Question

Let a pure $Si$ crystal has $5\times 10^{28}$ atoms $m^{-3}$. It is doped by parts per million concentration of pentavalent arsenic. If number of intrinsic pairs is $1.5\times 10^{16}{m}^{-3}$, then number of holes in doped crystal is

• A. $4.5\times 10^9{m}^{-3}$
• B. $\sim 10^{16}{m}^{-3}$
• C. $2.25\times 10^{32}{m}^{-3}$
• D. $5\times 10^{22}{m}^{-3}$

Answer 1

Answer: (A)

Total number of atoms $=5\times 10^{28}{m}^{-3}$
For every $10^6$ atoms, $1A-s$ is doped.
$1A-s$ contributely $1e^{-}$
$Ne=5\times 10^{28}/10^6=5\times 10^{22}$
Since, $n_e{n}_h=n_i^2$
The number of holes
$n_h=\left(2.25\times 10^{32}\right)/\left(5\times 10^{22}\right)$
$=4.5\times 10^9{m}^{-3}$