Numerical simulation of transient thermoreflectance of thin films in the picosecond regime

Transient thermoreflectance techniques, especially the picosecond transient thermoreflectance method (PTTR), provide a means of determining the thermo-physical properties of a thin film and of measuring thin film properties and temperature during manufacturing. In these techniques a pump and probe method is used to heat the sample and to measure the reflectance from it. It has been shown using a plane wave analysis and a one-dimensional thermal analysis based on uniform spatial irradiation that internal reflections caused by the spatial temperature field significantly affect the accuracy of the method in some materials. The internal reflection mechanism alters the temperature field as compared to that predicted without it. Criteria to define the range of importance of the internal reflection mechanism have been developed based on these assumptions. These results are extended using numerical analysis to investigate the effects of an incident Guassian beam instead of uniform irradiation. The code includes mechanisms to describe the temperature and intensity dependent absorption coefficients and index of refraction. It is found that the two-dimensional effects decrease the one dimensional normalized reflectance change by 24%. A technique for the incorporating the code into the analysis of the PTTR is described.