Methods of making optoelectronic devices containing functional elements made from layers liberated from natural and/or fabricated lamellar semiconductor donors. In one embodiment, a donor is provided, a layer is detached from the donor, and the layer is incorporated into an optoelectronic device as a functional element thereof. The thickness of the detached layer is tuned as needed to suit the functionality of the functional element. Examples of functional elements that can be made using detached layers include p-n junctions, Schotkey junctions, PIN junctions, and confinement layers, among others. Examples of optoelectronic devices that can incorporate detached layers include LEDs, laser diodes, MOSFET transistors, and MISFET transistors, among others.