What is the occupation number at room temperature of an electron state lying (a) 0.1 eVabove the Fermi level and (b) 0.1 eV below the Fermi level?

The occupation number of an electron state at a certain energy level can be calculated using the Fermi-Dirac distribution function, which is given by:

f(E) = 1 / (1 + exp[(E - E_f) / kT])

where:

• E is the energy of the state,
• E_f is the Fermi energy,
• k is the Boltzmann constant, and
• T is the temperature.

(a) For an electron state 0.1 eV above the Fermi level, the energy difference (E - E_f) is 0.1 eV. At room temperature (T = 300 K), and using the value of the Boltzmann constant in eV/K (k = 8.6173 x 10^-5 eV/K), the Fermi-Dirac distribution function becomes:

f(E) = 1 / (1 + exp[(0.1) / (8.6173 x 10^-5 x 300)])

Calculate the value inside the exponential function and then calculate the value of the Fermi-Dirac distribution function to find the occupation number.

(b) For an electron state 0.1 eV below the Fermi level, the energy difference (E - E_f) is -0.1 eV. The Fermi-Dirac distribution function becomes:

f(E) = 1 / (1 + exp[(-0.1) / (8.6173 x 10^-5 x 300)])

Again, calculate the value inside the exponential function and then calculate the value of the Fermi-Dirac distribution function to find the occupation number.