How is electron concentration maintained to hole concentration in intrinsic semiconductor?

Question

I know about E-H pair generation because of which in an intrinsic semiconductor the numbers of free electrons=number of holes. In terms of Fermi level, fermi level shifts when the temperature is varied and the product of the density of states and fermi function becomes asymmetrical. How it is then that electron conc. remains equal to hole concentration ?

With temperature Ef changes . Depending on the effective masses, Ef shifts either towards CB or VB. How is concentration still maintained from these equations in the picture?

Answer 1

Band wide state densities Nv and Np assume certain "effective masses" for conduction electrons and holes. Those effective masses make possible to bypass most of the complexity of the material, proper effective masses of electrons and holes make possible to apply simple gas-like behaviour equations to electrons and holes.

The effective mass of a hole is positive - that at least look problematic, because a hole is a lack of an electron. No, worry the effective mass of an electron at conduction band is negative - so much those electrons in crystal bonds differ from freely floating gas.

So, the classic band theory of semiconductors is a huge magician's trick. Continue it, make effective masses depend on temperature so that n=p. Ec and Ev also cannot be exact constants under temperature changes because the material lives under the changes.