For the quantum transport, we use the non-equilibrium Green’s function formalism [14]. We consider the coherent limit where it is equivalent to the Landaüer’s approach, and the current can be evaluated from the transmission as below: (2) where transmission is T(E) = tr(Γ s GΓ d G +). The Green’s function for the channel is (3) where I is an identity matrix and U L is the Laplace’s potential drop. Self-energies click here and broadening functions are and Γ s,d

= i[Σ s,d − Σ s,d +], respectively. are the contact Fermi functions. μ s,d are source/drain chemical potentials. μ d is shifted due to drain bias as μ d = μ o − qV d and μ s = μ o, where μ o is the equilibrium chemical potential. Results and discussion We next discuss the numerical results for a transistor with α = 0.4 and BWo = 0.1 eV. The transfer characteristics with V d = 0.16, 0.18 and 0.2 V are shown in Figure 2a. A steep subthreshold slope is obtained with a high on/off current ratio. The threshold voltage depends on the drain voltage V d, and it increases with the drain bias – a trend opposite to the drain-induced barrier

lowering of a FET. The subthreshold current much below the threshold voltage, which is due to the reflections from the barrier of the near-midgap state, decreases exponentially. Figure 2 Transport characteristics. (a) Transfer characteristics show steep subthreshold characteristics with drain-voltage dependent threshold voltage shift. (b) Output characteristics show a saturating behavior followed by a negative ACP-196 differential resistance. (c) With increasing drain bias, the C1GALT1 transmission window shrinks due to a spectral misalignment (Addition file 1). (d) The increasing Fermi function difference between the two

contacts and the decreasing transmission lead to an increasing and then decreasing T(E)[f s − f d] function. We further report the output characteristics in Figure 2b for V g = 0.04, 0.08, 0.12, 0.16, and 0.2 V, which show a negative differential resistance (NDR) behavior that is crucial for the low-power inverter operation (Additional file 1). The current cut-off mechanism is similar to the Bloch condition through minibands in superlattices, giving rise to an NDR event, when the drain voltage exceeds the miniband width [15, 16]. The miniband in superlattices is formed by the overlap of quantized states through tunnel barriers, inherently leading to small miniband widths and large effective masses [17]. The NDR events mediated by minibands have been reported in III-V heterostructures [18] and graphene superlattices [19]. However, the peak-to-valley ratio in such structures is limited to about 1.1 to 1.2. In comparison, the NDR feature reported for near-midgap state in this work shows a peak-to-valley ratio of greater than 103, which is important for the low-power operation.