Intrinsic semiconductor

An intrinsic semiconductor is pure, undoped semiconductor material — for this course, pure silicon with no deliberately added impurities. It is the baseline against which doped material is understood, and on its own it is a very poor conductor.

Where the carriers come from

In pure silicon at absolute zero, every valence electron is locked into a covalent bond and there are no free carriers at all. Raise the temperature and thermal energy starts breaking bonds: a bandgap-worth of energy promotes a valence electron into the conduction band, where it is free to move. That promoted electron is one free carrier; the empty bond it left behind is a hole, which acts as a mobile positive carrier. So in intrinsic material electrons and holes are always created in pairs — this is electron–hole pair generation — and they vanish in pairs when an electron falls back into a hole (recombination).

The intrinsic concentration: n = p = n_i

Because every free electron in pure silicon comes with exactly one hole, the electron and hole concentrations are equal:

$n=p=n_i$

where $n$ is the free-electron concentration (carriers per cm³), $p$ the hole concentration, and $n_i$ the Intrinsic carrier concentration — the common value they share in intrinsic material. In thermal equilibrium the generation rate equals the recombination rate, which is what holds $n$ and $p$ at this steady $n_i$.

For silicon at room temperature ($T=300\text{K}$), $n_i\approx 1.5\times 10^{10}{\text{cm}}^{-3}$. That sounds like a lot until you compare it with the density of silicon atoms, about $5\times 10^{22}{\text{cm}}^{-3}$: only about one atom in $10^{12}$ has contributed a free carrier. With so few mobile charges, intrinsic silicon conducts very poorly — far worse than a metal, though far better than a true insulator.

Why it matters

Intrinsic silicon by itself is not a useful device material — it is too resistive and its tiny carrier count is uncontrollable (it depends only on temperature). Its importance is conceptual: it defines $n_i$, and through the Mass-action law $np=n_i^2$, the intrinsic concentration sets the rule that every doped material must still obey. When you dope silicon you change the balance of $n$ and $p$ by many orders of magnitude, but their product is pinned to $n_i^2$ at a given temperature. So the intrinsic case is the anchor for understanding n-type and p-type material and everything built from them.