A high-voltage termination structure includes a peripheral voltage-spreading network. One or more trench structures are connected at least partly in series between first and second power supply voltages. The trench structures include first and second current-limiting structures connected in series with a semiconductor material, and also includes permanent charge in a trench-wall dielectric. The current-limiting structures in the trench structures are jointly connected in a series-parallel ladder configuration. The current-limiting structures, in combination with the semiconductor material, provide a voltage distribution between the core portion and the edge portion.