Achieving high carrier density and high mobility in graphene using monolayer tungsten oxyselenide


 Highly doped graphene holds promise for next-generation electronic and photonic devices. However, chemical doping cannot be precisely controlled, and introduces external disorder that significantly diminishes the carrier mobility and therefore the graphene conductivity. Here, we show that monolayer tungsten oxyselenide (TOS) created by oxidation of WSe2 acts as an efficient and low-disorder hole-dopant for graphene. When the TOS is directly in contact with graphene, the induced hole density is 3 × 1013 cm-2 , and the room-temperature mobility is 2,000 cm2 /V·s, far exceeding that of chemically-doped graphene. Inserting WSe2 layers between the TOS and graphene tunes the induced hole density as well as reduces charge disorder such that the mobility exceeds 20,000 cm2 /V·s and reaches the limit set by acoustic phonon scattering, resulting in sheet resistance below 50 Ω/□. An electrostatic model based on work-function mismatch accurately describes the tuning of the carrier density with WSe2 interlayer thickness. These films show unparalleled performance as transparent conductors at telecommunication wavelengths, as shown by measurements of transmittance in thin films and insertion loss in photonic ring resonators. This work opens up new avenues in optoelectronics incorporating two-dimensional heterostructures including infrared transparent conductors, electro-phase modulators, and various junction devices.

The development of versatile doping techniques capable of controlling carrier density over a wide range is a key to fabricating advanced electronic and photonic devices. [1][2][3] For graphene, doping is key to achieving high conductivity and tunable work function to realize its promise as a material for transparent electrodes and near-and mid-infrared (IR) photonics. 4,5 In this and other two-dimensional (2D) materials, conventional techniques such as ion implantation have not proven effective, 6 and surface-charge-transfer doping has instead been the most commonly employed technique. For example, hole-doping with NO2 gas achieves hole density < 2×10 12 cm -2 and sheet resistance of ~300 /□. 7 Wet chemical doping has been demonstrated using a variety of inorganic and organic dopants, and achieves higher densities (> 5×10 12 cm -2 ) with sheet resistance as low as 150~200 /□. [8][9][10] However, chemical doping can suffer from poor long-term stability and large device-to-device variability, [10][11] and introduces significant charge disorder which limits the carrier mobility to < 1,000 cm 2 /V⋅s. In contrast, solid-state dopants are preferable for doping graphene due to their high repeatability, CMOS compatibility, and long-term stability. For instance, nonstoichiometric insulators such as SiNx and AlOx [12][13] have been utilized to optimize charge injection in 2D semiconductors, but have not been widely studied for use with graphene.
Here, we demonstrate low-disorder and tunable high-density doping of graphene on the basis of work-function mismatch-induced charge transfer with a nearby two-dimensional layer using soli-state oxide. We utilize a high work-function monolayer tungsten oxyselenide (TOS) formed by room-temperature UV-ozone oxidation of WSe2 which we have previously shown that this process is self-limiting in nature 14 and thus allows precise layer-by-layer control as well as low disorder, a significant improvement over other oxidation technique with the advantage of starting from a crystalline layered source giving rise to reduced charge disorder. 15 We found that TOS layer induces high hole density of > 3 × 10 13 cm -2 in a neighboring graphene layer preserving high mobility (2,000 cm 2 /V⋅s) and low sheet resistance of 118 /□. When the TOS layer is separated from the graphene by WSe2, the mobility rises dramatically, in a similar fashion to modulation doping in III-V semiconductor heterostructures where the separation reduces impurity scattering. 16 As a result, the graphene shows phonon-limited mobility at densities of 5 ~ 10 × 10 12 cm -2 and further reduction of sheet resistance down to 48 /□. This highly conductive graphene is also highly transparent in the infrared: we demonstrate near-ideal transmittance (99.2%) and low insertion loss (0.012 dB/µm) at IR frequencies using the TOS-doped graphene. Figure 1a shows the process flow of fabricating TOS-doped monolayer graphene. The device is fabricated by first stacking 1L-WSe 2 , graphene, and bottom h-BN using a polycaprolactone (PCL) polymer-based dry transfer process. 