I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons equation inside and outside the semiconductor. To do so I need to supply it with some boundary conditions. Since the metal is a conductor the electrostatic potential should approach a constant at the metal boundary. Furthermore I should also specify the electrostatic potential in the vacuum region far away from the semiconductor, i.e. at infinity. But what should this value be? Obviously it should be a constant but I do not think it should be the same constant as in the metal. What are your thoughts on this?