The barrier layer 132 may include a material of which an energy band gap is greater than that of the channel layer 128. That is, in exemplary embodiments in accordance with principles of inventive concepts, the channel layer 128 may include the material of which the energy band gap is smaller than those of the barrier layer 132 and the second buffer layer 126 and, as a result, the channel layer 128 may have a quantum well structure. The barrier layer 132 may include silicon (Si), germanium (Ge), silicon-germanium (SiGe), or a III-V group compound. In other exemplary embodiments, the barrier layer 132 may be omitted.
The channel layer 128 and the barrier layer 132 may be formed as described with reference to FIG. 4.
Referring to FIGS. 13A and 13B, the barrier layer 132, the channel layer 128, the second buffer layer 126, the graphene layer 124 including the first and second doped regions r1 and r2, and the first buffer layer 122 may be sequentially patterned to form active patterns AP1 and AP2 on the substrate 100. An upper portion of the substrate 100 may be recessed during the patterning process. During the patterning process, the graphene layer 124 may be patterned to form a first doped pattern 104a including the first doped region r1 and a second doped pattern 104b including the second doped region r2, for example. The active patterns AP1 and AP2 may include a first active pattern AP1, including the first doped pattern 104a, and a second active pattern AP2, including the second doped pattern 104b.