Example

Question:

Suppose a pure Si crystal has \(5 \times 10^{28}\) atoms m\(^{-3}\). It is doped by 1 ppm concentration of pentavalent As. Calculate the number of electrons and holes. Given that \( n_i = 1.5 \times 10^{16} \) m\(^{-3}\).

Solution:

Thermally generated electrons (\( n_i \sim 10^{16} \) m\(^{-3}\)) are negligible compared to those produced by doping.
Therefore, \( n_e \approx N_D \).
Since \( n_e n_h = n_i^2 \), the number of holes: \[ n_h = \frac{n_i^2}{n_e} = \frac{(1.5 \times 10^{16})^2}{5 \times 10^{22}} = \frac{2.25 \times 10^{32}}{5 \times 10^{22}} = 4.5 \times 10^9~\text{m}^{-3} \]