For both of the Ga-and N-face triangular geometries that contain spontaneous and piezoelectric polarization source terms, the guess potential is obtained by numerically solving the dimensionless Poisson equation in Eq. ( ) without the S e ( x, ỹ) source term. In addition, the S D ( x, ỹ) source term in Eq. ( ) is approximated as a constant for this first iteration of the Poisson equation to obtain the guess potential. As discussed in Section 2, the spontaneous polarization source term yields a charge density at each of the three GaN/AlGaN interfaces for the triangular crosssection. From classical electrostatics, this interfacial charge density is formally represented by a Dirac delta function at each of the three interfaces. For example, the charge density at the polar interface for the Ga-face orientation is given by σ s = (0.0156 C/m 2 ) δ(ỹ + c √ 3/6) within the domain -c/2 ≤ x ≤ c/2, where c is the core side length. This delta function charge distribution is implemented in the rho_semipolar_inside.m m-file as a Gaussian function of the form ρ(