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Statistics of epitaxial graphene for Hall effect sensors
Accepted Manuscript Statistics of Epitaxial Graphene for Hall Effect Sensors Tymoteusz Ciuk, Wlodek Strupinski PII: DOI: Reference:
S0008-6223(15)00547-3 http://dx.doi.org/10.1016/j.carbon.2015.06.032 CARBON 10034
To appear in:
Carbon
Received Date: Accepted Date:
24 March 2015 15 June 2015
Please cite this article as: Ciuk, T., Strupinski, W., Statistics of Epitaxial Graphene for Hall Effect Sensors, Carbon (2015), doi: http://dx.doi.org/10.1016/j.carbon.2015.06.032
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Statistics of Epitaxial Graphene for Hall Effect Sensors Tymoteusz Ciuk1,2 and Wlodek Strupinski1* 1) Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland 2) Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
Key words: graphene, epitaxy, chemical vapor deposition, transport, bilayer, anisotropy, Hall effect, offset voltage
Abstract Epitaxial Chemical Vapor Deposition growth of graphene on silicon carbide is one of the most promising technologies to realize graphene-based electronics. Particularly, the quasifree-standing bilayer which comes through hydrogen atom intercalation of monolayer graphene grown on the Si-face of SiC offers high carrier mobility (as high as 5000[cm2/Vs]) and electrical stability throughout the device processing cycle. In this report, we present a statistical perspective on transport properties of QFS-bilayer graphene grown on 4H(0001) and 6H(0001) SiC, being a result of 460 individual processes on semi-insulating 10mm×10mm substrates. The mutual relation between charge carrier concentration and mobility is determined and analyzed to raise the awareness of the effect of SiC hexagonality on charge transport in graphene. Special attention is paid to the applicability of quasi-freestanding bilayer graphene on SiC, primarily in magnetic field detection. The issue of the stepedge-induced offset voltage anisotropy in Hall effect sensors is introduced and a method to minimize it is presented.
* corresponding author: [email protected] (Wlodek Strupinski)
1. Introduction Arguably, there are two most promising epitaxial technologies for wafer-scale production of graphene devices [1,2] – silicon atom sublimation from SiC surface [3-5] and Chemical Vapor Deposition (CVD) growth on SiC [6]. A CVD process typically involves methane, propane or acetylene as a carbon source. It enables a precise synthesis of a pre-defined number of carbon layers, including a sole buffer layer on the Si-face of SiC, and is less sensitive to SiC surface defects than sublimation. The CVD epitaxy has been studied for both Si-terminated and C-terminated SiC; however, more attention has been directed to SiC(0001) since Si-face growth kinetics foster higher accuracy. Growing graphene on the Si-face of SiC always involves the formation of a buffer layer [7] which is the first layer of carbon atoms covalently bonded to the substrate [8-10]. The buffer layer can be decoupled from the substrate through hydrogen atom intercalation [11-15]. The intercalating atoms diffuse underneath the buffer layer and bond themselves to the topmost Si atoms of the Si-terminated SiC surface, thus converting the buffer layer into a mostly sp2hybridized single graphene layer. Depending on the initial structure, the hydrogen atom intercalation allows different quasi-free-standing forms of graphene. As a result, a bare buffer layer on the Si-terminated SiC surface is turned into quasi-free-standing monolayer graphene (QFS-monolayer) and monolayer graphene (buffer layer + single graphene layer) on the Siterminated SiC surface is turned into quasi-free-standing bilayer graphene (QFS-bilayer). The significance of the quasi-free-standing forms of graphene on the Si-face of SiC is justified by the elimination of the buffer layer which constitutes a significant scatterer to charge carriers in graphene [10]. The resultant hydrogen-atom-intercalated graphene exhibits on average three times higher carrier mobility than the un-intercalated one and its p-type doping and carrier mobility is only slightly affected by the device fabrication. On the contrary the n-type doping of un-intercalated graphene on the Si-face of SiC, which is a consequence of the buffer layer’s pinning the Fermi level in graphene above the Dirac point, may be significantly shifted by the exposure to popular cleaning reagents and resists, including the change of the doping type. For these reasons, hydrogen-atom-intercalated graphene is better suited for electronics and sensor applications than un-intercalated graphene. Importantly, it has been observed in our samples that the hydrogen atom presence is stable up to 700°C,
which is high enough to meet the requirements of high-speed electronics and hightemperature sensing. Only at higher temperatures does a sample release hydrogen. The constantly growing demand for SiC as a base material for blue and white light emitting diodes has brought its prices down to a level comparable with that of InP which is widely employed in information and communications technology. The direct synthesis of graphene on SiC is not only cost-effective but assures continuity and uniformity of epitaxial graphene. In its hydrogen-intercalated quasi-free-standing form on the Si-face of SiC graphene has also proven to be largely resistant to popular cleaning procedures (SC-1 organic clean, SC-2 ionic clean, sulfuric acid/hydrogen peroxide mix, pressure rinsing and ultrasonic bath), resists and developers. For these reasons, QFS graphene on SiC should be considered a leading technology for graphene-enabled applications. In this report we present a general perspective on transport properties of quasi-free-standing bilayer graphene synthesized on Si-terminated 4H-SiC(0001) and 6H-SiC(0001) through epitaxial Chemical Vapor Deposition. The study covers a set of 380 samples grown on 4H substrates and 80 samples grown on 6H substrates, all 10mm×10mm in size and being a result of 460 individual processes. The impressive numbers provide a statistical perspective that clarifies the mutual relation between charge carrier concentration and mobility in QFS-bilayer graphene on SiC(0001) and sheds additional light on the origin of the doping type and level. The outcome of our research is compared with widely reported results and analyzed with an emphasis on the applicability of QFS-bilayer graphene in electronics and sensing. Special attention is paid to Hall-effect-based magnetic field detection. A method for minimizing the offset voltage which is enhanced by the step-edge-induced resistance anisotropy in epitaxial graphene on SiC [16] is presented.
