A method of fabricating a transistor device includes forming a non-crystalline germanium layer on a seed layer. The non-crystalline germanium layer is selectively locally heated to about a melting point thereof to form a single-crystalline germanium layer on the seed layer. The non-crystalline germanium layer may be selectively locally heated, for example, by applying a laser to a portion of the non-crystalline germanium layer. Related devices are also discussed.