A heterostructure field effect transistor is provided comprising a semiconductor wire comprising in its longitudinal direction a source and a drain region, a channel region in between the source and drain region and in its transversal direction for the source region, a source core region and a source shell region disposed around the source core region, the source shell region having in its transversal direction for the drain region, a drain core region and a drain shell region disposed around the drain core region, the drain shell region having in its transversal direction for the channel region, a channel core region and a channel shell region disposed around the channel core region; wherein the thickness of the channel shell region is smaller than the thickness of the source shell region and is smaller than the thickness of the drain shell region.