Abstract
In this paper, we present the modeling of long pulse laser thermal damage of Silicon using analytical solutions. Firstly, the two-dimensional axisymmetric physical model of the temperature rise problem for long pulse laser heating is established. By using the integral transformation method, analytical solutions of the heat conduction equation are obtained. Then, temperatures in the surface and inside of the Silicon are modeled, and the change characteristics and rules of the radial and axial distributions of temperature are studied. Finally, an analytical expression for the melting damage threshold of Silicon is given, and the threshold of different radial distances is analyzed.
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