Series and parallel connection of multiterminal quantum Hall-effect devices

Epitaxial graphene on silicon carbide is a promising material for the next generation of quantum Hall resistance standards. Single Hall bars made of graphene have already surpassed their state-of-the-art GaAs based counterparts as an R K /2 (R K = h/e 2 ) standard, showing at least the same precision and higher breakdown current density. Compared to single devices, quantum Hall arrays using parallel or series connection of multiple Hall bars can offer resistance values spanning several orders of magnitude and (in case of parallel connection) significantly larger measurement currents, but impose strict requirements on uniformity of the material. To evaluate the quality of the available material, we have fabricated arrays of 100 Hall bars connected in parallel on epitaxial graphene. One out of four devices has shown quantized resistance that matched the correct value of R K /200 within the measurement precision of 10 −4 at magnetic fields between 7 and 9 Tesla. The defective behaviour of other arrays is attributed mainly to non-uniform doping. This result confirms the acceptable quality of epitaxial graphene, pointing towards the feasibility of well above 90% yield of working Hall bars.

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“…If the multiple-connection technique 15,16 is used, the relative deviation of the Hall resistance R from its ideal value R H /N is…”

Section: Device Designmentioning

confidence: 99%

A prototype of RK/200 quantum Hall array resistance standard on epitaxial graphene

Lartsev

Lara‐Avila

Danilov

et al. 2015

Journal of Applied Physics

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“…Here, the graphene device was connected according to the triple-series connection scheme [22,23] (Fig. 1b), in which the respective equipotential terminals (contacts 1, 7, 8 and contacts 3, 4, 5) are connected outside of the cryostat to the nodes A and B, respectively.…”

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confidence: 99%

Towards a graphene-based quantum impedance standard

Kalmbach

Schurr

Ahlers

et al. 2014

Applied Physics Letters

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Precision measurements of the quantum Hall resistance with alternating current (ac) in the kHz range were performed on epitaxial graphene in order to assess its suitability as a quantum standard of impedance. The quantum Hall plateaus measured with alternating current were found to be flat within one part in 10 7 . This is much better than for plain GaAs quantum Hall devices and shows that the magnetic-fluxdependent capacitive ac losses of the graphene device are less critical. The observed frequency dependence of about -8×10 -8 /kHz is comparable in absolute value to the positive frequency dependence of plain GaAs devices, but the negative sign is attributed to stray capacitances which we believe can be minimized by a careful design of the graphene device. Further improvements thus may lead to a simpler and more user-friendly quantum standard for both resistance and impedance.Graphene is probably the most fascinating electronic material discovered in the last decades [1][2][3]. Among its various unique properties, an anomalous 'half-integer' quantum Hall effect (QHE) is most interesting for metrology, where the fact that the Hall resistance is quantized and depends only on fundamental constants is utilized for the representation and maintenance of the resistance unit, the ohm. Typically, twodimensional electron systems (2DES) realized in GaAs/AlGaAs heterostructures [4] are used for this purpose. The required relative measurement uncertainty of better than 1 part in 10 8 is, however, only obtained at strong magnetic fields around 10 tesla and at temperatures of 1.4 kelvin and below. In contrast, in graphene the cyclotron energy splitting between the Landau levels (which is the main factor determining the robustness of the quantized Hall resistance (QHR)) is so large that fingerprints of the QHE are even observed at room temperature [5]. Thus, with graphene a highly precise QHR standard working at low magnetic fields and temperatures above 4 kelvin is conceivable, which would be an enormous advantage for practical metrology. In fact, when measuring with direct current (dc), it has been demonstrated already that the precision of the QHE in high quality graphene devices matches that of GaAs devices [6][7][8][9]. However, in the forthcoming fundamental constant-based redefinition of the Système International d'Unités (SI) [10], also the impedance units (capacitance and inductance) will be traced to fundamental constants [11]. The most direct way to represent the impedance units is to use a quantum Hall resistance measured with alternating current (ac QHR). This has two advantages. Firstly, deriving the resistance and impedance units from the same quantum effect improves the consistency of the SI. And secondly, using the same QHE device at dc and at ac in one and the same cryomagnetic system would constitute a practical and economical advantage. Therefore, the question naturally arises whether graphene can replace GaAs also in the realm of impedance units, leading to an at least equally precise, but more userfriendl...

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“…The scheme of the interconnections for a series array of four Hall devices, with the voltage terminals connected in multiple series connection [12] using external bonding wires is presented in Fig. 1 (b).…”

Section: Fabrication Of Graphene Devicesmentioning

confidence: 99%

“…Other reference values can, at least in principle, be obtained by series or parallel connection of individual Hall devices [12]. Multiple-connected arrays of GaAs-based Hall devices have already been developed and used successfully for accurate scaling of dc resistances in the range 100 Ω -1.29 MΩ [13,14,15,16], but they are not in widespread use due to difficulties of reproducible fabrication of accurate and reliable devices with hundreds of contacts between individual Hall bars that should have very identical characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…The Hall devices which were all fabricated on the same chip were connected using triple series connection [12] and external bonding wires. Results of magneto-resistance measurements of the four Hall devices showed quantized plateaus of the Hall resistance starting at a relatively low magnetic field and allowed to perform the first precision measurement on a graphene-based QHR array.…”

Section: Introductionmentioning

confidence: 99%

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Mini array of quantum Hall devices based on epitaxial graphene

Новиков

Лебедева

Hämäläinen

et al. 2016

Journal of Applied Physics

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Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux R H,2 at filling factor ν = 2 starting from relatively low magnetic field (between 4 T and 5 T) when temperature was 1.5 K. Precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device.The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×R H,2 = 2h/e 2 was smaller than the relative standard uncertainty of the measurement (< 1×10 -7 ) limited by the used resistance bridge.

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Series and parallel connection of multiterminal quantum Hall-effect devices

Cited by 157 publications

References 11 publications

A prototype of RK/200 quantum Hall array resistance standard on epitaxial graphene

A prototype of RK/200 quantum Hall array resistance standard on epitaxial graphene

Towards a graphene-based quantum impedance standard

Mini array of quantum Hall devices based on epitaxial graphene

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