[Paper Review] Suppression of $1/f$ noise in graphene due to non-scalar mobility fluctuations induced by impurity motion

Masahiro Kamada, Weijun Zeng+6 more|arXiv (Cornell University)|Dec 22, 2021

Graphene research and applications4 citations

TL;DR

This study demonstrates direct experimental evidence that $1/f$ noise in high-mobility suspended graphene arises primarily from non-scalar, anisotropic mobility fluctuations due to mobile impurities forming dynamic clusters. Using a Corbino disk geometry, the authors observe strong magnetic field suppression of noise at $\mu_0B \approx 1$, confirming that the noise originates from correlated radial and azimuthal mobility fluctuations, with kinetic Monte Carlo modeling supporting collective impurity dynamics as the origin of long-time correlations and $1/f$ behavior.

ABSTRACT

Low frequency resistance variations due to mobility fluctuations is one of the key factors of $1/f$ noise in metallic conductors. According to theory, such noise in a two-dimensional (2D) device can be suppressed to zero at small magnetic fields, implying important technological benefits for low noise 2D devices. In this work, we provide direct evidence of anisotropic mobility fluctuations by demonstrating a strong field-induced suppression of noise in a high-mobility graphene Corbino disk, even though the device displays only a tiny amount of $1/f$ noise inherently. The suppression of the $1/f$ noise depends on charge density, showing less non-uniform mobility fluctuations away from the Dirac point with charge puddles. We model our results using a new approach based on impurity clustering dynamics and find our results consistent with the $1/f$ noise induced by scattering of carriers on mobile impurities forming clusters.

Motivation & Objective

• To identify the origin of $1/f$ noise in high-quality suspended graphene, particularly distinguishing between mobility fluctuations and other noise sources.
• To test the theoretical prediction that $1/f$ noise from isotropic mobility fluctuations should vanish at $\mu_0B = 1$ in Corbino geometry, which is sensitive only to diagonal conductivity.
• To investigate whether collective dynamics of mobile impurities—rather than isolated two-level systems—can generate genuine $1/f$ noise through long-time correlations.
• To model and validate the role of impurity clustering and anisotropic mobility fluctuations using kinetic Monte Carlo simulations and finite element method.
• To establish a direct link between magnetic field-dependent noise suppression and the intrinsic anisotropy of mobility fluctuations in 2D systems.

Proposed method

• Fabricated suspended monolayer graphene Corbino disks using a lift-off resist (LOR) sacrificial layer technique with electron-beam lithography and current annealing.
• Employed voltage-biased current fluctuation measurements with a transimpedance amplifier (SR570) and FFT analyzer (SRS 785) to extract power spectral density of $1/f$ noise.
• Used Corbino geometry to isolate the diagonal conductivity $\sigma_{xx}$, enabling detection of noise suppression when mobility fluctuations are isotropic.
• Performed kinetic Monte Carlo (kMC) simulations on a 50×50 square lattice to model thermally activated hopping of 25 defects with energy barrier $E_d = 4$ and $k_B T = 1.2$ and $2$.
• Calculated resistance fluctuations in radial and azimuthal directions using finite element method (FEM), assuming defect sites 10⁵ times more conductive than background.
• Computed correlation coefficients between radial and azimuthal resistance fluctuations to quantify anisotropy, comparing simulations with experimental data.

Experimental results

Research questions

• RQ1 Does $1/f$ noise in high-mobility graphene originate predominantly from mobility fluctuations, as predicted by theory?
• RQ2 Can magnetic field-induced suppression of noise in a Corbino geometry confirm the presence of non-scalar (anisotropic) mobility fluctuations?
• RQ3 To what extent do collective dynamics of mobile impurities—via cluster reshaping and long-range correlations—generate $1/f$ noise distinct from standard two-level system models?
• RQ4 How does the degree of anisotropy in mobility fluctuations depend on charge density and proximity to the Dirac point?
• RQ5 Can kinetic Monte Carlo simulations of defect motion reproduce the observed magnetic field dependence of $1/f$ noise in graphene?

Key findings

• A clear suppression of $1/f$ noise is observed in the Corbino graphene device at $\mu_0B \approx 1$, providing direct experimental evidence that the noise arises from mobility fluctuations.
• The noise suppression is strongest near the Dirac point and diminishes with increasing charge density, indicating reduced non-uniform mobility fluctuations away from charge puddles.
• Negative correlation between radial and azimuthal mobility fluctuations is observed, consistent with rotating or collectively reconfiguring impurity clusters.
• Kinetic Monte Carlo simulations reproduce the experimental noise suppression and anisotropy, supporting the model of long-time memory effects from infrequent hopping across large energy barriers.
• The results are inconsistent with standard $1/f$ noise models based on distributed two-level systems or trap states, instead pointing to collective impurity dynamics as the dominant mechanism.
• The study demonstrates that collective, non-exponential relaxation dynamics of mobile impurities can naturally produce $1/f$ noise over broad frequency ranges, offering a new physical origin distinct from conventional models.