Self-aligned local electrolyte gating of 2D materials with nanoscale resolution

In the effort to make 2D materials-based devices smaller, faster, and more efficient, it is important to control charge carrier at lengths approaching the nanometer scale. Traditional gating techniques based on capacitive coupling through a gate dielectric cannot generate strong and uniform electric fields at this scale due to divergence of the fields in dielectrics. This field divergence limits the gating strength, boundary sharpness, and pitch size of periodic structures, and restricts possible geometries of local gates (due to wire packaging), precluding certain device concepts, such as plasmonics and transformation optics based on metamaterials. Here we present a new gating concept based on a dielectric-free self-aligned electrolyte technique that allows spatially modulating charges with nanometer resolution. We employ a combination of a solid-polymer electrolyte gate and an ion-impenetrable e-beam-defined resist mask to locally create excess charges on top of the gated surface. Electrostatic simulations indicate high carrier density variations of $\Delta n =10^{14}\text{cm}^{-2}$ across a length of 10 nm at the mask boundaries on the surface of a 2D conductor, resulting in a sharp depletion region and a strong in-plane electric field of $6\times10^8 \text{Vm}^{-1}$ across the so-created junction. We apply this technique to the 2D material graphene to demonstrate the creation of tunable p-n junctions for optoelectronic applications. We also demonstrate the spatial versatility and self-aligned properties of this technique by introducing a novel graphene thermopile photodetector.

In the effort to make 2D materials-based devices smaller, faster, and more efficient, it is important to control charge carrier at lengths approaching the nanometer scale. Traditional gating techniques based on capacitive coupling through a gate dielectric cannot generate strong and uniform electric fields at this scale due to divergence of the fields in dielectrics. This field divergence limits the gating strength, boundary sharpness, and pitch size of periodic structures, and restricts possible geometries of local gates (due to wire packaging), precluding certain device concepts, such as plasmonics and transformation optics based on metamaterials.
Here we present a new gating concept based on a dielectric-free self-aligned electrolyte technique that allows spatially modulating charges with nanometer resolution. We employ a combination of a solid-polymer electrolyte gate and an ion-impenetrable e-beam-defined resist mask to locally create excess charges on top of the gated surface. Electrostatic simulations indicate high carrier density variations of ∆n = 10 14 cm −2 across a length of 10 nm at the mask boundaries on the surface of a 2D conductor, resulting in a sharp depletion region and a strong in-plane electric field of 6 × 10 8 V m −1 across the so-created junction. We apply this technique to the 2D material graphene to demonstrate the creation of tunable p-n junctions for optoelectronic applications. We also demonstrate the spatial versatility and self-aligned properties of this technique by introducing a novel graphene thermopile photodetector.
Keywords: graphene, 2D materials, nanoscale electrolyte gating, high carrier density, optoelectronics, p-n junctions, thermopile Modulation of charge carrier concentration of semiconductors lies at the heart of many electronic and optoelectronic device operation principles 1,2 . This modulation is especially essential for two-dimensional (2D) van der Waals materials 3-10 where it is usually much stronger (from 0.15 electrons/cell to 15 electrons/cell) compared to bulk materials and can be dynamically tuned with electrostatic gating methods. In recent years, rapidly developing device concepts and applications impose stronger and stronger requirements on the spatial resolution and highest-achievable carrier concentration of gating techniques. For example, a spatially sharp (∼10 nm) p-n junction and a high carrier density contrast across the junction is the key to the realization of concepts such as tunnel diodes 11 and negative electron refractive index 12 . A strong in-plane electric field across the junction as a result of the junction sharpness facilitates electron-hole pair separation in the photovoltaic (PV) effect 13 and thus can improve the quantum efficiency of PV-based solar cells and photodetectors 14 . Many novel device concepts also rely on the a) Contributed equally to this work b) Electronic mail: englund@mit.edu ability to create metamaterials with spatial carrier density variations down to the nanometer scale, including for instance graphene with periodically doped nanodisk or nanoribbon arrays for complete optical absorption in the visible and near-infrared 15,16 , graphene with doped waveguide, bend and resonator patterns for a plasmonbased nanophotonic network 17 , and superlattices based on graphene and other 2D materials for concepts such as electron beam supercollimation [18][19][20][21] . Implementing these concepts calls for a gating method that allows for sharp p-n junctions with narrow depletion regions (∼10 nm), large carrier density contrasts (10 14 cm −2 ), strong in-plane electric fields (6 × 10 8 V m −1 ), and the versatility to generate complex spatial doping profiles with a nanoscale resolution.
