A nanowire wrap-gate transistor is realized in a semiconductor material with a band gap narrower than Si. The strain relaxation in the nanowires allows the transistor to be placed on a large variety of substrates and heterostructures to be incorporated in the device. Various types of heterostructures should be introduced in the transistor to reduce the output conductance via reduced impact ionization rate, increase the current on/off ratio, reduction of the sub-threshold slope, reduction of transistor contact resistance and improved thermal stability. The parasitic capacitances should be minimized by the use of semi-insulating substrates and the use of cross-bar geometry between the source and drain access regions. The transistor may find applications in digital high frequency and low power circuits as well as in analogue high frequency circuits.