(2) or (3). As discussed further in Section 3, it is important to note that the HADOKEN code sets the zero of energy at the minimum of the conduction band edge for NWs obeying a charge-neutrality constraint. In contrast, the zero of energy is set at the outer shell edge for NWs constrained with an externally-pinned Fermi level. For computational convenience, the Schrödinger equation in the HADOKEN code is converted to a dimensionless form using the following reduced variables: x = x/ℓ 0 , ỹ = y/ℓ 0 , z = z/ℓ 0 , and E = ϵC, where ℓ 0 is a characteristic length scale, C = ℏ 2 /2m 0 ℓ 2 0 , and m 0 is the electron rest mass. Within the HADOKEN code, ℓ 0 is set to 10 nm, which correspondingly sets the energy scaling factor C to be 0.381 meV. Assuming translational invariance along the z-axis, the envelope wavefunction in Eq. ( ) can be factored as Ψ n (r) = e ikz ψ n (x, y)/