⇦Chinese Physics Letters, 2023, Vol. 40, No. 10, Article code 107201 Contrasting Transport Performance of Electron- and Hole-Doped Epitaxial Graphene for Quantum Resistance Metrology Xinyi Wan (万歆祎)1,2,3, Xiaodong Fan (范晓东)1,2,3*, Changwei Zhai (翟昌伟)4,5, Zhenyu Yang (杨镇宇)4,5, Lilong Hao (郝立龙)1,2,3, Lin Li (李林)1,2,3*, Yunfeng Lu (鲁云峰)4,5, and Changgan Zeng (曾长淦)1,2,3* Affiliations 1CAS Key Laboratory of Strongly Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei 230026, China 2International Center for Quantum Design of Functional Materials (ICQD), Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China 3Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China 4National Institute of Metrology, Beijing 100029, China 5Key Laboratory of Electrical Quantum Standards for State Market Regulation, Beijing 100029, China Received 1 August 2023; accepted manuscript online 7 September 2023; published online 13 October 2023 *Corresponding authors. Email: fanxd@ustc.edu.cn; lilin@ustc.edu.cn; cgzeng@ustc.edu.cn Citation Text: Wan X Y, Fan X D, Zhai C W et al. 2023 Chin. Phys. Lett. 40 107201    Abstract Epitaxial graphene grown on silicon carbide (SiC/graphene) is a promising solution for achieving a high-precision quantum Hall resistance standard. Previous research mainly focused on the quantum resistance metrology of n-type SiC/graphene, while a comprehensive understanding of the quantum resistance metrology behavior of graphene with different doping types is lacking. Here, we fabricated both n- and p-type SiC/graphene devices via polymer-assisted molecular adsorption and conducted systematic magneto-transport measurements in a wide parameter space of carrier density and temperature. It is demonstrated that n-type devices show greater potential for development of quantum resistance metrology compared with p-type devices, as evidenced by their higher carrier mobility, lower critical magnetic field for entering quantized Hall plateaus, and higher robustness of the quantum Hall effect against thermal degeneration. These discrepancies can be reasonably attributed to the weaker scattering from molecular dopants for n-type devices, which is further supported by the analyses on the quantum interference effect in multiple devices. These results enrich our understanding of the charged impurity on electronic transport performance of graphene and, more importantly, provide a useful reference for future development of graphene-based quantum resistance metrology.
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 DOI:10.1088/0256-307X/40/10/107201 © 2023 Chinese Physics Society Article Text Quantum Hall resistance depends exclusively on fundamental constants of nature, i.e., the Planck constant $h$, and the elementary charge $e$, which makes it a new metrological standard with high precision and repeatability for the unit ohm.[1] At present, the GaAs/AlGaAs heterostructure is the most widely used system for realization of the quantum Hall resistance standard (QHRS), with the Hall resistance accurately quantized within $1 \times 10^{-9}$.[2,3] However, achieving accuracy requires relatively low temperatures and high magnetic fields (e.g., $T \leqslant 1.5$ K and $B \approx 10$ T),[4] which strongly restricts the development of compact and portable metrology systems. Compared with the GaAs/AlGaAs heterostructure, graphene is a promising system that can be used to achieve the quantum Hall effect (QHE) under modest conditions, since it has an exceptionally larger energy gap between the zeroth and first Landau levels ($\Delta E_{01}$) due to its Dirac nature.[5,6] For instance, when the external magnetic field is 10 T, $\Delta E_{01}$ of graphene is more than six times that of the GaAs/AlGaAs system.[7] Among graphene systems prepared via different routes, SiC/graphene has attracted intense interest for development of next-generation QHRS.[8-10] The relatively large size of the as-grown graphene wafer allows a large breakdown current of the QHE. More importantly, the strong pinning effect of the graphene Fermi level, rooted in the charge transfer from the interfacial states of SiC, enables the realization of remarkably wide Hall plateaus.