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, $1 \,A - s$ is doped.
$1 \,A-s$ contributely $1 e^{-}$
$N e=5 \times 10^{28} / 10^{6}=5 \times 10^{22}$
Since, $ n_{e} n_{h}=n_{i}^{2}$
The number of holes
$n_{h}=\left(2.25 \times 10^{32}\right) /\left(5 \times 10^{22}\right)$
$=4.5 \times 10^{9} \,m ^{-3}$