The grain-boundary diffusion of dopants was reviewed. Literature data for thick and thin samples were analyzed by using an homogeneous semi-infinite substrate. It was concluded that grain boundary diffusion could be readily analyzed by using the correct model. It was shown that the ratio of grain boundary to bulk diffusivity ranged from 103 to 105 and was a function of temperature and dopant type. Data obtained from thin film systems were shown to be consistent with the Gilmer-Farrell thin film model. This model was used to deduce that diffusion in the polycrystalline material could be described by:

D(cm2/s) = 6.6 x 10-4exp[-1.87(eV)/kT]

A Physically Based Phenomenological Model using Boltzmann-Matano Analysis for Boron Diffusion from Polycrystalline Si intoSingle Crystal Si. A.D.Buonaquisti, W.Carter, P.H.Holloway: Thin Solid Films, 1983, 100[3], 235-48