Photoacoustic study of elastic deformations in silicon membranes

Abstract

In an optically excited semiconductor micromechanical structure, photogenerated carriers (plasma waves) can produce elastic deformations (local strains and stresses)–plasmaelastic (PE) deformations. On the other hand, the generation of excess carriers will produce heat due to carrier thermalization and recombination processes. The generated heat can produce other elastic deformations–thermoelastic (TE) deformations. For these two components of elastic deformation, it is possible to consider two types of elastic displacements (two mods of elastic vibrations): elastic expanding and elastic bending. A theoretical model of the photoacoustic (PA) signal for optically excited Si membranes is given, which includes thermal diffusion (TD), TE, and PE mechanisms, in order to study elastic expansion and bending. The relations for the PA amplitude and the phase of elastic expanding and bending in the excited membrane are derived. Analysis of the PA signal indicates that the TD component is dominant for all thicknesses and practically the entire range of observed frequencies. The calculated PA amplitude and phase spectra show that the PA elastic expanding component has a significant influence on the total PA signal at low frequencies. On the other side, the calculated PA spectra show that the PA elastic bending component has a significant influence on the total PA signal at high frequencies. Experimental PA signals of Si membranes were measured using the sample-gas-microphone detection technique with a transmission configuration in relation to the modulation frequency of the optical excitation for different membrane thicknesses. The experimental PA spectra were compared with the theoretical ones.