The Effect of an Internal Optically Absorbed Heat Source on the Photo-Thermoelastic Fields of a Silicon Half-Space Reinforced with 35 vol.% SiC Fibers: An Eigenvalue Approach

The photo-thermoelastic response of a silicon half-space reinforced by 35 vol.% SCS-6 SiC fibers aligned with the depth direction is studied when modulated light is absorbed inside the medium. Both consequences of the Beer–Lambert absorption are included in the governing equations: the thermalization of the photon energy in excess of the band gap, which acts as an internal heat source Q = Q0e−γx, and the photo-generation of excess carriers, which acts as a volumetric source G = G0e−γx in the carrier diffusion equation. The illuminated surface is in smooth contact with a rigid transparent window; it is thermally insulated except for the heat released by surface recombination, and the carriers recombine there with a finite surface recombination velocity, so that no surface value is prescribed. The effective thermal, expansion and elastic properties of the composite are obtained from micromechanics. The coupled equations are nondimensionalized, reduced by the normal mode technique and solved as a first-order vector–matrix system whose general solution is the sum of four decaying eigenmodes and a closed-form particular solution, which exists whenever the absorption coefficient differs from the characteristic roots. The solution is verified symbolically, against an independent finite-difference solution (agreement better than 3 × 10−4) and against the prescribed-amplitude case of earlier work. For 1 W cm−2 modulated at 10 Hz the surface temperature amplitude is 23–35 mK, the excess-carrier density reaches 5 × 1021 m−3 and the surface stresses reach 18 kPa. Weakly absorbed near-infrared light (1060 nm) lowers the surface temperature by 31% and the surface stress σyy by 41% relative to 980 nm, and moves the carrier maximum 0.1 mm below the surface, whereas strongly absorbed light behaves as surface heating.