Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of 100.Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is`7xx10^15`holes per cubic meter. Density of silicon is `5xx10^28`atoms per cubic metre.

Explanation

Total number of charge carriers initially
`= 2xx7xx10^15`
`= 14xx10^15/(Cubic meter)`
finally the total number of charge carriers
`= 14xx10^(17)/m^(3)`
We know the product of the concentrations of holes and conduction electrons remains almost the same.
Let 'x' be the number of holes.
So `(7xx10^(15))xx(7xx 10^(15))`
`= x xx(14^(17)-x)`
`rArr 14x xx10^17-x^2 = 49xx10^30`
`rArr x^2-14x xx10^17-49xx10^30 = 0`
`rArr x = (14xx10^17+-(14)^2xxsqrt(10^34+4xx49xx10^30))/(2)`
` = 10^17+-sqrt(10^34+4xx49xx10^30))/(2)`
` = (28.0007)/(2)xx10^17 = 14.00035xx10^17`
= increase in number of boles or the
number of atoms of Boron added
Now, `1386.035xx10^15 atom of `Si` in `1 m^3`.
`1` atom of Boron is added per
`(5xx10^28)/(1386.035xx10^15)`
`3.607xx10^15xx10^13`
`3.607xx10^10`