Question

The Fermi level of a n-type semiconductor at a temperature of 300 K is at a position 0.3 eV
below the conduction band. Find the position of fermi level at a temperature 320 K wrt to
the conduction band
(1) 0.26 eV (2) 0.28 eV (3) 0.34 eV (4) 0.32 eV

Answer 1

For the initial state of 300 K we can write

$$E_{F1}-E_C=kT_1\text{ln}\frac{n}{N_C}=-0.3 \text{ eV},$$

hence

$$k\text{ln}\frac{n}{N_C}=\frac{-0.3}{T_1}=-0.001 \text{ eV/K}.$$

For the next state for 320 K

$$E_{F2}-E_C=kT_2\text{ln}\frac{n}{N_C}=-0.001\cdot320=-0.32\text{ eV},$$

or

$$E_{F2}=E_C-0.32 \text{ eV}.$$