The invention relates to a semiconductor device with a heterojunction bipolar, in particular npn, transistor with an emitter region (1), a base region (2), and a collector region (3), which are provided with respectively a first, a second, and a third connection conductor (4, 5, 6), while the bandgap of the base region (2) is lower than that of the collector region (3) or of the emitter region (1), for example owing to the use of a silicon-germanium alloy instead of pure silicon. Such a device is very fast, but its transistor shows a relatively low BVceo. In a device according to the invention, the emitter region (1) or the base region (2) comprises a sub-region (1B, 2B) with a reduced doping concentration, which sub-region (1B, 2B) is provided with a further connection conductor (4B, 5B) which forms a Schottky junction with the sub-region (1B, 2B). Such a device results in a transistor with a particularly high cut-off frequency fT but with no or hardly any reduction of the BVceo. In a preferred embodiment, the emitter region (1) and its sub-region (1B), or the base region (2) and its sub-region (2B) both border the surface of the semiconductor body (10) and the further connection conductor (4B, 5B) forms part of the first or the second connection conductor (4, 5), as applicable. The invention also comprises a method of manufacturing a device according to the invention.