  Transition metal dichalcogenides (TMDCs), with their two-dimensional
structures and sizable bandgaps, are good candidates for barrier materials in
tunneling field-effect transistor (TFET) formed from atomic precision vertical
stacks of graphene and insulating crystals of a few atomic layers in thickness.
We report first-principles study of the electronic properties of the
Graphene/WS$_2$/Graphene sandwich structure revealing strong interface effects
on dielectric properties and predicting a high ON/OFF ratio with an appropriate
WS$_2$ thickness and a suitable range of the gate voltage. Both the band
spin-orbit coupling splitting and the dielectric constant of the WS$_2$ layer
depend on its thickness when in contact with the graphene electrodes,
indicating strong influence from graphene across the interfaces. The dielectric
constant is significantly reduced from the bulk WS$_2$ value. The effective
barrier height varies with WS$_2$ thickness and can be tuned by a gate voltage.
These results are critical for future nanoelectronic device designs.
