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⚛️ NEET Physics❓ Question

Energy bands: why does a semiconductor's resistance fall with temperature but a metal's rises?

Riya Singh12th Sample

23 Sept 2026 · 1 min read

Trying to write something poetic about the 'gap' between two bands and ended up with a physics doubt instead (occupational hazard).

NCERT says in a solid the energy levels of many atoms merge into bands, and what matters is the highest filled band (valence band) and the lowest empty band (conduction band). Conductors have overlapping bands or a tiny gap, insulators have a big gap above 3 eV, and semiconductors something less than 3 eV. Silicon 1.1 eV, germanium about 0.7 eV, diamond 5.4 eV.

My questions:

  1. At absolute zero, is a pure silicon crystal a conductor? My notes say 'semiconductor conducts a little', but that sounds wrong.
  2. Why does the resistivity of a semiconductor decrease when temperature is raised, but a metal does the opposite? I know the answer is something about number of carriers but I can't put it in a clean two-line form.
  3. If Ge has a smaller gap than Si, is it the better insulator at room temperature or the worse one? There's a question in my paper that I answered 50-50.

I'd be happy if someone could also tell me what 'intrinsic' means precisely here.

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6 answers & replies

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  • [+]Vivek Mishra12thSample· 26d ago

    Short answers. (1) At 0 K the valence band of pure Si is full and the conduction band is empty, no free electrons, so it acts like an insulator, not a conductor. It only starts to conduct when temperature gives electrons enough energy to jump the gap. So your note should say 'conducts a little at room temperature'.

    (3) Germanium has a smaller gap, so at the same temperature more electrons cross the gap. Ge has more intrinsic carriers and lower resistivity than Si. So it's the worse insulator.

  • [+]Dev Agarwal12thSample· 26d ago

    Larger the band gap, more the energy bands are separated so germanium with its 0.7 eV is bigger than silicon in energy, so it will have the greater resistance and fewer carriers at room temperature. Basically Si is the more conductive one. I did a quick glance at the table in the book and 0.7 looked bigger than 1.1 to me, maybe because of the decimal.

    • [+]Neel Chatterjee12thSample· 26d ago

      Dev, you've swapped it. 0.7 eV is smaller than 1.1 eV. Smaller gap = easier jump = more electrons in the conduction band = more conductive. So Ge conducts better than Si at the same temperature, as Vivek said. That is also why silicon is preferred for devices that run warm, since fewer carriers get thermally generated and the junction stays well behaved.

  • [+]Ishita GoyalDropperSample· 26d ago

    Two-line form for your (2):

    • Semiconductor: heating moves more electrons across the gap (and leaves holes behind), so the number of carriers rises sharply. That wins over the small extra scattering, so resistivity falls.
    • Metal: the number of free electrons is already huge and almost fixed; heating makes the lattice vibrate more, electrons scatter more often, relaxation time falls, so resistivity rises.

    (Same story in the ρ=m/ne2τ\rho = m/ne^2\tau formula: nn changes a lot for semiconductors, τ\tau changes for metals.)

    • [+]Riya Singh12thSample· 26d agoAuthor

      that clears it, thank you. Wrote a small verse about the full valence band waiting for a push. Will share maybe 🙂

  • [+]Kavya NaikDropperSample· 26d ago

    'Intrinsic' means pure, no dopant. In an intrinsic semiconductor the electrons in the conduction band and holes in the valence band are always created in pairs, so ne=nh=nin_e = n_h = n_i. Once you add a dopant (phosphorus, boron...) it becomes extrinsic and one kind of carrier dominates. NEET likes 'in an intrinsic semiconductor at room temperature, electron and hole concentrations are __': the answer is equal.

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