Rather than opening a gap in bilayer graphene, this tuned the magnitude of overlap in TGN. Based on the energy dispersion of biased TGN, wave vector relation with the energy (E-k relation) shows overlap between the conduction and valence band structures, which can be controlled by a perpendicular external electric field [6, 39]. The band overlap increases with GF120918 in vitro increasing external electric field which is independent of the electric field polarity. Moreover, it is shown that the effective mass remains constant when the external electric field is increased [3, 33].

As an essential parameter of TGNs, density of states (DOS) reveals the availability of energy states, which is defined as in [40, 41]. To obtain this amount, derivation of energy over the wave vector is required. Since DOS shows the number of available states at each energy level which can be occupied, therefore, DOS, as a function of wave vector, can be modeled as [39]

(2) where E is the energy band structure and A, B, C, D, and F are defined as A = −6.2832α, B = 14.3849α 2 β, , D = −9β 2, and . As shown in Figure 4, the DOS for ABA-stacked TGN at room temperature is plotted. As illustrated, the low-DOS spectrum exposes two prominent peaks around the Fermi energy [39]. Figure 4 The DOS of the TGN with ABA stacking. The electron concentration is calculated by integrating the Fermi probability distribution function over the energy as in [42]. Biased ABA-stacked TGN carrier concentration is modified as [43] (3) where , the MAPK inhibitor normalized Fermi energy is , and M and N are Fludarabine clinical trial defined as and . Based on this model, ABA-stacked TGN carrier concentration is a function these of normalized Fermi energy (η). The conductance of graphene at the Dirac point indicates minimum conductance at a charge neutrality point which depends on temperature. For a 1D TGN FET, the GNR channel is assumed to be ballistic. The current from source to drain can be given by the Boltzmann transport equation

in which the Landauer formula has been adopted [44, 45]. The number of modes in corporation with the Landauer formula indicates conductance of TGN that can be written as [32] (4) where the momentum (k) can be derived by using Cardano’s solution for cubic equations [46]. Equation 4 can be assumed in the form G = N 1 G 1 + N 2 G 2, where N 1 = 2αq 2/lh and N 2 = −6βq 2/lh. Since G 1 is an odd function, its value is equivalent to zero. Therefore, G = N 2 G 2[32], where (5) This equation can be numerically solved by employing the partial integration method and using the simplification form, where x = (E − Δ)/k B T and η = (E F − Δ)/k B T. Thus, the general conductance model of TGN will be obtained [32] as (6) It can be seen that the conductivity of TGN increases by raising the magnitude of gate voltage. In the Schottky contact, electrons can be injected directly from the metal into the empty space in the semiconductor.