Within the HADOKEN code, the π -1 m * ( x, ỹ)/m 0 "prefactor" term is calculated in n_e_prefactor.m, the summation n |ψ n ( x, ỹ)| 2 √ ϵ F -ϵ n is computed in psi_sqrt_eps_summation.m, and n_e_func.m utilizes the output of the previous two m-files to ultimately calculate S e as input to the Poisson equation. Thus far, neither the Fermi level nor the NW depletion region has been specified in our computational description. To more concretely describe these concepts, we first describe the Fermi level and depletion region for the (0001) Ga-face triangular core-shell nanowire depicted in Fig. . Due to surface states in these systems (discussed further in Section 4.2), the Fermi level is pinned 1.65 eV below the conduction band edge, as shown in Fig. . The corresponding NW depletion region, colored purple in Fig. , contains the positively-charged (ionized) donors that provide carriers in the NW (i.e., the purple-colored regions contribute a positive-valued dopant density, n D ). For NWs without a Fermi-pinning constraint, HADOKEN can use a charge neutrality condition (discussed further in Section 3) in combination with the solution of the depletion region to calculate ϵ F . The charge neutrality condition requires the total number of positive and negative charges over the entire NW to balance: