Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section B / B1 / a / Solution

For a single carrier type with unit Hall factor, the magnitude of the Hall voltage is $V_H=IB/(net)$, where $t$ is the slab thickness parallel to the magnetic field. ThereforeThe longitudinal electrical resistivity is $\rho =Rwt/L=1000(2\times 10^{-3})(0.5\times 10^{-3})/(5\times 10^{-3})=0.20\Omega \mathrm{m}$. Using $1/\rho =ne\mu$, the electron mobility magnitude isWithout the Hall polarity these data do not identify the carrier charge sign. The inference assumes one dominant carrier population; electron-hole compensation would require a multicarrier analysis.