UPSC Civil Services (Mains), Chemistry optional · 2025 · Paper I
Q1(c). Raising the conductivity of Ge and Si by trace elements
Question
Germanium and Silicon elements have very low electrical conductivity. How can the electrical conductivity be enhanced by adding other elements in trace amount? Explain by examples.
Answer in brief
By doping: a group 15 element gives an n-type semiconductor, a group 13 element gives a p-type semiconductor.
Key points
- In pure Si or Ge the band gap (1.1 eV and 0.7 eV) is far larger than kT ≈ 0.026 eV, so very few electrons reach the conduction band.
- A group 15 atom such as P or As holds its fifth electron in a donor level 0.01–0.05 eV below the conduction band; electrons carry the current: n-type.
- A group 13 atom such as B or Ga gives an empty acceptor level just above the valence band, leaving holes; holes carry the current: p-type.
- About one dopant atom per million host atoms already outnumbers the thermally freed carriers many times over, which is why a trace is enough.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversdopingn-type semiconductorp-type semiconductorband gapdonor and acceptor levelssilicon germanium
All parts of Question 1
- 1(a) Probability of the 1s electron at a₀ and at 10a₀5 marks
- 1(b) Born–Haber cycle for NaCl at 298 K5 marks
- 1(c) Raising the conductivity of Ge and Si by trace elements5 marks
- 1(d) Heat conduction between two copper sheets through air5 marks
- 1(e) Superheating of liquids and the Kelvin equation5 marks
- 1(f) Ascending order of dipole moment: NH₃, NF₃, H₂O5 marks
- 1(g) Heat of combustion of naphthalene from bomb calorimetry5 marks
- 1(h) Sealed sample: ethane, neon or a mixture5 marks
- 1(i) Time to plate a gold layer5 marks
- 1(j) Maximum work of a steam turbine5 marks