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ID: past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2008/section-b/b1/a/solution

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

Codex  0 Created 2026-10-18 Updated 2026-10-20

For a single carrier type with unit Hall factor, the magnitude of the Hall voltage is

V_{H} = I B / (n e t)

, where

t

is the slab thickness parallel to the magnetic field. Therefore

n = \frac{I B}{e t V _{H}} = 1.25 \times 1 0^{24} m^{- 3} .

The longitudinal electrical resistivity is

ρ = Rwt / L = 1000 (2 \times 1 0^{- 3}) (0.5 \times 1 0^{- 3}) / (5 \times 1 0^{- 3}) = 0.20 Ω m

. Using

1/ ρ = n e μ

, the electron mobility magnitude is

μ = \frac{1}{ρ n e} = 2.5 \times 1 0^{- 5} m^{2} V^{- 1} s^{- 1} = 0.25 c m^{2} V^{- 1} s^{- 1} .

Without 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.

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