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We survey impact-ionization coefficients for silicon, wide bandgap semiconductors (gallium nitride and 4H-silicon carbide), and ultrawide-bandgap semiconductors (aluminum gallium nitride, beta-gallium oxide, and diamond). We employ a custom genetic algorithm to fit those existing coefficients into a modified Thornber model. This fitting process leads to an estimation of material properties, such as ionization energy, optical-phonon energy, and mean free path. After evaluating electric-field profiles by solving the Poisson equation, we use the impact-ionization integral to fundamentally calculate the breakdown voltage and the critical field of various p-i-n structures. This work captures how the doping concentration and the thickness of the drift layer shape the breakdown voltage as well as the critical field achievable with a given material. It is observed that a wider bandgap is not the sole requirement for the achievement of a higher breakdown voltage. Impact-ionization coefficients and dielectric constants are additional material properties that influence the calculation of the breakdown voltage. The performance limits of diamond are found to be surprisingly poor for its large bandgap. Al x Ga 1- x N and <inline-formula> <tex-math notation="LaTeX">\beta </tex-math></inline-formula>-Ga 2 O 3 have almost the same performance limits, but it is observed that aluminum gallium nitride can outperform gallium oxide at high voltage if its background doping (doping floor) can be reduced.