Question

A silicon sample is uniformly doped with donor type impurities with a concentration of 10¹⁶/cm³. The electron and hole mobilities in the sample are 1200 cm²/V-s and 400 cm²/V-s respectively. Assume complete ionization of impurities. The charge of an electron is 1.6 × 10^-19C. The resistivity of the sample (in Ω-cm) is _____

Answer 1

Concept:

The conductivity of the sample \({\rm{\sigma }} = {\rm{q}}\left( {{\rm{n}}{{\rm{\mu }}_{\rm{n}}} + {\rm{p}}{{\rm{\mu }}_{\rm{p}}}} \right)\) if, n ≫ p, we can approximate \({\rm{\sigma }} \approx {\rm{qn}}{{\rm{\mu }}_{\rm{n}}}\)

Application: 

The conductivity of the sample \({\rm{\sigma }} = {\rm{q}}\left( {{\rm{n}}{{\rm{\mu }}_{\rm{n}}} + {\rm{p}}{{\rm{\mu }}_{\rm{p}}}} \right)\) since, n ≫ p, we can approximate \({\rm{\sigma }} \approx {\rm{qn}}{{\rm{\mu }}_{\rm{n}}}\)

Using \({\rm{n}} = {{\rm{N}}_{\rm{D}}} = {10^{16}}{\rm{c}}{{\rm{m}}^{ - 3}}\), we have \({\rm{\sigma }} = 1.6 \times {10^{ - 19}} \times {10^{16}} \times 1200\)

\(\Rightarrow {\rm{\sigma }} = 1.92\frac{{{\rm{mho}}}}{{{\rm{cm}}}}\)

Now, resistivity \({\rm{\rho }} = \frac{1}{{\rm{\sigma }}} = \frac{1}{{1.92}} = 0.52{\rm{\;\Omega cm}}\)