer films were synthesized by anodization of p + -type ͑100͒-oriented crystalline silicon ͑5-20 m⍀ cm͒ in an electrolyte composed of 1͑49% HF͒:1͑C 2 H 5 OH͒. Each set was made using a different supply of HF with one solution yielding single layer films with gravimetrically-determined porosities of 0.59 ͑J = 149 mA/ cm 2 ͒ and 0.52 ͑J = 101 mA/ cm 2 ͒, while the other resulted in films with porosities of 0.56 ͑J = 149 mA/ cm 2 ͒ and 0.46 ͑J = 101 mA/ cm 2 ͒. The difference in film porosity for the same applied current density is ascribed to slight differences in HF concentration in the two solutions. The single layer films were ϳ5 m thick. SLs with a binary periodic variation in porosity were formed by alternating the current density between the above values. Etching times were chosen so that the constituent layer thicknesses, d 1 and d 2 , were nearly equal ͓see Fig. 1͑a͔͒. SLs with modulation wavelengths of D = d 1 + d 2 from 37 nm to 167 nm were made for the Brillouin experiments. The porosities, refractive indices, and elastic properties of the SL constituent layers were taken to be the same as those of single layer films formed under identical conditions. It is noted that images like that of Fig. 1͑a͒ were not obtained for SLs with D Ͻ 500 nm. Indirect evidence of prescribed SL formation, however, was provided by measurements of overall SL film thickness ͑ϳ5 m͒ which was within 10% of the value calculated using known etch parameters.Brillouin scattering experiments were carried out in air at room temperature using a backscattering geometry ͓see Fig. 1͑b͔͒. Incident light o...

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

“…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. Furthermore, these light scattering experiments gave evidence of an additional Brillouin peak which was attributed to a surface-localized mode with a frequency within a one-dimensional hypersonic phononic band gap of the bulk longitudinal band structure centered at $16 GHz.…”

“…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.…”

Probing near-normally propagating bulk acoustic waves using pseudo-reflection geometry Brillouin spectroscopy

“…Experiments were also done on two porous silicon films made from p + -type (100)-oriented crystalline silicon under conditions similar to those given in Ref. 10. The films were ∼4.5 μm thick and had porosities of (58 ± 3)% and (50 ± 4)%.…”

“…1,[8][9][10] Unfortunately, this geometry allows access to bulk phonons of only a single wavevector magnitude.…”

One-Dimensional Phononic Crystals

“…Among these applications, one can mention (1) omnidirectional band gaps [55][56][57][58], (2) the possibility to engineer small-size sonic crystals with locally resonant band gaps in the audible frequency range [59], (3) hypersonic crystals [60][61][62][63] with high-frequency band gaps to enhance acousto-optical [49][50][51] or optomechanical [64,65] interaction and to realize stimulated emission of acoustic phonons [66], and (4) the possibility to enhance selective transmission through guided modes of a cavity layer inserted in the periodic structure [6,67] or by interface resonance modes induced by the superlattice/substrate interface [68][69][70]. The advantage of 1D systems lies in the fact that their design is more feasible and they require only relatively simple analytical and numerical calculations.…”