17 The heterostructure is then etched into Hall-bar structures for accurate extraction of carrier densities and conductivities of graphene, with edgecontacted metal electrodes (Cr/Au) formed using standard lithography processes (Fig. 1b). 18 Finally, the monolayer WSe 2 is oxidized into monolayer TOS at room temperature (RT) by exposing the sample to ozone under UV illumination for 30 min (see Methods for further device fabrication and UV-ozone oxidation details). In particular, the combination of UV and ozone is important as UV exposure creates local surface defects which facilitate the oxidation of the topmost WSe2 layer upon subsequent ozone exposure at room temperature. We note that this is in contrast to prior studies utilizing only ozone without any UV exposure 19 which required elevated temperature together with longer exposure time to completely oxidize the topmost WSe2 layer. We also note that another added benefit of our TOS-doping method is the self-cleaning nature of UVozone oxidation, as evidenced by the reduction in surface roughness due to the removal of polymer residue on the surface (Figs. S1b). This is further corroborated by the suppression of hysteresis arising from carrier (de-)trapping at the surface states formed by polymer residue 20 for all of our devices after oxidation (Figs. S2 and S3).
We first determine the type of the carriers induced in our TOS-doped monolayer graphene using Raman spectroscopy, as shown in Fig. 1c. We find a clear blueshift of both G and 2D peaks (18.1 and 4.3 cm −1 , respectively) to their original positions in pristine graphene, 21 which indicates that graphene gets hole-doped. This is corroborated by 2D / G ratio getting reduced by threefold and full-width half maxima (FWHM) of the G peak reduced from 7.3 to 5.9 cm −1 after oxidation (Fig.   1c, inset). Four-probe resistance ( 4p ) of graphene as a function of the back-gate bias ( GS ) at RT also shows a drastic shift of the Dirac peak from GS = 30 V to beyond the measurement range, after the formation of the TOS layer (Fig. 1d). This, together with the 4p decreasing with negative bias voltage, clearly indicates that an ultra-high density of holes is induced in graphene. As a result, the RT sheet resistance ( sh ) of our TOS-doped graphene shows a remarkably low value of ~118 /□ at zero gate bias voltage. Note that a weak secondary peak shown in sh can be attributed to small spatial inhomogeneity in the sample or formation of the moiré potential from an unintentional atomic alignment of graphene with the bottom h-BN. 22 We further note that any contribution of the TOS layer to the measured conductivity can be ruled out by independent electrical measurements which confirm that it is insulating (Fig. S4). To gain further insight into the nature of the TOS layer, we investigate its structural properties using selected-area electron diffraction (SAED). Figure 2a and b shows the SAED patterns of 1L-WSe 2 flake after oxidation, indicating complete disappearance of the hexagonal symmetry along the [0001] zone axis. This suggests that the resultant TOS layer is amorphous. However, few-layer WSe 2 shows hexagonal single-crystal diffraction patterns even after oxidation as shown in Figs. 2c and d, confirming that the UV-ozone process presented in our work is self-limiting in nature (only oxidizes the topmost layer) and thus the underlying WSe 2 layers remain in pristine form (see The self-limited nature of our oxidation process is further corroborated by the energy-dispersive X-ray spectroscopy (EDS) measurements of 1L-WSe2 that show the presence of selenium atoms even after oxidation (Table S1). We note that this self-limited nature allows for repeated oxidization and etching of multilayer WSe2 flake in a monolayer-by-monolayer fashion 14 ( Fig. S1a) as well as the removal of the TOS-doping method by simply etching the TOS layer, as indicated by the shift of the Dirac point back to GS = 0 V (Fig. S1c). On the atomistic level, this indicates that the TOS layer acts as a high diffusion barrier preventing further penetration of ozone molecules to the underlying layers. 