Conductivity Of Semiconductors

Conduction in a semiconductor is carried by both electrons and holes drifting under the applied field, so the total conductivity is (\sigma = e,(n_e \mu_e + n_h \mu_h)). For an intrinsic sample the two carrier densities are equal, (n_e = n_h = n_i), allowing the expression to be written as (\sigma = n_i,e,(\mu_e + \mu_h)). It is important to keep both terms because, although electrons and holes carry opposite charge and drift in opposite directions under the field, their currents add rather than cancel; a positive hole moving one way and a negative electron moving the other both transport positive charge in the same sense. Inserting (n_i = 2.4 \times 10^{19},\text{m}^{-3}), (e = 1.6 \times 10^{-19},\text{C}) and ((\mu_e + \mu_h) = 0.58,\text{m}^2\text{V}^{-1}\text{s}^{-1}) gives (\sigma = (2.4 \times 10^{19})(1.6 \times 10^{-19})(0.58) \approx 2.23,\text{S m}^{-1}). The value 1.50 wrongly uses only the electron mobility, dropping the hole contribution. The value 0.89 mistakenly subtracts the mobilities rather than adding them. The value 4.46 double counts by using (2n_i) for each carrier. As a sanity check, the corresponding resistivity is about (0.45,\Omega\text{m}), which lies sensibly between metals and insulators, confirming a semiconductor-scale conductivity.