Question

The electron mobility \( \mu_n \) in a non-degenerate germanium semiconductor at 300 K is 0.38 m$^2$/Vs. The electron diffusivity \( D_n \) at 300 K (in cm$^2$/s, rounded off to the nearest integer) is _________.

• A. 26
• B. 98
• C. 38
• D. 10

Hint:

To find the electron diffusivity, use the Einstein relation involving the Boltzmann constant, temperature, charge of an electron, and mobility. Don't forget to convert the result to the correct units.

Answer 1

The Correct Option is B

The electron diffusivity \( D_n \) is related to the electron mobility \( \mu_n \) by the Einstein relation: \[ D_n = \frac{k_B T}{q} \cdot \mu_n, \] where:
\( k_B = 1.38 \times 10^{-23} \, {J/K} \) (Boltzmann constant),
\( T = 300 \, {K} \) (temperature),
\( q = 1.6 \times 10^{-19} \, {C} \) (charge of an electron).
Substituting the given values: \[ D_n = \frac{(1.38 \times 10^{-23}) \cdot 300}{1.6 \times 10^{-19}} \cdot 0.38. \] \[ D_n = \frac{4.14 \times 10^{-21}}{1.6 \times 10^{-19}} \cdot 0.38 = 0.098 \, {m}^2/{s} = 98 \, {cm}^2/{s}. \] Thus, the correct answer is (B).