23 Figure 2e and f show the X-ray photoelectron spectroscopy (XPS) spectra of W 4f and Se 3d core levels before and after the oxidation of CVD monolayer WSe 2 . We find a dominant formation of multivalent oxidation states of W (W 5+ and W 6+ ) after the oxidation, which verifies that 1L-TOS is sub-stoichiometric. Note that weak W-O and Se-O signals present before oxidation are presumably attributed to intrinsic defects present in CVD grown samples. We further note that defects in amorphous nature of the TOS layer can cause surface adsorption of water and oxygen molecules leading to time-dependent degradation. 24 Figure S6 depicts the PMMA encapsulation layer as a potential solution to prevent this degradation. A slight initial decrease in the zero-gate bias hole density p of our TOS-doped graphene to 7 × 10 12 cm -2 immediately after the PMMA encapsulation can be attributed to chemical reaction with solvent at a high baking temperature of 180 ∘ C. However, p remains nominally unchanged thereafter (~14% decrease in p over one month after the PMMA encapsulation), showing the use of PMMA encapsulation to enhance the stability of our TOS-doping method.   (Fig. S7). We first focus on the case where the TOS is directly in contact with the graphene. We find that the hole density is 3.2 × 10 13 cm -2 at GS = 0 V, consistent with the estimate from the Raman measurements. Applying GS can further tune p up to 3.7 × 10 13 cm -2 , demonstrating that the back-gate capacitance is electrostatically decoupled from the top TOS layer.
This doping level is equivalent to ~1% of the graphene atomic density (3.82 × 10 15 cm -2 ), and similar to the maximum achievable in silicon using substitutional doping. 25 The doping level is also beyond what can be achieved by electrostatic gating through solid dielectrics. For example, a graphite back-gated structure with h-BN dielectric can only achieve carrier densities on the order of ~6 × 10 12 cm -2 in graphene, 26 and a perfect dielectric with a high electrical-breakdown dielectric strength of 1 V/nm can only accumulate ~2 × 10 13 cm -2 . The self-limiting nature of the oxidation process provides a straightforward method to tune the induced hole density: when multilayer WSe2 is utilized, the top layer is converted to TOS and the remaining layers remain pristine, increasing the separation between the dopant layer and the channel. As we vary the interlayer WSe2 thickness from 1 to 4 layers (1L to 4L), the induced p decreases monotonically to 0.4 × 10 13 cm -2 ( Fig. 3a and Fig. S8 at 1.5 K), and remains additionally tunable by the back-gate. The corresponding Fermi energy ( F ) can be extracted using the relation where CNP is the energy of charge neutrality point (Dirac point), ℏ is the reduced Planck constant, and F is the Fermi velocity in graphene (= 10 6 m/s). We find that EF can be tuned from -0.1 to -0.7 eV, by simply changing the WSe2 layer number together with the back gate (Fig. 3b).
We show the measured sheet resistance of the graphene in Figure 3c. At zero back gate voltage, the TOS-graphene sample shows sheet resistance (Rsh) of 118 /□. For comparison, the undoped graphene has Rsh of a few k/□ and state-of-the-art chemically-doped graphene has Rsh of ~140 /□, 4 demonstrating superiority of our doping method. Remarkably, for the 3L and 4L samples, Rsh is even smaller, falling below 50 /□ (see also Fig. S9). This indicates an increase in carrier mobility that more than offsets the reduced carrier density.
To explore the electrical performance of the TOS-doped graphene in more detail, we plot the carrier mobility (at RT) derived from the measured sheet resistance and carrier density in Figure   3d,e. With no interlayer WSe2, the mobility is ~2,000 cm 2 /V·s, more than an order of magnitude higher than that achieved in graphene with similar high carrier density induced by either chemical doping 4,8,9 or electrolyte gating. [27][28][29][30] In spite of this dramatic improvement, the mobility still falls below the limit predicted from acoustic phonon scattering, indicating dominant scattering from charged impurities. The density of such impurities can be estimated from the measured low- where is the impurity density, ℎ is the Planck constant, and is the elementary charge (Fig. S8b,c). 31 From this relation, we estimate of ~4.6 × 10 11 cm -2 , well below that of electrolyte-gated graphene (6 × 10 12 ~ 10 13 cm -2 ) 32 . This indicates that the charge disorder in the TOS layer is much lower than for other dopants.
