Atypical quantized resistances in millimeter-scale epitaxial graphene p-n junctions

Abstract

We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene p-n junction devices using simple ultraviolet photolithography, thereby significantly reducing device processing time compared to that of electron beam lithography typically used for obtaining sharp junctions. This work presents measurements yielding nonconventional, fractional multiples of the typical quantized Hall resistance at $\nu =2$ ($R_H\approx$ 12906 Ω) that take the form: $\frac{a}{b}{R}_H$. Here, a and b have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of R_H. Additionally, we provide a framework for exploring future device configurations using the LTspice circuit simulator as a guide to understand the abundance of available fractions one may be able to measure. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.

Introduction

Graphene has been extensively studied as a result of its great electrical and optical properties [[1], [2], [3], [4]]. Epitaxial graphene (EG) on silicon carbide (SiC), which can be grown on the centimeter scale and is one of the many methods of synthesizing graphene, exhibits properties that render it suitable for large-scale or high-current applications such as the continued development of quantized Hall resistance (QHR) standards [[5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]]. Though modern-day standards using millimeter-scale EG have been shown to have long-term electrical stability in ambient conditions, [16] these devices are, in most cases, only able to output a single value of quantized resistance ($\nu =2$ plateau) to a degree of accuracy which warrants possible use in metrology. The corresponding value is: $\frac{1}{2}\frac{h}{e^2}=\frac{1}{2}{R}_K=R_H$, where h is Planck's constant, e is the elementary charge, and R_K is the von Klitzing constant.

One milestone for graphene QHR standards would be the eventual accessibility of different resistance values that are well-quantized. One approach to reaching this goal includes creating quantum Hall arrays [[17], [18], [19]]. A major disadvantage to this approach is the requirement that many individual Hall bar devices be connected using a network of resistive interconnects, thereby increasing the total minimum device size and possibly lacking optimal contact resistances. The second approach involves building p-n junctions (pnJs) that operate in the quantum Hall regime, as has been previously demonstrated in EG with lateral dimensions on the order of 100 μm [20]. EG pnJs can be utilized to circumvent most of the technical difficulties resulting from the use of metallic contacts and multiple device interconnections. Research in developing materials for gating and preserving properties of large devices has seen limited success with amorphous boron nitride, [21,22] atomically-layered high-k dielectrics, [[23], [24], [25], [26]] Parylene, [[27], [28], [29]] and hexagonal boron nitride, [30,31] whereas other materials have been more successful, such as (poly)-methyl methacrylate ((P)MMA), ZEP520A photoresist, tetrafluoro-tetracyanoquinodimethane (F4TCNQ), and chromium tricarbonyl [16,32,33].

For millimeter-scale constructions, one major issue was fabricating correspondingly large pnJs. One of the major challenges of mass producing such devices with more than one pnJ has been the required use of electron beam lithography, a costly and time-consuming technique, for the fabrication of junctions that are abrupt, with n-type and p-type regions separated by a width on the scale of several hundreds of nanometers or smaller. This scale is necessary to ensure that the pnJ is sharp enough for dissipationless equilibration of Landauer-Büttiker edge states [20,34]. Junctions with too large a width, when dealing with bipolar interfaces, may effectively become resistive from non-quantization due to charge carrier values being in the neighborhood of the Dirac point.

In this work, we demonstrate how standard ultraviolet photolithography (UVP) and ZEP520A were used to build pnJs that have junction widths smaller than 200 nm on millimeter-scale EG devices. Quantum Hall transport measurements were performed and simulated for various p-n-p devices to verify expected behaviors of the longitudinal resistances in a two-junction device [35]. Furthermore, we use the LTspice current simulator [see notes] to examine the various rearrangements of the electric potential in the device when injecting current at up to three independent sites. We find that nonconventional fractions of the typical quantized Hall resistance, $R_H$, can be measured, thus validating the simulations.