A semiconductor device, e.g. a lateral DMOS transistor or bipolar transistor, has a main current path (20) extending through a high resistivity body portion (1) of one conductivity type. A minority-carrier injector region (6) which may be of the opposite conductivity type is provided in the body portion (1) in the vicinity of the current path (20) and serves with an applied forward-bias to inject minority charge carriers (16) which are characteristic of the opposite conductivity type into the body portion (1) to modulate the conductivity of the current path (20). In accordance with the invention one or more further regions (8) of the opposite conductivity type are located in the part of the body portion (1) in the vicinity of the current path (20) and within a minority-carrier diffusion length of the injector region (6) and/or of each other. These further regions (8) float at a potential dependant on the minority-carrier injection (16) from the injector region (6) and serve to inject minority charge carriers (18) into areas of the body portion (1) remote from the injector region (6) so as to modulate the conductivity of these areas of the current path (20). The floating regions (8) may be located within the spread of a depletion layer - (30) from a reverse-biased p-n junction (2) to increase the breakdown voltage of the junction (2). The body portion (1) may be, e.g., a MOST drain drift region or a bipolar transistor collector region or a thyristor base region.