The elements arsenic and phosphorus are common dopants in crystalline silicon that impart semiconductor properties to it via the introduction of p-type carriers into the silicon lattice. The doping process is carried out by a solid-state diffusion process at high temperature.

a. Compare the diffusion coefficients of arsenic and phosphorus in crystalline silicon at 600 and 1000 C. Why might such a high temperature be needed for the doping process?
b. At what temperature is the diffusion rate of arsenic-silicon equal to 12% of that for phosphorus-silicon? State all assumptions.