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Nowadays, the superior properties of carbon-based materials especially nano structural derivation like graphene and graphene oxide (GO) spot light to the researchers. The GO has been suggested as an alternate material in device miniaturization due to its atomic structure. The memristors and nonvolatile memories are settled in these categories as a solution for the scaling limitation problem in the Moor’s law. Therefore, the GO can influence the memristor performance and characteristics. The current–voltage characteristics as the most significant parameter in the memristor design are considered. On the other hand $I$–$V$ characteristic depends on the active layer (GO) bandgap energy in the metal/oxide/metal structure and therefore, needs to be explored. In the GO-based memristor, the bandgap energy can be changed by the percentage of the oxygen groups in comparison to the carbon on graphene sheets. Thus, the other parameters are overstated by the bandgap energy. In the presented work, the energy bandgap of a high epoxy group content of GO sheets is engineered. The opening of the bandgap in the graphene oxide by high epoxy groups content with the ratio of (O/C $=$ 50%) is studied. In other words, the oxygen adsorption effect on the Hamiltonian of the system is explored. For the proposed structure, the bandgap energy is modeled and the acceptable value (approximately equal to 2.799ev for epoxy groups) is obtained. Moreover, the hydroxyl group adsorption effect on the bandgap of the graphene oxide by high content hydroxyl group is considered (approximately equal to 2.647ev for epoxy groups). Consequently, the different absorption energy effects on the bandgap of the GO is participated and the opening bandgap in the range of 2ev to 3ev is obtained. The excitonic effect on the suggested model by epoxy groups and hydroxyl groups is explored and it is realized that the energy levels in the Dirac points of epoxy groups are closer than those of the hydroxyl groups.