A trench-gate semiconductor device (100) has a trench network (STR1, ITR1) surrounding a plurality of closed transistor cells (TCS). The trench network comprises segment trench regions (STR1) adjacent sides of the transistor cells (TCS) and intersection trench regions (ITR1) adjacent corners of the transistor cells. As shown in FIG. 16 which is a section view along the line II-II of FIG. 11, the intersection trench regions (ITR1) each include insulating material (21D) which extends from the bottom of the intersection trench region with a thickness which is greater than the thickness of the insulating material (21B1) at the bottom of the segment trench regions (STR1). The greater thickness of the insulating material (21D) extending from the bottom of the intersection trench regions (ITR1) is effective to increase the drain-source reverse breakdown voltage of the device (100). The insulating material (21D) which extends from the bottom of each intersection trench region (ITR1) may extend upwards to thicken the insulating material at the corners of the cells (TCS) over at least part of the vertical extent of the channel-accommodating body region (23) so as to increase the threshold voltage of the device.