2. Experimental details In this paper, we studied 460 quasi-free-standing bilayer graphene samples grown on the Siface of 10mm×10mm substrates, among these 380 on 4H-SiC(0001) (Cree Inc.) and 80 on 6H-SiC(0001) (II-VI Inc.). Each of the samples was grown using the epitaxial Chemical Vapor Deposition method on semi-insulating on-axis hexagonal SiC in a standard hot-wall CVD Aixtron VP508 reactor. Prior to growth, in-situ etching of the SiC surface was carried out in hydrogen atmosphere at 1600°C and chamber pressure of 100mbar, in an identical manner for all considered samples. Graphene synthesis was realized under laminar flow of argon. The process relies critically on the creation of dynamic flow conditions that control the silicon sublimation rate and enable mass transport of hydrocarbon molecules (propane or methane) to the SiC surface. The laminar gas flow over the SiC surface consists of adjacent layers moving at different velocities resulting from the shear stress between them. A ratio of the inertial and viscous forces is denoted as the Reynolds number. By tuning the value of the Reynolds number one forms an argon boundary layer, thick enough to prevent silicon sublimation yet allowing the diffusion of hydrocarbon to the SiC surface, thus enabling graphene epitaxy [6]. The growth process was followed by in situ hydrogen intercalation at ~1000°C in ~900mbar Ar atmosphere. The optimization of the growth conditions required the reactor’s hardware to be improved to assure favorable flow rates and laminarity of the carrier and precursor gases. Based on the Scanning Electron Microscopy and Raman Spectroscopy imaging, the total and the partial pressures along with the chamber temperature were optimized to suppress graphene’s vertical growth and favor its lateral expansion. Finally, the hydrogen atom intercalation conditions were brought to their possibly optimum values. The cumulative effect of these efforts led to a constantly increasing quality of the samples. The as grown samples were characterized in van der Pauw geometry with the use of a 0.55T Ecopia HMS-3000 Hall effect setup. For the purpose of the Hall effect characterization the four golden probes were placed in the four corners of each 10mm×10mm substrate. Beforehand, Cr/Au or In corner contacts were defined with the help of a mechanical mask. No significant difference was found between these two contact materials. For this reason, In was most often the choice.
Prior to the electrical measurement, out of the total number of 460 graphene samples 140 on 4H-SiC(0001) and 60 on 6H-SiC(0001) were inspected under an optical microscope and assigned a specific angle α of the SiC terraces configuration. The phenomenon of terrace formation is known as step bunching. It has its origin in the growth-preceding surface treatment during which atomic steps of SiC cluster to form macro steps, typically few nanometers in height. Fig.1 illustrates the adopted method for the angle assignment. The resultant is α ranging from 0° to 180° with the terraces running at an acute angle (α<90°), vertically (α=90°) or at an obtuse angle (90°<α<180°) calculated from the level. This method is slightly different than the one adopted in [16]. Fig.1 Schematic view of a 10mm×10mm SiC substrate and the adopted method for the angle α assignment of the terraces orientation with respect to the SiC substrate edges. Letters A-D indicate four corners of the substrate, where the four golden pins were placed during the standard Hall effect characterization in van der Pauw geometry. The red arrow marks the direction of the direct current forced between corners B and D, and the voltmeter indicates the offset voltage detected between corners A and C and related to the angle α.
In the standard van der Pauw method [17] for the sheet resistance determination, it is required to measure the RVERTICAL and RHORIZONTAL auxiliary resistances in the first place and based on the following relation exp(-πRVERTICAL/RS)+exp(-πRHORIZONTAL/RS)=1 numerically solve for the material’s sheet resistance RS. In the next step, carrier sheet density is determined based on the relation n=IB/UHalle, where n is the carrier concentration, I the applied direct current, B the magnetic induction, e is the unit charge and UHall comes as the average of two Hall voltages measured along the diagonal of the sample UAC and UBD that are the consequence of applying direct currents IBD and IAC, respectively. Since, in the single carrier model it is assumed that RS-1=enµ, where µ is the carrier mobility, µ may be calculated mathematically based on the knowledge of RS and n. In our study, in each Hall measurement the magnetic field was reversed so that the concentration n came as an average of two corresponding Hall voltages. Based on the macroscopic averaged transport properties of QFS-bilayer graphene measured on the surface of 10mm×10mm samples the statistical mean free path of charge carriers l was derived. In the equilibrium, the rate at which charge carriers receive their momentum from an external field is exactly equal to the rate at which they lose their momentum, hence the Drude
conductivity may be expressed as σ=RS-1=enµ=ne2τm/m*, where τm is the momentum relaxation time and m* is the effective mass of the charge carriers. Since m*=ħkF/VF and l= τmVF, where kF is the Fermi wave vector and VF is the Fermi velocity, the Drude conductivity takes the following form: σ=RS-1=ne2l/ħkF. The Fermi wave vector in graphene is defined as kF=
, where gs=2 is the spin degeneracy and gv=2 is the valley degeneracy. As a
result σ=RS-1=2e2kFl/h and the mean free path l=h/(2e2RSkF). Finally, the van der Pauw geometry was utilized to determine the step-edge-induced offset voltage anisotropy in epitaxial graphene on SiC. It had been observed that the step edges are more resistive than the terraces and it is very possible that the augmented resistivity is a result of a lowered carrier concentration within the step edge area; however, this mechanism could be further deepened by a possible scattering mechanism localized in the vicinity of the step edges [16]. Each of the 140 4H-SiC(0001) and 60 6H-SiC(0001) graphene samples that were inspected under an optical microscope and assigned a specific angle α of the SiC terraces configuration, were fed with 1mA direct current IBD forced between corners B and D. No magnetic field was applied (B=0T). The resultant offset voltage UAC induced along the opposite diagonal was measured and normalized by the factor (IBDRS), where RS is the sample’s sheet resistance, so that different samples could be compared. If the sheet resistance of epitaxial graphene on SiC was isotropic little if any voltage difference between corners A and C should occur. Since epitaxial graphene on SiC exhibits pronounced step-edge-induced anisotropy [16], the offset voltage UAC was analyzed as a function of the angle α to illustrate possible angle-dependence of the offset voltage.
3. Experimental results 3.1 The Effect of SiC Hexagonality The bilayer character of each individual sample was confirmed by Raman spectroscopy performed in a backscattering geometry using an inVia Renishaw microscope powered by a 532nm CW Nd:YAG laser. Fig.2 illustrates a representative map of the 2D band width within the terrace and step edge area. A detailed Raman discussion was presented in [16]. The roomtemperature Hall effect characterization of 380 4H-SiC(0001) and 80 6H-SiC(0001) 10mm×10mm quasi-free standing bilayer samples conducted in van der Pauw geometry proved p-type doping with hole concentration typically in the range 8×1012[cm-2] and 2×1013[cm-2]. From the data cloud presented in Fig.3 it is clearly visible that the intrinsic doping level in QFS-bilayer graphene grown on 6H-SiC(0001) substrates is slightly lower than on 4H-SiC(0001). Interestingly, in both plotted datasets (4H and 6H) the measured values of hole concentration appear to have a lower limit imposed by the substrate hexagonality but unrestricted upper limit so that even n≈+3.0×1013[cm-2] was measured. The large spread in hole mobility is a result of the accumulative experience in growth technology and reflects a steady increase in its maturity, but also a continuous improvement in the ex-situ preparation of SiC surface and the quality of commercial SiC wafers. As time passed even higher mobilities were obtained (up to 5000[cm2/Vs]) and the hole concentration would approach its steady substrate-dependent value. As a result, the topmost quality processes guaranteed little spread in carrier concentration and mobility.
