Imaging of Submicroampere Currents in Bilayer Graphene Using a Scanning Diamond Magnetometer

At a Glance

Metadata	Details
Publication Date	2022-05-05
Journal	Physical Review Applied
Authors	Marius L. Palm, William S. Huxter, Pol Welter, Stefan Ernst, Patrick Scheidegger
Institutions	ETH Zurich, National Institute for Materials Science
Citations	27
Analysis	Full AI Review Included

Executive Summary

Core Achievement: Demonstrated sensitive, non-invasive imaging of sub-µA current flow patterns in bilayer graphene (BLG) devices at room temperature using scanning Nitrogen-Vacancy (NV) diamond magnetometry.
High Sensitivity: Achieved an absolute magnetic field sensitivity of 4.6 nT (51 nT/sqrt(Hz)) and a corresponding current density sensitivity of 20 nA/µm (0.2 µA/(µm*sqrt(Hz))).
Resolution and Dynamic Range: Spatial resolution is 50-100 nm. A Bayesian quantum-phase unwrapping technique was introduced, increasing the magnetic field dynamic range by 6.5x (up to ±6.5 µT).
Non-Invasive Protocol: Developed methods, including dynamic back-gate toggling and synchronous differential imaging, to mitigate back-action effects (tip, laser, microwave) and reliably detect small (5-10%) changes in current flow.
Transport Physics Findings: Current density maps revealed local anomalies correlated with topography (likely hBN bubbles/dopants). Transport in the BLG devices was confirmed to be fully in the diffusive regime, with no signatures of hydrodynamic flow observed at room temperature.

Technical Specifications

Parameter	Value	Unit	Context
Magnetic Field Sensitivity (Absolute)	4.6	nT	120s averaging time per pixel
Magnetic Field Sensitivity (Per-root-Hz)	51	nT/sqrt(Hz)	Nominal NV center performance
Current Density Sensitivity (Absolute)	20	nA/µm	Extracted from 0.3 µA scan
Current Density Sensitivity (Per-root-Hz)	0.2	µA/(µm*sqrt(Hz))	Extracted from 0.3 µA scan
Spatial Resolution	50-100	nm	Achieved resolution in current maps
Minimum Current Imaged	0.3	µA	Demonstrated low-current imaging
NV Center Standoff Distance (z)	~100	nm	NV center to buried graphene sheet
hBN Encapsulation Thickness (Top)	11	nm	Device structure
hBN Encapsulation Thickness (Bottom)	27	nm	Device structure
Hall Mobility (Electrons)	3.3 x 10⁴	cm²/(Vs)	Conventional transport measurement
Mean Free Path (l_m)	0.4	µm	At carrier density 1 x 10¹² cm^-2
Measurement Temperature	Ambient	°C	Room temperature operation
Dynamic Range Increase (Phase Unwrapping)	6.5	x	Increase in maximum detectable field (B_max)
NV Center Spin Contrast (ε)	~26	%	Single diamond probe specification

Key Methodologies

Device Fabrication and Stacking:
- Bilayer graphene (BLG) was encapsulated between two hexagonal boron nitride (hBN) layers (11 nm top, 27 nm bottom).
- The stack was placed on a 4 nm thick graphite flake acting as a back-gate.
- Annealing was performed at 350 °C for 3 hours in an argon atmosphere.
- Contacts (Cr/Au) were defined using e-beam lithography and reactive ion etching (CHF₃/O₂).
AC Quantum Sensing Protocol:
- The technique utilizes a quantum lock-in amplifier concept, synchronizing the source-drain voltage (V_SD) modulation (50 kHz - 1.33 MHz) with microwave and laser pulses.
- All analog and digital signals were generated and synchronized using a multi-channel arbitrary waveform generator (AWG).
- Dynamical decoupling sequences (Spin Echo or N=128 refocusing pulses) were used to extend the coherent precession time (τ up to 48 µs) and maximize sensitivity to the AC magnetic field.
High Dynamic Range Phase Unwrapping:
- Variable Grid Method: Local refinement of pixel sizes (down to 10 nm) in high-current areas to ensure the true phase difference between adjacent pixels is less than π, allowing standard unwrapping algorithms to succeed.
- Bayesian Inference Method: An iterative two-step process using two images recorded with different interaction times (τ₁, τ₂). The algorithm incorporates spatial smoothness priors (neighboring pixels expected to have similar values) to robustly recover the true magnetic field map.
Current Density Reconstruction:
- The recovered magnetic field maps (B) were inverted to calculate the current density (J) using Biot and Savart’s law via an inverse filtering technique.
Mitigation of Back-Action and Stray Effects:
- The back-gate voltage (V_BG) was dynamically ramped to zero during laser pulses to mitigate photo-doping and carrier density drifts in the hBN encapsulation.
- Synchronous differential imaging was employed by toggling V_BG between measurement cycles to isolate small changes in current flow patterns induced by gate tuning, ensuring that spatial or temporal drifts do not create spurious signals.

Commercial Applications

Quantum Sensing and Metrology: The demonstrated room-temperature, high-sensitivity NV magnetometry technique is critical for developing robust, commercial quantum sensors capable of nanoscale magnetic field mapping.
2D Materials Characterization: Essential tool for quality control and defect analysis in van der Waals heterostructures (graphene, hBN, WTe₂). It allows for the direct visualization of conductivity variations, identifying performance-limiting factors like hBN bubbles or local doping anomalies.
Advanced Semiconductor Device Engineering: Used for non-invasive failure analysis and performance optimization in nanoscale electronic devices, mapping current paths, and studying the onset of non-linearity in transport phenomena.
Fundamental Condensed Matter Physics: Enables the study of exotic transport regimes (e.g., hydrodynamic electron flow, persistent edge currents, twist-angle disorder) in 2D materials at ambient conditions, expanding research beyond cryogenic requirements.
Micro-Electronics Reliability: Provides high-resolution current density maps necessary for validating simulations and optimizing the design of contacts and channel geometries in next-generation graphene-based electronics.

View Original Abstract

Nanoscale electronic transport gives rise to a number of intriguing physical\nphenomena that are accompanied by distinct spatial patterns of current flow.\nHere, we report on sensitive magnetic imaging of two-dimensional current\ndistributions in bilayer graphene at room temperature. By combining dynamical\nmodulation of the source-drain current with ac quantum sensing of a\nnitrogen-vacancy center in a diamond probe, we acquire magnetic field and\ncurrent density maps with excellent sensitivities of 4.6 nT and 20 nA/$\mu$m,\nrespectively. The spatial resolution is 50-100 nm. We further introduce a set\nof methods for increasing the technique’s dynamic range and for mitigating\nundesired back-action of magnetometry operation on the electronic transport.\nCurrent density maps reveal local variations in the flow pattern and global\ntuning of current flow via the back-gate potential. No signatures of\nhydrodynamic transport are observed. Our experiments demonstrate the\nfeasibility for imaging subtle features of nanoscale transport in\ntwo-dimensional materials and conductors.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevapplied.17.054008