Accurate analytical approximations for error function and its integral (semiconductor junctions)

Analytical expressions for the error function and the integral of the error function, which can be used in the calculation of electric field and potential distribution in semiconductor junctions with a Gaussian doping profile, are presented. For both functions, the complete x-interval, ranging from 0 to infinity, is handled with a single expression. The absolute accuracy of the analytical expressions for all x-values is better than +or-1.6*10^-9 for the error function and better than +or-3.7*10^-8 for the integral of the error function.