This paper describes an analytical method to deduce the steady-state, laser-induced temperature profile in an isotropic silicon substrate with a Guassian-shaped hole on its surface. Although effects of first-order specular reflection are included, the model is only applicable to holes that are not too deep. On carrying out a separate numerical finite-element analysis, the analytical method was found to be reasonably accurate. For a laser beam with a Gaussian intensity profile, it was found that the difference in results obtained by the two methods increases and then decreases as the Gaussian-shaped etched hole gets deeper. The analytical model tends to predict a lower peak temperature rise on the surface. Limitations of the analytical method are also discussed.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Acoustics and Ultrasonics
- Surfaces, Coatings and Films