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Degenerate versus non-degenerate semiconductors

Short answer

Non-degenerate semiconductors have doping low enough that the Fermi level lies in the band gap (more than a few kT from band edges), with n ≪ Nc, p ≪ Nv, and Boltzmann statistics apply. Degenerate semiconductors are so heavily doped (≈10¹⁹ cm⁻³) that the Fermi level enters the conduction or valence band, impurity bands merge, and they show metal‑like conductivity; Fermi‑Dirac statistics must be used.

Differentiate between non-degenerate and degenerate semiconductors.

A non-degenerate semiconductor has a carrier concentration much smaller than the effective density of states (n≪Ncn \ll N_c, p≪Nvp \ll N_v), so the Fermi level lies in the band gap at least a few kTkT from the band edges. A degenerate semiconductor is so heavily doped (above about 101910^{19} cm−3^{-3} in Si) that the Fermi level enters the conduction band (n+^+) or valence band (p+^+), and it behaves more like a metal.

   Non-degenerate n        Degenerate n+
  ---------- Ec          ~~~~~~~~~~ EF
  - - - - -  Ed          ---------- Ec
  .......... EF          ////////// impurity band
                          merged with CB
  ---------- Ev          ---------- Ev
PointNon-degenerateDegenerate
Doping levelLight/moderate (Nd≪NcN_d \ll N_c)Very heavy (Nd≳NcN_d \gtrsim N_c, about 101910^{19} to 102010^{20} cm−3^{-3})
Fermi levelIn the gap, more than about 3kT3kT from band edgeInside CB (n+^+) or VB (p+^+)
StatisticsBoltzmann approximation validFull Fermi-Dirac needed
np=ni2np = n_i^2HoldsDoes not hold
Impurity levelsDiscrete, isolated donor/acceptor levelsOverlap into an impurity band merging with the band
Band gapNormalSlightly reduced (band-gap narrowing)
BehaviourSemiconducting; conductivity rises with TMetal-like; weak temperature dependence
UsesOrdinary diodes, transistorsTunnel diodes, laser diodes, ohmic contacts

✓ Answer checked by Claude Opus 5.5 (high effort)

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