Calculate and plot the n-type doping efficiency for Phosphorus donor in Si at room temperature for the range of Nd from 1015 cm-3 to 5x1019 cm-3 . Assume that the donor ionization energy is 45meV. Doping efficiency is the fraction of donors that are ionized, Nd+ /Nd . Do it (a) using Boltzmann's approximation (b) exactly (Fermi-Dirac, so you -need to do numerical integration)