Direct fabrication and characterization of vertically stacked Graphene/h-BN/Graphene tunnel junctions

We have used a lithography free technique for the direct fabrication of vertically stacked two-dimensional (2D) material-based tunnel junctions and characterized by Raman, AFM, XPS. We fabricated Graphene/h-BN/Graphene devices by direct deposition of graphene (bottom layer), h-BN (insulating barrier) and graphene (top layer) sequentially using a plasma enhanced chemical vapor deposition on Si/SiO2 substrates. The thickness of the h-BN insulating layer was varied by tuning the plasma power and the deposition time. Samples were characterized by Raman, AFM, and XPS. The I-V data follows the barrier thickness dependent quantum tunneling behavior for equally doped graphene layers. The resonant tunneling behavior was observed at room temperature for oppositely doped graphene layers where hydrazine and ammonia were used for n-doping of one of the graphene layers. The resonance with negative differential conductance occurs when the band structures of the two electrodes are aligned. The doping effect of the resonant peak is observed for varying doping levels. The results are explained according to the Bardeen tunneling model.


Introduction
The tunneling transport phenomenon in quantum devices offers picosecond switching speeds and hence the possibility of designing very high-speed devices. Two-dimensional electron gas (2DEG) systems have played a vital role in the development of superior electronic devices [1]. However, one lesser-known device that utilized 2DEGs is a tunnel junction consisting of two such gases [2,3], realizing 2D-2D tunneling. Previous studies of 2D-2D tunneling were conducted on coupled electron gas systems in two closely placed quantum wells in AlGaAs/GaAs heterostructures [3,4]. In the case of unequal doping of the 2DEGs, it has been shown experimentally that, at a voltage bias corresponding to aligned band structures of the 2D systems, a sharp peak in the tunnel current occurs [1,[5][6][7][8]. This peak is referred as a resonant peak in the tunneling. It was claimed in the prior work that the width of this resonant peak was temperature independent (except possibly from inelastic effects) [6,[9][10][11].
Presence of negative differential resistance (NDR) is characteristic of the current-voltage relationship of a resonant tunneling device [12], enabling many unique applications [13]. The existence of devices with NDR has been reported since the late 1950's in devices that contained degenerately doped p-n junctions with thin oxide barriers (tunnel diodes) and double barrier heterojunction devices [14] where quantum tunneling effects are utilized. The NDR in the I-V characteristics of these devices has been used in many applications [15] involving microwave/ millimeter wave oscillators, high speed logic devices and switches.
With the advent of the new 2D electronic material systems, it has opened a new route for 2D-2D tunneling in such extended systems [16]. Two-dimensional(2D) materials such as graphene, hexagonal-boron nitride Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. metal dichalcogenides (TMDCs) and phosphorene etc have gained a vast interest due to their excellent performance in novel electronic, optoelectronic and photovoltaic applications [17][18][19][20][21][22]. Graphene and h-BN have been unsuitable for electronics applications which require tunable band gap materials since graphene is metallic while h-BN being wide band gap semiconductor [23]. Strong reactivity of phosphorene, with oxygen and water and requires to be sandwiched between layers of other materials if it is to last longer than a few hours [24]. TMDCs are much slower conductors of electrons than graphene or phosphorene, even though they are semiconducting and stable. In order to evade such limitations, researchers have attempted a combination of metallic (graphene etc), insulating (h-BN etc) and semiconducting (MoS 2 etc) [25]. 2D materials to facilitate functional heterostructure devices. Features of this approach include; adding some functionality into such 2D structures [26][27][28], combining into nanocomposites to optimize many inherent properties such as optical absorption etc [29,30] and, stacking them vertically layer-by-layer or arrange laterally by seamlessly stitched in-plane heterojunctions [31][32][33].
Heterostructures play a vital role in semiconductor industry. The newly developed monolayer 2D materials offer a platform that allows creation of heterostructures with a variety of novel properties [34].Many structural, physical, and chemical properties have been explored on Van der Waals heterostructures created by monolayers of multiple 2D materials with vertically stacked layered heterojunctions [35][36][37][38][39]. Since these heterostructures utilize the Van der Walls interlayer interaction, lattice matching is no longer a significant factor. The interface is atomically sharp, and the junction can be as thin as two atomic layers to reach the ultimate limits. Such stacks are very different from the traditional 3D semiconductor heterostructures, as each layer acts simultaneously as the bulk material and the surface and thereby reducing the amount of charge displacement within each layer. In addition, these structures are flexible and stable with compatible fabrication thin-film technologies.
In recent years, there have been various studies on graphene-2D materials heterostructures demonstrating novel charge transport properties across the interface [38,40,41]. Such graphene-TMDs structures have been introduced for various device applications and, also been of particular interest in the spectroscopy community [38,[42][43][44]. For example, many groups demonstrated the vertical tunneling transistors with high on-off ratios and large current densities that used TMDs thin layers as tunneling barriers and graphene as one or both electrodes [34,35,38,40,45].
An ideal 2D material for next generation of functional devices should meet the following important criteria. They must be (i) one-atom thick (for fastest conduction of electrons), (ii) be highly stable (even at high temperatures), (iii) possess a small and tunable band gap and, (iv) scalable in both synthesis and processing with the ability to integrate with existing technology etc.
Lithography methods in various forms are widely used in many research fields for making functional devices, including tunnel junctions. In the traditional top-down lithography technology, high-cost equipment including predesigned masks and collimated light sources are used, which also include complex and time-consuming production steps. Electron beam lithography has capability to write nanoscale patterns without using any physical mask [46], but again the expensive equipment and low patterning speed associated with it suppress its extensive applications [47]. Further, 2D materials having single or few atomic layers, are particularly sensitive to surface contaminants, including resist residues left behind by lithographical processes, which in turn modify the electrochemical potential and act as extra scattering sites. Though annealing techniques have been demonstrated to improve device mobility [48,49], they are not well controlled and do not always yield consistent results.
However, the employment of a vertical geometry enables overcome of both (i) the lithographical limitations inherent with in-planar geometry and (ii) poor scalability still sustaining large current modulations. Thus, there has been significantly increased interest on improving bottom-up techniques of lithography-free patterning in recent years. To achieve regular nanoscale patterns without using any mask, techniques like laser interference and nanosphere lithography have been developed as alternative routes [50]. Lithography-free fabrication techniques have been reported especially for simple geometries yielding simple, inexpensive [51], and free of resist processing with increased device throughput. Most importantly, lithography free techniques can be used by anybody who doesn't have access to clean room facility.
Here, we experimentally investigate the possibility of using graphene/h-BN/graphene in direct quantum tunnel junctions [75] and resonant tunneling devices. With the recent advancements of synthesis of graphene and h-BN on any arbitrary substrate using PECVD and fabrication of vertically stacked electronic devices using a simple lithography free technique allows us to address this question easily and rapidly since h-BN has great potential to be used as the tunneling barrier layer in functional heterostructure devices. The combination of graphene and h-BN opens up the exciting possibility of creating a new class of atomically thin multilayered heterostructures. In particular, this work focuses on the situations when the two graphene sheets have unequal doping, e.g., one is n-type (electron doped) in a single tunnel junction device and the other is p-type (hole doped). In this study, graphene and h-BN were directly deposited by radio frequency-plasma enhanced chemical vapor deposition (RF-PECVD) [76]. In the case of graphene, methane (CH 4 ) gas was used whilst ammonia borane was used for h-BN synthesis [77].