Fig.2 A representative Micro-Raman map (20µm×20µm) of quasi-free-standing hydrogenintercalated bilayer epitaxial CVD graphene on a semi-insulating on-axis Si-terminated SiC substrate. A prevailing number of our QFS-bilayer epitaxial CVD graphene samples on 4H-SiC(0001) falls within the range between n=+1.1×1013[cm-2] and n=+2.0×1013[cm-2]. This doping level is consistent with other reports on hydrogen-intercalated QFS-bilayer sublimated graphene: (+9.0×1012,+2.0×1013)[cm-2][18], (+8.0×1012,+1.4×1013)[cm-2][19], +8.7×1012[cm-2][20] and ca. +1.0×1013[cm-2][21]. The QFS-bilayer epitaxial CVD graphene samples on 6H-SiC(0001)
are mostly restricted to n=+8.5×1012[cm-2] and n=+1.5×1013[cm-2], compared with +6.5×1012[cm-2] in hydrogen-intercalated QFS-bilayer sublimated graphene [20]. Fig.3 Room-temperature Hall effect hole mobility and concentration in quasi-free-standing hydrogen-intercalated bilayer graphene measured in van der Pauw geometry on 380 4HSiC(0001) and 80 6H-SiC(0001) 10mm×10mm samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates. Marked with gray stripes are the expected doping levels calculated from the spontaneous polarization values of 6H-SiC and 4H-SiC polytypes based on [22]. The evident dependence of hole concentration on the SiC substrate hexagonality remains in agreement with the explanation for the origin of doping in QFS-bilayer graphene on silicon carbide described in [20,23]. The authors suggest that it is the spontaneous polarization of the substrate material that accounts for the observed carrier type and concentration. The intrinsic polarization can be interpreted as a superposition of localized dipoles due to the stacking faults along the <111> direction of an otherwise perfect cubic structure (3C-SiC) and hence it is an intrinsic feature of all hexagonal polytypes of SiC [24-26]. A quantum-mechanical calculation [22] based on [27] suggests the following values of the spontaneous polarization of SiC polytypes: P0=-4.8×10-2[C/m2] for 2H, P0=-2.3E×10-2[C/m2] for 4H, and P0=-1.5×102
[C/m2] for 6H. These numbers correspond to a sheet of pseudo-charge on the Si-face of the
SiC substrate n=P0/e and an induced charge equal in magnitude but with opposite sign on the other side of the interface, namely in graphene n=-P0/e. Based on these values one can calculate the expected hole concentration in any quasi-free-standing graphene on Siterminated hexagonal SiC to be n=+3.0×1013[m-2] for 2H, n=+1.4×1013[m-2] for 4H, and n=+9.3×1012[m-2] for 6H. The expected doping level in QFS graphene on 6H-SiC(0001) is surprisingly consistent with our experimental results for QFS-bilayer graphene on 6H-SiC(0001) and falls close to what is apparently a lower limit of carrier concentration. Instead, the expected doping in QFS graphene on 4H-SiC(0001) overestimates our empirical values by ca. 0.3×1013[cm-2], which suggests that either the intrinsic polarization of 4H-SiC should be reconsidered or there is an additional mechanism associated with the bulk crystal, graphene-SiC interface or most likely graphene itself that shifts the carrier concentration to lower values than suggested by the spontaneous polarization explanation.
From the data cloud in Fig.3 it is also evident that the substrate choice significantly affects the charge carrier mobility. The topmost mobilities in our QFS-bilayer graphene on 6HSiC(0001) reach 3000[cm2/Vs], while in QFS-bilayer graphene on 4H-SiC(0001) grown in comparable conditions they reach as high as 5000[cm2/Vs], which is more than in previous reports: 3700[cm2/Vs][18], 2300[cm2/Vs][19], 1250[cm2/Vs][21]. The quantitative difference between the two hexagonal polytypes is even more pronounced when one calculates the statistical mean free path of charge carriers based on the macroscopic transport properties RS and n. The mean free path of holes in our QFS-bilayer graphene on 4H-SiC(0001) is as long as 200nm and twice the highest value derived for our QFS-bilayer graphene on 6HSiC(0001).
Fig.4 Statistical mean free path of charge carriers in quasi-free-standing hydrogenintercalated bilayer graphene derived from macroscopic transport properties measured in van der Pauw geometry on 380 4H-SiC(0001) and 80 6H-SiC(0001) 10mm×10mm samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates.
Since growth conditions were comparable for 4H and 6H and both polytypes share almost identical dielectric permittivity we reason that the prominent statistical difference in charge carrier concentration has its origin in the spontaneous polarization but may be further affected by the varying density of charged impurities in high-purity semi-insulating 4H-SiC and the vanadium-compensated semi-insulating 6H-SiC. More complex to explain is the dissimilarity in carrier mobility and the statistical mean free path. Here the grounds could be manifold, including surface deviation from the ideal (0001), terrace density and their parallelism, number of point defects, pre-growth surface treatment and potentially many more factors to be identified and studied.
3.2 Hall Effect Sensor Performance Epitaxial graphene on SiC has been predominantly suggested for the technology of fieldeffect transistors [1,28-40]. The appropriateness of QFS-bilayer graphene is twofold. Bilayer graphene has been both theoretically and experimentally [41-43] confirmed to enable bandgap opening by applying vertical electric field across the two layers, sufficient enough to suppress the possible band-to-band tunneling in the off-state and thus allowing effective switching. Additionally, QFS-bilayer graphene on the Si-face of SiC exhibits on average three times higher carrier mobility than monolayer graphene on SiC(0001), reaching values as high as 5000[cm2/Vs] on 4H-SiC(0001) in well-established industrial-scale technology (Fig.3). High carrier mobility is necessary to maximize the GFET’s transconductance and intrinsic cut-off frequency. From the data cloud presented in Fig.3 it is clearly visible that the record mobilities in our as-grown QFS-bilayer graphene on the Si-face of semi-insulating SiC substrates inseparably correspond to a specific doping level induced by the substrate choice, namely n≈+9×1012[cm-2] for 6H and n≈+1.1×1013[cm-2] for 4H. This intrinsic restriction imposes an operating point of graphene far from the Dirac point and suggests that either it is consciously accepted as the device operating point or it is to be chemically downshifted towards the charge neutrality point. In contrast to transistors graphene’s potential applicability in Hall-effect-based magnetic field detection attracted less attention and was mainly reported for CVD copper-grown [44] and platinum-grown [45] transferred graphene. The Hall elements are usually designed as equalarm crosses and operate either in a direct current mode or a direct voltage mode. Assuming a single carrier model, the Hall voltage UHall in any two-dimensional materials is proportional to the forced current I, the applied magnetic field B and inversely proportional to sheet carrier concentration n, UHall= IB/ne. As a result, the current-mode sensitivity SI=( [V/AT] and the voltage-mode sensitivity SV=(
)/I=1/ne
)/V=µW/L [V/VT], where µ is the carrier
mobility and W/L are the dimensions of the graphene channel. Equally important as sensitivity is the magnetic resolution (Bmin [T/
]) or the minimum detectable field, defined as the
magnetic induction spectral density at which the Hall voltage UHall equals the noise voltage NV[T/
], namely NV=IBminSI. The magnetic resolution Bmin is proportional to µ-5/2n-1/2f-1/2
[45], where f is the measurement frequency. Therefore, Bmin will effectively improve with carrier mobility µ, and only moderately with carrier concentration n. Combining these two
