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A two-dimensional method based on numerical solution of the Boltzmann transport equation has been developed for calculating ion implantation profiles. The method is capable of treating arbitrarily contoured surfaces containing multiple layers of different materials. Calculations yield the concentration profile of the implanted ion, an estimate of the damage distribution, and concentration profiles from recoiled target atoms. Substantial differences are seen from one-dimensional and point-response two-dimensional methods when the interfaces are far from planar.