A hetero-structure field effect transistor, including: a first contact and a second contact; a hetero-junction structure (3,4,8,9), said hetero-junction structure including: a first layer made from a first semiconductor material; a second layer made from a second semiconductor material, and an interface at which said first layer and said second layer are in contact with each other, and along which a two dimensional electron gas is formed in a part of said first layer directly adjacent to said interface, for propagating of electrical signals from the first contact to the second contact or vice versa; said transistor further including: a gate structure provided at a side of said second layer opposite to the interface for controlling a conductance of a path through the hetero-junction structure, between the first contact and the second contact; a substrate layer made from a substrate semiconductor material, and a dielectric layer separating said first layer from said substrate layer; in which transistor said second contact includes an electrical connection between said substrate layer and said first layer, said electrical connection including a passage through at least said dielectric layer, said passage being filled with an electrically conducting material which is electrically connected to the first layer characterized in that said electrically conducting material has a higher conductivity than said first semiconductor material. a first contact and a second contact; a hetero-junction structure (3,4,8,9), said hetero-junction structure including: a first layer made from a first semiconductor material; a second layer made from a second semiconductor material, and an interface at which said first layer and said second layer are in contact with each other, and along which a two dimensional electron gas is formed in a part of said first layer directly adjacent to said interface, for propagating of electrical signals from the first contact to the second contact or vice versa; said transistor further including: a first layer made from a first semiconductor material; a second layer made from a second semiconductor material, and an interface at which said first layer and said second layer are in contact with each other, and along which a two dimensional electron gas is formed in a part of said first layer directly adjacent to said interface, for propagating of electrical signals from the first contact to the second contact or vice versa; said transistor further including: a gate structure provided at a side of said second layer opposite to the interface for controlling a conductance of a path through the hetero-junction structure, between the first contact and the second contact; a substrate layer made from a substrate semiconductor material, and a dielectric layer separating said first layer from said substrate layer; in which transistor said second contact includes an electrical connection between said substrate layer and said first layer, said electrical connection including a passage through at least said dielectric layer, said passage being filled with an electrically conducting material which is electrically connected to the first layer characterized in that said electrically conducting material has a higher conductivity than said first semiconductor material.