Comparing GaAs and graphene QHR standards for resistance realisation at SP
Tobias Bergsten
1
, Gunnar Eklund
1
and Hans He
2
1
SP Technical Research Institute of Sweden
2Chalmers University of Technology
tobias.bergsten@sp.se
Introduction
W
E present a comparison between QHR resistance realisation based on GaAs and graphene. This work was part of the EMRP1 project GraphOhm, which aimed at developing graphene QHR standards [1] with improved properties compared to GaAs, which has been the domi-nating material since the 1990s.The long term goal of GraphOhm is to simplify the re-alisation of the ohm and to make it more accessible to industrial users. Figure 1 illustrates one possible future thanks to the properties of graphene.
Figure 1: Resistance traceability chain at SP today, and in a possible
future. The properties of graphene allows higher temperatures and lower magnetic field for QHR standards, and in future commercial in-struments it may be possible to build the standard into the instrument.
Graphene
The Hall bars were fabricated from graphene grown epi-taxially by SiC sublimation at Link¨oping University. While the material was mostly single layer graphene, there was also a certain amount of bilayer included. The percent-age of bilayer varied in different areas of the chips, typi-cally between 1% and 30%. Figure 2 shows two Hall bars on the same chip with different amounts of bilayer. Al-though a QHR device with high bilayer content is unde-sirable, it may still work if there are uninterrupted paths of monolayer graphene between the contacts [2]. How-ever, the maximum measurement current will be lower with high bilayer content.
Figure 2: False colour optical transmission microscope images of
graphene Hall bars (beige) from different devices on the same chip. The bilayer content (darker areas) vary across the chip. Blue areas are SiC substrate and black areas are the metal contacts.
Tuning procedure
Before cooling the sample for measurements, it is possi-ble to tune the carrier density to an optimum value. A low carrier density (∼1011 cm−2) is desirable because it allows measurements at a relatively low magnetic field (less than 5 T). This tuning can be performed using the corona discharge (CD) gating technique [3]. Figure 3 il-lustrates the method. A CD device (the blue ”gun”) gener-ates ionised air molecules which settle on the chip, form-ing an electrostatic gate. By monitorform-ing the resistance we can tune the carrier density to a suitable level.
Figure 3: Carrier density tuning of the QHR device.
When operating the CD device, some ions will hit the connecting metal leads, rather than the Hall device. This will charge the leads, generating a high voltage because of the stray lead capacitances. The voltage can generate a spark on the chip which may destroy the device. Figure 4 illustrates what can happen. To avoid accidents like this we use a sourcemeter in voltage sourcing mode, using all the device connections. This way there is always a low impedance path for the excess charge on the leads.
Figure 4: QHR device destroyed by a spark during carrier density
tun-ing procedure.
QHR measurements
After tuning the carrier density we cool down the device and measure the longitudinal resistance while sweep-ing the magnetic field. The resistance needs to be es-sentially zero in order to measure accurately. As figure 5 demonstrates, the difference in tuning resistance be-tween a working (1.80 kΩ) and not working (1.85 kΩ) QHR
chip can be quite small. The minimum useful magnetic field for this chip was 6.5 T.
10 m 100 m 1 10 100 1 k 10 k Resistance ( W ) 10 8 6 4 2 0 Magnetic field (T) 0 -10 m Tuning resistance 2.00 kW (n=1.2´1011cm-2) 1.85 kW (n=2.2´1011cm-2) 1.80 kW (n=2.5´1011cm-2) 1.75 kW (n=2.7´1011cm-2)
Figure 5: Longitudinal resistance versus magnetic field for the same
device, but with different tuning resistance. Current: 43 μA.
Precision measurements were performed using two different graphene devices, and one GaAs device. The graphene devices were used at 4.2 K, while the GaAs de-vice was used at 2 K. One 100 Ω resistor in an oil bath and
one 10 kΩ resistor in a temperature controlled enclosure
was measured. In figure 6 the 10 kΩ results are shown,
either by direct comparison with QHR, or by comparison with the 100 Ω resistor as measured against QHR.
-6.445 -6.440 -6.435 -6.430 -6.425 -6.420
Deviation from nominal
(mW/W) 24 22 20 18 16 14 12 10
Date (of April 2016)
Graphene #1 Via 100 W Direct Graphene #2 Via 100 W Direct GaAs #1 Direct Average Graphene GaAs
Figure 6: QHR measurements of a 10 kΩ resistor. These results are
sim-ilar to the measurements reported in the summary.
Uncertainty budget
The uncertainty budget below is based on our stan-dard budget for QHR calibrations at SP. The main differ-ence between GaAs and graphene is the uncertainty in the quantisation of the QHR level. Our QHR cryostat can only reach a little below 2 K, which is too high for opti-mum performance of a GaAs based QHR standard, but with graphene the quantisation is excellent at 4 K. We can also use higher measurement current with graphene,[4] and in combination with the more stable temperature at 4 K the noise figure is slightly lower.
Table 1: Uncertainty budget for calibrating a 10 kΩ resistor using a
GaAs chip and a graphene chip. Uncertainty values are in nΩ/Ω.
Type GaAs Graphene
Quantisation B 12 3.0 Probe leakage B 0.9 0.9 CCC ratio B 0.8 0.8 CCC leakage B 1.1 1.1 Shunt resistor B 2.0 2.0 Lead resistance B 0.2 0.2 Noise (typical) A 2 1.5 Standard uncertainty 12.4 4.2 Expanded uncertanity (k=2) 25 8.4 Conclusions
We have found that graphene offers substantial im-provements for QHR metrology compared with GaAs. Measuring at 4 K simplifies the procedure and saves he-lium (or energy), and the uncertainty is lower by a factor of 3. The additional carrier density tuning procedure is quite straightforward and once an optimum tuning resis-tance has been established for a device, this procedure takes only minutes.
Acknowledgements
We would like to thank PTB for providing the GaAs QHR chip and Prof. Yakimova for fabricating the graphene material.
References
[1] A. Tzalenchuk et al., “Towards a quantum resistance standard based on epitax-ial graphene,” Nature nanotechnology, vol. 5, no. 3, pp. 186–189, 2010.
[2] T. Yager et al., “Express optical analysis of epitaxial graphene on SiC: Impact of morphology on quantum transport,” Nano Letters, vol. 13, no. 9, pp. 4217–4223, 2013.
[3] A. Lartsev et al., “Tuning carrier density across Dirac point in epitaxial graphene on SiC by corona discharge,” Applied Physics Letters, vol. 105, no. 6, 2014.
[4] R. Ribeiro-Palau et al., “Quantum hall resistance standard in graphene devices under relaxed experimental conditions,” Nature nanotechnology, vol. 10, no. 11, pp. 965–971, Sep 2015.
1The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
