Local wafer temperature non-uniformity correction with laser irradiation

The application of correcting small temperature non-uniformity on Silicon wafers using local irradiation with spatially scanning laser beams was analyzed. The objective of the study was to understand the specifications of such a laser beam to elevate the temperature of a wafer locally by 1 to 5°C. A detailed analytical model has been developed for predicting power level, exposure time, scanning speed, and the beam characteristics. The model has been derived by solving the three dimensional transient heat equation using Green´s function approach. Various wafer characteristics, such as the surface reflectivity, material absorption coefficient, and thermal properties have been built into the formulation as parameters, so that several what-if scenarios can be evaluated with ease and accuracy. Existing analytical methods in literature for prediction of laser irradiated substrate temperatures assume infinite thickness of the substrate. In this study, it has been found that this approximation could result in significant errors particularly for the present application of interest, where the wafer thickness is finite and the focus is on relatively small local temperature rise in short exposure durations. Numerical models were also developed to mimic some particular cases using a commercial finite volume method solver. The numerical and analytical results show an excellent agreement. The analytical model allows for a more diverse range of variables than the finite volume numerical models.