Physics · Semiconductor Electronics : Materials, Devices And Simple Circuits · NEET
It is true for both. In an intrinsic (pure) semiconductor ne = nh = ni, so their product is ni x ni = ni squared. When you dope the crystal it becomes extrinsic, and now ne is not equal to nh anymore, but their PRODUCT still equals ni squared. That is exactly why this law is powerful: it works for intrinsic and extrinsic semiconductors at the same temperature. NCERT gives it as equation 14.5: ne nh = ni squared, and calls it the electron and hole concentration in thermal equilibrium.
Adding donors floods the crystal with extra free electrons. With so many more electrons around, a hole is much more likely to meet an electron and be filled in (recombination). NCERT states this directly: the rate of recombination of holes increases due to the increase in the number of electrons, so the number of holes gets reduced further. The product ne x nh must stay equal to ni squared, so if ne shoots up, nh must drop to keep the product fixed.
The first one, ne = nh = ni, is ONLY for a pure intrinsic semiconductor where electrons and holes are made in equal pairs. The second one, ne x nh = ni squared, is the general mass action law that holds even after doping. In a doped crystal ne is no longer equal to nh, so you cannot use ne = nh = ni, but you can always use the product form to find the minority carrier once you know the majority carrier.
Use the mass action law and rearrange it. The majority carrier concentration roughly equals the dopant concentration (Nd for n-type, Na for p-type). Then the minority carrier = ni squared divided by the majority carrier. For example, in an n-type sample ne is approximately Nd, so nh = ni squared / ne = ni squared / Nd. Because you divide by a large majority number, the minority carrier comes out very small.
The FORM ne x nh = ni squared always holds, but the VALUE of ni depends strongly on temperature. As temperature rises, more electron-hole pairs are thermally generated, so ni increases, and therefore ni squared increases. The law is only valid at a fixed temperature (thermal equilibrium). Compare two different temperatures and the product ni squared is different at each.
No. The crystal stays electrically neutral, but that does NOT force ne = nh in a doped sample. In n-type, the extra electrons are balanced by the fixed positive donor ions locked in the lattice, so overall charge is still zero even though ne is much greater than nh. NCERT notes the crystal maintains overall charge neutrality because the added carriers are balanced by the ionised dopant charge.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
ne x nh = ni squared, where ne is the electron concentration, nh is the hole concentration, and ni is the intrinsic carrier concentration at that temperature. It holds in thermal equilibrium for both intrinsic and doped semiconductors.
Yes. In n-type, ne is much greater than nh, but their product is still ni squared. You can find the holes as nh = ni squared / ne.
The name is borrowed from chemistry. Just like a chemical equilibrium keeps the product of concentrations constant, the electron-hole generation and recombination equilibrium keeps ne x nh constant at ni squared.
ni is the intrinsic carrier concentration, the number of free electrons (equal to the number of holes) per cubic metre in a pure semiconductor at a given temperature. For silicon at room temperature ni is about 1.5 x 10 to the power 16 per cubic metre in NCERT examples.
Not in thermal equilibrium at a fixed temperature. The law fixes the product at exactly ni squared. Raising the temperature raises ni, so the product ni squared becomes larger, but at any single temperature it is fixed.
