18 May 2011 Transient analysis of thermal distorsion in a silicon substrate on incidence of a single soft x-ray FEL pulse
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Abstract
We discuss the dynamics of a silicon surface after incidence of a short, high energy pulse in the soft X-ray range. We focus on time-delays long enough after pulse incidence, so that the absorbed energy can be seen as a nonuniform time-dependent heat distribution in the solid. A model is developed using techniques of non-equilibrium hydro-thermodynamics, considering just the longitudinal and transverse acoustic phonon systems in the excited solid. The general theory leads to Maxwell-Cattaneo partial differential equations for the material medium n(r,t) and the energy h(r,t) volume densities; these reduce to the diffusion equation for the temperature T(r,t) and the usual thermo-mechanical elastic equation for the strain u(r,t) on further simplification. Here we solve the Maxwell-Cattaneo equation for T(r,t) and compare to previous results where the diffusion equation was used instead; the Maxwell- Cattaneo equation predicts faster cooling at short (dozens of fs, say) time delays. Previously obtained results for the strain field are briefly recalled.
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A. Rubens B. de Castro, A. R. Vasconcellos, R. Luzzi, "Transient analysis of thermal distorsion in a silicon substrate on incidence of a single soft x-ray FEL pulse", Proc. SPIE 8077, Damage to VUV, EUV, and X-ray Optics III, 80770A (18 May 2011); doi: 10.1117/12.887393; https://doi.org/10.1117/12.887393
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