Experimental
Graphene was directly deposited on Si/SiO 2 substrate using RF-PECVD technique developed in our laboratory [78]. A home-made split ring radiofrequency (13.56 MHz, Max. power 600 W) system was used for plasma generation. Proper cleaning of the substrate is a required to avoid any kind of contamination prior to synthesizing the graphene layer as a thin film on the entire Si/SiO 2 substrate. Therefore, all the substrates were sonicated in acetone for 10 min and dried in a flow of nitrogen before placing them inside the quartz reactor. Then the reactor was evacuated to a pressure lower than ∼5 mTorr and gradually heated to 650°C in a flowing gas mixture: Ar/H 2 (40 vol% argon, 60 vol% H 2 ) at a flow rate of ∼20 standard cubic centimeter per minute (sccm). The pressure was maintained at ∼200 mTorr during this temperature ramp. Hydrogen plasma was ignited at the power of 50 W for 20 min after the heating step. Pure CH 4 (99.8%) at a flow rate of ∼3 sccm was introduced into the growth chamber immediately after switching off the Ar/H 2 and plasma power of ∼80 W was maintained for 30∼120 min. The samples were then cooled down to room temperature at a rate 25°C min −1 . [79] Next, we prepared the sample for the deposition of h-BN using PECVD with ammonia borane (with 97% purity) as the source material [80]. The substrate with previously deposited graphene layer was covered with a circular shadow mask was placed inside the reactor at a desired position. Then, a ceramic boat containing borane ammonia borane was located in between the plasma reactor and the furnace. A heat belt was wrapped over the quartz tube covering the ceramic boat to sublime borane ammonia. Then the reactor was evacuated until the pressure lower than ∼5 mTorr and gradually heated to 750°C with the gas mixture: Ar/H 2 (40 vol % argon, 60 vol % H 2 ) at a flow rate of ∼50 sccm. The ceramic boat was heated gradually from room temperature up to 180°C and left for 45 min. and the plasma was maintained at 100 W [81]. The samples were then cooled down to room temperature at a rate 25°C min −1 . Finally, the third graphene layer was deposited as before using another mask with a smaller opening [34].
As prepared graphene shows p-type behaviour. To be used in resonant tunneling devices, it was n-doped by exposing to hydrazine at room temperature. The graphene sample was placed inside a reactor which was connected to a vial containing hydrazine. The reactor was pumped and hydrazine was admitted to a pressure of 10 Torr in sequence. We also synthesized n-type graphene directly by PECVD using anhydrous ammonia with CH 4 . Same procedure as in the synthesis of p-type graphene was followed except that ammonia gas was introduced along with CH 4 as a dopant for 10 min. Figure 1 shows the aforementioned sequential processes of fabricating graphene/h-BN/ graphene-based device. The top raw in figure 1 represents the schematic diagrams while the bottom raw show the optical images of the sample after each step. (a) bare Si/SiO 2 substrate (b) Si/SiO 2 substate completely coated with graphene (c) h-BN patch defined on the bottom graphene layer using a circular mask (6 mm diameter) (d) final graphene top layer deposited on the h-BN patch using a circular mask (3 mm diameter)

