= Measuring carrier concentration
Use a <Hall effect> measurement. Pass a known current $I$ through a thin rectangular specimen, apply a perpendicular magnetic field $B$, and measure the transverse <Hall voltage> $V_H$. For a uniform single-carrier sample of thickness $t$,
$$
R_H=\frac{V_Ht}{IB},\qquad
\boxed{n=\frac1{e|R_H|}=\frac{IB}{et|V_H|}}.
$$
The Hall-voltage sign identifies the carrier sign. Reverse $B$ and the current to separate the field-odd Hall signal from voltage-probe misalignment and offsets, and measure the specimen thickness accurately. The extraction assumes a one-carrier Hall factor near one. In intrinsic or mixed-carrier material, the <two-carrier Hall coefficient> is mobility weighted, so Hall voltage and conductivity need a two-carrier interpretation rather than this simple inverse formula.
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