With insertion of interlayer WSe2, the mobility improves dramatically, reaching values of ~17,000 cm 2 /V·s for the 3L sample and ~24,000 cm 2 /V·s for the 4L sample at zero gate voltage.
Remarkably, these values are at the limit set by longitudinal-acoustic (LA) phonon scattering. 18 This indicates that three layers of WSe2 (~2 nm) can screen the charged impurities in the TOS layer so that the impurity scattering is reduced by more than an order of magnitude. This is consistent with previous studies showing that the charged-impurity scattering rate decreases rapidly as a function of the distance between the impurities and the graphene layer. 33 The mobility improvement achieved in this way is analogous to the modulation doping technique in conventional semiconductor heterostructures, whereby the physical separation of dopant from the active channel drastically increases carrier mobility by minimizing impurity scattering by dopant atoms. 16 To understand the origin of the charge transfer between TOS and graphene, we focus on two important electrostatic boundary conditions imposed in our devices in equilibrium: (1) constant Fermi level EF across the entire system and (2) continuous vacuum level without any discontinuities. We first note that the charge neutrality point of graphene lies deep in the bandgap of WSe2, so that we can effectively treat WSe2 as a dielectric. 34 Therefore, the resultant electrostatic boundary condition in our TOS-doped graphene with interlayer WSe2 can be expressed in terms of the work function  of the individual layers (TOS and graphene) as where TOS (Gr) is the work function of TOS (graphene) with respect to the vacuum level, t is the distance between graphene and TOS, and  is the dielectric constant of WSe2. Here, we use  = 3.8. 35 The final term in eq. (2) is the potential drop developed across TOS and graphene as a result of charge transfer, which can be determined from Poisson's equation. 36 From eq. (2), p in graphene can be simply expressed in terms of t and the work-function mismatch between the two layers as p = (TOS -Gr)/t. We find that our model fits well our data for EF in our TOS-doped graphene as a function of t (Fig. 4a), indicating that the charge transfer is dictated by the work function mismatch between the two layers. Note that the extracted TOS of ~5.6 eV is in good correspondence with previous studies on non-stoichiometric tungsten oxides. 37 To validate our model of work-function mediated charge transfer, we study the TOS-doped graphene devices with different stacking orders of graphene and TOS layer (Gr/TOS and TOS/Gr) as well as with different insulating interlayer (TOS/2L h-BN/ Gr; Fig. S10). Raman spectra clearly show hole-doping of graphene irrespective of the stacking order or the type of insulating interlayer (Fig. 4b). This not only verifies the work-function mediated charge transfer but also rules out the possibility doping due to fixed dipoles, as seen for self-assembled monolayers and ferroelectric insulators. 38,39 The densities extracted from the Raman shifts of > 2.5 × 10 13 cm -2 for the TOS/graphene sample and ∼1 × 10 13 cm -2 for the graphene/TOS sample, as well as ~2 × 10 13  We next perform self-consistent electrostatic simulations using the extracted TOS of ~5.6 eV to gain further insight into the role of the WSe2 interlayer in the charge transfer process (simulation details can be found in our previous work). 40 The additional material parameters are provided in Table S2. Specifically, we study the effect of defects in WSe2 on the resultant p in graphene at RT as shown in Fig. 4c (here we assume that defects are equivalent to acceptors/donors A and D ).
