Extremely High Intrinsic Carrier Mobility and Quantum Hall Effect Of Single Crystalline Graphene Grown on Ge(110)

The successful synthesis of wafer‐scale single crystalline graphene on semiconducting Ge substrate has been considered a significant breakthrough toward the manufacturing of graphene‐based electronic and photonic devices; however, the assumed extremely high electrical mobility has not been found yet due to the lack of an adequate characterization method. Herein, state‐of‐the‐art transfer methods are developed to encapsulate the single crystalline graphene, which is grown on semiconducting Ge(110), in two hexagonal boron nitride (hBN) flakes, then acquire its inherent electrical mobility precisely via edge‐contact technique. It is found that single crystalline graphene grown on Ge(110) possesses a maximum carrier mobility of over 100 000 cm2 V−1 s−1 at low temperatures (2.3 K), which is superior to that obtained from graphene grown on other nonmetal substrates. Due to the extremely high mobility, well‐defined quantum Hall effect and Shubnikov‐de Haas oscillations can be observed at low temperatures as well. The study suggests that the excellent carrier mobility of graphene grown on Ge(110) may open an avenue to develop the practical graphene‐based nanodevices with high performance.


DOI: 10.1002/admi.202300482
and optical integrated devices with high performances. [5][6][7] Since the whole synthesis procedure avoids the use of metallic substrates, [8,9] it is compatible with modern semiconductor technology, thus permitting device downscaling and the extension of Moore's law. [10] In the past decade, single crystalline graphene has been successfully grown on Ge(110) and Ge(001), [11,12] and a number of technologies have been used to examine the charge transport properties of graphene, particularly their intrinsic carrier mobilities. For example, a mobility of only 1000 cm 2 V −1 s −1 is determined for graphene grown on Ge substrate using the traditional polymerassisted wet-transfer method. [1] The obtained value of carrier mobility is far below the expected one due to the inadequate transfer process. The carrier mobility increases to 7250 cm 2 V −1 s −1 when gold-coated graphene film is directly exfoliated from the underlying Ge substrate by using thermal-release tape (TRT). [2] Recently, an indirect characterization, known as terahertz time domain spectroscopy (THz-TDS), has been performed to determine the carrier mobility across the graphene on the intrinsic Ge(110) wafer. [11] This noncontact and nondestructive method shows the ultrahigh average mobility as 26351 cm 2 V −1 s −1 , even with the scattering effect of Ge substrate. However, a direct method to obtain the intrinsic carrier mobility of single crystalline graphene without the scattering effect of Ge substrate is still under demand. [13,14] In this work, by using hBN flake, single crystalline graphene without any undesirable residues coming from the transfer process can be directly peeled from Ge(110) substrate due to the extremely weak adhesion between graphene and the Ge substrate. [15] After printing graphene onto another piece of mechanically exfoliated hBN flake, a sandwich heterojunction of hBN/graphene/hBN is formed, in which encapsulated graphene is protected from external moisture and air, [16] and the scattering effect from semiconducting Ge substrate can be excluded. The sandwich structure is able to eliminate the possibility of mobility deterioration caused by transfer and substrateinduced long-range scattering remarkably. [13,17,18] A Hall bar device fabricated with the edge-contact technique is demonstrated to have maximum electron ( e ) and hole ( h ) mobilities of 96 000 and 100 000 cm 2 V −1 s −1 , respectively, at 2.3 K. [19] Moreover, due to the extremely high carrier mobility, both the Quantum Hall effect (QHE) and Shubnikov-de Haas oscillations (SdH) can be observed at low temperature in single crystalline graphene. [20] Our graphene-on-Ge platform may offer a promising pathway to realize advanced electronics, optoelectronics, and photonics. [21,22]

Preparation of hBN/Graphene/hBN Sandwich Structure
