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Hall Effect Mobility of Epitaxial Graphene Grown on Silicon Carbide

Epitaxial graphene films were grown in vacuo by silicon sublimation from the (0001) and (000-1) faces of 4H- and 6H-SiC. Hall effect mobilities and sheet carrier densities of the films were measured at 300 K and 77 K and the data depended on the growth face. About 40% of the samples exhibited holes as the dominant carrier, independent of face. Generally, mobilities increased with decreasing carrier density, independent of carrier type and substrate polytype. The contributions of scattering mechanisms to the conductivities of the films are discussed. The results suggest that for near-intrinsic carrier densities at 300 K epitaxial graphene mobilities will be ~150,000 cm2V-1s-1 on the (000-1) face and ~5,800 cm2V-1s-1 on the (0001) face.

Graphene has been identified as a promising material for use in future electronic devices [1][2][3], including digital switches and radio-frequency transistors [4][5]. Thin films of graphene can be formed either through exfoliation of bulk graphite [6] or by epitaxial growth on SiC [3], with epitaxial graphene (EG) being more amenable to large-scale device processing [1][2].
Recently, EG has been patterned into devices [1,[7][8][9][10][11] that have exhibited mobilities that are greater than or comparable to the mobilities of other high-mobility semiconductors including Si, Ge, GaN, and InAs [12][13][14]. However, most reports have neither cited the sheet carrier densities of the EG nor related those carrier densities to the mobilities in a systematic way. Such an approach would be of interest to determine if EG holds the promise of mobilities similar to recent reports of suspended exfoliated graphene at 300 K, e.g. ~200,000 cm 2 V -1 s -1 [15,16]. In this study, EG films were grown on semi-insulating SiC substrates and the Hall effect mobilities and sheet carrier densities were measured at both 300 K and 77 K to determine the relationship between the two properties. The conductivities of the EG films were also considered in order to begin to identify the scattering mechanisms affecting the mobilities. Understanding the relationship between mobility and carrier density as well as the scattering mechanisms limiting the film mobilities will be vital for designing the synthesis approach for future EG electronic devices.
Raman spectroscopy had been used previously to confirm the presence of graphene by observing the 2D peak at ~2700 cm -1 [18] and a correlation was observed between a finite resistance of the epitaxial film and the observation of the 2D peak. Therefore, the presence of EG was normally confirmed by measuring the resistance across the sample.
Hall effect measurements were performed on 44 "large area" (16 × 16 mm 2 ) samples and 386 "small area" (10 × 10 µm 2 ) samples that were patterned on the large area samples using standard photolithography techniques. Hall effect mobilities, µ, and sheet carrier densities, n s , of the large area samples were measured at 300 K and 77 K using copper pressure clips in a van der Pauw configuration, a magnetic field of ~2,060 G, and measurement currents of 1 to 100 µA.
Small area samples were measured at 300 K only using similar conditions. To test reproducibility, samples were often re-measured several times and the data were found to be within 5% of the original values.
Plots of the Hall mobilities and carrier densities for large area EG and small area EG are shown in Fig. 1(a) and Fig. 1(b [20]) are plotted in Fig. 1(b). The data from these other studies lies within the scatter of the data from this study, suggesting that the functional relationship between increasing mobility and decreasing carrier density is an intrinsic property of EG synthesized via the sublimation technique. The mobilities and carrier densities for both large and small area samples were found to vary over a large range, but the carrier densities for Si-face EG was always lower than for C-face EG grown simultaneously. Furthermore, not all samples were n-type; about 40% of the samples exhibited holes as the dominant carrier, independent of growth face.
