where e is the charge of an electron, ε( x, ỹ) is the spatially-dependent static dielectric constant, ρ D ( x, ỹ) is the charge density arising from the presence of ionized donors, ρ e ( x, ỹ) is the electron density, P (= P s +P p ) is the total polarization source term discussed previously (which is only relevant for the Ga-face or N-face triangular nanowires), and S D ( x, ỹ) and S e ( x, ỹ) are defined as source terms due to the ionized donors and electron density, respectively. In the HADOKEN code, ε * ( x, ỹ) is computed using the heaviside_core_poiss.m routine which is subsequently used as input for the "c" coefficient in the MATLAB PDE Toolbox assempde command. It is important to note that ∇ in Eq. ( ) is the twodimensional gradient operator (= [∂/∂x, ∂/∂y]) in regular (not reduced) variables. The S D ( x, ỹ) and S e ( x, ỹ) source terms in Eq. ( ) are discussed separately below, and the ∇ • P term is discussed in greater detail in Section 4.2. Finally, the HADOKEN code can utilize either Dirichlet or Neumann boundary conditions for Eq. ( ) where either V( x, ỹ) or its derivative, respectively, are set to zero at the outer shell boundary. For computational convenience, both S D ( x, ỹ) and S e ( x, ỹ) are expressed in terms of electron and donor number densities, n e and n D , within the HADOKEN code as