Methods of fabricating semiconductor devices or structures include bonding a layer of semiconductor material to another material at a temperature, and subsequently changing the temperature of the layer of semiconductor material. The another material may be selected to exhibit a coefficient of thermal expansion such that, as the temperature of the layer of semiconductor material is changed, a controlled and/or selected lattice parameter is imparted to or retained in the layer of 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 layer of semiconductor material having an average lattice parameter at room temperature proximate an average lattice parameter of the layer of semiconductor material previously attained at an elevated temperature.