Question

A crystal of intrinsic silicon at room temperature has a carrier concentration of $1.6\times {10}^{16}/m^3$. If the donor concentration level is $0.48\times {10}^{20}/m^3$, then the concentration of holes in the semiconductor is:

• A. $5.3\times {10}^{12}/m^3$
• B. $4\times {10}^{11}/m^3$
• C. $4\times {10}^{12}/m^3$
• D. $5.3\times {10}^{11}/m^3$

Answer 1

The correct option is A $5.3\times {10}^{12}/m^3$

Given : Donor concentration $n_e=0.48\times {10}^{20}$ $/m^3$

Carrier concentration of intrinsic silicon $n_i=1.6\times {10}^{16}$ $/m^3$

Let the concentration of holes be $n_h$

Using: $n_e{n}_h=n_i^2$ $⟹n_h=\frac{n_i^2}{n_e}$

$\therefore$ $n_h=\frac{(1.6\times {10}^{16}{)}^2}{0.48\times {10}^{20}}=5.3\times {10}^{12}$ $/m^3$