Question

Q3. Find the probability of occupying an energy state 0.2ev above the Fermi energy at 100K and 1000K. Also calculate the probability for the energy state 0.2eV below the Fermi level for same temperatures and comment on the results.​

Answer 1

At absolute temperature T=0, the probability is zero that any state with energy above the Fermi energy is occupied.

P(E)=

e

(E−E

F

)

lkT

+1

1

where k is the Boltzmann constant and E

F

is the Fermi energy. Now, E–E

F

=0.0620 eV

and

(E−E

F

)lkT=(0.0620eV)/(8.62×10

−5

eV/K)(320K)=2.248,

so

P(E)=

e

2.248

+1

1

=0.0955.

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