 Conductivity ratio of doped and intrinsic semiconductors

ID: conductivity-ratio-of-doped-and-intrinsic-semiconductors

n = p = n_{i}

, so

σ_{i} = e n_{i} (μ_{e} + μ_{h})

. In a fully ionised, uncompensated n-type sample with

N_{D} ≫ n_{i}

n ≃ N_{D}

p ≃ n_{i}^{2} / N_{D}

, and

\frac{σ _{d}}{σ _{i}} ≃ \frac{N _{D} μ _{e, d}}{n _{i} ( μ _{e, i} + μ _{h, i} )} .

Thus a carrier-density ratio alone is not generally the electrical conductivity ratio. If electron mobility is unchanged and electron transport dominates the intrinsic conductivity, it reduces to

N_{D} / n_{i}

; equal electron and hole mobilities instead give

N_{D} / (2 n_{i})

. Ionised-impurity scattering can change the doped mobility.

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