A semiconductor device includes: a semiconductor die having first and second opposite surfaces, a die pad having the first surface of the semiconductor die attached thereon, an electrically conductive ground pad at the second surface of the semiconductor die, a device package coupled with the semiconductor die with the ground pad lying between the semiconductor die and the package, and ground wiring or tracks for the semiconductor die between the second surface of the semiconductor die and the ground pad. A further ground connection may be provided between the ground pad at the second surface of the semiconductor die and the die pad having the semiconductor die attached thereon.