Introduction

Twisted bilayer graphene (tBLG), which consists of two single-layer graphene sheets with controlled twist angles, has attracted significant research interest because of its unique electronic band properties arising from the formation of a moiré superlattice1,2,3,4. Considerable attention has been given to exploring the intriguing properties of tBLG at small rotation angles, particularly at magic angles5,6. This emerging field, called twistronics, involves the manipulation of twist angles between homo- and heterostacked two-dimensional (2D) materials to create novel electronic and optical characteristics5,6,7,8,9. Despite extensive research on tBLG, most studies have focused primarily on the physics of magic angles in low-twist-angle tBLG. The investigation of the electronic properties of tBLG with moiré superlattice configurations has been limited to theoretical approaches that consider only a few specific angles5,6,10,11. Experimental investigations have also encountered challenges in precisely assembling two single-layer graphene sheets, preventing interlayer contamination, and minimizing wrinkle formation during the transfer process12,13.

In this study, we attempted to address the challenges associated with the precise assembly of tBLG structures by utilizing tBLG domains grown via chemical vapor deposition (CVD) with a Cu-Ni alloy metal catalyst thin film featuring a wide range of rotation angles from 0° to 30°. We employed Raman spectroscopy analysis of the G-peak and 2D-peak to determine the twist angle ranges and systematically investigated the electrical transport characteristics of tBLG within this twist angle range. We identified that high-angle tBLG (9 ~ 30°) exhibits more practically useful features than single-layer graphene. Additionally, scanning Kelvin probe microscopy (SKPM) measurements were performed to determine the work function values by comparing the experimental results with the theoretical calculations. Through a systematic analysis, we discovered that the electrical properties of tBLG are related to the twist-angle-dependent moiré period.

Results and discussion

Sample characterization and device fabrication

We employed a Cu (0.5 μm)/Ni (0.3 μm)/SiO2 substrate as a metal catalyst substrate for chemical vapor deposition (CVD) to limit the number of graphene layers added to bilayer graphene (BLG). As depicted in Fig. 1a, b, the optical microscopy (OM) and Raman Si peak intensity map** results reveal a substantial graphene domain consisting of both single-layer graphene (SLG) and BLG. Raman spectroscopy was utilized to verify the number of layers and stacking orientations14,15,16. The use of the Si peak intensity, which does not interfere with the graphene phonon mode, facilitated layer number identification based on the distinct optical absorption rate of graphene14. Si-peak intensity map** demonstrated uniform BLG regions, except for a small multilayer graphene (MLG) seed located at the center of the BLG domain. However, as illustrated in Fig. 1c, d, G- and 2D-peak intensity map** revealed intricate configurations within the BLG domain. These complex features in Raman G- and 2D-map** arise from differences in the stacking order of tBLG15.

Fig. 1: Sample preparation of twisted bilayer graphene (tBLG) field effect transistor (FET) device array sets.
figure 1

a Optical microscopy image of a chemical vapor deposition (CVD)-grown tBLG sample transferred onto SiO2. b–d Raman map** images of Si (500–550 cm−1), G (1500–1700 cm−1), and 2D (2600–2800 cm−1) bands, respectively. Raman map** was conducted using a 532 nm wavelength (2.33 eV) laser. e Optical microscopy image of the three sets of tBLG FET device arrays with electrodes. The yellow dashed line in the image denotes the edge of the CVD graphene area transferred onto a SiO2 substrate. The red, blue, and green dashed squares indicate individual sets of device arrays.

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Figure 1e shows an optical microscopy image of large-area graphene grown via CVD and transferred onto a substrate consisting of three sets of tBLG field-effect transistor (FET) device arrays. To minimize sample-to-sample variation, we fabricated tBLG FET device array sets on a single substrate. We analyzed the twist angle dependence of the electrical characteristics by examining approximately 35 devices in three array sets, with each array set consisting of 10–12 tBLG devices. CVD growth conditions were carefully chosen to produce optically distinguishable BLGs with diameters ranging from 50 to 100 μm (Supplementary Information Fig. S1). Following the identification of the candidate regions using optical microscopy, we verified the tBLG domain area and twist angle using Raman map** (Supplementary Information Fig. S2). Devices were fabricated using e-beam lithography, and each device was designed to be placed at a point with an even twist-angle distribution.