Characterization
Graphene and h-BN films were characterized by Raman spectroscopy with a spectral resolution better than 1 cm −1 . A Renishaw inVia spectrometer with a grating of 1800 lines mm −1 , a charge-coupled device (CCD) detector was used with 632 nm laser excitation. Figure 2 shows the Raman spectrum of graphene and h-BN. The Raman peaks of graphene appearing at 1346 cm −1 , 1596 cm −1 , 1628 cm −1 , and 2677 cm −1 are characteristic of D, G, D', and 2D bands of graphene. The D (1346 cm −1 ) band is known as the disorder band associated with the defects of graphene. G (1596 cm −1 ) is a primary in-plane vibrational mode involving the sp2 hybridized carbon atoms that comprises the graphene sheet. The D'-band (around 1628 cm −1 ) is associated with edges and structural disorder in graphene films [82]. is 0.82. The PECVD technique allows the growth of graphene on both conductive and insulated substrates with almost the same quality. The Raman spectrum of h-BN consisting of a peak at ∼1367 cm −1 with the FWHM of 13 cm −1 which is assigned to the high-frequency vibrational mode (E 2g ) [34].
X-ray photoemission spectroscopy was also used to analyze the synthesized 2D films. XPS analysis was performed using a VG Scientific MultiLab 3000 ultra-high vacuum surface analysis system with a dual-anode (Mg/Al) x-ray source, a CLAM4 hemispherical electron energy analyzer. and at a base pressure of 10 -9 Torr was used for x-ray photoelectron spectroscopy (XPS) measurements. The measurements were conducted using a non-monochromatized Al Kα x-ray radiation (hν ≈ 1486.6 eV) at a base pressure of 10 -9 Torr. The C-C (sp 2 ) peak of adventitious carbon at 284.5 eV was used for the binding energy (BE) calibration. Figure 3 shows the x-ray photo-emission spectroscopy (XPS) results of h-BN grown by PECVD. The survey spectrum shown in figure 3(a) clearly shows the presence of boron and nitrogen with the appearance of XPS peaks corresponding to B1s and N1s core electrons [34]. As expected, an additional peak corresponding to O1s core electrons is also present in the survey spectrum. The unexpected peak characteristic of C1s core electrons is presumably due to the carbon contamination resulting from previous synthesis of graphene in the same reactor. Figures 3 (b) and (c) show the high-resolution individual peaks, B1s and N1s at the binding energies (BE) 198.6 eV and 406.8 eV, respectively. These BEs are consistent with the reported XPS characteristic values for h-BN. Stoichiometry evaluation based on B1s and N1s peak areas gives B/N ratio of 1.08, suggesting equal composition of B and N elements in h-BN.     and frequency range 58−97 kHz. The average thicknesses of samples were found to be 2.23, 4.04, and 6.85 nm respectively [83] Figure 5 shows the tunneling I-V characteristic curves of three Graphene/h-BN/Graphene based single tunnel junctions with varying h-BN thicknesses (tunnel barrier widths). All three curves show exponential dependence of the current (I) with the bias voltage (V) at higher voltages. We also calculated the slope of the linear range of each curve about V=0 to evaluate the zero-bias conductivity (ZBC). The ZBC of the samples were found to be 1.760 GΩ −1 , 0.356 GΩ −1 and 0.025 GΩ −1 as the h-BN barrier width increases from the thinnest to the thickest, revealing the exponential dependence of the ZBC with the barrier width [34].

