Lixin Shen

Date of Award

Fall 2003

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Weizhong Dai


Heat transport through thin films or micro-objects is of vital importance in microtechnology applications. For instance, metal thin films are important components of microelectronic devices. The reduction of the device size to microscale has the advantage of enhancing the switching speed of the device. On the other hand, size reduction increases the rate of heat generation, which leads to a high thermal load on the microelectronic devices. Heat transfer at the microscale is also important for the thermal possessing of materials with a pulsed-laser. Examples in metal processing are laser micromachining, laser patterning, laser processing of diamond films from carbon ion implanted copper substrates, and laser surface hardening. In thermal processing of materials, microvoids may be found owing to thermal expansion. When such defects begin in the workpiece, their thermal energy in the neighborhood of the defects may be amplified, resulting in severe material damage and, consequently, total failure of the thermal processing. A detailed understanding of the way in which the local defects dissipate the thermal energy is then necessary not only to avoid the damage but also to improve the efficiency of the thermal processing.

The heat transport equation at the microscale is different from the traditional heat diffusion equation because a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study, we consider the heat transport equation in three-dimensional spherical coordinates and develop a three-level finite difference scheme for solving the heat transport equation in a microsphere. Stability of the scheme is proved in this dissertation. It is shown that the scheme is unconditionally stable. The scheme is then employed to investigate the temperature rise in a gold sphere subjected to a short-pulse laser. Numerical results are obtained for the cases that the laser irradiation is symmetric on the surface of the sphere, and the laser irradiation is from the top to a portion of the surface of the sphere.