Transient Analysis Of Thermal Distortion In A Silicon Substrate On Incidence Of A Single Soft X-ray Fel Pulse

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. © 2011 SPIE.8077De Castro, A.R.B., Vasconcellos, A.R., Luzzi, R., Thermo-elastic analysis of a silicon surface under X-ray free-electron-laser irradiation (2010) Rev. Sci. Instrum., 81. , art 073102de Castro A. R. B., Vasconcellos A. R. and Luzzi R., "Erratum: Thermo-elastic analysis of a silicon surface under X-ray freeelectron-laser irradiation (Rev. Sci. Instrum., 81, art 073102 (2010))", Rev. Sci. Instrum., submitted (2011)Luzzi, R., Vasconcellos, A.R., Ramos, J.G., (2002) Predictive Statistical Mechanics: A Non-equilibrium Ensemble Formalism, , Kluwer Academic, DorbrechtBoguliubov, N.N., (1962) Studies in Statistical Mechanics i, , North Holland, AmsterdamLandau, L.M., Lifschitz, E.M., (1986) Theory of Elasticity, , Pergamon, OxfordMorse, P.M., Feshbach, H., (1953) Methods of Theoretical Physics, , McGraw-Hill Book Company, N YorkDe Castro, A.R.B., Möller, T., Time-dependent strain analysis of mirrors illuminated with intense femtosecond pulses in the soft X-ray spectral range (2005) Rev. Sci. Instrum., 76. , art 06310