Methods of transferring a layer of semiconductor material from a first donor structure to a second structure include forming a generally planar weakened zone within the first donor structure defined by implanted ions therein. At least one of a concentration of the implanted ions and an elemental composition of the implanted ions may be formed to vary laterally across the generally planar weakened zone. The first donor structure may be bonded to a second structure, and the first donor structure may be fractured along the generally planar weakened zone, leaving the layer of semiconductor material bonded to the second structure. Semiconductor devices may be fabricated by forming active device structures on the transferred layer of semiconductor material. Semiconductor structures are fabricated using the described methods.