The concertration of hole-electron pairs in pire silicon at `T=300K` is `7xx10^(15` per cubic metre. Antimoy is doped into silicon in a proportion of `1` arom in `10^(7)` atoms. Assuming that half of the inpurity atoms contribute electrons in the conduction band, calculate the factor electrons in the conduction band, calculate the factor by which the number of charge carriers increase due to doping. the number of silicon atoms per cubic meter is `5xx10^(28)`.

Explanation

In pure semiconductor electron-hole pair `=7 times 10^(15)//m^(3)` total charge carrier `n_("total initial")=n_(h)+n_(e)=14 times 10^(15)` after doping donor impurity `N_(D)=(5 times 10^(28))/(10^(7))` and `n_(e)=N_(D)/2=2.5 times 10^(21)`
So `n_("final")=n_(h)+n_(e)`
`n_("final") approx n_(e) approx 2.5 times 10^(21)" "(because n_(e)">>"n_(h))`
Factor `=(n_("final")-n_("initial"))/n_("initial")`
`=(2.5 times 10^(21)-14 times 10^(15))/(14 times 10^(15))approx (2.5 times 10^(21))/(14 times 10^(15))1.8`