For defect densities lower than 5 × 10 11 cm -2 , our simulations show that p can be well understood in terms of eq. (2) for any layer number of WSe2 interlayers. However, p departs from eq. (2) at higher defect densities due to additional charge transfer from acceptors (donors) in WSe2 to graphene, which further decreases (increases) the resultant hole density in graphene. In our studies, we use high-purity flux-grown WSe2 with low defect densities (<10 11 cm -2 ). 41 Therefore, the simulations support the model of charge transfer dictated by work-function mismatch and validate the assumption of treating interlayer WSe2 as a simple dielectric. In this low defect density limit, our simulations further show that the induced charge densities in the WSe2 interlayer are orders of magnitude lower than that in graphene ( Fig. 4d and Fig. S14). This indicates that the electrical characteristics of our devices are dominated by the bottom graphene layer with negligible WSe2 contribution. We now explore the potential of TOS-doped graphene in optoelectronic applications. One immediate advantage of our technique is the ability to strongly suppress interband absorption for photon energies up to 2EF due to Pauli blocking. 5 Figure 5a shows the measured transmittance spectra of chemical vapor deposition (CVD)-grown 1L-WSe 2 /graphene films on quartz before and after UV-ozone oxidation (see Fig. S15 and Methods for the detailed measurement setup). Before oxidation, the transmittance is near graphene's intrinsic value (97.7%) for photon energies less than 1.4 eV since the top WSe2 is transparent in the near-IR region, and shows a dip at 1.67 eV that corresponds to the excitonic bandgap of WSe2. In contrast, the near-IR transmittance significantly improves after oxidation, increasing to 99.2% at telecommunication wavelengths ( ∼ 1550 nm). From the transmittance data, we can infer that EF of ∼0.6 eV for our TOS-doped graphene, in reasonable agreement with that from electrically measurements for the exfoliated sample discussed above (0.65 eV). Furthermore, the TOS-doped graphene is highly transparent even in the visible regime (see insets) indicated by the reduction of the WSe 2 absorption peak. The weak presence of the excitonic peak is due to thickness inhomogeneity in the top CVD-grown WSe2 layer within the area of illumination (∼6% of the area is covered by 2L-WSe 2 as shown in Finally, we demonstrate the ability to utilize TOS-doped graphene as a transparent gate electrode and high-speed phase-modulator in near-IR photonic circuits. 48 We probe the optical response of TOS-doped graphene embedded on planarized low loss silicon nitride (SiN) waveguides, in a microring resonator cavity ( Fig. 5c; see Methods for detailed fabrication processes). Notably, our planar photonic structure comprises a TOS/Gr/h-BN/SiN composite waveguide with a strong optical mode overlap when compared to out-of-plane measurements. The normalized ring transmission spectra show that the bare low-loss cavity is weakly coupled to the straight waveguide (under-coupled regime), thereby yielding a low extinction of ~3 dB on resonance, with narrow linewidth (Fig. 5d). After the transfer of WSe2/Gr/h-BN on the planarized SiN substrate, we extract an insertion loss of 0.077 ± 0.014 dB/µm in our composite waveguide from the optical response as shown in gray of Fig. 5d (see Methods and Supporting Information for insertion loss extraction). 49 We attribute the high insertion loss to the undoped graphene in WSe2/Gr/h-BN stack, which causes the resonator linewidth to broaden considerably, increasing the cavity loss and over-coupling the waveguide to the cavity. The insertion loss is lowered by about 85% to 0.012 ± 0.0022 dB/µm after UV-ozone oxidation, consistent with Pauli blocking of absorption. The significant lowering of insertion loss leads to the condition where the coupling rate between waveguide and ring resonator equals the optical decay rate (loss) in the cavity, thereby exhibiting a critically coupled resonance transmission response (shown in red in Fig. 5d), where the extinction is ~60 dB, with the spectral sharpening of the resonance. The 2% change measured in the out-of-plane transmission (Fig. 5a) is magnified to an 85% change in the in-plane transmission due to the enhanced optical mode overlap in integrated photonic circuits. This low insertion loss of 0.012 dB/µm uniquely places TOS-doped graphene as an ideal alternative to traditional transparent conducting materials such as ITO, which has at least two orders of higher insertion loss (1.6 dB/µm) with similar device geometries. 50

Conclusion
In this study, we utilize the work-function mediated charge transfer to achieve degenerate ptype doping of graphene using monolayer TOS prepared by a room-temperature UV-ozone oxidation of monolayer WSe2. Our TOS-doped graphene (1L-TOS/1L-Gr) shows excellent hole mobilities (~2,000 cm 2 /V⋅s) even at high hole density (>3 × 10 13 cm -2 ) which results in low sheet resistance (118 /□) at room temperature. We further demonstrate tunable carrier density together with enhanced mobility reaching the phonon-limited scattering rate at room temperature by inserting WSe2 interlayers, further reducing graphene sheet resistance to ~50 /□. Our selfconsistent electrostatic model based on work-function mismatch can well describe the charge transfer mechanism as well as the tunable carrier density with WSe2 interlayer. Finally, our TOSdoped graphene displays exceptionally high optical transmittance (>99%) and low insertion loss (0.012 dB/µm) at telecommunication wavelength. Our work opens up new avenues for incorporating vdW heterostructures into photonic circuits as a transparent gate electrode and highspeed phase-modulator for near-IR applications.

