  The transition metal carbides (namely MXenes) and their functionalized
derivatives exhibit various physical and chemical characteristics and offer
many potential applications in electronic devices and sensors. Using density
functional theory (DFT), it is revealed that the nearly free electron (NFE)
states are near the Fermi levels in hydroxyl (OH) functionalized MXenes. Most
of the OH-terminated MXene are metallic, but some of them, e.g. Sc2C(OH)2, are
semiconductors and the NFE states are conduction bands. In this paper, to
investigate the NFE states in MXenes, an attractive image-potential well model
is adopted. Compared the solutions of this model with the DFT calculations, it
is found that due to the overlap of spatially extensive wave functions of NFE
states and their hybridization between the artificial neighboring layers
imposed by the periodical boundary conditions (PBCs), the DFT results represent
the properties of multiple layers, intrinsically. Based on the DFT
calculations, it is found that the energy gap widths are affected by the
interlayer distances. We address that the energetics of the NFE states can be
modulated by the external electric fields and it is possible to convert
semiconducting MXenes into metals. This band-gap manipulation makes the
OH-terminated semiconducting MXenes an excellent candidate for electronic
switch applications. Finally, using a set of electron transport calculations,
I-V characteristics of Sc2C(OH)2 devices are investigated with the gate
voltages.
