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GATE 2023 EC Q.16: solution and answer

GATE 2023 · ECQ.16 · 1 mark · MCQ

In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

  1. (A)

    degenerate n-type.

  2. (B)

    degenerate p-type.

  3. (C)

    non-degenerate n-type.

  4. (D)

    non-degenerate p-type.

See the question in the paper
GATE 2023 EC question 16Tap to open full size

Answer and solution

ANSWER

The correct option is (A) degenerate n-type.

Official answer: ASource: Official answer key, GATE 2023 EC (IIT Kanpur)

  1. A semiconductor is called degenerate when the doping concentration is so high that the Fermi level moves out of the forbidden energy gap and into one of the allowed bands, rather than remaining within the gap as in a normal (non-degenerate) semiconductor.

  2. If lies inside the conduction band, this occurs specifically due to an extremely high concentration of donor (electron-donating) impurities — by definition, this is a degenerate n-type semiconductor.

  3. For comparison: if lies inside the valence band instead, the material is degenerate p-type, resulting from extremely high acceptor (hole-donating) doping.

  4. Since the question states lies in the conduction band, the semiconductor is degenerate n-type, i.e., option (A).

KEY IDEA

In a non-degenerate semiconductor, the Fermi level lies within the forbidden energy gap. When the doping (donor or acceptor) concentration becomes very high (typically approaching or exceeding the effective density of states, or ), the semiconductor becomes degenerate and moves out of the gap into the conduction band (for very heavy donor/n-type doping) or into the valence band (for very heavy acceptor/p-type doping).

WATCH OUT FOR

Confusing "degenerate" with mere heavy doping without connecting it to the Fermi level actually crossing into the band edge; or reversing n-type/p-type by forgetting that donor (electron) doping pushes E_F upward toward the conduction band while acceptor doping pushes it downward toward the valence band.

From the GATE 2023 EC paper. Every question of this paper · Download the full paper · All 9 Semiconductors questions, with notes

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