preconditions, an ideal material, characterized by high carrier mobility and relatively low carrier concentration, emerges. These requirements are approximated by graphene close to its charge neutrality point; however, commercial graphene available in a reliable industrial technology will be subject to the above reported restrictions. Commercially available Hall effect sensors based on standard bulk CMOS IC technology offer current-mode sensitivity of the order of 100[V/AT] [46]. This value is higher in GaAsbased elements – 200[V/AT] (Asahi Kasei Corp.) and may approach 700[V/AT] in 2DEG devices [47]. The theoretically calculated intrinsic current-mode sensitivity of our QFSbilayer epitaxial CVD graphene yields SI =70[V/AT] for 6H-SiC(0001) and SI =57[V/AT] for 4H-SiC(0001), since the as-grown samples exhibit different hexagonality-dependent minimum carrier concentration. Possible improvement of these values will require lowering the intrinsic concentration with carefully chosen chemical dopants. On the other hand, the substrate-limited minimum doping level n≈+1.1×1013[m-2] together with high carrier mobility µ=5000[cm2/Vs] in the top-quality QFS-bilayer graphene on 4H-SiC(0001) will offer high magnetic resolution Bmin. Yet sensitivity may not necessarily be the ultimate advantage of graphene-based Hall effect sensors. Traditionally, the thin-film active area of a Hall effect device is semiconducting and hence its transport properties degrade with temperature. Commercially available hightemperature Hall effect sensors operate at 200°C. Since QFS-bilayer graphene on SiC is gapless it may be suitable for temperatures above 200°C. In [44] the authors characterize a graphene-based Hall effect element at 400°C. The potential benefits of high-temperature sensing may prevail over the moderate sensitivity. A great significance should also be ascribed to the offset voltage of a Hall effect element. By definition the offset voltage occurs between the output electrodes when the Hall effect element is sourced with electric current but no magnetic field is yet applied. The offset voltage adds to the Hall voltage and constitutes an operating point of the device. In general, the offset voltage has its origin in the finite resolution of the geometry of the active area and in possible anisotropy in its electrical properties. When the active area of a Hall effect sensor is made of epitaxial graphene on SiC, the natural step-edge-induced electrical anisotropy of this material [16,34] may significantly increase the offset voltage, up to a level that excludes epitaxial graphene on SiC from this application.
In order to highlight this issue we present a qualitative observation of the step-edge-induced offset voltage anisotropy in epitaxial graphene on SiC derived from standard electrical characterization in van der Pauw geometry. 140 4H-SiC(0001) and 60 6H-SiC(0001) epitaxial CVD 10mm×10mm samples were inspected under an optical microscope and ascribed the specific angle α of the SiC terraces configuration (Fig.1). Each sample was fed with IBD =1mA direct current between corners B and D and the resultant step-edge-induced offset voltage UAC (B=0T) was analyzed as a the function of the angle α. In order to compare the 200 individual processes the offset voltage UAC was normalized with a factor (IBDRS). Fig.5 illustrates the resultant data cloud of the offset voltage (UAC/(IBDRS))100% as a function of the angle α. It is apparent from Fig.5 that at a given angle of the terrace configuration, the normalized values of the offset voltage span a certain range. This scatter in data has its origin in the varying average step edge height and density in different samples. An even more detailed analysis would require the offset voltage to be further normalized with the average step edge height and density exclusively determined for each individual sample. Unfortunately, such an extensive study has not been feasible.
Fig.5 Qualitative observation of the step-edge-induced offset voltage as a function of the angle α of the SiC terraces configuration measured in van der Pauw geometry in quasi-freestanding hydrogen-intercalated bilayer graphene on 140 4H-SiC(0001) and 60 6H-SiC(0001) 10mm×10mm samples grown in 200 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates.
From Fig.5 it is evident that the offset voltage in a Hall effect element made of epitaxial graphene on SiC depends on the cumulative number of SiC step edges that the two orthogonal components of the current need to pass and it may be significantly reduced by consciously orienting the element in a precise alignment with respect to the pattern of silicon carbide terraces and step edges. The two mutually equivalent optimum geometries correspond to the situation when the constant electric current flows either in the direction perpendicular or parallel to the pattern of silicon carbide terraces and step edges, so that its two orthogonal components pass an equal number of SiC step edges. Every other alignment will result in the offset voltage being higher than the minimum value. The engineering intuition tells that out of these two geometries the latter fosters more favorable transport conditions. Unfortunately, an
accurate determination of the possible angle-dependence of charge carrier mobility is not feasible in van der Pauw geometry since by definition both the sheet resistance and sheet carrier concentration are averaged over the entire area of the sample. The resultant average carrier mobility is therefore uniformly distributed in the function of the angle α of the SiC terraces configuration and the high-mobility samples are in no way related to a specific terrace angle. The above observation implies a great challenge for the technology of Hall effect sensors made of epitaxial graphene on SiC. The practical consequence for device processing engineers is to look for methods to intentionally reduce the effect of the step-edge-induced offset voltage anisotropy. Bearing in mind the potential suitability of QFS-bilayer hydrogenintercalated graphene on semi-insulating SiC for high-temperature magnetic field detection, this challenge may be worth the effort.
4. Conclusions We showed extensive statistics of transport properties of quasi-free-standing hydrogenintercalated bilayer graphene samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on the Si-face of semi-insulating on-axis silicon carbide substrates. The presented academic-scale technology is well-established and reliable. It offers high carrier mobility (5000[cm2/Vs]) and provides basis for large-scale industrial production of graphene for electronics and sensor applications. The mutual relation between charge carrier concentration and mobility proves that the as-grown samples exhibit different substratelimited minimum carrier concentration, namely n≈+9×1012[m-2] for 6H(0001) and n≈+1.1×1013[m-2] for 4H(0001), which is consistent with the spontaneous polarization explanation for the origin of the doping level in epitaxial graphene on hexagonal SiC. The study also reveals that the statistical mean free path of holes in our QFS-bilayer graphene on 4H-SiC(0001) is as long as 200nm and twice the highest value derived for QFS-bilayer graphene on 6H-SiC(0001).
The transport properties of our QFS-bilayer graphene together with its suitability for industrial-scale device processing technologies favor this material for application in transistors and magnetic field sensors. We clearly stress that the transport properties of epitaxial graphene on SiC are anisotropic, which has its origin in the characteristic morphology of the substrate. Particularly, in Hall effect sensors the step-edge-induced offset voltage anisotropy, which is a hazard to the device operation, need to be minimized by consciously orienting the Hall element, so that the constant electric current flows either in the direction perpendicular or parallel to the pattern of silicon carbide terraces and step edges.
Acknowledgements The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship. This work has been also partially supported by the National Centre for Research and Development under the GRAF-TECH/NCBiR/12/14/2013 “GRAFMAG” grant and from the National Science Centre under the PRELUDIUM 2013/11/N/ST3/04147 grant.
