Room-Temperature Graphene-Nanoribbon Tunneling Field-Effect Transistors

Controlled, tunable, and reversible negative-differential resistance (NDR) is observed in lithographically defined, atomically thin semiconducting graphene nanoribbon (GNR)-gated Esaki diode transistors at room temperature. Sub-10 nm-wide GNRs patterned by electron-beam lithography exhibit semiconducting energy bandgaps of ~0.2 eV extracted by electrical conductance spectroscopy measurements, indicating an atomically thin realization of the electronic properties of conventional 3D narrow-bandgap semiconductors such as InSb. A p–n junction is then formed in the GNR channel by electrostatic doping using graphene side gates, boosted by ions in a solid polymer electrolyte. Transistor characteristics of this gated GNR p–n junction exhibit reproducible and reversible NDR due to interband tunneling of carriers. All essential experimentally observed features are explained by an analytical model and are corroborated by a numerical atomistic simulation. The observation of tunable NDR in GNRs is conclusive proof of the existence of a lithographically defined bandgap and the thinnest possible realization of an Esaki diode. It paves the way for the thinnest scalable manifestation of low-power tunneling field-effect transistors (TFETs).


INTRODUCTION
The single-atom thickness of a two-dimensional (2D) sheet of graphene represents the ultimate limit of how thin one can make an electronically active material. [1][2][3] At present, there is no known way to scale a three-dimensional (3D) semiconductor to such a thickness. Structurally, this is not possible, because the chemical bonds are inherently 3D and a unit cell of the crystal cannot be completed in 2D. 4 Electronically, as a conventional 3D-crystal semiconductor is made thinner to approach the single-atom thickness limit, quantum confinement of electron states increases the energy bandgap. 4 As graphene has a two-atom basis, the onsite energies for an electron for the A-and B-atom sites are identical (both are carbon atoms) and the energy bandgap is zero. The zero gap prevents an appreciable modulation of the electronic conductivity upon sweeping the Fermi level through the Dirac point, preventing the realization of traditional Boolean On/Off electronic transistor switches. Nevertheless, several devices that exploit the uniqueness of the bandstructure and the density of states of graphene have been theoretically envisioned and experimentally demonstrated. 5,6 How can the bandgap be opened in an atomically thin material? One way is to break the chemical symmetry of graphene. This is achieved, e.g., in hexagonal boron nitride (hBN), where B and N are the nearest-neighbor atoms that straddle carbon in the same row of the periodic table. hBN is the compound-semiconductor analog of graphene, where the broken chemical symmetry due to the different on-site energies for the basis atoms opens a bandgap 5 eV. 7,8 Because of the large energy gap and chemical inertness, hBN has been used as an insulating barrier for atomically flat and clean van-der-Waals heterointerfaces. [9][10][11] It is possible that in the future similar atomically thin compound materials with bandgaps smaller than hBN will be discovered. A number of gapped semiconductors with broken chemical symmetry exist for thicknesses of tri-atomic layers and beyond, such as the threeatom-thick MoS 2 family, the four-atom-thick GaSe family, etc. [12][13][14] However, as the electrostatic scaling length of a transistor channel goes as λ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi where λ is the electrostatic scaling length, ε s and ε ox are the permittivities of semiconductor and gate oxide, and t s and t ox are the thicknesses of the semiconductor channel and the gate oxide, respectively; the thickness of the channel itself will soon become the limiting factor, for which a one-atom-thick material trumps all others. If chemical symmetry were to be preserved, other symmetries need to be broken to open gaps, e.g., by starting from zero-gap bilayer graphene (no more an atomically thin material) and applying a vertical electric field opens a bandgap. 15,16 Alternately, a gap can be opened by letting the atomic sites pucker out of plane. For example, this geometric symmetry breaking opens bandgaps in phosphorene. 17,18 Carbon nanotubes (CNTs) allow a way to break the cylindrical symmetry by requiring the electron wavefunction to satisfy periodic boundary conditions around the circumference. Depending on the chiral wrapping (armchair vs. zig-zag) and the radius, the density of electronic states of carbon nanotubes change from metallic to semiconducting. 19 Semiconducting nanotubes have been used to demonstrate highly scaled field-effect transistors (FETs) that help fight short-channel degradation because of exceptional electrostatic control in small geometries. 