The accurate modeling of temperature response of semiconductor production wafers during rapid thermal processing

When a production semiconductor with un-relaxed ion-implanted regions or wafer is subject to external irradiation, a portion of the incident energy is absorbed within the wafer volume, rather than at the surface. The volume absorption will alter the distribution energy within the wafer, resulting in temperature non-uniformity. In order to access the contribution of the volume absorption and emission processes the mathematical model and Fortran code was developed. The energy equation is solved in conjunction with the radiation problem. The one-dimensional transient problem is solved using the Crank-Nicholson scheme. Input to the model includes material properties specified in a look-up table form. The spectral ellipsometry is used to determine the optical properties of the ion-implanted model. The model shows the difference in the surface temperature of the wafer similar to the results observed experimentally