Acoustic investigation of porous silicon layers

Fonseca, R. J. M. da; Saurel, J; Foucaran, A.; Camassel, Jean; Massone, E.; Taliercio, Thierry; Boumaïza, Y.

doi:10.1007/bf00352128

Cited by 54 publications

(48 citation statements)

References 18 publications

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“…However, excepting some simple empirical relations [2], a general theoretical modeling tool able to recover experimental data and to predict material properties at particular pore sizes and shapes is still missing. As the continuum theory fails to apply at the length scale of pores in nano-PSi we propose a discrete homogenization model and show that under certain regularity assumptions (such as uniformity of shapes and distributions of the pores) the method predicts a mechanical macroscopic behavior that fits remarkably well the experimental data reported in [3][4][5][6] for a wide range of porosities. The method can be easily extend in order to include much more complicated situations such as: other porous semiconductors, more complex microscopic symmetries, compositional effects (like back-bond oxidation) and mechanical related behavior including joint bulk and surface effects.…”

mentioning

confidence: 52%

“…The right-hand-side in (6) is linear in E as it can be easily seen by inspection in (3) and (4). Using the solution of (6) in (2) we are lead toŴ (E) = W (E, {ũ(E)}) so that the macroscopic elasticity can be computed as…”

Section: Discrete Homogenizationmentioning

confidence: 96%

“…The simplest pore shape is the union of three cylinders with equal square cross-section, described by P = [3][4][5][6]. Only in the case of a pore with cubic symmetry the macroscopic response has the same symmetry as the bulk Si.…”

Section: Elastic Constants For Nano-psi With Cubic Symmetrymentioning

confidence: 99%

“…where R = C 12 /C 11 while, experimental data for the Young modulus are those reported in [3][4][5][6] obtained respectively using: X-ray diffraction, acoustic methods, nano-indentation and Brillouin spectroscopy. We remark that:…”

Section: Elastic Constants For Nano-psi With Cubic Symmetrymentioning

confidence: 99%

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Modeling macroscopic elasticity of porous silicon

Magoariec

Danescu

2009

Phys. Status Solidi (c)

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In this paper we present a model able to predict the elastic properties of nano‐porous silicon (nano‐PSi). Initially developed by Keating [1] for the elastic response of nonprimitive lattices in the harmonic regime, the model accounts for near neighbors (NN) and next‐near‐neighbors (NNN) interactions and leads to numerical results in very good agreement with existent experimental data.We performed numerical tests covering a wide range of porosities between bulk silicon and 90% porosity.We also evidence the significant interplay between the cubic symmetry of the bulk silicon and the shape of the pores. This is of special interest in the case of nano‐PSi due to directional electrochemical etching process and leads, in general, to macroscopic anisotropic elastic response. Our method can be easily extended to cover other porous materials and/or more surface effects like, for example, the back‐bond oxidation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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mentioning

confidence: 52%

Section: Discrete Homogenizationmentioning

confidence: 96%

Section: Elastic Constants For Nano-psi With Cubic Symmetrymentioning

confidence: 99%

Section: Elastic Constants For Nano-psi With Cubic Symmetrymentioning

confidence: 99%

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Modeling macroscopic elasticity of porous silicon

Magoariec

Danescu

2009

Phys. Status Solidi (c)

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“…The mass density q j is a function of the porosity and is described by q j ¼ q 0 ð1 À P j Þ, where q 0 ¼ 2:330 g=cm 3 is the mass density of bulk silicon and P j is the porosity in the j-th layer. The acoustic velocity dependence on porosity is given empirically by 25,26 …”

Section: Theoretical Modelmentioning

confidence: 99%

Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

Lazcano

Arriaga

Aliev

2014

Journal of Applied Physics

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We report the theoretical calculations and the experimental demonstration of acoustic Bloch oscillations and Wannier-Stark ladders in linear tilted multilayer structures based on porous silicon. The considered structures consist of layers with constant porosity alternated by layers with a linear gradient in the parameter g ¼ 1=v 2L along the growth direction in order to tilt the acoustic band gap. The purpose of this gradient is to mimic the tilted electronic miniband structure of a superlattice semiconductor under an external electric field. In this way, acoustic Wannier-Stark ladders of equidistant modes are formed and they were experimentally confirmed in the transmission spectrum around 1.2 GHz. Their frequency separation defines the period of the acoustic Bloch oscillations. We fabricated three different structures with the same thicknesses but different values in the g parameter to observe the effect on the period of the Bloch oscillations. We measured the acoustic transmission spectra in the frequency domain, and by using the Fourier transform, we obtained the transmission in the time domain. The transmission spectra of the fabricated samples show acoustic Bloch oscillations with periods of 27, 24, and 19 ns. The experimental results are in good agreement with the transfer matrix calculations. The observed phenomenon is the acoustic counterpart of the well known electronic Bloch oscillations. V C 2014 AIP Publishing LLC.

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Structural and Acoustic Properties of ZnO Thin Films Prepared by Spray

Amlouk

Touhari

Belgacem

et al. 1997

phys. stat. sol. (a)

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ZnO thin films have been grown on glass substrates using the spray pyrolysis technique. The depositions were carried out in the range of substrate temperatures from 400 to 500 °C. Highly c‐axis oriented ZnO films, having a strong (002) X‐ray diffraction line, are obtained at lower temperatures (400 to 420 °C). Film surfaces were analysed by contact Atomic Force Microscopy (AFM). On the other hand, we have used scanning microscopy performed at a frequency of 570 MHz to reach a microechography and acoustic signature V(z) of our samples in order to understand their qualities.

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Acoustic investigation of porous silicon layers

Cited by 54 publications

References 18 publications

Modeling macroscopic elasticity of porous silicon

Modeling macroscopic elasticity of porous silicon

Experimental and theoretical demonstration of acoustic Bloch oscillations in porous silicon structures

Structural and Acoustic Properties of ZnO Thin Films Prepared by Spray

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