Fermi function numeric calculation - Example

1. Calculate the Fermi function at 6.25 eV if E_F = 6.25 eV and T = 300 K. Repeat at T = 950 K assuming that the Fermi energy does not change. At what temperature does the probability that an energy level at E = 5.95 eV is empty equal 1 %.
   Answer: At 300 K the probability of occupancy equals:
   f(E = 6.5 eV) = 1/(1+ exp(0.25/0.0258)) = 6.5 x 10^-5
   At 950 K (where kT = 81.8 meV) the probability equals:
   f(E = 6.5 eV) = 1/(1+ exp(0.25/0.0818)) = 4.5 %
   The occupancy probability at E = 5.95 must equal 0.99 or:
   f(E = 5.95 eV) = 1/(1+ exp(-0.3 eV/kT)) = 0.99
   so that
   exp(-0.3 eV/kT) = 0.01 or T = - q 0.03/k/ln(0.01) = 758 K