Methods of fabricating a semiconductor structure include providing a semiconductor-on-insulator (SOI) substrate including a base substrate, a strained stressor layer above the base substrate, a surface semiconductor layer, and a dielectric layer between the stressor layer and the surface semiconductor layer. Ions are implanted into or through a first region of the stressor layer, and additional semiconductor material is formed on the surface semiconductor layer above the first region of the stressor layer. The strain state in the first region of the surface semiconductor layer above the first region of the stressor layer is altered, and a trench structure is formed at least partially into the base substrate. The strain state is altered in a second region of the surface semiconductor layer above the second region of the stressor layer. Semiconductor structures are fabricated using such methods.