In the manufacture of a semiconductor power device such as a trench-gate power MOSFET, a source region (13) is formed using a sidewall extension (30) of an upstanding insulated-gate structure (11, 21, 22). The sidewall extension (30) forms a step with an adjacent surface area (10a') of a body region (15) of a first conductivity type and comprises doped semiconductor material (13a) of opposite, second conductivity type which is separated from the gate (11) by insulating material (22). The body region (15) provides a channel-accommodating portion (15a) adjacent to the gate structure (11, 21, 22) and also comprises a localised high-doped portion (15b) which extends to a greater depth in the semiconductor body (10) than the shallow p-n junction between the source region (13) and the channel-accommodating portion (15a), and preferably deeper even than the bottom of the trench (20) of a trench-gate device. This high-doped portion (15b) is formed by introducing dopant of the first conductivity type into the semiconductor body (10) via the stepped-down adjacent surface area (10a') while using the stepped-up sidewall extension (30) comprising the doped source region material (13a) to mask the underlying channel area. Source electrode material (33) is deposited over the step so as to contact the doped semiconductor material (13a) of the sidewall extension (30) and the adjacent surface area (10a') of the high-doped portion (15b).