In Fig. 1(a), it appears that the lowest measured EG carrier densities are approaching the intrinsic carrier density, n i , of graphene. The intrinsic carrier density can be determined using the equation n i = (π/6)(kT/ħv F ) 2 [22], where k is Boltzmann's constant, T is the sample temperature, ħ is the reduced Planck constant, and v F is the Fermi velocity. The intrinsic carrier density has previously been determined to be (8.5 ± 0.5) × 10 10 cm -2 at 300 K [22][23] and, based on the 300 K value, n i at 77 K was calculated to be (5.5 ± 0.5) × 10 9 cm -2 . It is evident that as n s approaches n i , the projected 300 K mobility for C-face EG, increases to ~150,000 cm 2 V -1 s -1 and the projected 300 K mobility for Si-face EG, increases to ~5,800 cm 2 V -1 s -1 . The projected C-face mobility is comparable to the reported intrinsic mobility of exfoliated graphene at 300 K due only to electron-phonon scattering, ~200,000 cm 2 V -1 s -1 [24] and the mobilities reported from suspended exfoliated graphene at 300 K, ~200,000 cm 2 V -1 s -1 [15][16]. Additionally, this suggests that the mobility of C-face EG at near-intrinsic carrier densities will be dominated by electronphonon scattering.
The doping mechanism of EG is not understood at this time. Generally, the samples' dominant carrier type remained the same at 77 K as it had been at 300 K and the samples' mobilities generally increased as the temperature decreased. Also, the EG mobilities increase and the carrier densities decrease as the sample size decreases and whether samples were large or small, the highest hole mobilities are greater than the highest electron mobilities. The mobility increase at 77 K for the individual large area C-face samples was up to a factor of ~4 and the carrier densities decrease was by a factor of ~5.5 times relative to 300 K values. The changes were more dramatic for the Si-face samples, where mobilities increased by ~4 to 13.5 times, while the carrier densities decreased by ~6 to 28 times.
In an attempt to understand the observed differences in the temperature dependence of the mobilities, the conductivities, σ (σ = n s eµ, where e is the electron charge [26]), of the data found in Fig. 1 is shown in Fig. 2(a) for large area samples and Fig. 2(b) for small area samples.
The C-face conductivities (at constant temperature) that are shown in Fig. 2 exhibit a sublinear dependence on carrier density for n s > 10 13 cm -2 . The sublinear dependence is consistent with a scattering due to charged impurities, where σ ~ n s for n s >> n i [25,27], with other potential sublinear scattering mechanisms suppressing the conductivity. The behavior of the C-face conductivity plotted in Fig. 2 is in contrast to the behavior of the Si-face conductivity shown in  [25,[28][29]. Therefore, the dependence of Si-face EG conductivity may result from inherently thinner films [3] and the well-known stepped morphology of EG graphene due to the underlying SiC substrate [11]. Furthermore, single or bilayer Si-face EG has an interfacial layer that differs significantly from the bonding between the C-face EG and the SiC substrate [30], which could give rise to interfacial point defects.
Therefore, for n s >> n i , it is also attractive to consider that further suppression of conductivity may be due to scattering from point defects in the interfacial layer, where σ is expected to be constant with carrier density [25]. Interestingly, at 300 K, scattering from phonons should be the dominant scattering mechanism for epitaxial graphene on SiC [31], while scattering from charged impurities should dominate at lower temperatures [25]. However, the behavior of the large area C-face and Si-face conductivities shown in Fig. 2(a) remains the same at 77 K as at 300 K. This similar behavior suggests that the scattering mechanisms present at 300 K are not significantly affected by lowering the temperature only to 77 K; lowering the temperature further may be required to achieve a change in the conductivity behavior of the EG films.
Hall effect mobilities and sheet carrier densities were obtained for large area (16 × 16 mm 2 ) and small area (10 × 10 µm 2 ) EG films synthesized on SiC by the sublimation method.
Unlike previous reports, sample with holes as dominant carriers were observed in EG films synthesized on both substrate faces. The mobilities were found to strongly depend on substrate face, and the mobilities were found to increase with decreasing carrier density on both faces, independent of carrier type or substrate polytype. Taken together, these results imply that it should be possible to produce graphene-based devices with mobilities approaching 150,000 cm 2 V -1 s -1 (5,800 cm 2 V -1 s -1 ) at 300 K when the carrier density of the C-face (Si-face) EG is reduced to intrinsic levels. Also, through comparison with results from other laboratories, the relationship between mobility and carrier density reported here may be an intrinsic property of EG synthesized via the sublimation technique.  [7], C-face with electrons at 1.4 K ( ) [19], C-face with electrons at 4.2 K ( ) [20], and a Si-face sample at 4 K with electrons [1] is an open hexagon.