I agree that only the position of the bands relative to the Fermi level should be important.
However, I observe the following:
When I look at the same system and increase the size of the unit cell, the slope of the curves in the previous picture increases. This means that the shift of the band structure values due to charge addition is increased by using bigger cells (only the values are shifted, the look of the band structure is not influenced). The Fermi level changes as a result, too.
By looking at the Fermi level versus the system size for different doping levels, I obtain the attached picture ("fermi_dependency.png"). Only for big cells, the Fermi level is independent of the cell size.
The observed effect is interesting for us because it correlates with the observed shift of the transfer characteristic of our CNTFET (see
http://quantumwise.com/forum/index.php?topic=2670.msg12714#msg12714). The charged CNT is used as electrodes for the transistor.
We think that the observed effect (shift of the transfer characteristic) comes from electrostatics inside the cell, because the additional charge increases the electrostatic effects inside the cell. Therefore, a bigger cell is needed so that the manipulation of the field by the Neumann boundaries is small.
We know what to do against this effect (using small amounts of charge and big cells), but we don't understand the effect yet.
Maybe someone can enlighten us.