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S0008-6223(15)00547-3 http://dx.doi.org/10.1016/j.carbon.2015.06.032 CARBON 10034
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Please cite this article as: Ciuk, T., Strupinski, W., Statistics of Epitaxial Graphene for Hall Effect Sensors, Carbon (2015), doi: http://dx.doi.org/10.1016/j.carbon.2015.06.032
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Statistics of Epitaxial Graphene for Hall Effect Sensors Tymoteusz Ciuk1,2 and Wlodek Strupinski1* 1) Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland 2) Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
Key words: graphene, epitaxy, chemical vapor deposition, transport, bilayer, anisotropy, Hall effect, offset voltage
Abstract Epitaxial Chemical Vapor Deposition growth of graphene on silicon carbide is one of the most promising technologies to realize graphene-based electronics. Particularly, the quasifree-standing bilayer which comes through hydrogen atom intercalation of monolayer graphene grown on the Si-face of SiC offers high carrier mobility (as high as 5000[cm2/Vs]) and electrical stability throughout the device processing cycle. In this report, we present a statistical perspective on transport properties of QFS-bilayer graphene grown on 4H(0001) and 6H(0001) SiC, being a result of 460 individual processes on semi-insulating 10mm×10mm substrates. The mutual relation between charge carrier concentration and mobility is determined and analyzed to raise the awareness of the effect of SiC hexagonality on charge transport in graphene. Special attention is paid to the applicability of quasi-freestanding bilayer graphene on SiC, primarily in magnetic field detection. The issue of the stepedge-induced offset voltage anisotropy in Hall effect sensors is introduced and a method to minimize it is presented.
* corresponding author: [email protected] (Wlodek Strupinski)
1. Introduction Arguably, there are two most promising epitaxial technologies for wafer-scale production of graphene devices [1,2] – silicon atom sublimation from SiC surface [3-5] and Chemical Vapor Deposition (CVD) growth on SiC [6]. A CVD process typically involves methane, propane or acetylene as a carbon source. It enables a precise synthesis of a pre-defined number of carbon layers, including a sole buffer layer on the Si-face of SiC, and is less sensitive to SiC surface defects than sublimation. The CVD epitaxy has been studied for both Si-terminated and C-terminated SiC; however, more attention has been directed to SiC(0001) since Si-face growth kinetics foster higher accuracy. Growing graphene on the Si-face of SiC always involves the formation of a buffer layer [7] which is the first layer of carbon atoms covalently bonded to the substrate [8-10]. The buffer layer can be decoupled from the substrate through hydrogen atom intercalation [11-15]. The intercalating atoms diffuse underneath the buffer layer and bond themselves to the topmost Si atoms of the Si-terminated SiC surface, thus converting the buffer layer into a mostly sp2hybridized single graphene layer. Depending on the initial structure, the hydrogen atom intercalation allows different quasi-free-standing forms of graphene. As a result, a bare buffer layer on the Si-terminated SiC surface is turned into quasi-free-standing monolayer graphene (QFS-monolayer) and monolayer graphene (buffer layer + single graphene layer) on the Siterminated SiC surface is turned into quasi-free-standing bilayer graphene (QFS-bilayer). The significance of the quasi-free-standing forms of graphene on the Si-face of SiC is justified by the elimination of the buffer layer which constitutes a significant scatterer to charge carriers in graphene [10]. The resultant hydrogen-atom-intercalated graphene exhibits on average three times higher carrier mobility than the un-intercalated one and its p-type doping and carrier mobility is only slightly affected by the device fabrication. On the contrary the n-type doping of un-intercalated graphene on the Si-face of SiC, which is a consequence of the buffer layer’s pinning the Fermi level in graphene above the Dirac point, may be significantly shifted by the exposure to popular cleaning reagents and resists, including the change of the doping type. For these reasons, hydrogen-atom-intercalated graphene is better suited for electronics and sensor applications than un-intercalated graphene. Importantly, it has been observed in our samples that the hydrogen atom presence is stable up to 700°C,
which is high enough to meet the requirements of high-speed electronics and hightemperature sensing. Only at higher temperatures does a sample release hydrogen. The constantly growing demand for SiC as a base material for blue and white light emitting diodes has brought its prices down to a level comparable with that of InP which is widely employed in information and communications technology. The direct synthesis of graphene on SiC is not only cost-effective but assures continuity and uniformity of epitaxial graphene. In its hydrogen-intercalated quasi-free-standing form on the Si-face of SiC graphene has also proven to be largely resistant to popular cleaning procedures (SC-1 organic clean, SC-2 ionic clean, sulfuric acid/hydrogen peroxide mix, pressure rinsing and ultrasonic bath), resists and developers. For these reasons, QFS graphene on SiC should be considered a leading technology for graphene-enabled applications. In this report we present a general perspective on transport properties of quasi-free-standing bilayer graphene synthesized on Si-terminated 4H-SiC(0001) and 6H-SiC(0001) through epitaxial Chemical Vapor Deposition. The study covers a set of 380 samples grown on 4H substrates and 80 samples grown on 6H substrates, all 10mm×10mm in size and being a result of 460 individual processes. The impressive numbers provide a statistical perspective that clarifies the mutual relation between charge carrier concentration and mobility in QFS-bilayer graphene on SiC(0001) and sheds additional light on the origin of the doping type and level. The outcome of our research is compared with widely reported results and analyzed with an emphasis on the applicability of QFS-bilayer graphene in electronics and sensing. Special attention is paid to Hall-effect-based magnetic field detection. A method for minimizing the offset voltage which is enhanced by the step-edge-induced resistance anisotropy in epitaxial graphene on SiC [16] is presented.
2. Experimental details In this paper, we studied 460 quasi-free-standing bilayer graphene samples grown on the Siface of 10mm×10mm substrates, among these 380 on 4H-SiC(0001) (Cree Inc.) and 80 on 6H-SiC(0001) (II-VI Inc.). Each of the samples was grown using the epitaxial Chemical Vapor Deposition method on semi-insulating on-axis hexagonal SiC in a standard hot-wall CVD Aixtron VP508 reactor. Prior to growth, in-situ etching of the SiC surface was carried out in hydrogen atmosphere at 1600°C and chamber pressure of 100mbar, in an identical manner for all considered samples. Graphene synthesis was realized under laminar flow of argon. The process relies critically on the creation of dynamic flow conditions that control the silicon sublimation rate and enable mass transport of hydrocarbon molecules (propane or methane) to the SiC surface. The laminar gas flow over the SiC surface consists of adjacent layers moving at different velocities resulting from the shear stress between them. A ratio of the inertial and viscous forces is denoted as the Reynolds number. By tuning the value of the Reynolds number one forms an argon boundary layer, thick enough to prevent silicon sublimation yet allowing the diffusion of hydrocarbon to the SiC surface, thus enabling graphene epitaxy [6]. The growth process was followed by in situ hydrogen intercalation at ~1000°C in ~900mbar Ar atmosphere. The optimization of the growth conditions required the reactor’s hardware to be improved to assure favorable flow rates and laminarity of the carrier and precursor gases. Based on the Scanning Electron Microscopy and Raman Spectroscopy imaging, the total and the partial pressures along with the chamber temperature were optimized to suppress graphene’s vertical growth and favor its lateral expansion. Finally, the hydrogen atom intercalation conditions were brought to their possibly optimum values. The cumulative effect of these efforts led to a constantly increasing quality of the samples. The as grown samples were characterized in van der Pauw geometry with the use of a 0.55T Ecopia HMS-3000 Hall effect setup. For the purpose of the Hall effect characterization the four golden probes were placed in the four corners of each 10mm×10mm substrate. Beforehand, Cr/Au or In corner contacts were defined with the help of a mechanical mask. No significant difference was found between these two contact materials. For this reason, In was most often the choice.
