Simulation of Phosphorus Diffusion in Silicon Using a Pair Diffusion Model with a Reduced Number of Parameters

Abstract

In this work, we describe a general model for dopant diffusion via dopant‐defect pairs containing all possible charge states of species under the assumption of local equilibrium for electronic processes, but not for chemical processes. We present a method by which the unknown parameters can be reduced efficiently. With the aid of this method all the backward reaction rate coefficients can be replaced by the forward reaction rate coefficients and two new parameters. Introducing the intrinsic diffusion coefficient, one of the two new parameters can be replaced, too. Thus, we have only one constant parameter instead of all backward reaction rate coefficients, and additionally the model automatically yields the correct results in the intrinsic case. In our model we use the barrier energy for the Frenkel pair mechanism and the point defect parameters which we have determined from gold diffusion experiments previously. We present several simulations of phosphorus diffusion and compare the results with experiments published in the literature. Very good agreement between simulations and experiments has been obtained. As a result we suggest a complete set of parameters for phosphorus diffusion in silicon for the temperature range from 900 to 1200°C.