Methods of fabricating a semiconductor device include forming a first semiconductor layer of a first conductivity type and having a first dopant concentration, and forming a second semiconductor layer on the first semiconductor layer. The second semiconductor layer has a second dopant concentration that is less than the first dopant concentration. Ions are implanted into the second semiconductor layer to form an implanted region of the first conductivity type extending through the second semiconductor layer to contact the first semiconductor layer. A first electrode is formed on the implantedregion of the second semiconductor layer, and a second electrode is formed on a non-implanted region of the second semiconductor layer. Related devices are also discussed.