Ultrafast Laser Induced Thermo-Elasto-Visco-Plastodynamics in Single Crystalline Silicon
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A comprehensive model for describing the fundamental mechanism dictating the interaction of ultrafast laser pulse with single crystalline silicon wafer is formulated. The need for establishing the feasibility of employing lasers of subpicosecond pulse width in Laser Induced Stress Waves Thermometry (LISWT) for single crystalline silicon processing motivated the work. The model formulation developed is of a hyperbolic type capable of characterizing non-thermal melting and thermo-elastoviscoplastic deformation as functions of laser input parameters and ambient temperature. A plastic constitutive law is followed to describe the complex elasto-viscoplastic responses in silicon undergoing Rapid Thermal Processing (RTP) annealing at elevated temperatures. A system of nine first-order hyperbolic equations applicable to describing 3-D elasto-viscoplastic wave motions in silicon is developed. The group velocities of certain selected frequency components are shown to be viable thermal indicators, thus establishing the feasibility of exploiting nanosecond laser induced propagating stress waves for the high-resolution thermal profiling of silicon wafers. Femtosecond laser induced transport dynamics in silicon is formulated based on the relaxation-time approximation of the Boltzmann equation. Temperature-dependent multi-phonons, free-carrier absorptions, and the recombination and impact ionization processes governing the laser model and carrier numbers are considered using a set of balance equations. The balance equation of lattice energy and equations of motion of both parabolic and hyperbolic types are derived to describe the complex thermo-elastoplastodynamic behaviors of the material in response to ultrafast laser pulsing. The solution strategy implemented includes a multi-time scale axisymmetric model of finite geometry and a staggered-grid finite difference scheme that allows both velocity and stress be simultaneously determined without having to solve for displacements. Transport phenomena initiated by femtosecond pulses including the spatial and temporal evolutions of electron and lattice temperatures, along with electron-hole carrier density, are found to be functions of laser fluence and pulse width. The femtosecond laser heating model that admits hyperbolic energy transport is shown to remedy the dilemma that thermal disturbances propagate with infinite speed. Non-thermal melting fluence is examined favorably against published experimental data. That it is feasible to explore femtosecond laser induced displacement and stress components for 1K resolution thermal profiling is one of the conclusions reached.