20 Nanotubes remain highly attractive for electronic switches. Significant progress has been made in the separation of semiconducting and metallic tubes. 21 Techniques are being developed to assemble them in specified locations. A lack of precise control over the diameter and chirality results in a lack of control over the bandgap, which is required to make identical electronic switches in large numbers. For large-area applications where high-performance is not necessary, (CNT) FETs are making progress. 22 Transistor on/off switching characteristics that beat the fundamental room-temperature "Boltzmann" limit of (kT/q).ln (10) 60 mV/decade were observed in carbon nanotube channel transistors. 23 This observation spurred significant recent interest in an energy-efficient tunneling FETs (TFETs) in several 3D material systems. 24 However, as the transistor size is scaled, the energy bandgaps of 3D tunneling junctions increase due to quantum confinement, 4 exponentially reducing the on-state tunneling current. This necessitates the use of intrinsically reduced dimensional 2D or one-dimensional (1D) semiconductor materials for scaled TFETs. In an in-plane 2D semiconductor tunnel junction, electrons that are incident on the potential barrier at non-90°a ngles have their tunneling probabilities lowered exponentially; 25,26 this severe filtering rule reduces the tunneling efficiency, suggesting 1D channels as the most energy-efficient for nanoscale TFETs. This is borne out in benchmarking efforts by the semiconductor industry; a GNR-TFET can outperform all currently conceived low-power switches based on charge, spin, excitons, and negative capacitance under the energy-delay product metric. 27 Semiconducting graphene nanoribbons (GNRs) with perfectly controlled edges are the most desirable channel materials for TFETs, [26][27][28][29] although not without their own slew of fabrication challenges. Although CNTs are perfectly cylindrical, GNRs lay flat on a substrate and have broken bonds at the edge. This apparent problem may well become a defining feature. It has proven chemically difficult to dope a CNT by the substitution of donor or acceptor atoms, because there are no sites available for covalent bonding. This opportunity is available in GNRs. The possibility of large-area 2D lithographic patterning, the ability to grow largearea graphene, 30 the excellent heat dissipation on account of laying flat on the substrate, 31 and all the other reasons described above make GNR TFETs a difficult, yet desirable challenge. In this work, we present the experimental realization of a roomtemperature GNR-TFET. Although the techniques used here, and the performance, are far from what is desired of a highperformance TFET, our demonstration proves conclusively that the dream of a lithographically defined atomically thin 1D TFET platform is not just conceptually sound, it is experimentally feasible. The theoretical analysis of experiments helps identify the research directions that can take this initial demonstration to a truly attractive low-power sub-Boltzmann switch.

RESULTS AND DISCUSSION
In a recent work, 32,33 we experimentally showed that lithographically defined atomically thin,~10 nm-wide GNR-FETs (not TFETs) could mimic the electronic behavior of InSb nanowire FETs 34 in switching, showing the opening of an energy bandgap of the order of~0.2 eV (the bandgap of InSb is~0.17 eV). In Fig. 1a, we show an image of a similarly fabricated sub-10 nm back-gated GNR-FET, but now with two additional side gates to enable the Esaki diode formation, and realization of a GNR TFET. The entire graphene region, the long GNR channel, and the side gates are patterned from a monolayer chemical vapor deposition (CVD)grown graphene using electron-beam lithography (Supplementary Fig. S1). The source and drain contacts to the GNR are made to zero-gap wide 2D graphene regions. 32,33 Figure 1b shows the measured temperature-dependent transfer characteristics and Fig.  1c shows the conductance spectrum measured at 4 K without side-gate bias for the "control" GNR-FET. The conductance modulation and its temperature dependence indicates the opening of an energy bandgap of~0.2 eV for the GNR channel. The measured data and its temperature dependence looks remarkably similar to that of an InSb nanowire FET of gap~0.17 eV. 34 However, as the GNRs are lithographically defined, they remain atomically thin as opposed to carbon nanotubes and InSb nanowires, and can be produced in large and reproducible quantities because of significant advances in lithography. For example, the widths of fins in current Si FinFETs are well below 10 nm 35 and such processing tools can be brought to action to mass produce tightly controlled narrow GNRs in the future if there is promise in their behavior.
