A semiconductor cooling arrangement wherein a semiconductor is affixed to a thermally and electrically conducting carrier such as by brazing. The coefficient of thermal expansion of the semiconductor and carrier are closely matched to one another so that during operation they will not be overstressed mechanically due to thermal cycling. Electrical connection is made to the semiconductor and carrier, and a porous metal heat exchanger is thermally connected to the carrier. The heat exchanger is positioned within an electrically insulating cooling assembly having cooling oil flowing therethrough. The arrangement is particularly well adapted for the cooling of high power switching elements in a power bridge.