The intrinsic charge carriers in pure Silicon are 2.0 ×1016 m−3. On doping with Indium, the hole density increases to 4 ×1022 m−3. The electron density in the doped Silicon is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1010 m−3
Doping with indium, a trivalent (acceptor) impurity, makes the silicon p-type, with holes as majority carriers. In thermal equilibrium the product of the electron and hole densities stays equal to the square of the intrinsic density (the law of mass action), so extra holes mean fewer electrons.
\( n_e n_h = n_i^{2} \)
\( \displaystyle n_e = \frac{n_i^{2}}{n_h} = \frac{(2.0\times10^{16}\,\mathrm{m^{-3}})^{2}}{4\times10^{22}\,\mathrm{m^{-3}}} \)
\( \displaystyle n_e = \frac{4\times10^{32}}{4\times10^{22}}\,\mathrm{m^{-3}} \)
\( n_e = 10^{10}\,\mathrm{m^{-3}} \)