Prior to the electrical measurement, out of the total number of 460 graphene samples 140 on 4H-SiC(0001) and 60 on 6H-SiC(0001) were inspected under an optical microscope and assigned a specific angle α of the SiC terraces configuration. The phenomenon of terrace formation is known as step bunching. It has its origin in the growth-preceding surface treatment during which atomic steps of SiC cluster to form macro steps, typically few nanometers in height. Fig.1 illustrates the adopted method for the angle assignment. The resultant is α ranging from 0° to 180° with the terraces running at an acute angle (α<90°), vertically (α=90°) or at an obtuse angle (90°<α<180°) calculated from the level. This method is slightly different than the one adopted in [16]. Fig.1 Schematic view of a 10mm×10mm SiC substrate and the adopted method for the angle α assignment of the terraces orientation with respect to the SiC substrate edges. Letters A-D indicate four corners of the substrate, where the four golden pins were placed during the standard Hall effect characterization in van der Pauw geometry. The red arrow marks the direction of the direct current forced between corners B and D, and the voltmeter indicates the offset voltage detected between corners A and C and related to the angle α.
In the standard van der Pauw method [17] for the sheet resistance determination, it is required to measure the RVERTICAL and RHORIZONTAL auxiliary resistances in the first place and based on the following relation exp(-πRVERTICAL/RS)+exp(-πRHORIZONTAL/RS)=1 numerically solve for the material’s sheet resistance RS. In the next step, carrier sheet density is determined based on the relation n=IB/UHalle, where n is the carrier concentration, I the applied direct current, B the magnetic induction, e is the unit charge and UHall comes as the average of two Hall voltages measured along the diagonal of the sample UAC and UBD that are the consequence of applying direct currents IBD and IAC, respectively. Since, in the single carrier model it is assumed that RS-1=enµ, where µ is the carrier mobility, µ may be calculated mathematically based on the knowledge of RS and n. In our study, in each Hall measurement the magnetic field was reversed so that the concentration n came as an average of two corresponding Hall voltages. Based on the macroscopic averaged transport properties of QFS-bilayer graphene measured on the surface of 10mm×10mm samples the statistical mean free path of charge carriers l was derived. In the equilibrium, the rate at which charge carriers receive their momentum from an external field is exactly equal to the rate at which they lose their momentum, hence the Drude
conductivity may be expressed as σ=RS-1=enµ=ne2τm/m*, where τm is the momentum relaxation time and m* is the effective mass of the charge carriers. Since m*=ħkF/VF and l= τmVF, where kF is the Fermi wave vector and VF is the Fermi velocity, the Drude conductivity takes the following form: σ=RS-1=ne2l/ħkF. The Fermi wave vector in graphene is defined as kF=
, where gs=2 is the spin degeneracy and gv=2 is the valley degeneracy. As a
result σ=RS-1=2e2kFl/h and the mean free path l=h/(2e2RSkF). Finally, the van der Pauw geometry was utilized to determine the step-edge-induced offset voltage anisotropy in epitaxial graphene on SiC. It had been observed that the step edges are more resistive than the terraces and it is very possible that the augmented resistivity is a result of a lowered carrier concentration within the step edge area; however, this mechanism could be further deepened by a possible scattering mechanism localized in the vicinity of the step edges [16]. Each of the 140 4H-SiC(0001) and 60 6H-SiC(0001) graphene samples that were inspected under an optical microscope and assigned a specific angle α of the SiC terraces configuration, were fed with 1mA direct current IBD forced between corners B and D. No magnetic field was applied (B=0T). The resultant offset voltage UAC induced along the opposite diagonal was measured and normalized by the factor (IBDRS), where RS is the sample’s sheet resistance, so that different samples could be compared. If the sheet resistance of epitaxial graphene on SiC was isotropic little if any voltage difference between corners A and C should occur. Since epitaxial graphene on SiC exhibits pronounced step-edge-induced anisotropy [16], the offset voltage UAC was analyzed as a function of the angle α to illustrate possible angle-dependence of the offset voltage.
3. Experimental results 3.1 The Effect of SiC Hexagonality The bilayer character of each individual sample was confirmed by Raman spectroscopy performed in a backscattering geometry using an inVia Renishaw microscope powered by a 532nm CW Nd:YAG laser. Fig.2 illustrates a representative map of the 2D band width within the terrace and step edge area. A detailed Raman discussion was presented in [16]. The roomtemperature Hall effect characterization of 380 4H-SiC(0001) and 80 6H-SiC(0001) 10mm×10mm quasi-free standing bilayer samples conducted in van der Pauw geometry proved p-type doping with hole concentration typically in the range 8×1012[cm-2] and 2×1013[cm-2]. From the data cloud presented in Fig.3 it is clearly visible that the intrinsic doping level in QFS-bilayer graphene grown on 6H-SiC(0001) substrates is slightly lower than on 4H-SiC(0001). Interestingly, in both plotted datasets (4H and 6H) the measured values of hole concentration appear to have a lower limit imposed by the substrate hexagonality but unrestricted upper limit so that even n≈+3.0×1013[cm-2] was measured. The large spread in hole mobility is a result of the accumulative experience in growth technology and reflects a steady increase in its maturity, but also a continuous improvement in the ex-situ preparation of SiC surface and the quality of commercial SiC wafers. As time passed even higher mobilities were obtained (up to 5000[cm2/Vs]) and the hole concentration would approach its steady substrate-dependent value. As a result, the topmost quality processes guaranteed little spread in carrier concentration and mobility.
