Physics · Semiconductor Electronics : Materials, Devices And Simple Circuits · NEET
No. The relation ne = nh is true ONLY for an intrinsic (pure) semiconductor. There, thermal energy breaks a covalent bond and each broken bond releases exactly one electron and leaves exactly one hole, so they are created in equal pairs. Once you dope the material (extrinsic semiconductor), the dopant adds extra carriers of one kind, so ne is no longer equal to nh.
ni is the intrinsic carrier concentration, the common value of ne and nh in a pure semiconductor at a given temperature. It is measured as number of carriers per unit volume (per cubic metre). Because ne = nh in a pure sample, we give both one single name ni. It is a property of the material and the temperature only.
No, that is the most common mistake. In n-type, donors give extra electrons so ne is much greater than nh. In p-type, acceptors give extra holes so nh is much greater than ne. The equal-pair rule ne = nh = ni is broken by doping. For doped material you instead use the mass action law ne x nh = ni squared.
At room temperature ni for silicon is about 1.5 x 10 to the power 16 per cubic metre and for germanium about 2.4 x 10 to the power 19 per cubic metre. Germanium has a smaller band gap (0.72 eV vs 1.1 eV for silicon), so more bonds break and ni is larger. These values are only for pure material.
Think of the source. The only way to make a free carrier in pure material is to break a covalent bond using thermal energy. Breaking one bond does two things at once: it frees one electron and it leaves behind one hole. There is no process here that makes an electron without a hole. So counting them always gives the same number, ne = nh.
Yes, strongly. Higher temperature gives more thermal energy, so more bonds break, so both ne and nh rise together and ni increases. That is why the conductivity of a semiconductor increases (resistance decreases) as temperature rises. At T = 0 K almost no bonds are broken, ni is nearly zero, and the pure semiconductor behaves like an insulator.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a pure semiconductor, ne = nh = ni, where ne is the number of free electrons per unit volume, nh is the number of holes per unit volume, and ni is called the intrinsic carrier concentration. This is NCERT equation 14.1.
Because each carrier pair is made by breaking one covalent bond, and one broken bond frees exactly one electron and creates exactly one hole. They are always produced in equal numbers, so ne = nh.
ni is a concentration, so its SI unit is number per cubic metre (per m cubed). Some books quote it per cubic centimetre; be careful to match units in numerical problems.
Germanium has a larger ni (about 2.4 x 10^19 per m cubed) than silicon (about 1.5 x 10^16 per m cubed) because germanium has a smaller energy gap, so more bonds break at the same temperature.
ne = nh = ni describes pure material only. The mass action law ne x nh = ni squared is the more general relation that also holds after doping, when ne is no longer equal to nh.