We then test the effect of side gates to introduce a p-n junction in the GNR channel ( Supplementary Fig. S2). Although techniques to chemically dope GNRs have been reported, [36][37][38][39][40] they have yet to provide the degree of control necessary for the demonstration of the TFET action. We have therefore chosen a solid polymer electrolyte gate in this work to enable the side gates to dope the GNR channel locally ( Supplementary Fig. S2). Although both solid polymer electrolytes 41 and ionic liquids 42 are frequently used to gate organic and inorganic FETs, we choose a solid polymer electrolyte, because it is solid state and has a low gate to source leakage current. 43 Furthermore, the electrolytes polyethylene oxide (PEO) and LiClO 4 s have been used previously to induce charge carrier densities in 2D graphene greater than n~10 13 cm −2 . 44 Figure 2a schematically shows how the polarity of the gate sets the channel doping: when a negative voltage is applied to side-gate 2, the positive Li ions are attracted to the gate pad and the negative ClO 4 ions to the GNR channel. This causes the GNR channel to be doped p-type. Then a higher positive back-gate voltage should be necessary to move the Fermi level to its chargeneutrality point. The experimental positive shift in the chargeneutrality point is picked up in the measured room-temperature transfer curve shown in Fig. 2d. By varying the side-gate voltage, the measured drain current in Fig. 2d shows that the GNR channel can be doped n-or p-type by a single side gate. Figure 2c schematically shows that if voltages of opposite polarity are applied to the two side gates, a p-n junction should form in the GNR channel. Figure 3a shows the transfer characteristics of the device when the side gates are biased with opposite polarity. Two chargeneutrality points appear in the experimentally measured transfer characteristics, proving the formation of a p-n junction in the GNR channel. 36 Although the measurement was conducted at room temperature, any possibility of Joule heating was ruled out during the operation, based on the low drain voltage of 0.2 V and excellent heat dissipation of graphene, there might be a very little chance for the heat to affect the device performance. The voltage difference between two current minima increases with the strength of the side-gate bias, as indicated by the circles in the figure. This is simply because the side gates are far more effective in doping the GNR channel than the back gate. The use of ions, their unfettered access to the GNR channel, and their inability to participate in the electron current transport are responsible for this significant enhancement. Figure 3b shows the calculated transfer characteristics of the GNR-TFET using a simple analytical model. 32 The simple model uses thermionic emission and tunneling currents in the channel, appropriately gated with the device capacitances, and captures the entire region of operation of the experimentally measured transfer curve, including the splitting and movement of the charge-neutrality points (see Supplementary Section 3 and Fig. S3). This agreement also indicates the band-like transport in the GNR channel (as opposed to hopping) and the successful realization of a gated GNR p-n junction. The comparison between experiment and model showed that the charge-neutrality points (Fig. 3a) are changing exponentially, while the points (Fig. 3b) are changing linearly. The difference could possibly be attributed to the difference in ion mobility between Li + and ClO 4 − . Whereas in the modeling work, the Li + and ClO 4 − ions respond at the same rate to the same potential, in reality the movement is likely to be different because of differences in ion size, mobility, and changes in local dynamics with changing ion concentration. In addition, as shown in this comparison between experiment and model, the on-current density of 6 μA/10 nm at a supply voltage of 0.2 V was experimentally obtained, while that of 40 μA/10 nm at a supply voltage of 0.2 V was extracted by the model. The degraded oncurrent density of the GNR-FET compared with the modeled value was presumably due to the imperfect characteristic of the formed GNR such as edge disorder and defects. This difference of around ten times between experiment and model can also be found in ref. 28 The currents in Fig. 3 are at a fixed drain bias of 0.2 V; the proof of tunneling is in the I d − V ds output characteristics of the GNR TFETs shown in Fig. 4.   