| Abstract: | In this paper a variational principle has been formulated for obtaining an approximate solution of Poisson's equation for the potential of a donor ion embedded in Si. A comparison of a two parameter approximate analytical potential with the exact numerical potential shows excellent agreement for several electron concentrations. It is also found that the present theory, using the concept of a “spatially variable dielectric constant,” leads to a donor-ion potential which deviates significantly from the potential of Dingle, which has been the traditional starting point of calculations of electron mobility limited by ionized-impurity scattering. |
