In the manufacture of a trench-gate semiconductor device, for example a MOSFET or an IGBT, a starting semiconductor body (10) has two top layers (13, 15) provided for forming the source and body regions. Gate material (11null) is provided in a trench (20) with a trench etchant mask (51, FIG. 2) still present so that the gate material (11null) forms a protruding step (30) from the adjacent surface (10a) of the semiconductor body, and a side wall spacer (32) is then formed in the step (30) to replace the mask (51). The source region (13) is formed self-aligned with the protruding trench-gate structure with a lateral extent determined by the spacer (32, FIG. 5), and the gate (11) is then provided with an insulating overlayer (18, FIG. 6). Forming the sidewall spacer (32) when the protruding trench-gate structure has a well-defined edge provided by the gate material (11null) allows better definition of the source region (13) compared with a prior-art process in which the gate insulating overlayer is provided in the trench before causing the trench-gate structure to have the protruding step for the sidewall spacer.