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III-nitride semiconductors combine a wide bandgap with low sheet resistance and, thus, can be used for efficient power electronics. Their lateral architecture also enables monolithic integration on cost-effective silicon. However, electric-field crowding, as well as surface and buffer trapping, limit the breakdown voltage, degrade dynamic performance and reduce reliability. Here we report intrinsic polarization superjunctions in III-nitride heterostructures for efficient power electronics. We use the spontaneous and piezoelectric polarization fields to induce matched mobile electrons in a two-dimensional electron gas and mobile holes in a two-dimensional hole gas, forming an intrinsically charge-balanced superjunction without intentional doping. With an ohmic contact to the two-dimensional hole gas, both carrier types can be dynamically depleted during switching, which preserves drift-region charge neutrality, producing a nearly uniform electric field and increasing the breakdown voltage under operating conditions. We use the approach to create gallium-nitride-on-silicon polarization superjunction Schottky barrier diodes with a breakdown voltage exceeding 3.9 kV and a specific ON resistance as low as 4.7 mΩ cm 2 , as well as polarization superjunction transistors with a breakdown voltage exceeding 3.4 kV. The devices exhibit a near-ideal dynamic ON-resistance degradation of less than 15% up to 3 kV, as well as repeatable, temperature-stable and avalanche-like breakdown.