A phosphorus‑doped silicon wafer has a donor concentration $N_D=2\times 10^{17}{\text{cm}}^{-3}$ and a measured resistivity of $0.02\Omega \cdot \text{cm}$. Assuming electrons are the only significant carriers, determine the electron mobility ${\mu }_n$. (Take $q=1.6\times 10^{-19}\text{C}$.)

Step-by-step solution

1. Calculate the conductivity: $\sigma =\frac{1}{\rho }=\frac{1}{0.02}=50{\text{Scm}}^{-1}$.
2. For an n‑type semiconductor where holes are negligible, $\sigma =q{N}_D{\mu }_n$.
3. Re‑arrange to find mobility: ${\mu }_n=\frac{\sigma }{q{N}_D}$.
4. Substitute the values: $q{N}_D=1.6\times 10^{-19}\times 2\times 10^{17}=3.2\times 10^{-2}{\text{Ccm}}^{-3}$.
5. Thus ${\mu }_n=\frac{50}{3.2\times 10^{-2}}\approx 1.56\times 10^3{\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$.
6. Round to two significant figures: ${\mu }_n\approx 1.6\times 10^3{\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$.

Concept tested: Conductivity and carrier mobility in doped silicon

Published 11 September 2026 · How this solution was prepared and checked