Methods of fabricating semiconductor devices or structures include forming structures of a semiconductor material overlying a layer of a compliant material, subsequently changing the viscosity of the compliant material to relax the semiconductor material structures, and utilizing the relaxed semiconductor material structures as a seed layer in forming a continuous layer of relaxed semiconductor material. In some embodiments, the layer of semiconductor material may comprise a III-V type semiconductor material, such as, for example, indium gallium nitride. Novel intermediate structures are formed during such methods. Engineered substrates include a continuous layer of semiconductor material having a relaxed lattice structure.