With the source terms properly computed, the dimensionless Poisson equation can now be solved for the guess potential for the Ga-and N-face triangular geometries. Specifically, the S D ( x, ỹ) and ∇ • P source terms are used as input for the "f" coefficient in the MATLAB PDE Toolbox assempde function . Since the dielectric constant has a spatial dependence in the Poisson equation, the heaviside_core_poiss.m m-file (which returns a value of 1 for inputted ( x, ỹ) values that lie within the core region of the nanowire and 0 otherwise) is used to construct an appropriately scaled ε * ( x, ỹ) term, which is used as the "c" coefficient in the assempde solver. Finally, a boundary condition matrix, b, which enforces Dirichlet or Neumann boundary conditions for V( x, ỹ) at the outer shell boundary, is used as input to assempde. Researchers interested in applying different boundary conditions can simply modify the boundary condition matrix, b, to suit their specific needs (see Ref. for the MATLAB documentation on modifying this variable). The electrostatic potential energy, V( x, ỹ), is then computed and stored in the global variable V_poisson.