[11] These advantages will definitely benefit achievement of high-precision quantized resistance. However, the interlayer charge transfer process also gives rise to strong n-type doping in the pristine SiC/graphene samples (carrier density: 10$^{12}$–$10^{13}$ cm$^{-2}$),[12] and additional carrier density control is thus needed to enter a well-defined quantized Hall region within a small magnetic field. Traditional gate-voltage tuning usually induces a leakage current, which influences the accurate measurement of the quantum Hall resistance. Alternatively, chemical doping has been demonstrated to be an effective route in these circumstances.[13-15] For instance, by adsorbing 2,3,5,6-tetrafluoro-tetracyano-quino-dimethane (F4TCNQ) molecules on the surface of SiC/graphene, the carrier density can be reduced to the order of 10$^{10}$–$10^{11}$ cm$^{-2}$.[16,17] Actually, due to the special ambipolar electric field effects of graphene,[18] it is highly promising that one can obtain p-type doping SiC/graphene by further tuning across the Dirac point using molecular adsorption. However, prior studies have predominantly concentrated on quantum resistance metrology of n-type devices, with limited investigations on p-type devices.[8-10,19,20] Considering that the transport performance normally shows clear asymmetry between the n- and p-sides for many graphene devices,[21-26] comparing the quantum Hall performance of SiC/graphene devices with different doping types is of vital importance for both transport studies and quantum metrology applications.
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Fig. 1. The SiC/graphene device and basic transport characterizations. (a) An optical image of the SiC/graphene Hall bar device. The edges of graphene are indicated by white dashed lines. (b) A schematic diagram of molecular adsorption using the PMMA-F4TCNQ dopant, which is separated from the graphene layer by a PMMA spacer. (c) Symmetrized Hall curves of the SiC/graphene device before (black) and after (red) molecular adsorption.
The graphene samples were epitaxially grown on 4H-SiC substrates via the thermal decomposition of SiC in an argon atmosphere, and their high quality was carefully checked before device fabrication (see Fig. S1 in the Supplemental Materials). Figure 1(a) shows a typical optical image of the SiC/graphene device before F4TCNQ adsorption. A standard Hall bar was patterned using electron beam lithography and oxygen reactive ion etching, and Ti/Pd/Au films with thicknesses of 1/60/20 nm, respectively, were deposited as electrode materials via e-beam evaporation. The typical Hall measurement results at 5 K for such a pristine SiC/graphene device are shown in Fig. 1(c) (black curve). It is clear that the device is indeed n-type doping, and the carrier density is calculated to be $2.3 \times 10^{12}$ cm$^{-2}$, which is too high to observe the QHE within the range of the measuring magnetic field ($B \leqslant 9$ T). Surface molecular adsorption, instead of conventional gate-voltage tuning, was then utilized to achieve the desired carrier density, as schematically shown in Fig. 1(b). In this work, the dopant blend we used was PMMA-F4TCNQ (a concentration of 7 wt% of F4TCNQ in PMMA), which was spin-coated onto a spacing layer of PMMA and then annealed at temperatures above the PMMA glass transition temperature. Here, the aim of the addition of the PMMA spacer layer is to improve the carrier mobility.[16] The red curve in Fig. 1(c) exhibits the Hall resistance for the same SiC/graphene device after molecular adsorption. The device remains n-type doping, while the extracted carrier density is $1.9 \times 10^{11}$ cm$^{-2}$, almost one order of magnitude lower than the pristine device. This change is accompanied by an increase in carrier mobility from its original value of $\sim$ $1200$ cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$ to $\sim$  $11000$ cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$. As a consequence, well-defined quantized Hall plateaus at the Landau level (LL) filling factors $v=\pm 2$ can be achieved at a magnetic field smaller than 3 T. These results clearly demonstrate that such polymer-assisted molecular adsorption is an effective way to achieve high-quality quantum Hall devices. By varying