Direct quantum tunneling
We will simulate the tunneling current using the following formalism [6]. The tunneling current, I can be expressed as, where, α and β represent the top (T) and bottom (B) electrodes with energies, E α and E β respectively, g s = 2 is the spin degeneracy and g ν is the valley degeneracy, τ αβ and τ βα are the tunneling rates for electrons tunneling from top → bottom and bottom → top respectively and f T and f B are Fermi occupation factor for the top and bottom electrodes given by, The tunneling current can be simplified as, is the density of states in the top (bottom) electrode, T(E) is the transmission probability at the given energy. Figure 5(b) shows the tunneling current calculated for varying h-BN thicknesses according to equation (3). In the simulation, we assumed relativistic density of states of graphene, DOS(E)∼|E| and restricted the energy integral limits μ and μ+eV, where μ is the chemical potential.
It is also assumed that there is no in-plane momentum conservation, The calculated tunneling currents qualitatively agree very well with the experimental results for appropriate h-BN thicknesses.

Resonant tunneling with unequal doping
Here the same sequential processes were used for fabricating p-graphene/h-BN/n-graphene based device [84]. First n type graphene (n-graphene) was deposited using PECVD using NH 3 in addition to CH 4 on a Si/SiO 2 substrate. Next, through a mask with a circular opening, h-BN was deposited on previously deposited graphene again using PECVD with ammonia borane as described before. Finally, the third p-type graphene (p-graphene) layer was deposited using another mask with a smaller opening. The thermopower of p and n-graphene was measured using the analog-subtraction method developed in our laboratory. Two miniature thermocouples (Chromel (KP)/Au−7 at. % Fe (Au/Fe); 100 μm diameter) and a resistive heater were used for the measurements. The as deposited graphene was found to be p-type with the thermopower of +60 μV K −1 . In order to n-dope graphene, it was exposed to hydrazine. Figure 6(a) shows the thermopower response of graphene when exposed to hydrazine at room temperature. The downward arrows indicate where hydrazine was introduced to a pressure of 3, 7 and 10 Torr. After the first exposure to 3 Torr, the thermopower decreased and turned negative and eventually saturated at a value ∼10 μV K −1 . Further exposure to the pressures of 7 Torr and 10 Torr resulted in saturating the thermopower at∼−55 and ∼−80 μV K −1 respectively. The n-doped graphene with ammonia shows the thermopower ∼250 μV K −1 ( figure 6(b)). Figure 7(a) shows the I-V characteristics of p-Graphene/h-BN/n-Graphene samples with 3 different levels of n-doping. The I-V curves of all three samples show the presence of a pronounced peak in the current corresponding to negative differential conductance (NDC) whose peak current value and the voltage value depend on the doping level of the n-layer. It is assumed that the doping level of the p-layer is the same as it's due to the intrinsic doping presumably due to an electrochemically mediated charge transfer process [85] under the ambient conditions. It can be seen that the peak current and the peak voltage increase when the doping level of the n-layer increases. Figure 7

Conclusion
In conclusion, we have demonstrated a direct method for fabricating devices with atomically thin tunnel barriers by direct deposition of h-BN with graphene (doped and undoped) active electrode layers on a Si/SiO 2 substrate using a PECVD method. A variety of devices including unequally doped graphene electrodes separated by a thin h-BN layer were also fabricated by using different doping methods of these materials for the upper and lower electrodes. Our measurements of the electron tunnel current through the barrier demonstrate that the h-BN films act as a good tunnel barrier. Current-voltage measurements for different BN thicknesses and equally doped graphene based single barrier tunneling shows linear I-V characteristics at low bias but shows an exponential dependence at higher bias. The tunnelling devices consisting of unequally doped graphene with a single barrier shows resonant quantum tunneling with the presence of a pronounced peak in the current corresponding to negative differential conductance (NDC) whose peak current value and the voltage value depend on the doping levels. The results are explained according to the modified Bardeen tunneling model.