The breakdown voltage of planar junctions (both non-punch-through and punchthrough cases) equipped with field plate and guard ring is determined by evaluating the ionization integral using the potential distribution computed by solving Poisson's equation in two-dimensions, by finite difference method. The influence of various parameters such as substrate doping concentration, n-layer thickness, field oxide thickness, cylindrical junction curvature, field plate width, and the spacing between field plate and guard ring, on the breakdown voltage is extensively studied. It is shown that an optimum value exists for the field oxide thickness to realize maximum breakdown voltage. The study also shows that the optimum oxide thickness depends upon cylindrical junction curvature, substrate doping concentration, and n-layer thickness. It is further shown that the permittivity of passivant dielectric layer deposited over field plate structure influences the breakdown voltage when breakdown takes place at the field plate edge. The numerical results are compared with the experimental data and good agreement between the two is observed. Based on this two-dimensional study, design guidelines are provided for achieving breakdown voltages close to maximum realizable values, by conserving the device area and reducing the ionization at the field plate edge. The results presented in this paper clearly demonstrate the superiority of the field plate design employing punch-through structures over non-punch-through structures in realizing a given breakdown voltage.