Raman spectra feature-induced twist angle classification

A random twist-angle distribution is characteristic of tBLG grown on a Cu/Ni metal catalyst thin film. Raman spectroscopy is a nondestructive method that provides a convenient method for determining the twist angle by analyzing the distinct features of the phonon modes associated with each stacking angle15. We analyzed the twist-angle dependence using the G peak (~1580 cm−1) and 2D peak (~2670 cm−1) information obtained from Raman spectroscopy using a 532 nm laser (2.33 eV) because these peaks exhibit clear features that depend on the twist angle15,17. Figure 2a, b presents the Raman spectra of the G-peak and 2D-peak of the tBLG devices, respectively (the full spectra are shown in Supplementary Information Fig. S3). As illustrated in Fig. 2a, the G peak is nearly independent of the twist angle, except in the middle range, where it is significantly enhanced when the laser energy matches the energy difference between the conduction and valence van Hove singularities15. The G-peak enhancement angle can be calculated as

$$\theta =3a{E}_{{laser}}/{{\hbar }}{v}_{f}4\pi ,$$

where \(a\) is the lattice parameter of graphene (2.46 Å), \(\hslash\) is the reduced Plank’s constant, and \({v}_{f}\) is the Fermi velocity in monolayer graphene (106 m/s)15. For a sample with a laser excitation energy of 532 nm (2.33 eV), the G peak enhancement angle was calculated to be 11.9°15. Figure 2b illustrates the variations in the 2D-peak Raman spectra of the tBLG channels. As the graphene 2D peak is sensitive to changes in the electronic and phonon band structures due to the double-resonance Raman scattering process18,19, it exhibits twist angle dependency15,17.

Fig. 2: Raman spectroscopy analysis of tBLG FET devices.
figure 2

G-peak (a) and 2D-peak (b) spectra of the tBLG devices. Raman spectra were acquired using a ×100 objective and a 532 nm laser (2.33 eV) with a spot size of ~1 μm. The Raman spectra are arranged in increasing order of twist angle from bottom to top. The inset in a shows magnified G-peaks, which are in the twist angle-independent range. G-peak (c) and 2D-peak (d) integral intensity variations as a function of the twist angle. e Relative 2D peak blueshifts with respect to the value of single-layer graphene. f FWHM values of the 2D peak for the tBLG samples. Both the G-peak and 2D-peak spectra were fitted with a single Lorentzian for simplicity. The gray lines in (d–f) represent the trends of the experimental Raman characteristics from reference15. g Schematic illustration of the moiré pattern in five tBLG structures classified by the stacking angle range. L-BG, M-BG, and H-BG indicate low, middle, and high rotation angle ranges between two graphene layers, respectively. LM-BG and MH-BG represent intermediate angles between low and middle and between middle and high angles, respectively.

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To determine the twist angle using the Raman 2D peak, information on the integral intensity, blueshift, and full width at half maximum (FWHM) from the 2D peaks was extracted and compared with the experimental results (gray lines in Fig. 2d–f) reported in a previous study15. Based on the observed trends of the G and 2D peaks, the twist angles of the tBLG channels were determined more accurately. Initially, the twist angles were categorized as low-angle (L-BG; 0°–9°), middle-angle (M-BG; 11°–13°), and high-angle (H-BG; 20°––30°) regimes based on the trend in the integral intensity of the 2D peak. Specifically, tBLGs with G-peak enhancement were designated M-BGs. In addition, intermediate angles between low and middle (LM-BG; 9°–11°) and between middle and high (MH-BG; 13°–20°) were determined. The most challenging task was arranging the H-BG regime because of similarities in G- and 2D-peak related values, as well as twist angle independence. To determine the twist angles in the high-angle regime, a D-like peak intensity analysis was conducted (Supplementary Information Fig. S4). This method of identification has limitations when determining the accurate twist angle of an arbitrary tBLG; however, by arranging the angles in increasing or decreasing orders of magnitude, the identification of inflection points enables a clear classification within the specified ranges and orders.