the thickness of the PMMA layer or the annealing time, the final doping level of SiC/graphene can be readily controlled. Figure S2 in the Supplemental Materials displays the raw data of magneto-transport measurements at 5 K for SiC/graphene devices processed under different parameters. From the Hall data shown in Fig. S2(a), the estimated carrier densities for the n-type devices range from $0.5 \times 10^{11}$ cm$^{-2}$ to $3.9 \times 10^{11}$ cm$^{-2}$. By further decreasing the thickness of the PMMA layer or increasing the annealing time, we can also obtain p-type doping devices, possessing nearly identical doping levels [Fig. S2(c)], which facilitates a direct comparison of their quantum Hall performance. In Figs. 2(a) and 2(c), we first plot the quantum Hall performance for n- and p-type devices that possess a relatively low doping level ($n_{\rm e1}=n_{\rm h1} = 0.5\times 10^{11}$ cm$^{-2}$). For either the n- or p-type devices, well-defined quantized Hall plateaus, accomplished by the longitudinal resistivity $\rho_{xx}$ approaching 0 $\Omega$ [see Figs. S2(b) and S2(d)], are clearly seen. The accessibility of exact Hall quantization at such a low carrier density normally corresponds to the suppression of electron–hole puddles in the graphene layer,[27] which further demonstrates the maintenance of high sample quality after F4TCNQ adsorption. Nevertheless, clear variations between these two devices are still evident. When increasing the magnetic field, the Hall resistivity for the n-type device enters the quantized plateaus prior to that of the p-type device and, accordingly, the longitudinal resistivity $\rho_{xx}$ of the n-type device also approaches 0 $\Omega$ at a smaller field. A similar difference in the quantum Hall performance also holds for the SiC devices that possess higher carrier densities, as typically shown in Figs. 2(b) and 2(d) ($n_{\rm e2}=n_{\rm h2} = 2.5\times 10^{11}$ cm$^{-2}$). To provide a more intuitive comparison, we then define the critical magnetic field $B_{\rm c}$ as the magnetic field at which the residual longitudinal resistivity drops to 10 $\Omega$ [inset of Fig. 2(e)]. Figure 2(e) shows the estimated $B_{\rm c}$ for SiC/graphene devices with different doping levels. For all the devices, the $B_{\rm c}$ of the p-type device is consistently higher than that of the n-type device when their carrier densities are nearly the same. This implies that there are larger LLs broadening in the p-type devices, which hinders the achievement of quantum Hall states. Meanwhile, we also compare the carrier mobilities of various devices. As demonstrated in Fig. 2(f), for both the n- and p-type devices, the carrier mobility decreases as the carrier density increases, which is commonly seen in graphene samples.[6,28-30] Taking the n-type devices for example, the carrier mobility can achieve $\sim$ $19900$ cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$ when the carrier density is $0.5 \times 10^{11}$ cm$^{-2}$, and remains above 7700 cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$, even when the carrier density increases up to $3.9 \times 10^{11}$ cm$^{-2}$, which further demonstrate the high quality of our devices.[9,10] As a comparison, the p-type devices possess lower mobility within the examined carrier density range, indicating the enhanced carrier scattering in these devices.
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Fig. 2. Quantum Hall performance of SiC/graphene devices. [(a), (b)] Hall resistivity as a function of the magnetic field for n-type ($n_{\rm e1}$, $n_{\rm e2}$) and p-type ($n_{\rm h1}$, $n_{\rm h2}$) devices. Here, (a) $n_{\rm e1}=n_{\rm h1} = 0.5\times 10^{11}$ cm$^{-2}$, and (b) $n_{\rm e2}=n_{\rm h2} = 2.5\times 10^{11}$ cm$^{-2}$. [(c), (d)] Magnetic-field-dependent longitudinal resistivity $\rho_{xx}$ of n-type and p-type devices. (e) The extracted $B_{\rm c}$ for devices with different carrier densities. Here, $B_{\rm c}$ is defined as the magnetic field at which the residual $\rho_{xx}$ reduces to 10 $\Omega$. Inset: an enlarged view of the $\rho_{xx}$–$B$ curve for the device with a carrier density of $n_{\rm e1}$. (f) The calculated carrier mobility for devices with different carrier densities.