The state-of-the-art electrostatic gating technique for modulating charge carrier concentration and creating p-n junctions is the metal-dielectric split gate technique [22][23][24] . This method is based on the electric field effect 25 in which electric voltages are applied across a gate dielectric to induce extra charges on the 2D material surface. A pn junction can be created by applying opposing electric potentials to the two sides of a boundary to induce charges with opposite polarities. Although this technique is convenient, several limitations restrict its use when more extreme requirements are desirable: In terms of carrier density contrast, dielectric-based gating can only induce a carrier concentration variation ∆n of less than 2 × 10 13 cm −2 for typical dielectrics such as SiO 2 , HfO 2 , SiN, and hexagonal-BN, due to a maximal applicable voltage across the dielectrics before the dielectric breakdown (molecular bond breakage and defects) [26][27][28] . In terms of junction sharpness, the carrier density has a slowly varying profile across the junction due to electric field divergence in dielectrics, with a characteristic length similar to the thickness of the dielectric, making it hard to create sharp junctions at nanoscale unless with extremely thin (a few nanometers) dielectrics which typically has undesirable leakage and tunneling currents. Furthermore, due to wire-packaging difficulties and fabrication limitation of the electrodes, complex gating patterns and device geometries with large numbers of gating electrodes at the nanoscale is practically challenging.
In this paper we present a self-aligned gating concept with a spatial resolution down to sub-10 nm based on electrolytic gating. In contrast to dielectric-based gating, electrolyte gating can concentrate excess charges directly on the surface of the 2D material and reach a capacitance of C = 3.2 µF cm −2 (250 times higher than a typical 300 nm SiO 2 gate) [29][30][31] , which enables carrier density modification up to ∆n = 10 14 cm −2 . Since patterning of electrolyte is challenging, a general method for local electrolyte gates at nanoscale has not been demonstrated so far. To achieve this goal we introduce a lithographical masking technique based on e-beam over-exposed Poly(methyl methacrylate) (PMMA) that can screen ions in electrolyte. This e-beam patterned mask can prevent the mask-protected areas from being in contact with, and thus modulated by, the electrolyte gate. The mask hence effectively creates lithographically-defined local electrolyte gates with versatile geometries and feature sizes down to several nanometers. Figure 1(a) illustrates the technique for a graphene sheet. When a voltage is applied between the electrolyte top gate and the graphene, ions in the electrolyte accumulate on the graphene surface, only in regions that are uncovered by the PMMA mask, creating a self-aligned electrolyte gating pattern defined by the shape of the mask. An additional SiO 2 back gate allows weak p or n doping of the regions covered by the mask.
For an electrolyte gate voltage of 1 V, a carrier density contrast of ∆n > 10 14 cm −2 can be created at the PMMA mask boundary across only a few nanometers, as shown in the blue curve in Figure 1(c), produced by finite element simulations with COMSOL-Multiphysics 32 . Plotted in Figure 1(d) in the blue curve is the calculated in-plane electric field intensity across the junction, showing a maximum magnitude as high as E in-plane = 600 MV m −1 at the close vicinity of the mask boundary. The simulation assumes a Stern-Gouy-Chapman electrical double layer model 33 of the electrolyte ions and calculates the electric potential and the flux of ions under the influence of both ion diffusion due to the ionic con-centration gradient and ion migration due to the electric field. This process is governed by the Poisson-Nernst-Planck equations. Additional details about the double layer model and parameters used in the simulation are in the Supplementary Information.
For comparison, the simulated doping contrast and the in-plane electric field are much lower in a metal-dielectric split gate, as indicated in the red curves in Figure 1(c) and (d), rescaled for better visibility with factors of 5 and 10, respectively. A carrier density contrast of at most ∆n = 2 × 10 13 cm −2 (1 order of magnitude lower than that with the electrolyte-PMMA-mask technique) across a length scale of ∼ 100 nm is induced when a voltage of ∼ 60 V is applied, corresponding to an in-plane electric field of E in-plane = 13.5 MV m −1 (∼ 40 times lower than that with the electrolyte-PMMA-mask technique). This simulation assumes a dielectric constant of 3.9 (SiO 2 ) and a thickness of 60 nm for the gate dielectric, and a gap of 100 nm between the two gate electrodes, which are typical values in the literature 22,23 . The dielectric thickness and the gap width between the gate electrodes are the limiting factors for the junction sharpness. To achieve a sharpness of only a few nanometers, both the dielectric and the gap width have to be only a few nanometers in size too (see Supplementary Information). The former would result in undesirable leaking and tunneling currents and the latter is currently challenging from a fabrication standpoint.
