Question

When a semiconducting material is doped with an impurity, new acceptor levels are created. In a particular thermal collision, a valence electron receives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the top edge of the valence band and that the temperature T is equal to 300 K, find the energy of the acceptor levels above the valence band.

Answer 1

Before the thermal excitation, the electron was located at the top of the valence band.
After the thermal excitation, the electron was present in the acceptor level.
This implies that the energy gap between the valence band and the acceptor level is equal to the energy absorbed by the electron in thermal excitation.
Thus,
2kT = Energy gap between the acceptor level and the valence band

\[\Rightarrow E = 2 \times 1 . 38 \times  {10}^{- 23}  \times 300  \] 

\[ \Rightarrow E = (2 \times 1 . 38 \times 3) \times  {10}^{- 21} \] J

\[ \Rightarrow E = \left( \frac{6 \times 1 . 38}{1 . 6} \right) \times \frac{{10}^{- 21}}{{10}^{- 19}} \] eV

\[ \Rightarrow E = \left( \frac{6 \times 1 . 38}{1 . 6} \right) \times  {10}^{- 2}   \]eV 

\[ \Rightarrow E = 5 . 175 \times  {10}^{- 2}  \] eV

\[ \Rightarrow E = 51 . 75  \] meV