Assume Silicon (bandgap 1.12 eV) at room temperature (300K) with the Fermi level located exactly in the middle of the bandgap. Answer the following...

Assume Silicon (bandgap 1.12 eV) at room temperature (300K) with the Fermi level located exactly in the middle of the bandgap. Answer the following questions.

a) What is the probability that a state located at the bottom of the conduction band is filled?

b) What is the probability that a state located at the top of the valence band is empty?

c) What is the density of states (in 1/eV-cm3) in the conduction band, gc(E), at an energy 26 meV above Ec?

d) What is the density of states (in 1/eV-cm3) in the valence band, gv(E), at an energy 26 meV below Ec?

Hint: For part c and d, you must perform the calculations in SI units, and convert the unit of final results back to 1/eV-cm3.