Question

Suppose a pure Si crystal has $5\times {10}^{28}{\text{atom m}}^{–3}$. It is doped with $1\text{ppm}$ concentration of pentavalent Arsenic. Calculate the number of holes $(n_i=2.5\times {10}^{16}{\text{m}}^{–3})$.

• A. $8\times {10}^9{\text{m}}^{-3}$
  
• B. $1.25\times {10}^{10}{\text{m}}^{-3}$
• C. $6.25\times {10}^{22}{\text{m}}^{-3}$
• D. $4.5\times {10}^{22}{\text{m}}^{-3}$

Answer 1

The correct option is B $1.25\times {10}^{10}{\text{m}}^{-3}$

Thermally generated electrons $=2.5\times {10}^{16}{\text{m}}^{–3}$ are very small as compared to dopant.
$\therefore n_e;N_D$
Dopant concentration $=\frac{5\times {10}^{28}}{{10}^6}=5\times {10}^{22}{\text{m}}^{-3}$
$n_e\times n_h=(n_i{)}^2$
$\therefore n_h=\frac{(2.5\times {10}^{16}{)}^2}{5\times {10}^{22}}=\frac{6.25}{5}\times {10}^{10}$
$n_h=1.25\times {10}^{10}{\text{m}}^{-3}$