Figure 4a shows the measured output characteristics of the GNR-TFET measured at room temperature with the two side gates oppositely biased at ±2.0 V, for various back-gate voltage and drain voltages. A clear and reproducible negative-differential resistance (NDR) is observed at room temperature for a range of back-gate voltages and for negative drain bias voltages. The NDR vanishes for positive drain voltages. If the opposite polarity sidegate voltages are removed, the NDR also vanishes for negative drain voltages, as shown in Fig. 4b. The measured roomtemperature characteristics of Fig. 4b are that of a p-channel GNR-FET with no tunneling, whereas that in Fig. 4a is that of a GNR-TFET. This is the report of NDR in a GNR-TFET. The same analytical model that was used for the transfer characteristics in Fig. 3b also qualitatively reproduces the GNR-TFET output characteristics as shown in Fig. 4c. The fact that the model is able to reproduce all essential features of the device attests to its qualitative accuracy. However, the extreme quantized nature of the GNR electronic states implies that the measured experimental data be compared with an atomistic simulation for quantitative insight.
Before setting up the atomistic model, in Fig. 5 we have explained the measured operation regimes of the GNR-TFET through energy-band diagrams. The NDR due to Esaki tunneling should be observed only for negative drain voltages, because the source-end of the GNR is doped p-type by side-gate 1. Under these conditions, the GNR pn junction is under a small forward bias, the regime for interband Esaki tunneling of electrons from the conduction band in the n-side to the empty valence-band states in the p-side. The NDR occurs at the drain bias when the band edges go out of alignment. For positive drain voltages, no NDR is expected, because the current is due to interband Zener tunneling, for which there is no chance for band edges to go out of alignment as indicated in Fig. 5. In Fig. 4a, it is also observed that for positive drain voltages the current monotonically increases and does not turn off. The on/off switching in Fig. 4b, although modest, is much more pronounced when the side gates are not biased. This is because to switch the device off, the back gate must stretch the junction tunneling distance and lower the tunneling probability. However, it is unable to so because the far stronger electrostatic doping of the two side gates boosted by the polymer electrolyte overrides this desired back-gate control. Thus,  As side-gate 1 is on the source side and is negatively biased, it makes the GNR source p-type, setting the polarity of the GNR p-n junction. When the drain voltage is large and negative, the p-n diode is forward biased and the normal diode thermionic on-current flows. For small forward biases for smaller negative drain voltages, interband Esaki tunneling current flows from the n-conduction band states to the pvalence-band states, leading to NDR. For positive drain voltages, the GNR is reverse biased and interband Zener tunneling current flows in the device although the polymer electrolyte is useful for demonstrating the NDR action, the monotonic increase of the drain current under Zener tunneling also exposes its limitation. To achieve gain in a GNR-TFET, it is desirable that the Zener current saturates and is controlled by the (back) gate voltage as indicated by the gray lines in Fig. 5. These observations point towards the need of direct donor and acceptor doping in the GNR channel without polymer electrolytes in future embodiments, and also underlines the need for narrower GNRs with increased bandgaps in the future. To solidify this qualitative observation, we have employed a comprehensive electrostatic and quantum transport simulation.