In Figure 1a, wafer-scale single crystalline graphene has been grown at 916°C on Ge(110) substrate using atmosphericpressure CVD furnace in a methane gas environment. [2,23] More growth parameters are shown in Table S1 in the Supporting Information. The Raman spectra shown in Figure S1 (Supporting Information) suggest the synthesized graphene wafer possesses high crystalline quality and good uniformity. In Figure 1b-i, a piece of graphene/Ge(110) (1 × 1 cm 2 ) sample is cut from the wafer, and then a thin hBN flake with a thickness of ≈35 nm is mechanically applied to the graphene, and the corresponding SEM image of hBN/graphene/Ge(110) is shown in Figure 1c. Due to the extremely weak adhesion between graphene and the Ge(110), monolayer graphene can be peeled from Ge(110) substrate directly using the bilayer stack consisting of a slice of polyvinyl alcohol (PVA) and a larger slice of polydimethylsiloxane (PDMS), as shown in Figure 1b-ii. A SEM image of graphenepeeled Ge(110) substrate and an optical image of hBN/graphene on bilayer stack are shown in Figure 1d,e, respectively. Upon printing to another exfoliated hBN flake covered SiO 2 substrate, the sandwich of hBN/graphene/hBN is formed (Figure 1b-iii and iv) and an optical image is shown in Figure 1f. The formation process of hBN/graphene/hBN sandwich structure can www.advancedsciencenews.com www.advmatinterfaces.de be monitored by Raman spectra, as displayed in Figure 1g. For hBN/graphene/hBN sandwich structure, the intensity ratio I 2D /I G of graphene is the highest, which is due to the fact that encapsulated graphene by hBN is protected from external environment and the charge doping from substrate can been eliminated significantly. [24,25] Finally, using the edge-contact technique, Hall bar device is fabricated on hBN/graphene/hBN sandwich structure (Figure 1b-v) and the corresponding cross section transmission electron microscope (TEM) image is shown in Figure 1h. A certain slope of the edge formed in cross section ensures 1D edge contact between exposed graphene and metal lead because of lateral etching. [19] Compared with 2D surface contact interface, 1D edge contacts present no contaminations between graphene and metal. Therefore, electrons can travel freely between graphene and metal, ensuring better electrical conductivity. [19] In addition, a high-resolution cross-section STEM image (Figure 1i) from the red box in (h) reveals a clean interface between graphene and layered hBN, which reduces long-range and short-range scattering in graphene and thus increases carrier mobility. [26,27]

Raman Characterization of hBN/Graphene/hBN Sandwich Structure
Traditional wet-transferred graphene methods result in increased charge doping and strain fluctuations due to residual polymers and metal ions, which reduces the quality of the graphene crystal. [28] Using wet-transferred technology, the graphene grown on Ge(110) is wet-transferred on SiO 2 substrate and the crystal quality of graphene is evidenced by the extremely low I D/G (≈0.025) of D peak and G peak as shown in Figure S2a and S2b (Supporting Information). [29] However, the intensity ratio I 2D/G of 2D peak and G peak in wet-transferred graphene can only reach ≈2.1 as shown in Figure S2c (Supporting Information). The low I 2D/G originates from the dangling bonds of the SiO 2 substrateas well as the contamination-induced doping, which damages the ballistic transport of charge carriers. [24,30] Furthermore, the wettransferred graphene shows an average hydrostatic strain as large as 0.18% in Figure S2d (Supporting Information) calculated as [31,32] where 0 is the G peak position at zero strain, Δ G is the frequency shift of the G peak, and is the Grüneisen parameter (slope of Δ 2D /Δ G , where Δ 2D is the frequency shift of the 2D peak), which is 2.2 in freestanding graphene. The unexpected strain fluctuations and charge doping seriously weaken the electrical properties of graphene by enhanced scattering effect and the all-dry transfer method will avoid these drawbacks. [33] In the all-dry transfer case, the Raman characterization of hBN/graphene/hBN sandwich structure in Figure S3a (Supporting Information) shows a weak G peak at 1584 cm −1 and a strong 2D peaks at 2692 cm −1 , in which the I 2D/G is as high as ≈7.6 in six Raman spectra as shown in Figure 2a (more details shown in Figure S3b,c, Supporting Information). The high I 2D/G indicates that the graphene/hBN interface is free from charge doping induced by either substrate or external contaminations, thus facilitating more efficient charge transport through the clean interface. [29] Besides, the lack of D peak in sandwiched graphene suggests the all-dry transfer process is nondestructive. The charge doping and local strain induced by substrate together with the external contaminations will both seriously degrade the carrier transport in graphene. To qualitatively determine the dominant disorder source, the spatially resolved Raman spectra measurement in an area of 20 μm × 20 μm (red dashed box in Figure S3a, Supporting Information) is performed to obtain the position of the 2D peak ( 2D ) and G peak ( G ). Using