Diffusion characteristics of boron and phosphorus in polycrystalline silicon

Abstract

Grain boundary diffusion of dopants (boron and phosphorous) in silicon is discussed. The appropriate models and equations are presented both for semi-infinite and for thin film boundary conditions. Data reported in the literature for both thick and thin samples have generally been analyzed using models appropriate to diffusion in a homogeneous semi-infinite substrate. These data were reanalyzed using the appropriate boundary conditions and a more realistic model of the inhomogeneous nature of diffusion in polycrystalline samples. It was shown that, even though the relation between diffusion depth and time may be the same from bulk and grain boundary models, the diffusion coefficients determined from assuming the homogeneous semi-infinite solid may be several orders of magnitude in error for the pre-exponential factor, and the activation energy will also be wrong. Grain boundary diffusion coefficients for arsenic, boron and phosphorus in silicon were determined.