Next, we aim to provide a primary explanation for different performances between the n- and p-type devices, taking into account that the carrier tuning is achieved using molecular doping instead of conventional electrostatic gating. For the PMMA-F4TCNQ dopant used in our experiments [Fig. 1(b)], F4TCNQ molecules will diffuse through the PMMA layer and reach the graphene surface when the annealing temperature exceeds the glass transition temperature of PMMA.[16,17] Then, the F4TCNQ molecules could act as electron acceptors, resulting in p-doping effects on the graphene via charge transfer.[16] Since the pristine SiC/graphene device is highly n-doping, the final obtained p-type devices will definitely possess a higher concentration of F4TCNQ anions on the graphene surface compared with the n-type devices with similar carrier density. Moreover, it has been reported that the p–n asymmetry in carrier mobility of graphene devices was always attributed to the variations in the scattering cross section within the framework of relativistic quantum systems.[21,31,32] When the carriers are attracted to charged impurities, their interaction with the impurities is relatively stronger, leading to a larger scattering cross section. This results in a higher probability of scattering events, which in turn reduces the carrier mobility. However, when the carriers are repelled by the charged impurities, their interaction is weaker.[33] In our devices, F4TCNQ anions act as electron acceptors, which reasonably scatter holes more strongly. These two issues collectively lead to stronger charged-impurity scattering, and thus lower carrier mobility in p-type SiC/graphene devices.
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Fig. 3. Low-field magneto-transport behavior. [(a), (b)] Magnetoconductivity curves at 5 K for (a) n-type and (b) p-type devices with different carrier densities. Here, $\Delta \sigma (B)=\sigma (B)-\sigma (0)$ corresponds to the change in conductivity relative to the zero-field value. The solid lines are the fitting results using the typical WL formula for graphene. (c) The extracted values of the phase coherence length at 5 K.
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Fig. 4. The evolution of quantum Hall performance with increasing temperatures. [(a), (b)] Magnetic field dependence of (a) Hall resistivity $\rho_{xy}$ and (b) longitudinal resistivity $\rho_{xx}$ for an n-type device at various temperatures. [(c), (d)] Magnetic field dependence of (c) $\rho_{xy}$ and (d) $\rho_{xx}$ for a p-type device with similar carrier density. (e) The extracted critical magnetic field $B_{\rm c}$ at different temperatures for both the devices. Here, the definition of $B_{\rm c}$ is the same as that in Fig. 2(e). The data above 30 K are not shown since the residual $\rho_{xx}$ is above 10 $\Omega$ within the measured field range. (f) The temperature-dependent residual $\rho_{xx}$ at 6 T. Inset: an enlarged view of the $\rho_{xx}$ vs $B$ curve at 5 K for the n-type device.
