Fermi level in extrinsic semiconductors

prudhvi mohan

Fermi level in an extrinsic semiconductor(after attaining thermal equilibrium) is said to be invariant (constant ) , and the proof uses the fact 'no current must flow thorough any cross-section'..But I don't think its true, charge will be transported due to diffusion and this is countered by drift current( Fermi level must vary for drift to occur) ? Please tell me my mistake