The numerical atomistic simulation of the GNR-TFET characteristics is performed using a self-consistent solution of Poisson equation for electrostatics and Schrodinger equation for the electronic bandstructure and quantum transport. For the quantum mechanical portion of the atomistic simulation a p-d tight-binding basis set was used 45 for determining the energy bandstructure and the transmission formalism was used for calculating the current. Scattering effects are not explicitly included, but lumped into an effective mean-free path and contact resistances ( Supplementary Figs S4 and S5). Figure 6a shows the results of the atomistic simulation of the GNR-TFET output characteristics superposed on the measured experimental data. The agreement supports the qualitative analysis and the analytical models, and also offers quantitative insight. For example, the shift in the NDR peak with increasing side-gate doping occurs as the tunneling energy window indicated in Fig. 6b is widened. The energyresolved current spectrum indicates the peak current flows near the middle of the tunneling window. Although this feature is similar to the increase in Esaki tunneling current as a pn diode is doped heavier, the energy-resolved local density of states (LDOS) in Fig. 6c shows a very abrupt tunnel junction with reflections and interference of electron waves occurring over~4 nm as visible in the LDOS oscillations. Such features are not captured easily in a typical effective mass Wentzel-Kramers-Brillouin (WKB) approximation. The agreement between the experimental data and the numerical model in Fig. 6a also highlights the importance of the atomistic modeling. The performance will continue to improve as the side gate is brought closer to the GNR, while preventing leakage. In addition, the performance will continue to improve if the width is scaled down from the~10 nm to~5 nm, but it will start degrading if the GNR width is scaled down even lower. This is because the I off decreases when the GNR is scaled to smaller widths exponentially as~1/W, but the interband tunneling oncurrent I on decreases with the GNR width exponentially.
To conclude, we have experimentally demonstrated roomtemperature operation of atomically thin GNR TFETs. Every feature in the operating characteristics can be understood from a combination of lithographically defined bandgaps and gated interband Easki and Zener tunneling current flow. The measured NDR tunneling current density is~1 mA/μm shown in Fig. 4. The larger-than-intended drain voltages necessary are significantly limited by contact and access resistances, as discussed in the Supplementary Materials. The on/off ratio is limited by both the contacts and the wide GNR width. The measured switching performance of these GNR TFETs at this stage are a far cry from what may be considered attractive for realistic applications; scaling of the GNR width and lower contact resistances are predicted to take the GNR-TFET performance close to those predicted in refs. 27,28 However, the observation of roomtemperature gate-tunable NDR in GNR channels is remarkable in its own right. In addition to proving the concept of atomically thin 1D TFETs based on GNRs, the shortcomings of the device reported here also clearly lay down the challenges ahead. Indeed, the control of narrow GNR widths on hBN with controlled edges and orientations, although challenging, was recently reported, 46,47 which would be beneficial to exploit the inherent advantages of GNRs. The single most challenging task at this juncture to which no clear solution is in sight is to dope the GNR by taking advantage of the broken bonds at the edges. This step would mark a significant breakthrough, because it will not only enable completely controlled GNR TFETs, but also the simpler GNR-FETs −the ideal nanoscale transistors that carbon nanotubes have promised all along.

Device fabrication
The GNRs were fabricated by electron-beam lithography (EBL). Hydrogen silsesquioxane (HSQ) diluted with methylisobutylketone is used as a negative electron-beam resist to pattern the GNRs and the details of the entire EBL process have been discussed in previous publications. 33,48 Figure S1a shows the width of patterned HSQ lines as a function of the electron-beam dose. The width from the scanning electron microscope image in Fig. S1b is proportional to the line dose of the electron beam. After etching away the uncovered graphene by O 2 plasma, the GNR width remains sub-10 nm, showing that the HSQ width is successfully transferred onto the graphene layer. Cr (5 nm)/Au (150 nm) were deposited by e-beam evaporation to form source/drain (S/D), side-gate, and back-gate metal electrodes. The S/D metals sit on top of the zero-bandgap 2D graphene regions to decrease the contact resistance. Unless otherwise stated, all materials were obtained from Sigma Aldrich. One gram of PEO (M w 100,000 g/mol) was dissolved in 38 g of acetonitrile by mixing with a Teflon stir bar in a Teflon beaker. As commercial PEO contains micrometer-sized particles of SiO 2 , the solution is purified by centrifugation. To purify, the solution is transferred to two 50 mL centrifuge tubes (VWR) and centrifuged at 19,000 × g for 5 min. The transparent supernatant is returned to the Teflon beaker, whereas the precipitate is discarded. Battery-grade LiClO 4 (0.12 g; 99.99% purity) is added to the PEO/acetonitrile solution and stirred for several hours. This PEO:LiClO 4 ratio corresponds to an ether oxygen to Li ratio of 20:1. The solution is spin-coated onto the GNR-TFET at a spin-speed of 1000 RPM for 30 s and annealed for 5 min at 95°C. This anneal temperature is well above the melting temperature (60°C) of the polymer electrolyte at an ether oxygen to lithium ratio of 20:1. 49 The sample is cooled to room temperature by removing it from the hotplate and placing it directly on a cleanroom wipe on the counter top. The thickness of the (PEO) 20 :LiClO 4 film is 100 nm, measured by ellipsometry. The side-gate metal and the electrolyte act as electrostatic doping agents by manipulating the electric potential of GNRs through mobile Li+ and ClO À 4 ions in PEO, thus creating a p-n junction.