Figure 2g illustrates the five representative lattice structures used to classify the distinct structural features observed in each twist angle regime. When two graphene layers are stacked at a specific twist angle, they form a hexagonal moiré pattern that acts as a superlattice modulator. This superstructure has a considerably larger periodicity than the graphene lattice that arises from the commensurate stacking orders of the AA and AB structural alternations5,20. The twist angle (θ) and the moiré period (D) in tBLG are related through the equation \(D=a/\left[2\sin \left(\theta /2\right)\right]\), where \(a\) is the graphene lattice constant13,21,22. This finding demonstrates that the period of the moiré pattern rapidly decreases as the twist angle increases beyond the L-BG regime, followed by a less conspicuous angle dependency in the higher twist angle range. This trend is indicated by the bright dotted pattern in Fig. 2g. The representative tBLG illustrations are obtained at the mean values of the stacking angles of L-BG (red: 1.15°), LM-BG (blue: 9.71°), M-BG (magenta: 12.53°), MH-BG (green: 18.43°), and H-BG (purple: 25.25°), with calculated D values of 12.26, 1.45, 1.13, 0.77 and 0.56 nm, respectively.

Twist angle-dependent electrical transport characteristics

Figure 3a–c shows optical microscopy images and Raman G- and 2D-map** images of seven tBLG devices arranged in an array, which includes four specific angle regimes. The twist angles were verified using Raman spectroscopy (Supplementary Information Figs. S3 and S4). Furthermore, these analyses were confirmed using two additional tBLG device array sets that were prepared and constructed independently (Supplementary Information Figs. S6−S8). Figure 3d shows the current-gate voltage curve, which shows the transport characteristics of the tBLG FET in the seven channels of the device array presented in Fig. 3a–c (the FET transport characteristics of all the devices in the three array sets are shown in Supplementary Information Fig. S5). Interestingly, the electrical transport characteristics can also be classified into two groups based on the trend of the moiré period: the L-BG regime and other higher regimes (LM-BG, M-BG, MH-BG, and H-BG regimes).

Fig. 3: Electrical transport characteristics of tBLG FET devices.
figure 3

a Optical microscopy image of an array of tBLG FET devices. The color of the dashed circle corresponds to the twist angle range. b, c Raman intensity map** images of the G-peak (1500–1700 cm−1) and 2D-peak (2600–2800 cm−1), respectively. The scale bar in (a–c) is 10 μm. d Representative electrical transport characteristics of the tBLG FETs demonstrated in (a–c) for specific twist angle regimes. All tBLG channels were designed to be 5 × 5 μm2 with Au/Cr metallic contacts. Twist angle dependence of the gate voltage at the charge neutral point (CNP) (e), residual carrier density at the CNP (f), resistance at the CNP (g), and effective mobility (h) of all the tBLG FET devices in the three-device array sets. Each square point represents the mean value for a particular angle range. The x-axis and y-axis error bars represent the standard deviations of the values.

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To extract the primary parameters, we used Drude model fitting (Supplementary Information Fig. S5). The gate voltage dependence of the resistance is governed by four parameters: the charge neutral point (CNP) voltage (VCNP), contact resistance (RC), residual carrier density at the CNP (n0), and field-effect mobility (μ). The resistance profiles of the tBLG FETs were fitted using the following equation23:

$$R=2{R}_{c}+\frac{L/W}{q\mu \sqrt{{\left(\frac{{C}_{{ox}}\left({V}_{G}-{V}_{{CNP}}\right)}{q}\right)}^{2}+{n}_{0}^{2}}},$$

where L and W denote the length and width of the tBLG channel, respectively, q is the electric charge, VG is the applied back-gate voltage, and COX is the gate capacitance of SiO2. The contact resistance (RC) was assumed to be independent of the twist angle. Figure 3e–h presents the mean values and standard deviations of VCNP, n0, RCNP, and μ, obtained from all 32 devices of the three array sets, as functions of the twist angle.

