Question

Suppose a pure Si crystal has $5\times {10}^{28}$ atoms per $m^3$. It is doped by $1$ ppm concentration of pentavalent As. Calculate the number of electrons and holes. Given that $n_i=1.5\times {10}^{16}$ per $m^3$.

Answer 1

a)Number of electrons $=5\times {10}^{22}{m}^3$

b)Number of holes $=4.5\times {10}^9{m}^3$

a)Each Arsenic atom will provide one electron.

Hence,

$Numberofelectrons=NumberofAsatoms$

Number of electrons $=\frac{5\times {10}^{28}}{{10}^6}=5\times {10}^{22}{m}^3$

b)We know

$n{i}^2=numberofelectrons\times numberofholes$

Number of holes $=\frac{n{i}^2}{numberofelecrons}$

Number of holes $=\frac{1.5\times {10}^{16}}{5}\times {10}^{22}$

Number of holes $=\frac{2.25\times {10}^{32}}{5}\times {10}^{22}$

Number of holes $=4.5\times {10}^9{m}^3$