In a pure semiconductor the concentration of conduction electrons is \( 6\times10^{13} \) cm-3. The total number of holes in this semiconductor of dimensions (1 cm × 1 mm × 1 mm) will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 6\times10^{11} \)
In a pure (intrinsic) semiconductor every conduction electron leaves behind one hole, so \( n_h = n_e \). The total number of holes is this concentration times the volume, with all lengths in cm.
\( n_h = n_e = 6\times10^{13}\,\mathrm{cm^{-3}} \)
\( 1\,\mathrm{mm} = 0.1\,\mathrm{cm} \)
\( \displaystyle V = 1\,\mathrm{cm} \times 0.1\,\mathrm{cm} \times 0.1\,\mathrm{cm} = 10^{-2}\,\mathrm{cm^{3}} \)
\( \displaystyle N_h = 6\times10^{13}\,\mathrm{cm^{-3}} \times 10^{-2}\,\mathrm{cm^{3}} = 6\times10^{11} \)