Relatively strong charged-impurity scattering may also be the reason for the higher $B_{\rm c}$ of the p-type devices, as it can destroy cyclotron motions of electrons and therefore lead to LL broadening.[34] Motivated by this assumption, we further compare the magnetoresistance behavior between devices with different doping types. From the typical magnetoresistance curves shown in Figs. 2(c) and 2(d), a sharp resistivity peak of $\rho_{xx}$ occurs at the zero field, together with a clear negative magnetoresistance effect in the low-field regime [see the data for more devices in Figs. S2(b) and S2(d)]. These observations can be attributed to the emergence of weak localization (WL) effects, a typical phenomenon of quantum interference in solids.[35-37] As demonstrated in Figs. 3(a) and 3(b), the low-field data for most devices can be ably fitted using the typical WL formula for graphene (as detailed in Section I in the Supplemental Material).[38] From the results shown in Fig. 3(c), the extracted phase coherence length $L_{\phi}$ for n-type devices increases with increasing carrier density. These results are consistent with previous graphene devices,[30,39-42] and are usually explained as the strong screening effects on the fluctuating background potential.[43] However, for the p-type devices, $L_{\phi}$ conversely decreases with increasing carrier density, with the magnitude much smaller than the n-type counterparts. As discussed above, for the p-type devices processed by molecular adsorption, increasing carrier density corresponds to higher density of interfacial F4TCNQ anions and thus stronger inelastic scattering. Therefore, the as-induced enhanced scatterings on the carriers could break the phase coherence and account for the reduction in $L_{\phi}$.[44,45] These analyses further support our view presented above: namely, relatively strong charged-impurity scattering from F4TCNQ anions could greatly limit the performance of the quantum resistance metrology of p-type SiC/graphene devices. We then investigated the robustness of the QHE for our SiC/graphene devices at elevated temperatures. Figure S3 presents the raw data of magneto-transport measurements for two typical devices across a range of temperatures, while the symmetrized curves are plotted in Figs. 4(a)–4(d). From the low-field Hall data, the carrier densities for the examined n- and p-type devices were calculated to be $2.0 \times 10^{11}$ cm$^{-2}$ and $1.6 \times 10^{11}$ cm$^{-2}$, respectively. For both the devices, well-defined quantized Hall plateaus at the LL filling factor $v=\pm 2$ persist at temperatures up to 100 K, indicating their potential in the development of quantum metrology of resistance in modest conditions. Nevertheless, as the temperature increases, a gradually higher magnetic field is always needed to enter quantized Hall plateaus and, simultaneously, the corresponding minimum value of the longitudinal resistivity monotonically increases. These trends can be more clearly seen in Figs. 4(e) and 4(f), which show the critical magnetic field $B_{\rm c}$ and the residual $\rho_{xx}$ at 6 T as functions of temperature, while the thermal-induced LL broadening is the main issue accounting for them. Moreover, the as-extracted phase coherence length also reduces with increasing temperature for both the devices [see Fig. S4(c)], mainly due to the enhanced electron–electron interaction.[46] From Fig. 4(f), we can also conclude that the robustness of QHE under thermal degeneration for the p-type device is weaker than the n-type device, as manifested by the more rapid increase in residual $\rho_{xx}$. The temperature dependence of the conductivity curves can be ably fitted using the variable range hopping formula (see Fig. S5).[47-49] The localization length $\xi$ at 6 T for the p-type device is estimated to be 97 nm, while $\xi$ is 30 nm for the n-type device, which further supports the conclusion that there are larger LLs broadening in p-type devices. In summary, our experiments clearly demonstrate that polymer-assisted molecular adsorption can effectively tune the carrier density, and even the polarity of epitaxial graphene, while maintaining its advantages for the realization of QHRS under modest conditions. The as-obtained n-type devices normally exhibit greater potential for the development of quantum resistance metrology than the p-type devices due to weaker charged-impurity scatterings, which is concluded by measuring the quantum Hall, magnetoresistance, and quantum interference effects in various molecular-adsorption-processed SiC/graphene samples. Our study further reveals the impact of molecular dopants on the quantum Hall performance of graphene, which provides essential insights into how to obtain high-quality graphene devices for the development of quantum resistance metrology. Acknowledgments. This work was supported by the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-046), the National Natural Science Foundation of China (Grant Nos. 92165201, 11974324, and 12104435), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302800), the Anhui Initiative in Quantum Information Technologies (Grant No. AHY170000), Hefei Science Center CAS (Grant No. 2020HSC-UE014), and the Fundamental Research Funds for the Central Universities (Grant Nos. WK3510000013 and WK2310000104). L.L. was also supported by USTC Tang Scholar. Part of this work was carried out at the Center for Micro- and Nanoscale Research and Fabrication, University of Science and Technology of China. 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