Hi,
The potential looks flat-enough. However, I agree that the behavior of this device is quite weird, and I think it is mostly related to the fact that the device is very short, even including doping.
For bulk silicon, the depletion region at the doping that you have considered is around 20 nanometers. For a 2D material, screening will be less effective, and therefore the depletion region will be even larger.
If you don't want to increase further the size of the device, the only solution would be to keep increasing the doping, until the potential in the central region is fully screened. But since your device is very short, you might need to go to quite large values of doping.
Regards,
Daniele