Fabrication and characterization of graphene device
WSe2, graphene, and h-BN flakes were prepared on SiO2/Si substrate by mechanical exfoliation.
The thickness of each flake was determined by the contrast difference in optical microscopic images and Raman spectra. Only monolayer graphene was used while the WSe 2 thickness varied from 1L to 5L to see the layer dependence. The stacking of flakes was conducted by the dry transfer method using PCL polymer at 50∼58 ∘ C to pick up flakes that are then transferred onto a 285-nm   . S13).

Transmittance measurements
The transmittance of CVD-grown 1L-WSe 2 /Gr directly on a quartz substrate (purchased from 2D Semiconductors) was measured under ambient condition using a custom setup built around a Nikon TE-300 inverted microscope as shown in Fig. S15. The output of a tungsten halogen lamp was focused onto a 50 m pinhole and an aspheric condenser lens to obtain collimated white light, which was focused at the sample plane through the quartz substrate using a long working distance 50x objective (0.55 NA). The transmitted light was collected with a 40x (0.6 NA) objective focused at the sample plane from below and was sent to an f/4 spectrograph (Princeton Instruments SpectraPro HRS300) equipped with a cooled InGaAs array detector (Princeton Instruments PylonIR). Order sorting filters were used to avoid higher-order diffraction signals. Transmittance was calculated by dividing the transmitted intensity measured on the sample by the transmitted intensity through a nearby blank area of quartz, with dark counts subtracted from both measurements. The system was optimized to ensure that the instrument error was <0.5% over the whole spectral range for each measurement as indicated shaded area of the spectrum.

Fabrication of SiN photonic platform with TOS-doped graphene
To fabricate low-loss silicon nitride waveguides, we use e-beam lithography to define 1300 nm wide waveguides on a stack of 360 nm PECVD SiO2 hard mask and 330 nm high silicon nitride conditions. Finally, UV-oxone oxidation is performed to oxidize WSe2 into TOS and dope graphene. Notably, microring resonators allows for high fidelity measurement of the optical propagation loss induced by TOS-doped graphene due to the enhanced sensitivity of a high-quality factor (Q) cavity (~ 300,000 in our case) to small changes in phase and absorption.

Optical loss measurement and insertion loss estimation
We couple transverse electric (TE) polarized light from a tunable near-infrared laser (1550 ~ 1650 nm) to the input of the SiN microring resonator (Input of schematic in Fig. 5c) using a tapered single-mode fiber, which is then collected from the SiN ring output, using a similar tapered fiber.
Transmission measurements were taken from the same device before transfer to account for the insertion loss of planarized SiN substrates, once after the transfer to account for the insertion loss due to undoped graphene, and finally, after UV-ozone oxidation to measure the propagation loss

Data availability
The data that support the findings within this paper are available from the corresponding authors upon reasonable request.