The VCNP, n0, and RCNP of the L-BG regime exhibit higher magnitudes than the values obtained in the other regimes, whereas μ shows the opposite trend, as illustrated in Fig. 3e–h. Among these parameters, n0 represents the carrier concentration at VCNP, where the carrier-inducing effect is minimized by adjusting the gate voltage bias. Therefore, only the thermally generated electron-hole pairs and charge puddles induced by charged impurities on the SiO2 substrate may vary n0. However, despite fabricating all the tBLG device arrays on a single substrate, to avoid sample-to-sample variations and minimize the areal-charged impurity inhomogeneity, n0 exhibited distinct moiré-related twist angle trends.

In the case of AB-stacked multilayer graphene, the do** level decreases as the number of layers increases due to the increased interlayer spacing24,25. However, in the case of tBLG, the atomic corrugation of the moiré pattern arises from the alternating interlayer distances. It reaches a minimum for AB stacking (3.34 Å) and a maximum for AA stacking (3.61 Å)26. Moreover, a large-period moiré pattern with small twist angles leads to atomic-level corrugations, resulting in a decrease in carrier density. In contrast, a high twist angle indicates single-layer behavior due to reduced corrugation with a significantly small period27. According to the analysis of the electrical transport characteristics of the tBLG FETs, the tBLG channels in the high-angle regime (9–30°) exhibited a ~20% decrease in VCNP, a ~30% decrease in n0, a ~40% decrease in RCNP, and a ~170% increase in μ compared to those in the L-BG regime. Notably, several of these features exceed the behavior of single-layer graphene, as theoretically predicted. High-angle tBLGs exhibit the same VCNP values but a >80% decrease in RCNP values and a three- or fourfold improvement in mobility compared to the SLG channel. These improvements were confirmed in other independent sets of array devices (Supplementary Information Figs. S7 and S8).

Twist angle-dependent work function characteristics

Although the electrical transport characteristics of the tBLG FETs were analyzed, the relationship between the twist angle-dependent do** state and the moiré period D remains unclear. To further investigate the twist angle-dependent electrical transport characteristics, we performed scanning Kelvin probe microscopy (SKPM) measurements to determine the work function (Φ). SKPM is an experimental technique based on atomic force microscopy (AFM) that allows the measurement of the local contact potential difference (CPD) between a metallic tip and the sample surface. The CPD is related to the surface potential variation (VCPD) of the sample through the equation \({V}_{{CPD}}=\left({\Phi }_{{tip}}-{\Phi }_{{sample}}\right)/\left(-q\right)\), where q is the elementary charge28. To explore the connection between the twist-angle-dependent work function and electrical transport characteristics, three devices were selected from each of the L-BG, M-BG, and H-BG regimes, and representative results are presented for each regime (the full data are provided in Supplementary Information Fig. S9).

Figure 4a–c display SKPM images and line profiles of the L-BG, M-BG, and H-BG channels, respectively. The relative surface potential difference (ΔVCPD) was obtained using the relationship \(\Delta {V}_{{CPD}}=\Delta {V}_{{CP}{D}_{-}g}-\Delta {V}_{{CP}{D}_{-}e}\), where VCPD_g and VCPD_e are the average VCPD of the graphene and electrode surfaces, respectively29. Consequently, the average ΔVCPD values are ranked in the following order: L-BG (31.42 ± 5.73 mV) > M-BG (16.88 ± 2.66) \(\cong\) H-BG (16.62 ± 2.90 mV) > Au electrode (0; reference). The work function values of the tBLG samples are calculated as follows: \({\Phi }_{{sample}}={\Phi }_{{electroce}}-e\Delta {V}_{{CPD}}\), where Φelectrode is 5.1 eV for the work function of the Au electrode, resulting in ΦL-BG (~5.07 eV), ΦM-BG (~5.08 eV), and ΦH-BG ( ~ 5.08 eV), as shown in Fig. 4d (red dots).

