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Energy bands: conductor, insulator and semiconductor

Short answer

Energy bands are quasi-continuous allowed energy ranges separated by gaps. In conducters, bands overlap or are partly filled, giving high conductivity and positive temperature coefficient. Insulators have a large band gap (>5 eV) and extremely high resistivity. Semiconductors have a small gap (~1 eV), conductivity increasing with temperature, and can be doped.

What are energy bands? Distinguish between a conductor, an insulator and a semiconductor on the basis of energy diagram. Write two characteristic features to [?] (rest of the question is cut off in the scan).

An energy band is a set of very closely spaced allowed energy levels in a solid. When NN atoms come together, each atomic level splits into NN levels because the outer orbitals overlap (Pauli principle); these form a nearly continuous band. Bands are separated by forbidden gaps EgE_g in which no electron states exist. The highest band containing valence electrons is the valence band (VB) and the next higher band is the conduction band (CB).

Conductor, semiconductor and insulator

  Conductor        Semiconductor     Insulator
 +---------+       +---------+      +---------+
 |   CB    |       |   CB    |      |   CB    |
 |#########|       +---------+      +---------+
 +---------+          Eg ~ 1 eV
 |#########| overlap +---------+       Eg > 5 eV
 |   VB    |       |#########|
 +---------+       |#  VB   #|      +---------+
  (or partly       +---------+      |#########|
   filled band)                     |#  VB   #|
                                    +---------+
  ### = filled with electrons
PointConductorSemiconductorInsulator
Band gap EgE_gNone (bands overlap or band half-filled)Small, about 1 eV (Si 1.1, Ge 0.67)Large, > 5 eV (diamond 5.5)
Electrons in CB at 300 KVery manyFew (thermally excited)Practically none
Resistivity (Ω m)10−810^{-8} to 10−610^{-6}10−410^{-4} to 10310^{3}101010^{10} to 102010^{20}
Temperature coefficientPositiveNegativeNegative (very high R)
ExamplesCu, Al, AgSi, Ge, GaAsGlass, mica, diamond
  • Conductor: VB and CB overlap (e.g. Mg) or the highest band is only half filled (e.g. Na, Cu). Free electrons exist even at 0 K, so a small field produces a large current.
  • Semiconductor: at 0 K the VB is full and the CB empty, so it behaves as an insulator. At room temperature some electrons gain enough thermal energy to jump the small gap, leaving holes, so conduction increases with temperature.
  • Insulator: the gap is so large that thermal or ordinary electric field energy cannot lift electrons into the CB.

Two characteristic features of each

(The rest of the question is cut off; the usual demand is two features of each type.)

  • Conductors: (1) high conductivity due to a large number of free electrons; (2) resistance rises with temperature, because lattice vibrations scatter electrons more.
  • Semiconductors: (1) conductivity rises sharply with temperature (negative temperature coefficient); (2) conductivity can be controlled by doping, producing n-type or p-type material, with both electrons and holes as carriers.
  • Insulators: (1) very high resistivity and high dielectric strength; (2) they break down and conduct only under very high fields or temperatures.

✓ Answer checked by Claude Opus 5.5 (high effort)

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