A semiconductor device, such as a MOSFET or PN diode rectifier, has a p-n junction (24) between a first device region (23) and an underlying voltage-sustaining zone (20). Trenched field-shaping regions (40) extend through the voltage-sustaining zone (20) to improve the voltage-blocking and on-resistance characteristics of the device. The trenched field-shaping region (40) comprises a resistive path (42) accommodated in a trench (41) that has an insulating layer (44) at its side-walls. The insulating layer (44) dielectrically couples potential from the resistive path (42) to the voltage-sustaining zone (20) that is depleted in a voltage-blocking mode of operation of the device. The insulating layer (44) extends at the side-walls of the trench (41) to an upper level (81) that is higher than a lower level (82) at which the resistive path (42) starts in the trench (41). This lower level (82) is more closely aligned to the p-n junction (24) and is protected by the insulating layer (44) extending to the higher level (81). This construction enables the electric field distribution in the voltage-sustaining zone (20) to be improved by aligning very closely the start of the potential drop along the resistive path (42) with the p-n junction depth (d).