Fig.2 A representative Micro-Raman map (20µm×20µm) of quasi-free-standing hydrogenintercalated bilayer epitaxial CVD graphene on a semi-insulating on-axis Si-terminated SiC substrate. A prevailing number of our QFS-bilayer epitaxial CVD graphene samples on 4H-SiC(0001) falls within the range between n=+1.1×1013[cm-2] and n=+2.0×1013[cm-2]. This doping level is consistent with other reports on hydrogen-intercalated QFS-bilayer sublimated graphene: (+9.0×1012,+2.0×1013)[cm-2][18], (+8.0×1012,+1.4×1013)[cm-2][19], +8.7×1012[cm-2][20] and ca. +1.0×1013[cm-2][21]. The QFS-bilayer epitaxial CVD graphene samples on 6H-SiC(0001)
are mostly restricted to n=+8.5×1012[cm-2] and n=+1.5×1013[cm-2], compared with +6.5×1012[cm-2] in hydrogen-intercalated QFS-bilayer sublimated graphene [20]. Fig.3 Room-temperature Hall effect hole mobility and concentration in quasi-free-standing hydrogen-intercalated bilayer graphene measured in van der Pauw geometry on 380 4HSiC(0001) and 80 6H-SiC(0001) 10mm×10mm samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates. Marked with gray stripes are the expected doping levels calculated from the spontaneous polarization values of 6H-SiC and 4H-SiC polytypes based on [22]. The evident dependence of hole concentration on the SiC substrate hexagonality remains in agreement with the explanation for the origin of doping in QFS-bilayer graphene on silicon carbide described in [20,23]. The authors suggest that it is the spontaneous polarization of the substrate material that accounts for the observed carrier type and concentration. The intrinsic polarization can be interpreted as a superposition of localized dipoles due to the stacking faults along the <111> direction of an otherwise perfect cubic structure (3C-SiC) and hence it is an intrinsic feature of all hexagonal polytypes of SiC [24-26]. A quantum-mechanical calculation [22] based on [27] suggests the following values of the spontaneous polarization of SiC polytypes: P0=-4.8×10-2[C/m2] for 2H, P0=-2.3E×10-2[C/m2] for 4H, and P0=-1.5×102
[C/m2] for 6H. These numbers correspond to a sheet of pseudo-charge on the Si-face of the
SiC substrate n=P0/e and an induced charge equal in magnitude but with opposite sign on the other side of the interface, namely in graphene n=-P0/e. Based on these values one can calculate the expected hole concentration in any quasi-free-standing graphene on Siterminated hexagonal SiC to be n=+3.0×1013[m-2] for 2H, n=+1.4×1013[m-2] for 4H, and n=+9.3×1012[m-2] for 6H. The expected doping level in QFS graphene on 6H-SiC(0001) is surprisingly consistent with our experimental results for QFS-bilayer graphene on 6H-SiC(0001) and falls close to what is apparently a lower limit of carrier concentration. Instead, the expected doping in QFS graphene on 4H-SiC(0001) overestimates our empirical values by ca. 0.3×1013[cm-2], which suggests that either the intrinsic polarization of 4H-SiC should be reconsidered or there is an additional mechanism associated with the bulk crystal, graphene-SiC interface or most likely graphene itself that shifts the carrier concentration to lower values than suggested by the spontaneous polarization explanation.
From the data cloud in Fig.3 it is also evident that the substrate choice significantly affects the charge carrier mobility. The topmost mobilities in our QFS-bilayer graphene on 6HSiC(0001) reach 3000[cm2/Vs], while in QFS-bilayer graphene on 4H-SiC(0001) grown in comparable conditions they reach as high as 5000[cm2/Vs], which is more than in previous reports: 3700[cm2/Vs][18], 2300[cm2/Vs][19], 1250[cm2/Vs][21]. The quantitative difference between the two hexagonal polytypes is even more pronounced when one calculates the statistical mean free path of charge carriers based on the macroscopic transport properties RS and n. The mean free path of holes in our QFS-bilayer graphene on 4H-SiC(0001) is as long as 200nm and twice the highest value derived for our QFS-bilayer graphene on 6HSiC(0001).
Fig.4 Statistical mean free path of charge carriers in quasi-free-standing hydrogenintercalated bilayer graphene derived from macroscopic transport properties measured in van der Pauw geometry on 380 4H-SiC(0001) and 80 6H-SiC(0001) 10mm×10mm samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates.
Since growth conditions were comparable for 4H and 6H and both polytypes share almost identical dielectric permittivity we reason that the prominent statistical difference in charge carrier concentration has its origin in the spontaneous polarization but may be further affected by the varying density of charged impurities in high-purity semi-insulating 4H-SiC and the vanadium-compensated semi-insulating 6H-SiC. More complex to explain is the dissimilarity in carrier mobility and the statistical mean free path. Here the grounds could be manifold, including surface deviation from the ideal (0001), terrace density and their parallelism, number of point defects, pre-growth surface treatment and potentially many more factors to be identified and studied.
3.2 Hall Effect Sensor Performance Epitaxial graphene on SiC has been predominantly suggested for the technology of fieldeffect transistors [1,28-40]. The appropriateness of QFS-bilayer graphene is twofold. Bilayer graphene has been both theoretically and experimentally [41-43] confirmed to enable bandgap opening by applying vertical electric field across the two layers, sufficient enough to suppress the possible band-to-band tunneling in the off-state and thus allowing effective switching. Additionally, QFS-bilayer graphene on the Si-face of SiC exhibits on average three times higher carrier mobility than monolayer graphene on SiC(0001), reaching values as high as 5000[cm2/Vs] on 4H-SiC(0001) in well-established industrial-scale technology (Fig.3). High carrier mobility is necessary to maximize the GFET’s transconductance and intrinsic cut-off frequency. From the data cloud presented in Fig.3 it is clearly visible that the record mobilities in our as-grown QFS-bilayer graphene on the Si-face of semi-insulating SiC substrates inseparably correspond to a specific doping level induced by the substrate choice, namely n≈+9×1012[cm-2] for 6H and n≈+1.1×1013[cm-2] for 4H. This intrinsic restriction imposes an operating point of graphene far from the Dirac point and suggests that either it is consciously accepted as the device operating point or it is to be chemically downshifted towards the charge neutrality point. In contrast to transistors graphene’s potential applicability in Hall-effect-based magnetic field detection attracted less attention and was mainly reported for CVD copper-grown [44] and platinum-grown [45] transferred graphene. The Hall elements are usually designed as equalarm crosses and operate either in a direct current mode or a direct voltage mode. Assuming a single carrier model, the Hall voltage UHall in any two-dimensional materials is proportional to the forced current I, the applied magnetic field B and inversely proportional to sheet carrier concentration n, UHall= IB/ne. As a result, the current-mode sensitivity SI=( [V/AT] and the voltage-mode sensitivity SV=(
)/I=1/ne
)/V=µW/L [V/VT], where µ is the carrier
mobility and W/L are the dimensions of the graphene channel. Equally important as sensitivity is the magnetic resolution (Bmin [T/
]) or the minimum detectable field, defined as the
magnetic induction spectral density at which the Hall voltage UHall equals the noise voltage NV[T/
], namely NV=IBminSI. The magnetic resolution Bmin is proportional to µ-5/2n-1/2f-1/2
[45], where f is the measurement frequency. Therefore, Bmin will effectively improve with carrier mobility µ, and only moderately with carrier concentration n. Combining these two
