Breakdown of the quantum in epitaxial

T.J.B.M. Janssen∗, S. Rozhko∗, A. Tzalenchuk∗, J.A. Alexander-Webber†, R.J. Nicholas† ∗ National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK † Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK

(corresponding author; [email protected])

Abstract—We present the space defined by the quantum TABLE I Hall effect breakdown in gated epitaxial graphene on MATERIAL COMPARISON FOR QHE BREAKDOWN CUURENT DENSITY jc SiC (SiC/G) as a function of , current, carrier density, AT ν =2 and magnetic field. At 2 K, breakdown currents (Ic) almost 2 orders of magnitude greater than in GaAs devices are observed. Material ¯hωc τe jc jc Width We use this knowledge to explore the potential of using graphene 1 1 as a high temperature (> 2 K) and low magnetic field (< 5 T) (meV) (ps) (A m− ) (A m− )(µm) quantum resistance standard. Theory Exp. Index Terms—Graphene, measurement standards, quantum GaAs (7 T) 12 100 2.9 1.4 35 Hall effect, quantum resistance standard. InSb (7 T) 40 500 2.6 0.3 600 Graphene (7 T) 105 80 7.3 4.3 35 I. INTRODUCTION (14 T) 150 30 23 15 35 The quantum Hall effect (QHE) observed in two dimen- (17 T) 165 16 36 30 5 sional electron (2DEGs) is defined by a vanishing (23 T) 200 6 71 43 5 longitudinal resistivity ρxx =0and a quantised Hall resistance 2 ρxy = h/νe for ν = integer. Ever since its first observation, the QHE has been used as a quantum electrical resistance in a 35 µm wide channel near the current contacts). This standard which has been most extensively developed using in turn implies that the charge carriers in graphene must be GaAs devices [?]. In recent years, since the first isolation of very efficient in losing their energy to the lattice, a property graphene and the observation of the integer QHE [?], [?], which makes this material so attractive for modern electronics the attention of quantum Hall labs has turned to where the power densities are limiting performance. This graphene as a potentially more readily accessible resistance property is somewhat counter intuitive given that the available standard capable of operating at higher and mea- spectrum for scattering is very limited (up to room- surement currents with lower magnetic fields. This is in part temperature polar-optical phonon scattering and piezoelectric due to its large energy gaps (hω¯ c) arising from the acoustic phonon scattering are negligible). high electron velocity at the Dirac point. Recent experimental The measured electron relaxation rates [?], [?] can be used work [?], [?] has also shown that it has high electron-phonon with the bootstrap-type electron heating model of Komiyama energy relaxation rates (τe), an order of magnitude faster and Kawaguchi [?] to predict the QHE breakdown current. than in GaAs heterostructures, which play an important role This model is based on the runaway heating which occurs in determining the high current breakdown of the QHE. In when the quantum Hall effect begins to break down. Within particular, polymer gated epitaxial graphene on SiC has been this model, for graphene, the breakdown field Ey is predicted shown to be an exceptional candidate for metrology [?], [?], to be and the universality of quantisation between it and GaAs has been shown to be accurate within a relative uncertainty of 4¯hωc 11 Ey = . (1) 8.6 10− [?]. eτ × e In order to achieve an accuracy approaching this level at a We see in Table ?? that with typical parameters for graphene low magnetic field and high temperature we need to have a (τe = 80 ps and ¯hωc = 105 meV) we can expect a breakdown detailed understanding of the breakdown mechanism and ex- current 3 times higher than for GaAs (τe = 100 ps and plore the phase space for quantised resistance measurements. ¯hω = 12 meV 9 c at the same magnetic field of 7 T) [?]. These The aim is to achieve an accuracy level of 1 part in 10 in a results suggest that the intrinsic properties of graphene make it table-top cryogen-free system which could, in future, provide a much better choice for the realisation of a quantum resistance fully automated quantum Hall measurements. standard than traditional GaAs.

II. BREAKDOWN MECHANISM III. PRECISION MEASUREMENTS The extremely large breakdown currents observed in SiC/G Precision measurements require a good signal-to-noise ratio imply there is significant heating of the electron in the in order to obtain the desirable uncertainty within a reasonable quantum Hall state (for 100 µA this is more than 100 µW measurement time. For a typical measurement of the quantum

978-1-4799-2479-0/14/$31.00 ©2014 IEEE 40 source using our photochemical gating technology. For the illuminated sample, with low carrier density, the deviation at ν =2from the expected value did not exceed 0.35 ppm in the range 3 4 T, and the deviation increased up to − 1.9 ppm at magnetic field 2.5 T. The observed deviation for the illuminated sample at B =8.0 T was about 0.15 ppm where the breakdown current was 41 µA at 1.2 K.

IV. C ONCLUSION In conclusion, we have investigated the detailed QHE breakdown mechanism in graphene on SiC devices. We have shown that the intrinsic breakdown current is significantly larger than that for GaAs devices under the same experimental conditions. These conditions imply that it will be possible Fig. 1. Rxx (red) and Rxy (black) measurements on a 10 µm wide graphene on SiC device at approximately 3 K. The blue triangle are the measured to make a quantum Hall standard which will operate under breakdown current. much less stringent conditions than traditional systems. First measurements on a small graphene on SiC device indicate that this will indeed be possible if the carrier density can be tuned Hall plateau at ν =2to 100 Ω we use a ratio on the cryogenic to an optimal value. current comparator bridge of 2065:16. The measurement cur- rent in the 100 Ω is set to 3 mA so that the power ACKNOWLEDGMENT dissipation is less than 1 mW which in turn implies a current This work has been funded by the NMS under IRD of about 25 µA in the quantum Hall device. In other words the Graphene project, EU FP7 project ConceptGraphene, EU measurement is 0.3 V which for a typical voltage noise EMRP project GraphOhm. We which to acknowledge our level of 1 nV/√Hz results in 1 ppb in about 5 minutes. These collaborators at Chalmers University and Linkoping¨ University requirements together with the data in Table ?? suggest that a both in Sweden. device of approximately 10 µm wide should be sufficient to REFERENCES make accurate QHE measurements around 5 T. Figure 1 shows the results for a 10 µm wide SiC/G device. [1] B. Jeckelmann, and B. 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