Question

a) (10 points) Calculate the occupation probability f(E), that is the probability that a state will be occupied, at 293 K for a state at the bottom of the conduction band in germanium. The energy of the gap is Eg= 0.67 eV and assume that the Fermi energy lies in the middle of the gap. b) (20 points) Aluminum is a good electrical conductor with a density of 2.7 g/cm3 and a molar mass of 27 g/mol. Each aluminum atom contributes 3 free electrons for conduction with mobility u = 0.0012 m?/Vs. Calculate the electrical conductivity and the mean free path between collisions using the quantum model for conduction.

Answer 1

B)

Solution: - given :-: density = 2.7 glems molar mass 279 Imol Mobility , ME 0.0012 may Each aluminium atom contributes 3.free electrons. Electrical conductivity = net m Relaxation time I - mu .. as drift velocity Vo - UE - EET T = mel е. :, Electrical conductivity P² ( o an ne² mel e m

r=neel Now , volume = molar mass Dens nsity E 27 2.7 10cm3 Free elections of aluminjum atom 3 No. of free electrons in one mole of Al =3 No. :: electron density 3 No cm-3 10 = 3 X 6.02 X 1023 10 = 18.06 X 1022 cm3 = 1.806 X 1023 cm -3 nel :: Electrical conductivity 1.806 x 1023 X 1.6 X 10-19 X 0.0012 - (10-2)3 -0.0034675 X 10 23-1976 0.00 346 45 x 10 10 F o = 3,467X10

Mean free path between collisions! As there is no external electric field 2. Mean free path = 0