Transient analysis of thermal distorsion in a silicon substrate on incidence of a single soft x-ray FEL pulse

A. Rubens B. de Castro; A. R. Vasconcellos; R. Luzzi

doi:10.1117/12.887393

18 May 2011 Transient analysis of thermal distorsion in a silicon substrate on incidence of a single soft x-ray FEL pulse

A. Rubens B. de Castro, A. R. Vasconcellos, R. Luzzi

Author Affiliations +

Proceedings Volume 8077, Damage to VUV, EUV, and X-ray Optics III; 80770A (2011) https://doi.org/10.1117/12.887393
Event: SPIE Optics + Optoelectronics, 2011, Prague, Czech Republic

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.

Citation Download Citation

A. Rubens B. de Castro, A. R. Vasconcellos, and 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); https://doi.org/10.1117/12.887393

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