Two-dimensional diffraction of plasma, thermal, and elastic waves generated by an infrared laser pulse in semiconductors

When a $1064\mathrm{nm}$ laser pulse is focused at the surface of silicon, it has been observed that the material contracts whereas heating should produce expansion. In addition to the usual thermal acoustic source, a nonthermal sound generation results of photoexcitation of electron-hole pairs. To describe the optoacoustic effect in semiconductors, it is thus necessary to account for thermoelastic and other deformation sources simultaneously. The acoustic signal is then strongly dependent on the nature of the space-time evolution of both the photoexcited charge carriers and temperature. In this paper, assuming line focusing of the laser pulses, a model is implemented that accounts for the two-dimensional (2D) character of charge carrier motion and heat conduction. Relevant differential equations are coupled together and with the wave motion equation to describe acoustic diffraction. Three sets of equations are linearized in a 2D Fourier domain and solutions are found with an appeal to convenient boundary conditions. The conditions for 2D diffraction of plasma, thermal, and elastic waves are analyzed. Experiments are performed on a $5\mathrm{mm}$ thick silicon plate with a Nd:yttrium aluminum garnet laser that delivers $20\mathrm{ns}$ pulses. Signals are measured for epicenter and off epicenter positions. Very good agreement is obtained with calculated signals for both positions demonstrating that both sound generation mechanism and anisotropy are accurately taken into account. In addition to the expected material contraction accompanying quasilongitudinal bulk acoustic waves, the other remarkable feature is the change in the shape of the signals observed for a same angle, but for two laser energies. The results emphasize the nonlinear photoacoustic response of the material, with respect to the laser energy. It is accurately represented by the calculations, assuming prevailing of Auger electron-hole recombination process and nonlinear dependency of charge carrier lifetime with respect to its density.

Figure 1

Group velocity curves (km/s) in the plane $(x_1,x_2)$ of the silicon sample.

Figure 2

Pulsed and CW lasers location with respect to the sample geometry.

Figure 3

Experimental (up) and calculated (down) signals in silicon for two source-receiver directions: $\theta =0$ (a) and (c) and $\theta =35°$ (b) and (d); and two incident laser energies: $I_1=7.5\mathrm{mJ}{\mathrm{m}}^{-1}$ (a) and (b) and $I_2=200\mathrm{mJ}{\mathrm{m}}^{-1}$ (c) and (d).