Fig. 4: Surface potential and work function analysis of the L-BG, M-BG, and H-BG devices.
figure 4

Scanning Kelvin probe microscopy (SKPM) surface potential results (30 × 30 μm scan) and line profiles of the tBLG FET device channels of L-BG (a), M-BG (b), and H-BG (c). The white dashed line in the surface potential result indicates the position of the line profile. The line profile intersects the tBLG channel and Au electrodes on both sides. d Work function (Φ) calculated from the SKPM surface potential and Fermi energy (EF) calculated from the VCNP through FET measurements. e Intrinsic work function (Φ0 = Φ – EF) calculated from experimental Φ and EF values and the theoretically calculated work function model. f Energy band diagram showing the relationship between Φ, eΔV, EF, and Φ0 at L-BG, M-BG, and H-BG.

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In addition, first-principles calculations were performed on the angle-dependent work functions based on density functional theory30,31,32 (see Methods for details), as illustrated in Fig. 4e. The calculation considers the work function at the undoped intrinsic state (Φ0); therefore, the experimental work function value must be corrected using Fermi energy (EF) compensation. The Fermi level of tBLG is tuned by the gate voltage bias and follows the relation \({E}_{{F}_{-}{tBLG}}=\hslash {v}_{F}{sign}\left(\Delta {V}_{g}\right){\left(\pi \alpha \left|\Delta {V}_{g}\right|\right)}^{1/2}\), where \(\alpha =7.1\times {10}^{10}c{m}^{-2}{V}^{-1}\) is the gate capacitance in electron charge and \({v}_{F}=1\times {10}^{6}m/s\) is the Fermi velocity of SLG29,33,34. The change in EF from the intrinsic level is calculated using the VCNP obtained from the electrical transport analysis, as illustrated in Fig. 4d (blue dots). Therefore, the experimental Φ0 (Fig. 4e) is calculated using Φ and EF (Fig. 4d) using the relationship between these values (Φ0 = Φ – EF) (Fig. 4f). The moiré patterns of twisted bilayers with small twist angles are characterized by periodically arranged AA and AB stacking configurations, and such distinctive stacking becomes obscure as the angle increases. Thus, the variation in the work function with the twist angle can be understood as the cumulative effect of the work functions from these mixed stackings. For the AA-stacked region, the interlayer distance decreases as the angle increases, while the opposite trend is observed for the AB-stacked region. We also demonstrated that the work functions for homogeneous AA and AB stacked bilayers decrease as the interlayer distance increases, as shown in our newly added Supplementary Fig. S10. Because the rate of change for work function variations with respect to interlayer distances is more pronounced in AA stacking than in AB stacking, an increase in the work function around the L-BG regime could be more noticeable. Beyond this regime, the distinction between AA and AB stacking becomes less pronounced, leading to a uniform work function independent of the twist angle. The computed work functions of the tBLG increased slightly from the intrinsic value of the Bernal-stacked BLG and became saturated when the angle exceeded 9°. This weak dependence of the work functions was consistent with the experimental trend. Additionally, in the case of higher do** for L-BG, these two stacking alterations in the tBLG moiré pattern may affect the higher do** for L-BG compared to the other regimes. Therefore, we suspect that the variation in the local stacking order may change the local screening for given extrinsic do** sources such that apparent angle-dependent do** may occur.