Analytical model approach
We have used a simple drift-diffusion analytical model to capture the correct electrostatics of the problem ( Supplementary Fig. S4), before applying a full quantum transport + electrostatics to explain the expeimentally measured device characteristics. The current is the integral of the charge and mobility over the entire channel length. The charge density at a specific location is calculated based on the channel potential and density of states of graphene. The channel potential is solved based on the chargeneutrality equation.

Atomic non-equilibrium Green's function approach
The experimental data were also correlated with an atomistic nonequilibrium Green's function approach based on a p/d orbital tight-binding (p/d TB) model 50 in which {p z , d yz , d zx } orbitals are included ( Supplementary  Fig. S5). Although there have been several theoretical studies about GNR TFETs, most of them are limited to the simple p z orbital tight-binding (p z TB) model 51,52 in which only the p z orbital is included in calculations and some of them are limited to the WKB approximations. 28 The simple p z TB model only works for 2D graphene without considering edge effects. The p/d TB model, however, is more accurate than the simple p z TB model in terms of the bandstructure, as it is calibrated to first-principle calculations and explicitly includes passivated hydrogen atoms in the Hamiltonian matrix. 50

DATA AVAILABILITY
All data derived from the experiments and calculations of this study are available from the corresponding author upon reasonable request.  Figure S3. Graphene nanoribbon tunnel-field effect transistor device geometry top and side views, and the corresponding simple circuit model that is used for analytical modeling. Figure S4. Effective mobility μeff as a function of the channel length L is obtained from the experimentally measured the ID-VD characteristics through fitting [9] to an analytical formula [10]. The effective mobility calculated from an analytical relation between long channel mobility to the short channel mobility is fitted to the previously calculated effective mobility with a least square fit. The mean free path λ of 793 nm and long channel mobility of 707 cm 2 /Vs give the best fit. 4 Figure S5. Current spectrum and density of state for the doping of 2.2 x10 13 / cm 2 . Figure S2 shows normalized ID as a function of normalized VBG at with ion-assisted and without ion-assisted electrostatic doping. It shows that side gates (without ions) can modulate the charge carrier density in the GNR channel, but needing much higher side gate voltages compared to the side gates with ions. It also shows that ions in the polymer minimize the parastic capacitance and can enhance the GNR channel controllability to form an abrupt pn Esaki junction in the GNR.

Supplementary Discussion
Analytical modeling of the GNR device characteristics : Figure S3 shows and Cq is the density-of-states or quantum capacitance of the graphene nanoribbon channel. 5 The current is calculated by the the Shockley gradual channel drift-diffusion model where q is the electron charge, W and L are the width and length of the GNR, n(x) the carrier density in the channel at x, the coordinate from the source to drain. The drift velocity of carriers is where m is the electron mobility, vsat the saturation velocity, and F is the electric field in the xdirection. The carrier density is related to the local channel potential, the bandgap by where  Using this electrostatics model, we added a simple analytical WKB component to the current to further capture the NDR as indicated in Fig 4(c), under the appropriate bias conditions to compare to the experimental measurement in Fig 4(a). Even though the calculated current is much larger 6 than experimental results due to the lack of the additional contact resistance in the simple model, the IPEAK -Ivalley in the NDR region is very close, and the model also captures the correct polarity for the Esaki NDR tunneling in the -ve bias, and the Zener interband tunneling in the forward bias condition. For higher precision, a numerical simulation combining electrostatics with quantum transport is next described.

