Physics · Semiconductor Electronics : Materials, Devices And Simple Circuits · NEET
| Band gap Eg | Metal: 0 eV (bands overlap) | Insulator: greater than 3 eV (e.g. diamond 6 eV) |
| Free carriers at room temp | Metal: very large number | Insulator: almost none |
| Resistivity | Metal: lowest | Insulator: highest |
| Semiconductor (middle) | Eg small, 0 to 3 eV (Si 1.1, Ge 0.7) | Few carriers, resistivity in between; rises when heated |
Metals: Eg = 0 eV (the valence band and conduction band overlap, so there is no forbidden gap at all). Semiconductors: Eg is small, roughly 0 to 3 eV. Standard NCERT values are Silicon = 1.1 eV and Germanium = 0.7 eV. Insulators: Eg is large, usually more than 3 eV, for example diamond has Eg = 6 eV. NEET often asks you to just remember the order: metal (0) is less than semiconductor (small) is less than insulator (large).
In a metal the highest filled band is either only partly filled, or the valence band and conduction band overlap. Because free energy levels sit right next to the filled ones, an electron needs almost no energy to move into an empty level and carry current, so Eg = 0. In an insulator the valence band is completely full and is separated from the empty conduction band by a wide forbidden gap (more than 3 eV). Room temperature heat (about 0.026 eV) is far too small to push an electron across that wide gap, so no current flows.
About 3 eV is a rough guide, not a sharp law. A material with Eg near 1 eV is clearly a semiconductor and one near 6 eV is clearly an insulator. Materials in between (like some oxides with Eg around 3 to 4 eV) can behave either way. For NEET, use Eg less than about 3 eV = semiconductor and Eg greater than about 3 eV = insulator, and remember the classic examples (Si 1.1, Ge 0.7, diamond 6).
Yes, at the same temperature. A bigger Eg means fewer electrons can jump into the conduction band, so there are fewer free charge carriers, which means higher resistivity. That is exactly why insulators (large Eg) have the highest resistivity, semiconductors (small Eg) are in the middle, and metals (Eg = 0, many free electrons) have the lowest resistivity. This ordering is directly asked in NEET.
In a metal, electrons already occupy energy levels in the conduction region (overlap), so free electrons are available with no energy input. In a semiconductor at 0 K the conduction band is empty and the valence band is full, so it acts like an insulator; heat then lifts a few electrons across the small gap. In an insulator the conduction band stays empty at ordinary temperatures because the gap is too wide to cross.
On the basis of electrical conductivity, which one of the following materials has the smallest resistivity?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Band gap (Eg) is the minimum energy an electron needs to jump from the filled valence band to the empty conduction band, measured in electron-volts (eV).
Silicon has Eg = 1.1 eV and Germanium has Eg = 0.7 eV. Germanium has the smaller gap, so at a given temperature it produces slightly more free carriers than silicon.
The insulator has the largest band gap (more than about 3 eV, e.g. diamond 6 eV). The metal has the smallest, Eg = 0. The semiconductor is in between.
The band gap decreases very slightly as temperature rises, but the big effect for NEET is that more electrons gain enough energy to cross the gap, so semiconductor conductivity increases with temperature.
At 0 K no heat energy is available, so no electron can cross even the small gap. The valence band stays full and the conduction band empty, so the semiconductor behaves like an insulator.
