Sketch the Fermi-Dirac distribution function, F(E), alongside the energy band diagram for an n-type semiconductor, indicating the position of the Fermi level, EF, and the donor levels.  
 
Sketch the energy band diagram for a metal, indicating the position of the Fermi level.
 
At a temperature of 300 K silicon has an energy gap of 1.1 eV. Calculate the probability that a particular electron energy state at the bottom of the conduction band for intrinsic silicon is occupied at 300 K. 

Use the expression for F(E) on the formula sheet to derive the probability that, for this semiconductor, 

i)  a state at the bottom of the conduction band is occupied at 0 K

ii)  a state at the top of the valence band is occupied at 0 K. 

Explain how the values you obtain can be deduced from physical considerations alone.