An n-type Si sample has been doped with 1015 phosphorus atoms cm-3. The donor energy level for P in Si is 0.045 eV below the conduction band edge energy.

a.   Calculate the room temperature conductivity of the sample.

b.   Estimate the temperature above which the sample behaves as if intrinsic.

c.   Estimate to within 20 percent the lowest temperature above which all the donors are ionized.

d.  Sketch schematically the dependence of the electron concentration in the conduction band on the temperature as log(n) versus 1/T, and mark the various important regions and critical temperatures.  For each region draw an energy band diagram that clearly shows from where the electrons are excited into the conduction band.

e.  Sketch schematically the dependence of the conductivity on the temperature as log(σ) versus 1/T and mark the various critical temperatures and other relevant information.