--- title: "Degenerate versus non-degenerate semiconductors" subject: "Electrical Engineering Material" chapter: 6 key: "semester_3/electrical_engineering_material:degenerate-nondegenerate" source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/degenerate-nondegenerate site: BCT Engineering --- # Degenerate versus non-degenerate semiconductors Electrical Engineering Material · Chapter 6: Semiconductors - Asked in: 2080 Baisakh, 4 marks; 2078 Bhadra, 4 marks; 2074 Chaitra, 6 marks; 2071 Chaitra, 4 marks; 2069 Asar, 4 marks (asked 5 times) - Video: [DEGENERATIVE AND NON DEGENERATIVE SEMICONDUCTOR | SEMICONDUCTOR DOPING | IMPURITY CONCENTRATION |](https://www.youtube.com/watch?v=_oTYuhIMw8U) — Electronic Gyan - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/degenerate-nondegenerate - Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6 ## Question Differentiate between non-degenerate and 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. ## Answer A **non-degenerate** semiconductor has a carrier concentration much smaller than the effective density of states ($n \ll N_c$, $p \ll N_v$), so the Fermi level lies in the band gap at least a few $kT$ from the band edges. A **degenerate** semiconductor is so heavily doped (above about $10^{19}$ cm$^{-3}$ in Si) that the Fermi level enters the conduction band (n$^+$) or valence band (p$^+$), and it behaves more like a metal. ```text Non-degenerate n Degenerate n+ ---------- Ec ~~~~~~~~~~ EF - - - - - Ed ---------- Ec .......... EF ////////// impurity band merged with CB ---------- Ev ---------- Ev ``` | Point | Non-degenerate | Degenerate | |---|---|---| | Doping level | Light/moderate ($N_d \ll N_c$) | Very heavy ($N_d \gtrsim N_c$, about $10^{19}$ to $10^{20}$ cm$^{-3}$) | | Fermi level | In the gap, more than about $3kT$ from band edge | Inside CB (n$^+$) or VB (p$^+$) | | Statistics | Boltzmann approximation valid | Full Fermi-Dirac needed | | $np = n_i^2$ | Holds | Does not hold | | Impurity levels | Discrete, isolated donor/acceptor levels | Overlap into an impurity band merging with the band | | Band gap | Normal | Slightly reduced (band-gap narrowing) | | Behaviour | Semiconducting; conductivity rises with T | Metal-like; weak temperature dependence | | Uses | Ordinary diodes, transistors | Tunnel diodes, laser diodes, ohmic contacts | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where is the Fermi level in a degenerate n+ semiconductor? A. In the band gap, a few kT below Ec B. Inside the conduction band C. At mid-gap D. In the valence band Answer: B. Heavy doping pushes EF into the band (n+ or p+). (Key point: Fermi level position) 2. Which statistics apply? A. Degenerate: Boltzmann; non-degenerate: Fermi-Dirac B. Both: Boltzmann C. Non-degenerate: Boltzmann approximation; degenerate: full Fermi-Dirac D. Both: Bose-Einstein Answer: C. Boltzmann fails when EF is in or near a band. (Key point: Statistics) 3. Does np = ni^2 hold? A. Yes for degenerate only B. Yes for both C. No for both D. Yes for non-degenerate, no for degenerate Answer: D. The law relies on the Boltzmann approximation. (Key point: Mass-action law) 4. How does a degenerate semiconductor behave? A. Metal-like with weak temperature dependence; used in tunnel diodes and ohmic contacts B. Conductivity rises strongly with T, used in ordinary diodes C. Insulating with no carriers D. It has a widened band gap Answer: A. Heavy doping gives metal-like conduction. 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