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Self-similar solutions for a free boundary problem in the doping of semiconductors

We study the development of concentration profiles in a semi-infinite slab of semi-conductor material, in which impurities have been implanted at a high concentration. When the implant is uniform throughout the slab, no impurities can pass through the face of the slab, and the vacancy concentration at the surface is kept at its equilibrium value, it is shown that the density profiles of impurities, vacancies and host atoms may have self-similar form. The analysis is constructive and yields qualitative properties of the profiles and the front.