A pure silicon crystal has \(5\times10^{28}\) atoms per m3. It is doped with phosphorus. The electron concentration of the doped crystal is \(1.5\times10^{23}\ \mathrm{m^{-3}}\), and the thermally generated electrons are negligible. The doping concentration of phosphorus is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 ppm
Phosphorus is pentavalent. Each phosphorus atom gives one free electron. As the thermal electrons are negligible, \( n_e \) is equal to the number of phosphorus atoms per m3, \( N_D \).
\( \begin{aligned} \frac{N_D}{N} &= \frac{n_e}{N} \\ &= \frac{1.5\times10^{23}}{5\times10^{28}} \\ &= 3\times10^{-6} \end{aligned} \)
One part in \( 10^{6} \) is 1 ppm, so the doping concentration is 3 ppm.
NCERT (2026-27):
n-type semiconductor – “… Thus, the pentavalent dopant is donating one extra electron for conduction and hence is known as donor impurity. …”
Example 14.2 – “… Note that thermally generated electrons (ni ~1016 m–3) are negligibly small as compared to those produced by doping. Therefore, ne ≈ ND.”