Let `(Delta)E`denote the energy gap between the valence band and the conduction band.The population of conduction electrons (and of the holes)is roughly proportional to `e^(-Delta E//2kT).`Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room tempareture 300K.`(Delta E)`for silicon is 1.1 ev and for diamond is 6.0eV.How many conduction electrons are likely to be in one cubic meter of diamond ?

Explanation

Give `n = e^(-DeltaE/2KT)`
`Delta E(Diamond) = 6eV`
`Delta E(Si) = 1.1ev.`
`n_1 = e^(-DeltaE_1/2KT)`
`= (-6)/(e^2xx300xx8.62xx10^(-5))`
`n_2 = e^(-DeltaE_2)/ (2KT)`
`= ((-11)/e^2xx300xx8.62xx10^(-5))`
`(n_1)/(n_2) = (4.14722xx10^(-51))/(5.7979xx10^(-10))`
`= 7.15xx10^(-42)`
Due to more `Delta E`, the conduction electrons per cubie metre in diamond is alomst zero.