In summary, our self-aligned electrolyte gating technique can enable nanometer-sharp junctions, and carrier density contrast and in-plane electric field orders of magnitude higher than split metal gate structures.
To implement this self-aligned electrolyte gating technique with the screening mask, the choice of material for the mask is essential. Two requirements need to be met: (1) To ensure high spatial resolution of the self-aligned local electrolyte gates, the lithographyical resolution of the mask has to be high; (2) To ensure reliable spatial selectivity and doping level control, the mask must be impenetrable to ions in the electrolyte with no leaks.
One candidate for the mask is the e-beam resist PMMA. Commonly used as a high-resolution positivetone e-beam resist 34,35 , PMMA becomes a negativetone resist when exposed at a much higher dose (∼ 20 000 µC cm −2 ), where it is cross-linked and transformed into graphitic nanostructures from a polymeric resist carbonization process 36,37 . Cross-linked PMMA allows sub-10 nm e-beam lithography resolution 36 . In separate experiments, we measured negligible current between a graphene sheet covered by cross-linked PMMA (∼ 300 nm thickness) and the electrolyte gate, verifying that the mask is essentially impermeable to ions in solid polymer electrolyte PEO−LiClO 4 . These cyclic voltammetry (CV) results are in the Supplementary Information.
The spatial patterning resolution of the self-aligned gates is determined by two factors: the e-beam lithography resolution of the screening mask and the Debye length of the electrolyte. As mentioned above, the ebeam resolution is ∼ 10 nm and the Debye length is ∼ 1 nm 38 , so the spatial resolution for patterning local electrolyte gates using this technique is dominated by the e-beam resolution which is 10 nm. The simulation in the inset of Figure 1(c) indicates a well-defined carrier density modulation profile resulting from periodic local electrolyte gates with a half-pitch of 10 nm. Figure 1(b) shows scanning-electron-micrographs (SEMs) of two examples of PMMA mask on graphene with nanometer feature size and different geometries, including disks and ribbons.
As proof-of-principle studies, we will now apply this technique to demonstrate two different device concepts: a graphene p-n junction and a graphene compact thermopile. Figure 2 shows a graphene p-n junction and the dynamical tuning of its doping level and photoresponse. The structure of the p-n junction device, shown in Large-range doping level control of the two regions in a p-n junction can be achieved by tuning electrolyte top gate and SiO 2 back gate voltages, where V tg controls the mask-uncovered region and V bg mostly controls the mask-covered region. Figure 2(c) shows the channel resistance R versus V tg and V bg , showing four distinct characteristic regions that indicate gate-voltage-tunable charge density at a p-n interface 39 . Two intersecting lines of high resistance (white dashed), representing charge neutrality points of the two regions respectively, divide the resistance map into four low-resistance regions: p-n, p-p, n-p, and n-n. A vertical line trace of the 2D resistance Photoresponse observed at the graphene p-n junction can also be dynamically tuned by the gate voltages. Figure 2(a) (bottom panel) shows the spatially-resolved open-circuit photovoltage map of the device under zero bias voltage across the channel, conducted on a nearinfrared (λ = 1.55 µm) confocal scanning microscopy setup at room temperature. As the laser excitation is scanned over the device, a large photovoltage V ph is observed at the self-aligned electrolyte gate defined junction. This photovoltage V ph at the junction as a function of V tg and V bg , plotted in Figure 2(d), exhibits a distinct six-fold pattern with alternating photovoltage signs, showing a strong dependence of the photoresponse on the relative doping level of the graphene junction. This six-fold pattern indicates a photo-induced hot carrier-assisted photoresponse process at the graphene p-n junction known as the photo-thermoelectric (PTE) effect 40 . A vertical line trace of the 2D photovoltage map along the same dotted gray line, plotted in the red curve of Figure 2(b), shows typical non-monotonic gate voltage dependence as a result of the PTE effect.