Conclusion

In conclusion, our study systematically investigated the twist angle-dependent electrical transport characteristics of tBLG within a twist angle range of 0–30°. By utilizing CVD-grown tBLG domains and conducting Raman spectroscopy, we precisely determined the twist angle ranges and systematically explored the electrical properties of tBLG. Our findings reveal that the electrical properties of tBLG FETs follow twist-angle-dependent moiré period trends. Moreover, our systematic investigation demonstrated that tBLG with a high twist angle (9–30°) exhibits enhanced conductivity and mobility compared with single-layer graphene. To complement the electrical transport analysis, SKPM was employed to determine the work function values, which were consistent with the calculations from first principles. This study contributes significantly to advancing our understanding of tBLG and its potential role in future electronic devices.

Methods

Graphene growth using Cu/Ni thin films

To grow tBLG, we used a Cu/Ni film as a metal catalyst. First, Ni was deposited on a thermally oxidized SiO2 substrate using an e-beam evaporator, followed by the deposition of Cu through DC sputtering. The Cu and Ni thicknesses were fixed at 500 nm and 300 nm, respectively. The Cu/Ni/SiO2 substrate was loaded into a tube-type thermal CVD chamber for tBLG growth. During the growth process, a mixture of H2 (10 sccm) and CH4 (5 sccm) gases was added, and the temperature was maintained at 1000 °C for 15 min. After growth, the gas mixture was substituted with Ar gas (100 sccm), and the sample was rapidly cooled by moving the heater to the cooling zone.

Raman spectroscopy

Raman map** images and single spectra were obtained using a confocal Raman measurement system (Witec alpha 300 R). The excitation laser had a wavelength of 532 nm (2.33 eV), and the spot size was ~1 µm for all Raman measurements. During the Raman map** process, the laser power was maintained below 5 mW, and each spot was measured for 0.5 s. To obtain a single Raman spectrum, data were collected for 60 s (12 times with 5 s each) at a constant laser power of 5 mW. The intensities of the Si, G and 2D peaks were measured at the center of the FET channels and subsequently compared after normalization to the Si peak intensity on the SiO2 substrate.

Device fabrication and electrical property measurement

Graphene was transferred onto a thermally oxidized SiO2 (300 nm) substrate using conventional wet transfer. E-beam lithography was used to define the patterns of the alignment markers, electrical pads, and graphene channels. Under high vacuum (~10−6 Torr), we deposited a 10 nm thick Cr layer followed by a 30 nm thick Au layer using an e-beam evaporator. The current‒voltage transport characteristics of the FET device were measured at room temperature in a high vacuum (~10–6 Torr) using a Keithley 4200 semiconductor parameter analyzer.

SKPM measurement

The topography and contact potential difference between the graphene-metal and metal-metal interfaces were measured using the AFM and SKPM modes, respectively, of an NX10 (Park systems) instrument under ambient conditions. We utilized an NCST Au cantilever (k = 7.4 N/m, f = ~160 kHz) to obtain topography and surface potential scan images.

Density functional theory calculations

We performed first-principles electronic structure calculations based on density functional theory (DFT). We used the norm-conserving pseudopotentials29 of the Ceperley–Alder exchange-correlation functional30 in the local-density approximation (LDA) to DFT, as implemented in the SIESTA code31. An atomic orbital basis with a double-zeta polarization expanded the electronic wave functions, and the atomic structures were relaxed until all the atomic forces were smaller than 0.01 eV Å−1. Real-space grids were generated with a 200 Ry cutoff energy. To avoid interference between the layers, we used a vacuum space of 16 Å. For the Bernal stacked bilayer graphene at 0°, we sampled the Brillouin zone using a 50 × 50 × 1 Monkhorst–Pack k-point mesh during structural optimization. For 5.08°, 9.43°, 13.17°, 21.79°, 27.80° and 29.41°, we used 3 × 3 × 1, 6 × 6 × 1, 9 × 9 × 1, 20 × 20 × 1, 15 × 15 × 1, and 4 × 4 × 1 k-point meshes, respectively. To achieve more precise results for the electronic structure simulations on 0° bilayer graphene, we increased the k-point mesh to 100 × 100 × 1. Bilayer graphene at other angles was similarly sampled using a k-grid, maintaining the same equivalent density as the 0° bilayer graphene.