Methods Operating principle A near-midgap state in the zigzag graphene nanoribbon (zzGNR)  with periodic edge roughness is extensively studied in . In this work, we study novel device characteristics where the channel consists of a 1-nm wide zzGNR as shown in Figure 1a. The device structure is shown in Figure 1b, where the channel is gated by two side gates to create an electric field in the width direction. For such a side-gated nanoribbon, we show the electronic structure in Figure 1c
using extended Hückel STA-9090 molecular weight theory (see [8–12] for the detailed model). The two interesting electronic structure features are a significant band gap opening of about 2 eV, which is not very sensitive to the external electric field, and secondly a near-midgap state with a finite bandwidth, the bandwidth and dispersion of which can be manipulated by the gate-induced electric field. In Figure 1d, we show the dependence of the bandwidth on the gate voltage in the limit of relative permittivity
of the gate dielectric to be much larger than that of the nanoribbon. Figure 1 Device structure and operating principle of an electronic structure modulation transistor. (a) The channel consists of a 1-nm wide hydrogenated zigzag graphene nanoribbon with edge roughness. (b) The channel is side-gated to create an electric field in the width direction. Gate dielectric
surrounds the channel and is not shown for clarity. (c) For such a ribbon, a near-midgap state with AZD1480 chemical structure a small bandwidth is observed which can be modulated by the gate-induced electric field (left = 0 V/nm electric field, middle = 0.2 V/nm electric field, right = zoomed bandwidth comparison for the two electric fields). (d) The bandwidth of the near-midgap state is linearly dependent on the gate voltage . Such a bandwidth modulation can be understood in terms of the real-space localization of the wavefunction for various momentum values. At the Γ point, the wavefunction of the near-midgap state is distributed throughout the nanoribbon width, whereas at the X point is localized on the pristine edge. Additionally, the wavefunctions are localized on Vasopressin Receptor only one sublattice of graphene . By applying a positive gate voltage at this edge, the energy find more values shift downward, thereby increasing the bandwidth as shown in Figure 1c. One should note that such modulation may happen due to intrinsic or extrinsic electric fields. In case of gate-voltage-induced modulation (extrinsic electric field) as shown in Figure 1d, the BW is given as follows: (1) where α is a dimensionless parameter, called the modulation factor. BWo is the residual BW at zero gate voltage (Mag ≡ absolute magnitude) and V g is the applied gate voltage. In Figure 1d, α = 0.47 and BWo = 0.12 eV.