Question

The drift mobility of electron in an n-type Si crystal doped with \( 10^{16} \, \text{cm}^{-3} \) phosphorous atoms is \(\underline{\hspace{1cm}}\) (round off to nearest integer).

Hint:

For drift mobility in semiconductors, use the relation \( \sigma = q n \mu \), where \( q \) is the charge, \( n \) is the charge concentration, and \( \mu \) is the drift mobility.

Answer 1

Correct Answer: 210

The electrical conductivity \( \sigma \) for a semiconductor is given by the equation:
\[ \sigma = q n \mu \] Where:
- \( q = 1.6 \times 10^{-19} \, \text{C} \) (charge of an electron),
- \( n = 1.45 \times 10^{10} \, \text{cm}^{-3} \) (intrinsic charge concentration of Si),
- \( \mu = 1350 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1} \) (drift mobility).
Rearranging the formula to solve for drift mobility \( \mu \), we get:
\[ \mu = \frac{\sigma}{q n} \] Substituting the given values:
\[ \mu = \frac{1350}{(1.6 \times 10^{-19})(1.45 \times 10^{10})} = 210 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}. \] Thus, the drift mobility of electrons in the n-type Si crystal is approximately \( 210 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1} \).