Question

Determine for what energy above ef (in terms of kt) the f-d probability function is within 1% of the boltzmann approximation.

Answer 1

Consider the expression for the difference of Fermi-Dirac function and Boltzmann approximation.

Here, is the energy above Fermi level, is Fermi energy, is Boltzmann constant and is temperature.

Multiply in numerator and denominator.

The value of is very small. Neglect the value of the expression.

Hence, the energy above Fermi energy the Fermi–Dirac probability function is within 1 percent of the Boltzmann approximation is .