Next we demonstrate a compact graphene thermopile in the mid-infrared that takes advantage of the flexible gating geometries enabled by this self-aligned technique. In this design a complex doping pattern of graphene is created to enhance the photodetector's photovoltage responsivity. For PTE effect, the photovoltage generated can be expressed as V ph = S(n, x)∆T (x)dx, where S is the Seebeck coefficient of graphene, a function of charge carrier density, and ∆T is the increase in electron temperature from the environment. For free-space incident light that typically has a spherical Gaussian profile, the temperature gradient points in the radial direction, so the photovoltage is maximized when it is collected radially. The designed thermopile geometry, whose equivalent circuit diagram is illustrated in Figure 3(a), consists of several thermocouples connected in series whose photovoltages are all collected in the radial direction. Each graphene segment is considered a voltage source with a resistance. For the photovoltage to sum up along the meandering graphene channel, each segment is p− or n−doped in an alternating fashion so that neighboring photovoltages point in opposite directions (Seebeck coefficient has opposite signs). The alternating doping is achieved using our gating technique by covering every other segments with the PMMA mask and applying positive V tg and negative V bg respectively. Compared to existing graphene thermopiles such as that in ref. 41 , this approach eliminates the need for embedded gates and external wiring of thermocouples, enabling a compact thermopile based solely on graphene. The achievable nanoscale dimensions and the more complex geometries could lead to more efficient photovoltage collection.
Spatially-resolved open-circuit photovoltage mapping of this thermopile is conducted on a confocal scanning microscopy setup with a mid-infrared laser source at two wavelengths λ = 8.58 µm and λ = 7.15 µm. The photovoltage between several sets of terminals (indicated with numbers in Figure 3(a)) are measured to study the individual contributions of thermocouples. As the laser spot is scanned over the device, a maximal photovoltage V ph is observed at the center of the thermopile, as shown in the photovoltage spatial maps in the inset of Figure 3(b).
The spatial maximum for responsivity is then plotted as a function of the number of voltage source segments between the terminals. The well-fitted linear relation at both wavelengths confirms the summation of photovoltages from each individual segment. The maximal responsivity of this device is 26.2 mV W −1 . Compared to a previous graphene thermocouple with only one single p-n junction, studied in similar conditions 42 , the carefully designed doping pattern of graphene results in an about 7 times enhancement in photovoltage responsivity. Further optimization of parameters including device dimension and the number of voltage segments can be done to achieve higher responsivity.
The flexibility to tailor the dimension and geometry of electrolyte gates on 2D materials at the nanoscale with strong doping ability expands the possibility of 2Dmaterial-based tunable optoelectronic devices. Also, the non-destructive fabrication procedure maintains the high quality of the 2D material samples since there is no need for nanopatterning of graphene itself in harsh environments, and the cross-linked PMMA has previously been shown to have insignificant effect on the mobility of graphene 43 . Moreover, the broadband optical transparency of the PMMA mask also ensures non-interfered optical spectroscopy on the fabricated device. These are important practical considerations that can be crucial for the experimental implementation of many novel device concepts such as the compact thermopile we have demonstrated above. Plasmonics in graphene would be another example. To achieve a plasmonic resonant wavelength of 5 µm or less, graphene nanostructures need to have a feature size as small as 10 nm. This typically requires direct patterning of the graphene sheet, which on this small scale would create significant edge scattering and reduce carrier mobility, limiting the quality factor of the graphene plasmonic resonances 44 . The nanoscale electrolytic gating scheme proposed here would be an alternative and promising way of generating tunable graphene plasmons with an improved quality factor and a broader wavelength range.
To conclude, we have proposed and numerically simulated a self-aligned local electrolyte gating method of 2D materials that allows for a carrier density contrast of more than ∆n = 10 14 cm −2 across a length of 10 nm and an in-plane electric field of 600 MV m −1 . We have also developed an experimental implementation of this technique and demonstrated two different device concepts based on graphene, including a single p-n junction with tunable doping level and photoresponse and a novel compact thermopile with enhanced photovoltage responsivity in the mid-infrared. This novel nanoscale electrolytic gating scheme is a promising and versatile experimental approach to numerous 2D material-based device concepts in tunable nanophotonics and optoelectronics, and can potentially be used for other low-dimensional material classes too.