The Fermi-Dirac Distribution for semiconductors is given by where E is the electron energy EF the Fermi energy T the absolute temperature and k is the Boltzmann’s constant 1380 x 10-23 JK-1 In a part

To solve for E, we need to rearrange the Fermi-Dirac Distribution equation to isolate E:

Taking the natural logarithm of both sides:

Rearranging:

Now we can substitute the given values:

Simplifying:

Multiplying both sides by -1/kT:

Finally, solving for E:

Therefore, the probability of finding an electron at an energy of E is 89% when E = 0.874 eV (to three decimal places).