A method includes providing a wafer that has a semiconductor layer having an insulator layer disposed on the semiconductor layer. The insulator layer has openings made therein to expose a surface of the semiconductor layer, where each opening corresponds to a location of what will become a transistor channel in the semiconductor layer disposed beneath a gate stack. The method further includes depositing a high dielectric constant gate insulator layer so as to cover the exposed surface of the semiconductor layer and sidewalls of the insulator layer; depositing a gate metal layer that overlies the high dielectric constant gate insulator layer; and implanting Carbon through the gate metal layer and the underlying high dielectric constant gate insulator layer so as to form in an upper portion of the semiconductor layer a Carbon-implanted region having a concentration of Carbon selected to establish a voltage threshold of the transistor.