A quantum well transistor or high electron mobility transistor may be formed using a replacement metal gate process. A dummy gate electrode may be used to define sidewall spacers and source drain contact metallizations. The dummy gate electrode may be removed and the remaining structure used as a mask to etch a doped layer to form sources and drains self-aligned to said opening. A high dielectric constant material may coat the sides of said opening and then a metal gate electrode may be deposited. As a result, the sources and drains are self-aligned to the metal gate electrode. In addition, the metal gate electrode is isolated from an underlying barrier layer by the high dielectric constant material.