Majority and minority carriers

In a doped semiconductor the two carrier types are present in wildly different amounts. The majority carrier is the one Doping makes abundant; the minority carrier is the one the Mass-action law suppresses. Which is which depends entirely on the doping type.

• N-type silicon: donors flood the material with electrons, so electrons are the majority carrier and holes are the minority carrier.
• P-type silicon: acceptors flood the material with holes, so holes are the majority carrier and electrons are the minority carrier.

The roles simply swap between n-type and p-type.

How lopsided the populations are

The numbers are extreme, and they follow directly from the Mass-action law $np=n_i^2$. In n-type silicon with donor concentration $N_D$, the majority concentration is $n\approx N_D$ and the minority concentration is

$p\approx \frac{n_i^2}{N_D}.$

For $N_D=10^{16}{\text{cm}}^{-3}$ and $n_i=1.5\times 10^{10}{\text{cm}}^{-3}$ this gives $n\approx 10^{16}$ majority electrons but only $p\approx 2.25\times 10^4$ minority holes per cm³ — an imbalance of about $10^{11}$ to one. The symmetric statement holds in p-type material: $p\approx N_A$ majority holes, $n\approx n_i^2/N_A$ minority electrons. Raising the doping pushes the majority count up and the minority count proportionally further down.

Why minority carriers matter despite being scarce

It would be easy to dismiss minority carriers — they are outnumbered by a factor of $10^{10}$ or more. But they are the carriers that do the work in the “off” state of a PN junction. Under reverse bias the majority carriers are all pushed away from the junction and cannot cross; the only current that flows is the Reverse saturation current $I_S$, and it is carried entirely by the few minority carriers (the stray holes in the n-side and stray electrons in the p-side) that wander into the junction’s field and get swept across.

So the asymmetry cuts both ways. The huge majority population is what gives doped silicon its useful conductivity and supplies the large forward diffusion current; the tiny minority population is what determines leakage, reverse saturation current, and ultimately the temperature sensitivity of every diode and transistor (minority concentrations scale as $n_i^2$, which is fiercely temperature-dependent — see Intrinsic carrier concentration).