Your system is not really periodic, it is a 2D quantum dot - I suppose. You should consider increasing the in-plane lattice parameters and using non-periodic boundary conditions (Dirichlet and/or Neumann) in the Poisson solver settings to avoid interaction between periodic images.
In addition, there is no guarantee that your dot is unstable and would form some weird structure. Would it make more sense to put in on some substrate, instead of having it free-standing.