the vector-decomposition model, the relationship between 2D and G in graphene is summarized in Figure 2b, where strain and charge doping are optically separated on the axis for strain (red dotted line) and doping (green dotted line). [31] Similar to the wettransferred graphene, the slope (Δ 2D /Δ G ) of dry-transferred graphene is about 2.2 and parallel to the strain axis, suggesting that strain is the dominant disorder in both cases rather than charge doping. For cursory estimation of hydrostatic strain from G peak, the wet-transferred graphene on SiO 2 exhibits a red shift (namely, tensile strain) while dry-transferred graphene encapsulated in hBN tends to exhibit a blue shift (namely, compressive strain) and is closer to the freestanding point (black dot), indicating a smaller degree of strain inhomogeneity. In particular, the anomalous up shift of 2D peak in hBN/graphene/hBN sandwich structure can be attributed to the reduced electron-phonon coupling at high-symmetry point K caused by dielectric screening from thick hBN substrate, which is also known as the tuned Cohen anomaly. [34] Following the formula (1) above, the exact value of the hydrostatic strain in dry-assembled graphene is extracted and summarized in Figure 2c, where the spatially resolved mapping of and its histogram are plotted. On the one hand, the all-dry transferred graphene manifests smaller average strain value (-0.05%) and distribution range (-0.2% to 0.1%) compared to wet-transferred graphene to SiO2 substrate ( Figure S2d, Supporting Information). As a result, the strain-induced local pseudomagnetic fields in graphene is reduced and the corresponding intravalley scattering is suppressed, thus facilitating the more efficient movement of the carriers. [35,36] On the other hand, the all-dry transferred graphene illustrates a smaller random strain fluctuation which can be reflected by the full width at half maximum (FWHM) of the 2D peak (Γ 2D ). In general, the reduced random strain variations can lead to a narrower 2D peak. [33] Extracted by Lorentz fitting, the Γ 2D of all-dry transferred graphene (Figure 2d) shows an average value of 18.8 cm −1 , which is much smaller than the value of 32.5 cm −1 for the wet-transferred graphene ( Figure S2a, Supporting Information). It indicates the fact that the graphene transferred by the dryassembled process exhibits less random strain fluctuations than that obtained by the wet transfer, which is conducive to improve the carrier mobility by the considerable suppression of scattering effects.

The Electrical Transport Measurements
The edge-contact Hall bar device is fabricated in the hBN/graphene/hBN sandwich structure as shown in the inset of Figure 3a. To eliminate the influence of contact resistance, all electrical transports are performed by Kelvin fourterminal configuration at 2.3 K (pale blue) and 300 K (pink). [30] As a consequence of the linear dispersion relationship at the Dirac point of the graphene, [37] the four-terminal resistance R xx (determined by V xx /I as shown in the inset of Figure 3a) of Hall bar device exhibits a sharp peak as a function of back-gate voltage V bg . The sharp peak, also known as the charge neutrality point (V CNP ), is located at −5 V, which manifests slight n doping existing due to the graphene-Cr work function difference. [19] Compared with the R xx at 300 K, the low-temperature (2.3 K) resistance R xx increases by a factor of 1.3 at V Dirac due to the suppressed thermal activation. It should be noted that the high ratio of maximum resistance peak under low temperature and room temperature usually occurs in the disorder-suppressed monolayer graphene. [30] The conductivity is determined by = R xx W/L, where the W and L are width and length of device channel, respectively. By performing the Hall measurements with magnetic field B = 0.25 T, the back-gate voltage dependent carrier density n can be calculated by dividing the R xy /B = 1/ne (details shown in Figure  S4a, Supporting Information). The Hall resistance R xy is obtained from V xy /I as illustrated in the inset of Figure 3a. Afterward, the relationship between conductivity and charge carrier density n is shown in Figure 3b. At low carrier density (n < 5 × 10 11 cm −2 ), the low-temperature − n curve is consistent with the linear Drude model, [38] but the self-consistent Boltzmann model fits the curve better at high carrier density, as demonstrated in Figure S4b (Supporting Information). [39] To extrapolate the disorder-induced charge carrier density fluctuations n*, the relationship between log( ) and log(n) is shown in Figure 3c. [36] The exact value of the n* (guided by gray