Chapter 15, Problem 15E.2AE

Interpretation Introduction

Interpretation:

The energy above Fermi energy $\left(1.00eV\right)$ at which the probability has fallen to $0.25$ at $298K$ has to be calculated.

Concept Introduction:

Probability can be calculated using Fermi-Dirac distribution as follows,

  $f\left(E\right)=\frac{1}{e^{\frac{\left(E-E_F\right)}{kT}}+1}$

This expression can be simplified as follows, when $E>E_F.$

  $f\left(E\right)\approx e^{\frac{-\left(E-E_F\right)}{kT}}$

Where,

$f\left(E\right)=$ probability

$E_F=$ Fermi energy

$E=$ energy

$k=$ Boltzmann constant

$T=$ Temperature