When a (semi)conductor is connected to a voltage bias, a charge is injected by the electrodes. When steady state is reached (constant current flow), does the total charge of the (semi)conductor differ when compared to when a voltage bias is zero? If yes, where does this extra charge come from?
Depending on the boundary conditions doping profile, current density voltage characteristic, etc., of a semiconductor sample you can get a total non-zero charge in a piece of semiconductor upon applying a voltage which is different from the zero voltage and current case. Due to charge conservation this charge must of course come from outside the semiconductor region considered. On the other hand, when you include the metal contacts in a Gauss surface enclosing the semiconductor, the total charge in this region will be zero because the electric field in the metal contacts are negligible even with a current is flowing.