Precision Measurements and Advanced Applications of Epitaxial Graphene-Based Quantum Hall Array Resistance Standards

Cheng-Hsueh Yang^1,2*, Wei-Chen Lin^1,3,4, Dean G. Jarrett¹, David B. Newell¹, Linli Meng⁵, Albert F. Rigosi¹, Randolph E. Elmquist¹, Ching-Chen Yeh^1,2, Yanfei Yang¹, Alireza Panna¹, Chi-Te Liang^2,6,7

¹Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Maryland, Taiwan
²Department of Physics, National Taiwan University, Taipei, Taiwan
³Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan
⁴Taiwan International Graduate Program (TIGP), Academia Sinica, Taipei, Taiwan
⁵Graphene Waves, LLC, Maryland, USA
⁶Centre for Quantum Science and Engineering (CQSE), National Taiwan University, Taipei, Taiwan
⁷Taiwan Semiconductor Research Institute (TSRI), Hsinchu, Taiwan

* Presenter:Cheng-Hsueh Yang, email:d09245007@g.ntu.edu.tw

In alignment with the redefinition of the International System of Units (SI), the implementation of the Kibble balance and quantum Hall resistance standards (QHRS) has become increasingly important in the field of metrology. This work initially employed a cryogenic current comparator (CCC) along with oil-bathed artefact resistors as reference standards, to directly compare epitaxial graphene (EG)-based QHRS and quantum Hall array resistance standards (QHARS) fabricated on silicon carbide (SiC) substrates. Due to mechanical stresses and strains, artefact standard resistors require long-term scaling. Consequently, our research also demonstrates the use of EG-based 12.9 kΩ QHRS, along with 1 kΩ, and 1 MΩ QHARS, as standard resistors, achieving parts-per-billion (ppb) precision through inter-device comparison via CCC. Furthermore, we propose a mathematical approach to optimizing the total number of device elements required to achieve larger quantized resistances in EG-based QHARS. This method leverages star-mesh transformations to generate fractal-like or recursive device designs, yielding extremely high resistances (up to 1 EΩ, potentially the highest resistance with practical applications) while remaining feasible with modern fabrication techniques. Our study provides important insights into the quantum Hall effect and metrology, contributing to the future development and application of advanced standard resistors.

Keywords: Quantum Hall effect, Graphene, Graphene Hall resistance standard, Cryogenic current comparator (CCC), Quantum Hall arrays