preconditions, an ideal material, characterized by high carrier mobility and relatively low carrier concentration, emerges. These requirements are approximated by graphene close to its charge neutrality point; however, commercial graphene available in a reliable industrial technology will be subject to the above reported restrictions. Commercially available Hall effect sensors based on standard bulk CMOS IC technology offer current-mode sensitivity of the order of 100[V/AT] [46]. This value is higher in GaAsbased elements – 200[V/AT] (Asahi Kasei Corp.) and may approach 700[V/AT] in 2DEG devices [47]. The theoretically calculated intrinsic current-mode sensitivity of our QFSbilayer epitaxial CVD graphene yields SI =70[V/AT] for 6H-SiC(0001) and SI =57[V/AT] for 4H-SiC(0001), since the as-grown samples exhibit different hexagonality-dependent minimum carrier concentration. Possible improvement of these values will require lowering the intrinsic concentration with carefully chosen chemical dopants. On the other hand, the substrate-limited minimum doping level n≈+1.1×1013[m-2] together with high carrier mobility µ=5000[cm2/Vs] in the top-quality QFS-bilayer graphene on 4H-SiC(0001) will offer high magnetic resolution Bmin. Yet sensitivity may not necessarily be the ultimate advantage of graphene-based Hall effect sensors. Traditionally, the thin-film active area of a Hall effect device is semiconducting and hence its transport properties degrade with temperature. Commercially available hightemperature Hall effect sensors operate at 200°C. Since QFS-bilayer graphene on SiC is gapless it may be suitable for temperatures above 200°C. In [44] the authors characterize a graphene-based Hall effect element at 400°C. The potential benefits of high-temperature sensing may prevail over the moderate sensitivity. A great significance should also be ascribed to the offset voltage of a Hall effect element. By definition the offset voltage occurs between the output electrodes when the Hall effect element is sourced with electric current but no magnetic field is yet applied. The offset voltage adds to the Hall voltage and constitutes an operating point of the device. In general, the offset voltage has its origin in the finite resolution of the geometry of the active area and in possible anisotropy in its electrical properties. When the active area of a Hall effect sensor is made of epitaxial graphene on SiC, the natural step-edge-induced electrical anisotropy of this material [16,34] may significantly increase the offset voltage, up to a level that excludes epitaxial graphene on SiC from this application.
In order to highlight this issue we present a qualitative observation of the step-edge-induced offset voltage anisotropy in epitaxial graphene on SiC derived from standard electrical characterization in van der Pauw geometry. 140 4H-SiC(0001) and 60 6H-SiC(0001) epitaxial CVD 10mm×10mm samples were inspected under an optical microscope and ascribed the specific angle α of the SiC terraces configuration (Fig.1). Each sample was fed with IBD =1mA direct current between corners B and D and the resultant step-edge-induced offset voltage UAC (B=0T) was analyzed as a the function of the angle α. In order to compare the 200 individual processes the offset voltage UAC was normalized with a factor (IBDRS). Fig.5 illustrates the resultant data cloud of the offset voltage (UAC/(IBDRS))100% as a function of the angle α. It is apparent from Fig.5 that at a given angle of the terrace configuration, the normalized values of the offset voltage span a certain range. This scatter in data has its origin in the varying average step edge height and density in different samples. An even more detailed analysis would require the offset voltage to be further normalized with the average step edge height and density exclusively determined for each individual sample. Unfortunately, such an extensive study has not been feasible.
Fig.5 Qualitative observation of the step-edge-induced offset voltage as a function of the angle α of the SiC terraces configuration measured in van der Pauw geometry in quasi-freestanding hydrogen-intercalated bilayer graphene on 140 4H-SiC(0001) and 60 6H-SiC(0001) 10mm×10mm samples grown in 200 individual epitaxial Chemical Vapor Deposition processes on semi-insulating on-axis Si-terminated substrates.
From Fig.5 it is evident that the offset voltage in a Hall effect element made of epitaxial graphene on SiC depends on the cumulative number of SiC step edges that the two orthogonal components of the current need to pass and it may be significantly reduced by consciously orienting the element in a precise alignment with respect to the pattern of silicon carbide terraces and step edges. The two mutually equivalent optimum geometries correspond to the situation when the constant electric current flows either in the direction perpendicular or parallel to the pattern of silicon carbide terraces and step edges, so that its two orthogonal components pass an equal number of SiC step edges. Every other alignment will result in the offset voltage being higher than the minimum value. The engineering intuition tells that out of these two geometries the latter fosters more favorable transport conditions. Unfortunately, an
accurate determination of the possible angle-dependence of charge carrier mobility is not feasible in van der Pauw geometry since by definition both the sheet resistance and sheet carrier concentration are averaged over the entire area of the sample. The resultant average carrier mobility is therefore uniformly distributed in the function of the angle α of the SiC terraces configuration and the high-mobility samples are in no way related to a specific terrace angle. The above observation implies a great challenge for the technology of Hall effect sensors made of epitaxial graphene on SiC. The practical consequence for device processing engineers is to look for methods to intentionally reduce the effect of the step-edge-induced offset voltage anisotropy. Bearing in mind the potential suitability of QFS-bilayer hydrogenintercalated graphene on semi-insulating SiC for high-temperature magnetic field detection, this challenge may be worth the effort.
4. Conclusions We showed extensive statistics of transport properties of quasi-free-standing hydrogenintercalated bilayer graphene samples grown in 460 individual epitaxial Chemical Vapor Deposition processes on the Si-face of semi-insulating on-axis silicon carbide substrates. The presented academic-scale technology is well-established and reliable. It offers high carrier mobility (5000[cm2/Vs]) and provides basis for large-scale industrial production of graphene for electronics and sensor applications. The mutual relation between charge carrier concentration and mobility proves that the as-grown samples exhibit different substratelimited minimum carrier concentration, namely n≈+9×1012[m-2] for 6H(0001) and n≈+1.1×1013[m-2] for 4H(0001), which is consistent with the spontaneous polarization explanation for the origin of the doping level in epitaxial graphene on hexagonal SiC. The study also reveals that the statistical mean free path of holes in our QFS-bilayer graphene on 4H-SiC(0001) is as long as 200nm and twice the highest value derived for QFS-bilayer graphene on 6H-SiC(0001).
The transport properties of our QFS-bilayer graphene together with its suitability for industrial-scale device processing technologies favor this material for application in transistors and magnetic field sensors. We clearly stress that the transport properties of epitaxial graphene on SiC are anisotropic, which has its origin in the characteristic morphology of the substrate. Particularly, in Hall effect sensors the step-edge-induced offset voltage anisotropy, which is a hazard to the device operation, need to be minimized by consciously orienting the Hall element, so that the constant electric current flows either in the direction perpendicular or parallel to the pattern of silicon carbide terraces and step edges.
Acknowledgements The research leading to these results has received funding from the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship. This work has been also partially supported by the National Centre for Research and Development under the GRAF-TECH/NCBiR/12/14/2013 “GRAFMAG” grant and from the National Science Centre under the PRELUDIUM 2013/11/N/ST3/04147 grant.
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