Laser-based measurement of elastic and mechanical properties of layered polycrystalline silicon structures with projection masks

Abstract

Using Rayleigh surface acoustic waves (SAW), the Young's modulus, the density and the thickness of polycrystalline Silicon-Germanium (SiGe) films deposited on silicon and SiO 2 were measured, in excellent agreement with theory. The dispersion curve of the propagating SAW is calculated with a Boundary Element Method (BEM)-Model based on Green's functions.The propagating SAW is generated with a nanosecond laser in a narrowband scheme projecting stripes from a mask on the surface of the sample. For this purpose a glass mask and a liquid crystal display (LCD) mask are used. The slope of the SAW is then measured using a probe beam setup. From the wavelength of the mask and the frequency of the measured SAW, the dispersion curve is determined point by point.Fitting the BEM-Model to the measured nonlinear dispersion curve provides several physical parameters simultaneously. In the present work this is demonstrated for the Young's modulus, the density and the thickness of SiGe films.The results from the narrowband scheme measurement are in excellent agreement with separated measurements of the thickness (profilometer), the density (balance) and the Young's modulus (nanoindenter).

Linearized forward and inverse problems of the resonant ultrasound spectroscopy for the evaluation of thin surface layers

“…The relative frequency shifts Dx/x are plotted both in linear coordinates (left vertical axis) and in logarithmic coordinates (right vertical axis), which enables the comparison of all models for the whole range of relative thicknesses h/d 3 . It is clearly seen that for all the displayed modes, the linearized approximation sufficiently agrees with the nonlinear models for h/d 3 indeed fails for h/d 3 10 À4 (oscillations for mode No. 1 and a systematic declination for mode No.…”

“…(4)] induce incomparably smaller errors than the final linearization of the direct problem. However, for h/d 3 10 À2 , the linearized direct problem gives sufficiently accurate results.…”

“…Either the times-of-flight of extremely short ultrasonic pulses through the thickness of the layer can be measured (picosecond pulse-echo technique), 1,2 wherefrom the longitudinal elastic modulus in direction perpendicular to the layer can be estimated, or the dispersion curves of Rayleigh waves propagating along the surface on which the layer is deposited can be experimentally determined, which enables the velocity of surface waves in the layer to be evaluated. [3][4][5][6] The third possibility is to use the resonant ultrasound spectroscopy 7-10 (RUS), i.e., to compare the resonant spectra of free elastic (ultrasonic) vibrations of a chosen specimen of the substrate material measured with and without the layer deposited on it. As long as the difference between these two spectra is measurable, the in-plane (possibly anisotropic) properties of the layer can be estimated.…”

Mess- und Analysemethoden in der Laserakustik bei breitbandiger Laseranregung

“…Wird ein einzelner, fokussierter Laserpuls zur Ultraschallanregung verwendet, erzeugt dieser Ultraschallwellen mit einer großen Frequenzbandbreite [5]. Andererseits kann eine schmalbandige Anregung realisiert werden, indem Projektionsmasken für die gewünschte Wellenlänge oder das Interferenzmuster durch die Überlagerung zweier Teilstrahlen verwendet werden [6,7]. Überschreitet die Energiedichte des Anregelaserstrahls die Zerstörschwelle des zu untersuchenden Materials, ist die Anregung ablativ, ansonsten thermoelastisch.…”

Coherent control of surface plasmon polariton mediated optical transmission

“…These waves can be generated by a laser pulse in structures similar to those showing EOT [20][21][22]. SAWs are known to change the dielectric function of the material in which they propagate via the photoelastic effect [23] and coherent control of acoustical phonons has been demonstrated [24].…”