A semiconductor has equal electron and hole concentration of `2 xx 10^(8) m^(-3)`. On doping with a certain impurity, the eletron concendration increases to `4 xx 10^(10) m^(-3)`, then the new hole concentration of the semiconductor is

Options

A. `10^(6) m^(-3)`
B. `10^(8) m^(-3)`
C. `10^(10) m^(-3)`
D. `10^(12) m^(-3)`

Answer

a

Explanation

Electron concentration `n_(e) = 2 xx 10^(6) m^(-3)`
Hole concentration, `n_(h) = 2 xx 10^(8) m^(-3)`
after doping with a impurity the new electron concentration, `n_(e) = 4 xx 10^(10) m^(-3)`
New hole concentration, n_(n) = ?`
We know that, `n_(e) xx n_(h) = h_(i)^(2)`
and `n_(e) xx n_(h) = n_(i)^(2)`
`:. n_(e) xx n_(h) = n_(e) = xx n_(h)`
`n'_(h) = (n_(e) xx n_(h))/(n_(e)) = (2 xx 10^(8) xx 2 xx 10^(8))/(4 xx 10^(10)) // m^(3) = 10^(8) // m^(3)`
`implies n_(h) = 10^(8) m^(-3)`