A modeling study of mechanisms for NDR in graphene-BN-graphene heterostructures

Heterostructures made out of 2D materials are being actively investigated for a variety of device applications. In this work, we discuss recent results on modeling electrical transport through graphene ? Boron Nitride (BN) ? graphene heterostructures. The main result is that there are two potential mechanisms for negative differential resistance (NDR). We also show how the increase in BN layers changes the device conductance. Non-idealities in the sizes of the layers can alter the device characteristics from a perfectly aligned device. We have initiated this study by varying the size of the layers forming the heterostructure, and report that the peak position and peak to valley ratio of the NDR peak are altered. Finally, we discuss the role of electron-phonon scattering in altering the NDR peak. The calculations of electron transport are carried out using the pi-orbital tight binding Hamiltonian, with electron-phonon scattering. Monolayer graphene and hexagonal BN can be stacked to form heterostructures, with the graphene and BN being the conducting and insulating layers, respectively [1] [2]. The electrical characteristics of such devices are determined by the bandstructure of the underlying materials and the size/shape of the layers. They can further be tuned by the gate voltage and doping. The magnitude of current in these devices are limited by both the width of the graphene sheet and the tunneling through the heterostructure. Figures 1 and 2 show the heterostructure device [1]. While the alignment of the layers is ideal in Figure 1, the layers are of different sizes in Figure 2. The width of the device is Nx, the overlap region of the two graphene sheets is Ny, and the number of BN layers is Nz. When the gate voltage (Vg) is zero and the Fermi energies of the top and bottom graphene layers are at / close to their respective Dirac points, Figure 3 shows two negative differential peaks (red curve). These peaks arise due to a Fabrey-Perot like mechanism due to the quantum box formed by the three layers of the heterostructure [3]. We also remark that the number of resonant peaks is mainly controlled by the overlap length Ny when Nx of the top and bottom layers are identical. When the gate voltage is non zero, the Fermi energy of the graphene sheets are shifted from the Dirac point, and this leads to the second mechanism for current flow. When the applied source-to-drain bias (Vb) is such that the Fermi energies are aligned, electrons can efficiently tunnel from the top to the bottom graphene sheets [3] [4]. This results in a large peak in the current-voltage characteristics (blue curve of Figure 3). The current-voltage characteristics are sensitive to the dimensions of the top and bottom layers for small widths of the heterostructure layers, when the Fabrey-Perot mechanism is in play. Figure 4 shows the current-voltage characteristics for nominally identical devices except when the bottom layer has a width of Nx=62 (blue curve) as opposed to Nx=122 (red curve) at Vg=0V. Clearly, while the NDR features are preserved, detailed features such as the peak location and peak to valley ratio are affected. In contrast, the NDR features are altered to a smaller extent at non zero gate voltages when the second mechanism discussed above is at play (results are not shown here). A single BN layer turns out to be a strong tunnel barrier. Figure 5 shows that increase of number of BN layers by two decreases the low bias conductance by over hundred times (the results are similar for higher biases and are not shown). The small bias conductance with three BN layers is significantly smaller than the quantum of conductance for these narrow width devices. The role of phonon scattering (with both elastic and inelastic scattering) is shown in Figure 6. The main observation is that the NDR peak due to the mechanism of tunneling between graphene layers when the Dirac points are aligned is less affected by electron-phonon scattering (large peak near Vb=