Unified Model for Laser Doping of Silicon from Precursors

Laser doping of silicon with the help of precursors is well established in photovoltaics. Upon illumination with the constant or pulsed laser beam, the silicon melts and doping atoms from the doping precursor diffuse into the melted silicon. With the proper laser parameters, after resolidification, the silicon is doped without any lattice defects. Depending on laser energy and on the kind of precursor, the precursor either melts or evaporates during the laser process. For high enough laser energies, even parts of the silicon's surface evaporate. Here, we present a unified model and simulation program, which considers all these cases. We exemplify our model with experiments and simulations of laser doping from a boron oxide precursor layer. In contrast to previous models, we are able to predict not only the width and depth of the patterns on the deformed silicon surface but also the doping profiles over a wide range of laser energies. In addition, we also show that the diffusion of the boron atoms in the molten Si is boosted by a thermally induced convection in the silicon melt: the Gaussian intensity distribution of the laser beam increases the temperature-gradient-induced surface tension gradient, causing the molten Si to circulate by Marangoni convection. Laser pulse energy densities above H > 2.8 J/cm² lead not only to evaporation of the precursor, but also to a partial evaporation of the molten silicon. Without considering the evaporation of Si, it is not possible to correctly predict the doping profiles for high laser energies. About 50% of the evaporated materials recondense and resolidify on the wafer surface. The recondensed material from each laser pulse forms a dopant source for the subsequent laser pulses.