Crossed Fields: The Hall Effect — Question 4

Question 4

Combining longitudinal resistance with a Hall measurement separates density and mobility

A single-electron-carrier strip has length L=.0200 m, width w=.00500 m and thickness t=.000200 m. At I=.0100 A, its longitudinal voltage is .400 V. With B=.500 T, its upper-minus-lower Hall voltage is +2.00 mV. Use e=$1.60\times10^{-19}$ C and $\sigma=ne\mu$.

1. Find conductivity and the signed Hall coefficient $R_H=E_y/(J_xB)$.

2. Find electron density n and mobility mu.

Question 4 - Solution

Combining longitudinal resistance with a Hall measurement separates density and mobility

(a) Method and calculation

$$\sigma=\frac{IL}{V_xwt}=500\,\mathrm{S/m}.$$$$R_H=-\frac{V_Ht}{IB}=-8.00\times10^{-5}\,\mathrm{m^3/C}.$$

(b) Interpretation and further calculation

$$n=\frac1{e|R_H|}=7.8125\times10^{22}\,\mathrm{m^{-3}}.$$$$\mu=\frac\sigma{ne}=\sigma|R_H|=.0400\,\mathrm{m^2/(V\,s)}.$$

Physical check

A conductivity measurement alone constrains the product of carrier density and mobility, not either separately.