dashed line) is 3 × 10 10 at 2.3 K and 9 × 10 10 cm −2 at 300 K, respectively, which is much smaller than the wet-transferred graphene devices on SiO 2 substrate (> 1 × 10 11 cm −2 ). [38] This small fluctuation in carrier density is attributed to the reduction of doping-and strain-induced disorder during the dry transfer process, which coincides with the results of Raman characterization. [40] According to mobility equation of D = /ne from Drude model, the mobility D as a function of the charge carrier density n is plotted in Figure 3d. Near the charge neutrality point at 2.3 K, the maximum mobilities of electrons ( e ) and holes ( h ) are 9.6 × 10 4 and 1.0 × 10 5 cm 2 V −1 s −1 , respectively. The carrier mobility can also be estimated from the linear fitting near Dirac point in Figure S4b (Supporting Information), and the maximum mobilities of electrons and holes are 8.3 × 10 4 and 11.5 × 10 4 cm 2 V −1 s −1 , respectively, which are approximate to the values mentioned earlier. Furthermore, as the temperature is elevated to room temperature (300 K), the maximum mobilities of electrons ( e ) and holes ( h ) change to 4.6 × 10 4 and 6.0 × 10 4 cm 2 V −1 s −1 , respectively. Our study suggests that the edge-contact Hall bar device built on hBN/graphene/hBN sandwich structure provides an unique architecture to acquire the accurate mobility of 2D materials, and the estimated carrier mobility of single crystalline graphene grown on Ge(110) is found to be much higher than those prepared on other nonmetallic substrates (semiconductors or insulators) including sapphire, SiO 2 , hBN, SiC, and Si 3 N 4 as shown in Figure 3e. [2,15,[41][42][43][44][45][46][47][48][49][50][51][52][53][54] The ultrahigh mobility found in the edge-contact Hall bar device built on hBN/graphene/hBN sandwich structure is further verified by other four parallel devices, as depicted in Figure  S5 in the Supporting Information. For other four devices, the mobilities obtained at 2.3 K are distributed in the range of 4.5 × 10 4 -7.7 × 10 4 cm 2 V −1 s −1 . And, the corresponding carrier density fluctuations n* vary from 6.3 × 10 10 to 3.7 × 10 10 cm −2 as show in Figure S6 (Supporting Information).

The QHE and SdH Oscillations
The ultrahigh carrier mobility enables the observation of novel physical phenomena in the edge-contact Hall bar device, including half-inter QHE and SdH oscillations, as shown in Figure 4. Below a fixed back-gate voltage V bg = 35 V, the well-defined plateaux of Hall resistance R xy (blue) and the oscillatory longitudinal magnetoresistance R xx (red) are observed, as shown in Figure 4a. The quantized conductance (R −1 xy ) of plateaux in Figure 4a are in accordance with the following formula [20] R −1 xy = ±g s (n + 1∕2) e 2 ∕h (2) where g s is the degeneracy of the Landau level of graphene (equal to four), ± represents the electrons and holes, respectively, n is an integer, e represents the elementary charge, and h is the Planck constant. With a back-gate voltage V bg = 35 V, the filling factors = ± g s (n + 1/2) = 10, 14, 18… (denoted as black dashed line) are observed. Decreasing the back-gate voltage V bg to 5 V, the lower filling factors = 2, 6, 10 are observed as displayed in inset of Figure 4a. In integer quantum Hall states, the oscillations of magnetoresistance R xx occur when the quantization Hall resistance R xy appears, which is well described by where R(B,T) is the amplitude of the SdH oscillations, B F is the frequency of the oscillations, and is the Berry's phase of graphene. [20] The magnetoresistance show more SdH oscillations due to the increased Landau level density of states (DOS) at high carrier density. An increased back-gate voltage of 45 V leads to more Landau levels being occupied by electrons, as shown in Figure S7 (Supporting Information), confirming the enhanced electron-electron interactions by the observation of the fractional quantum Hall effect. [55] Both quantum Hall effect and the SdH oscillations provide a convincing evidence for the existence of extremely high mobility in the edge-contact Hall bar device built on hBN/graphene/hBN sandwich structure, in which the single crystalline graphene is initially grown on Ge(110) substate.
The QHE and SdH oscillations are observed for both electrons and holes by altering the V bg across the Dirac point with a fixed magnetic field B (5 T). In the case of electrons (V bg − V CNP > 0) or holes (V bg − V CNP < 0) filling Landau levels, the quantum Hall plateaux (blue) and symmetric SdH oscillations (red) occur synchronously, as shown in Figure 4b, in which the plateaux of the Hall resistance are denoted by black dashed line.