Atomic Non-equilibrium Green's function approach:
The simulated structure is a p-n diode with the length of the p-and n-type regions equal to 30 nm. The effective doping density is assumed to reflect electrostatic doping. Since the simulation is conducted in a ballistic regime, a more realistic comparison with experimental data requires taking into account scattering. The ratio between the ballistic current and the scattering limited current is calculated from [1].
This equation requires the mean free path for scattering, λ, to calculate the scattering limited current. The mean free path for scattering is calculated from the effective mobility μeff extracted from the measured ID-VD characteristics of the GNRFET structure. The measured ID-VD characteristics are fitted with the analytical model [2], allowing μeff only as a fitting parameter [3].
The mean free path is then obtained by fitting the μeff vs. channel length curve to the experimental data. For a given λ, the μeff can be calculated from the relationship between the long channel mobility μlong and μeff [1]: A mean free path = 793 nm and μlong = 707 cm 2 /Vs give the best fit to the measured data using least square method as shown in Fig. S4. After the ballistic current is calculated from 7 quantum transport calculations, the scattering limited current is calculated from Eq. 1 using λ = 793 nm. It is noted that the results in the fig. S4 was extracted from epi-graphene but the scattering caused by GNR edge should be comparable to that from CVD graphene since the entire process integration including GNR formation is identical both of them. Then the series resistance RSD is tuned to match the simulated thermionic current part with experimental data. The resulting RSD is 300 Ωm. The trend and the shape of the calculated ID-VD matches well the experimental data.
However, the simulation data are for a symmetrically doped un-gated p-n diode while the experimental data are for a tunneling transistor with a p-n junction and a back-gate. Therefore, the results need some interpretations. The experimental ID-VD characteristics show no NDR at VG = 0 V. This indicates that when no back-gate voltage is applied, the effective doping concentration of either p-or n-doped region is not big enough to allow (Esaki) tunneling to occur. This can be explained by the following. Without a voltage applied to the side gates, the original GNR is a strong p-type. With a side-gate voltage VG1 = -2 V, the GNR under the side-gate G1 becomes a weak n-type while a side-gate voltage VG2 = 2 V gives an even stronger p-type for the GNR under the side-gate G2. This implies that, without a back-gate voltage, the p-n junction doping concentration is asymmetric (p+++-n−). Only when a back-gate voltage is applied, the overall bands are shifted down (because the back-gate covers the whole region of the GNR) and the effective doping concentration of the n-doped region starts to be comparable to that of p-dope region and hence the ID-VD characteristic shows a strong NDR. When the NDR peak becomes the largest, the p-n doping is the closest to symmetric. Therefore, the effective doping concentrations in the experimental structure can be estimated by comparing the tunneling current at the maximum NDR peak of the experimental data to the NDR peak of the simulation data. Since the NDR peak in the simulation data with NS = ND = 5.5x10 13 cm −2 is similar to the maximum NDR peak current 8 in the experimental data at VG =1.5 V, the effective doping concentrations of the p-and n-doped regions created experimentally are estimated to be 5.5x10 13 cm −2 .
Notice that not only the peak is similar, but the overall shape including the drain voltage VD where the NDR occurs is also very similar. Both the tunneling current and the drain voltage at the NDR peak are determined by tunneling window EFD -EFS where EFS/EFD is the source/drain Fermi level as shown in Fig. S5. Therefore, the tunneling window for different back-gate bias VG in experiment can be estimated from the simulation results as well. These results as a whole confirm a successful creation of a GNR tunneling transistor with a capability of the back-gate controlling the tunneling current magnitude. Optimizing the GNR TFET structure is beyond the scope of this article, but one can argue that doping modulation in TFETs can drastically change their on/off current [4]