Semiconductor device including a metal carrier substrate. Above the carrier substrate a first semiconductor layer of Alx1Gay1Inz1N (x1+y1+z1=1, x1≧0, y1≧0, z1≧0) is formed. A second semiconductor layer of Alx2Gay2Inz2N (x2+y2+z2=1, x2>x1, y2≧0, z2≧0) is arranged on the first semiconductor layer and a gate region is arranged on the second semiconductor layer. The semiconductor device furthermore includes a source region and a drain region, wherein one of these regions is electrically coupled to the metal carrier substrate and includes a conductive region extending through the first semiconductor layer.