Question

A pure $Si$ crystal has $5 \times 10^{22}$ atoms $m^{-3}$. It is doped by $1$ ppm concentration of pentavalent As. The number of holes is $(n_i^2, = n_pn_e)$ (Take $n_i = 1.5 \times 10^{16}\, m^{-3})$

• A. $4.5 \times 10^9\, m^{-3}$
• B. $4 .5 \times 10^6\, m^{-3}$
• C. $2.5 \times 10^9\, m^{-3}$
• D. $2.5 \times 10^6 \,m^{-3}$

Answer 1

Answer: (A)

The electron and holes concentration in a semiconductor in thermal equilibrium is
$n_{e} n_{h} = n_{i}^{2} $
or $n_{h} = \frac{n_{i}^{2}}{n_{e}} $
Here, $n_{i} = 1.5 \times 10^{16}m^{-3}, $
$ n_{e} = 5\times 10^{22} m^{-3} $
$ \therefore n_{h} = \frac{\left(1.5\times 10^{16}\right)^{2}}{\left(5\times 10^{22}\right)} $
$= \frac{2.25\times 10^{32}}{5\times 10^{22}}$
$ = 4.5 \times 10^{9} m^{-3}$