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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q4(a)(ii). Conduction in semiconductors

  • 5 marks
  • Answered
Question

Explain the conduction mechanism in semiconductors.

Answer in brief

A semiconductor has a filled valence band separated from an empty conduction band by a small gap. Electrons promoted across the gap (by heat, or from donor impurities) carry current in the conduction band, and the holes they leave carry current in the valence band. Conductivity therefore rises with temperature.

Key points

  • in a solid the atomic orbitals merge into bands. The valence band is full and the conduction band empty, separated by a band gap E_g: small in a semiconductor (Si 1.11 eV, Ge 0.72 eV), large in an insulator, absent in a metal.
  • thermal energy promotes a few electrons across the gap. Each leaves a positive hole in the valence band. Electrons move in the conduction band; holes move as neighbouring electrons fill them. Carrier number ∝ e^(-E_g/2kT), so…
  • Si doped with a Group 15 atom (P, As). The fifth electron sits in a donor level just below the conduction band and is easily excited into it: electrons are the majority carriers.
  • Si doped with a Group 13 atom (B, Ga). Each creates an empty acceptor level just above the valence band; electrons jump into it and leave mobile holes, the majority carriers.

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

  1. Band picture: in a solid the atomic orbitals merge into bands. The valence band is full and the conduction band empty, separated by a band gap E_g: small in a semiconductor (Si 1.11 eV, Ge 0.72 eV), large in an insulator, absent in a metal.
  2. Intrinsic semiconduction (pure Si, Ge): thermal energy promotes a few electrons across the gap. Each leaves a positive hole in the valence band. Electrons move in the conduction band; holes move as neighbouring electrons fill them. Carrier number ∝ e^(-E_g/2kT), so conductivity rises with temperature, the opposite of a metal.
  3. n-type (extrinsic): Si doped with a Group 15 atom (P, As). The fifth electron sits in a donor level just below the conduction band and is easily excited into it: electrons are the majority carriers.
  4. p-type: Si doped with a Group 13 atom (B, Ga). Each creates an empty acceptor level just above the valence band; electrons jump into it and leave mobile holes, the majority carriers.
  5. Non-stoichiometric oxides behave the same way: ZnO with excess Zn is n-type, Ni₁₋ₓO and Fe₁₋ₓO (metal deficient, some M³⁺) are p-type.

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Model answer to Q4(a)(ii), 2018 Paper I: solution page 23
Solution page 23 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 4