Minority charge suppression in extrinsic semiconductors

Minority carrier suppression is the reduction of the minority carrier concentration far below $n_i$ when a semiconductor is doped. Adding donors increases electrons and at the same time decreases holes (and vice versa for acceptors).

Reason

In thermal equilibrium, the mass action law holds for a non-degenerate semiconductor:

$$np = n_i^2$$

$n_i^2$ depends only on the material and temperature, not on doping. So if doping raises the majority concentration, the minority concentration must fall by the same factor. Physically, the large number of electrons increases the recombination rate with holes, so fewer holes survive.

Example

Si at 300 K, $n_i = 1.45\times10^{10}$ cm$^{-3}$, doped with $N_d = 10^{16}$ cm$^{-3}$:

$$\begin{aligned} n &\approx N_d = 10^{16}\ \text{cm}^{-3} \\ p &= \frac{n_i^2}{n} = \frac{(1.45\times10^{10})^2}{10^{16}} = 2.1\times10^{4}\ \text{cm}^{-3} \end{aligned}$$

The hole concentration falls from $1.45\times10^{10}$ to $2.1\times10^4$ cm$^{-3}$, nearly a million times smaller.

Consequences

• Conductivity is due almost entirely to majority carriers: $\sigma \approx eN_d\mu_e$.
• Minority carriers, though few, control pn junction reverse saturation current and transistor action.