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We employ scanning probe microscopy to reveal atomic structures and nanoscale morphology of graphene-based electronic devices (i.e. a graphene sheet supported by an insulating silicon dioxide substrate) for the first time. Atomic resolution STM images reveal the presence of a strong spatially dependent perturbation, which breaks the hexagonal lattice symmetry of the graphitic lattice. Structural corrugations of the graphene sheet partially conform to the underlying silicon oxide substrate. These effects are obscured or modified on graphene devices processed with normal lithographic methods, as they are covered with a layer of photoresist residue. We enable our experiments by a novel cleaning process to produce atomically-clean graphene sheets.
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We review our recent work on the physical mechanisms limiting the mobility of graphene on SiO2. We have used intentional addition of charged scattering impurities and systematic variation of the dielectric environment to differentiate the effects of charged impurities and short-range scatterers. The results show that charged impurities indeed lead to a conductivity linear in density in graphene, with a scattering magnitude that agrees quantitatively with theoretical estimates [1]; increased dielectric screening reduces scattering from charged impurities, but increases scattering from short-range scatterers [2]. We evaluate the effects of the corrugations (ripples) of graphene on SiO2 on transport by measuring the height-height correlation function. The results show that the corrugations cannot mimic long-range (charged impurity) scattering effects, and have too small an amplitude-to-wavelength ratio to significantly affect the observed mobility via short-range scattering [3, 4]. Temperature-dependent measurements show that longitudinal acoustic phonons in graphene produce a resistivity linear in temperature and independent of carrier density [5]; at higher temperatures, polar optical phonons of the SiO2 substrate give rise to an activated, carrier density-dependent resistivity [5]. Together the results paint a complete picture of charge carrier transport in graphene on SiO2 in the diffusive regime.
We present spatially resolved Raman images of the G and 2D lines of single-layer graphene flakes. The spatial fluctuations of G and 2D lines are correlated and are thus shown to be affiliated with local doping domains. We investigate the position of the 2D line -- the most significant Raman peak to identify single-layer graphene -- as a function of charging up to |n|~4 10^12 cm^-2. Contrary to the G line which exhibits a strong and symmetric stiffening with respect to electron and hole-doping, the 2D line shows a weak and slightly asymmetric stiffening for low doping. Additionally, the line width of the 2D line is, in contrast to the G line, doping-independent making this quantity a reliable measure for identifying single-layer graphene.
The linear dispersion relation in graphene[1,2] gives rise to a surprising prediction: the resistivity due to isotropic scatterers (e.g. white-noise disorder[3] or phonons[4-8]) is independent of carrier density n. Here we show that acoustic phonon scattering[4-6] is indeed independent of n, and places an intrinsic limit on the resistivity in graphene of only 30 Ohm at room temperature (RT). At a technologically-relevant carrier density of 10^12 cm^-2, the mean free path for electron-acoustic phonon scattering is >2 microns, and the intrinsic mobility limit is 2x10^5 cm^2/Vs, exceeding the highest known inorganic semiconductor (InSb, ~7.7x10^4 cm^2/Vs[9]) and semiconducting carbon nanotubes (~1x10^5 cm^2/Vs[10]). We also show that extrinsic scattering by surface phonons of the SiO2 substrate[11,12] adds a strong temperature dependent resistivity above ~200 K[8], limiting the RT mobility to ~4x10^4 cm^2/Vs, pointing out the importance of substrate choice for graphene devices[13].
Twisted double bilayer graphene has recently emerged as an interesting moire material that exhibits strong correlation phenomena that are tunable by an applied electric field. Here we study the atomic and electronic properties of three different graphene double bilayers: double bilayers composed of two AB stacked bilayers (AB/AB), double bilayers composed of two AA stacked bilayers (AA/AA) as well as heterosystems composed of one AB and one AA bilayer (AB/AA). The atomic structure is determined using classical force fields. We find that the inner layers of the double bilayer exhibit significant in-plane and out-of-plane relaxations, similar to twisted bilayer graphene. The relaxations of the outer layers depend on the stacking: atoms in AB bilayers follow the relaxations of the inner layers, while atoms in AA bilayers attempt to avoid higher-energy AA stacking. For the relaxed structures, we calculate the electronic band structures using the tight-binding method. All double bilayers exhibit flat bands at small twist angles, but the shape of the bands depends sensitively on the stacking of the outer layers. To gain further insight, we study the evolution of the band structure as the outer layers are rigidly moved away from the inner layers, while preserving their atomic relaxations. This reveals that the hybridization with the outer layers results in an additional flattening of the inner-layer flat band manifold. Our results establish AA/AA and AB/AA twisted double bilayers as interesting moire materials with different flat band physics compared to the widely studied AB/AB system.
Using micro-Raman spectroscopy and scanning tunneling microscopy, we study the relationship between structural distortion and electrical hole doping of graphene on a silicon dioxide substrate. The observed upshift of the Raman G band represents charge doping and not compressive strain. Two independent factors control the doping: (1) the degree of graphene coupling to the substrate, and (2) exposure to oxygen and moisture. Thermal annealing induces a pronounced structural distortion due to close coupling to SiO2 and activates the ability of diatomic oxygen to accept charge from graphene. Gas flow experiments show that dry oxygen reversibly dopes graphene; doping becomes stronger and more irreversible in the presence of moisture and over long periods of time. We propose that oxygen molecular anions are stabilized by water solvation and electrostatic binding to the silicon dioxide surface.
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