[Paper Review] Grain Boundaries in Graphene on SiC(000$\bar{1}$) Substrate

Yann Tison, Jérôme Lagoute+8 more|arXiv (Cornell University)|Dec 10, 2014

Graphene research and applications40 references60 citations

TL;DR

This study combines scanning tunneling microscopy and spectroscopy with first-principles calculations to investigate grain boundaries (GBs) in epitaxial graphene on SiC(000¯1). It identifies a critical misorientation angle θc = 19 ± 2° for the buckling transition and demonstrates that a highly ordered θ = 33 ± 2° GB—composed of alternating pentagons and heptagons—exhibits strong valley polarization, enabling all-electric valleytronic devices.

ABSTRACT

Grain boundaries in epitaxial graphene on the SiC(000$\bar{1}$) substrate are studied using scanning tunneling microscopy and spectroscopy. All investigated small-angle grain boundaries show pronounced out-of-plane buckling induced by the strain fields of constituent dislocations. The ensemble of observations allows to determine the critical misorientation angle of buckling transition $ heta_c = 19 \pm~2^\circ$. Periodic structures are found among the flat large-angle grain boundaries. In particular, the observed $ heta = 33\pm2^\circ$ highly ordered grain boundary is assigned to the previously proposed lowest formation energy structural motif composed of a continuous chain of edge-sharing alternating pentagons and heptagons. This periodic grain boundary defect is predicted to exhibit strong valley filtering of charge carriers thus promising the practical realization of all-electric valleytronic devices.

Motivation & Objective

• To understand the atomic structure and electronic properties of grain boundaries (GBs) in epitaxial graphene grown on SiC(000¯1).
• To determine the critical misorientation angle (θc) at which GBs transition from flat to buckled morphology due to strain relief.
• To identify and characterize highly ordered large-angle GBs and assess their potential for valleytronic applications.
• To link experimentally observed STM/STS features with first-principles simulations and non-equilibrium Green’s function calculations.
• To evaluate the potential of periodic GBs for valley-polarized charge transport in graphene-based nanoelectronics.

Proposed method

• Performed low-temperature ultrahigh-vacuum scanning tunneling microscopy (STM) and spectroscopy (STS) on epitaxial graphene grown on SiC(000¯1) at 1300 °C.
• Acquired atomic-resolution STM images and dI/dV spectra using electrochemically etched W tips to probe local electronic structure.
• Used first-principles density functional theory (DFT) calculations within the Tersoff-Hamann approximation to simulate STM images and electronic density of states.
• Applied non-equilibrium Green’s function (NEGF) transport calculations with a nearest-neighbor tight-binding Hamiltonian to model ballistic electron transmission across the GB.
• Mapped transmission probabilities T(k||, E) and valley polarization Pτ(ϑ, E) as functions of momentum k|| and incidence angle ϑ.
• Correlated experimental STM topography and spectroscopy with simulated images and electronic states to assign the atomic structure of the GB.

Experimental results

Research questions

• RQ1 What is the critical misorientation angle θc at which grain boundaries in epitaxial graphene on SiC(000¯1) transition from flat to buckled morphology?
• RQ2 What is the atomic structure of the highly ordered large-angle grain boundary observed at θ ≈ 33°, and how does it relate to theoretical predictions?
• RQ3 Do the observed periodic grain boundaries support localized electronic states and exhibit valley-polarized transport?
• RQ4 How does the electronic structure of the GB, particularly its van Hove singularities, correlate with experimental STS measurements?
• RQ5 Can the periodic GB defect function as a valley filter in graphene, enabling all-electric control of valley polarization?

Key findings

• The critical misorientation angle for the buckling transition from flat to buckled grain boundaries is determined to be θc = 19 ± 2°, confirming theoretical predictions.
• A highly ordered grain boundary with θ = 33 ± 2° is identified as a continuous chain of edge-sharing alternating pentagons and heptagons, matching the lowest-energy structural motif predicted by theory.
• Scanning tunneling spectroscopy reveals localized electronic states at the GB, with van Hove singularities observed at E = −0.55 eV (P1) and E = 0.25 eV (P2), consistent with theoretical simulations.
• First-principles simulations reproduce the experimental STM topography, including the periodic zigzag pattern and bright corner features, with a periodicity of 0.9 nm.
• Non-equilibrium Green’s function calculations show that charge carriers transmitted across the θ = 32.2° GB exhibit strong valley polarization, with complete valley filtering achievable at oblique incidence angles.
• The valley polarization Pτ(ϑ, E) shows a nearly linear dependence on the incidence angle ϑ, indicating robust, all-electric control of valley degree of freedom in the GB.