Mumbai University > First Year Engineering > Sem 1 > Applied Physics 1

Marks: 3M

Year: May 2016

Given:

$T_1= 27^0 C = 300K$

$E_R = 5.6 eV=5.6 x 1.6 x 10^{-19} J$

Find:

$f (E_c)$

Solution:

The probability that an electron being thermally promoted to the conduction band is given as

$f(E_c) = \frac{1}{1 + exp \bigg(\frac{E_g}{2KT}\bigg)}$

where k is the Boltzmann constant.

Substituting the given data for $E_R$, T, k into above equation, we get

$f (E_c) = \frac{1}{1 + exp\bigg(\frac{5.6 \times 1.6 \times 10^{-19}}{2 \times 1.38 \times 10^{-23}\times 300}\bigg)}$

$f (E_c) = 1.7 \times 10^{-47}$

Since the probability $f (E_c)$ is extremely small, electrons cannot be thermally promoted to the conduction band of diamond at $27^0 C$.