Meanwhile, the ultrahigh mobility in graphene can also be proved by the robustness of the magneto-oscillations to temperature dependence. [56] The magnetic oscillation curves under variable temperature are shown in Figure 4c, where the SdH oscillations gradually weaken with increasing temperature, and disappear when the temperature approaches 100 K. The SdH oscillations are able to preserve over a wide temperature range, indicating the strong robustness of carrier transport to external thermal fluctuations, which can be further utilized in quantized Hall resistance (QHR) applications. [57] Arising from the symmetric band structure of graphene, [37] Landau levels in the quantum Hall regime can be filled by both electrons or holes. Hence, the relationship of Landau index n (nth minimum R xx ) and 1/B are plotted in the fan diagram in Figure 4d. At different back-gate voltages, the nonzero intercept of linear fit to the data with Landau index n and 1/B symmetrically converge on both sides of the n-index axis. The dry transfer of graphene assisted with hBN offers an appropriate method to explore the inherent carrier mobility of graphene grown on Ge(110) substrate. The SdH oscillations over a wide range of back-gate voltages once again prove the extremely high intrinsic carrier mobility of CVD graphene, which sets a solid foundation for the applications of nonmetal grown graphene.

Conclusion
In summary, the advanced dry-transferred method together with the edge-contact technique are developed to pick up the graphene directly from Ge(110) substrate, and form high quality Hall bar device built on hBN/graphene/hBN sandwich structure. The transport measurements of Hall bar device in both low temperature and room temperature demonstrate that the graphene grown on Ge(110) possess extremely high carrier mobility, which is further verified by the observation of the well-defined QHE and SdH oscillations. The superiority of the mobility in graphene grown on Ge(110) may open an avenue to drive the semiconductor process-compatible nonmetal graphene toward more promising applications.

Experimental Section
Dry Transfer Process: First, PVA film was prepared by dropping PVA solution (8%) on the glass slide and dried it in the atmosphere. Then a piece of polydimethylsiloxane (PDMS, 1 ×1 cm 2 ) block was attached on the glass slide, and the prepared PVA film was cut to 2 × 2 mm in size and placed on PDMS to form a stack of PVA/PDMS film. Prior to the transfer of graphene, the hBN flakes with a thickness of around 30-40 nm was mechanically exfoliated on the surface of the graphene. With the optical examination, the polymer stack was positioned in a micromanipulator. With a slight horizontal inclination, the stack was dropped down at the desired position. Afterward, the sample was heated to 75°C at first and the stack was brought into mechanical contact with the hBN/graphene on Ge substrate from one side slowly. When the PVA film completely covered the hBN/graphene, the temperature of sample continued to be kept at 75°C for 3 min and then cooled down to room temperature. Rapidly, the graphene was picked up from the Ge substrate and optical examination was performed before the graphene/hBN/PVA/PDMS stack was transferred to another exfoliated hBN flake on SiO 2 substrate. At 80°C, PVA and PDMS could be easily separated due to the weak adhesion between them while the graphene/hBN hybrid would be released to another slice of hBN.
Device Fabrication: The edge-contact Hall bar device fabrication consists of two key steps, namely, the exposure of the edge of the encapsulated graphene layer and the deposition of metal electrodes. To define the shape of Hall bar device, a poly(methyl methacrylate) (PMMA) film was spin coated as a mask and then the electron beam lithography (EBL, Zeiss Sigma system) was used to pattern the PMMA layer to define the device shape. Afterward the hBN/graphene/hBN stack was etched in an RIE system with a mixture of O 2 (4 sccm) and CHF 3 (40 sccm) gases under 60 W at a pressure of 10 Pa. The PMMA layer with acetone was dissolved. Afterward, the Methyl methacrylate (MMA) and PMMA layers were spin coated, respectively, before the EBL process. Developing immediately after EBL process, 10 nm Cr and 80 nm Au were deposited to form the electrical contact between Cr/Au electrodes and graphene by electron beam evaporation (EBE) system. After the lift-off process, the devices were annealed in ambient pressure with a mixture of Ar (200 sccm) and H 2 (20 sccm) at 250°C for 3 h to remove residual polymer.
Raman Measurement: The Raman spectra of hBN/graphene/hBN sandwich structure was measured using a micro-Raman spectroscope (HR800, Horiba) in ambient environment. In order to eliminate the parasitic thermal effects and guarantee the signal-to-noise ratio, the power of laser with a wavelength of 514 nm was set to the minimum value of 5 mW. The diameter of laser spot is about 1 μm.
Transport Measurement: The transport measurement was performed by a physical property measurement system (PPMS-9T, Quantum Design) from 2.3 to 300 K. In order to apply a back-gate voltage to alter the carrier density of the graphene in Hall device, an external Keithley 2400 SourceMeter was utilized.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.