Computer modeling of the temperature rise and carrier concentration induced in silicon by nanosecond laser pulses

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Abstract
A set of simultaneous equations for lattice temperature, carrier concentration, and carrier temperature is numerically solved for typical nanosecond laser pulses. The temperature dependences of the thermal conductivity and lattice absorption are included, as well as the free carrier absorption and reflection. Carrier diffusion and electronic heat conduction are taken into account, and Auger recombination is assumed to be the dominant recombination mechanism. The calculations show that while free carrier absorption plays a major role in annealing with 1.06-μm radiation, only lattice absorption is important at wavelengths corresponding to photon energies well above the band gap. The Auger recombination coefficient is not a sensitive parameter, and the energy relaxation time does not affect the annealing results unless it is comparable to the pulse length. The results of the calculations are consistent with the hypothesis that the observed increase in silicon reflectivity is due to surface melting of the material. When literature values are used for all relevant parameters, the model predicts melt threshold energies which are in agreement with published experimental values.