In a pure semiconductor, the number of conduction electrons is 6 × 1018 per cubic metre. In a sample of this semiconductor of dimensions 1 cm × 1 cm × 1 mm, the number of holes would be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 × 1011
In a pure (intrinsic) semiconductor, every electron that enters the conduction band leaves a hole behind, so the number of holes equals the number of conduction electrons.
\( \displaystyle V = 1\,\mathrm{cm} \times 1\,\mathrm{cm} \times 1\,\mathrm{mm} = (10^{-2}\,\mathrm{m})(10^{-2}\,\mathrm{m})(10^{-3}\,\mathrm{m}) = 10^{-7}\,\mathrm{m^{3}} \)
\( \displaystyle N_h = N_e = n_i V = 6\times10^{18}\,\mathrm{m^{-3}} \times 10^{-7}\,\mathrm{m^{3}} \)
\( \displaystyle N_h = 6\times10^{11} \)