Solution for the electric potential distribution produced by sphere-plane electrodes using the method of images

Dall’Agnol, Fernando F.; Mammana, Victor Pellegrini

doi:10.1590/s1806-11172009005000004

Cited by 15 publications

(8 citation statements)

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“…The approximate force between the tip and the graphite as a function of bias voltage was calculated using the method of images [17]. The tip is modeled as a biased conducting sphere of radius 20 nm and the graphite is modeled as an infinite grounded conducting plane.…”

Section: Resultsmentioning

confidence: 99%

New scanning tunneling microscopy technique enables systematic study of the unique electronic transition from graphite to graphene

Yang

Barber

et al. 2012

Carbon

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A series of measurements using a novel technique called electrostatic-manipulation scanning tunneling microscopy were performed on a highly-oriented pyrolytic graphite (HOPG) surface.The electrostatic interaction between the STM tip and the sample can be tuned to produce both reversible and irreversible large-scale vertical movement of the HOPG surface. Under this influence, atomic-resolution STM images reveal that a continuous electronic reconstruction transition from a triangular symmetry, where only alternate atoms are imaged, to a honeycomb structure can be systematically controlled. First-principles calculations reveal that this transition can be related to vertical displacements of the top layer of graphite relative to the bulk. Detailed analysis of the band structure predicts that a transition from parabolic to linear bands occurs after a 0.09 nm displacement of the top layer.

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Section: Resultsmentioning

confidence: 99%

New scanning tunneling microscopy technique enables systematic study of the unique electronic transition from graphite to graphene

Yang

Barber

et al. 2012

Carbon

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“…Ref. 28. The solution takes the form of a set of point charges Q n and −Q n at positions (x, y, Z n ) and (x, y, −Z n ), where the origin is chosen on the backgate, and the center of the tip is at (x, y, Z 0 ).…”

Section: Electric Field Profile Under a Tipmentioning

confidence: 99%

Electric field control of soliton motion and stacking in trilayer graphene

et al. 2014

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The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition which is usually controlled by a state variable such as temperature or pressure. In the case of trilayer graphene, there are two common stacking configurations (Bernal and rhombohedral) which exhibit very different electronic properties [1][2][3][4][5][6][7][8][9][10][11]. In graphene flakes with both stacking configurations, the region between them consists of a localized strain soliton where the carbon atoms of one graphene layer shift by the carbon-carbon bond distance [12][13][14][15][16][17][18]. Here we show the ability to move this strain soliton with a perpendicular electric field and hence control the stacking configuration of trilayer graphene with only an external voltage. Moreover, we find that the free energy difference between the two stacking configurations scales quadratically with electric field, and thus rhombohedral stacking is favored as the electric field increases. This ability to control the stacking order in graphene opens the way to novel devices which combine structural and electrical properties. * leroy@physics.arizona.edu 2 Multilayer graphene has attracted interest in large part due to the ability to induce a sizable band gap with the application of an electric field. The exact nature of the electronic properties of multilayer graphene is controlled both by the number of layers as well as their stacking configuration. The equilibrium in-plane crystal structure of graphene is hexagonal [19], and deviations from this equilibrium require a large amount of energy. Upon stacking multiple graphene sheets, Bernal-stacking -where the A-sublattice of one layer resides above the B-sublattice of the other layer -represents the lowest energy stacking configuration. Thus under normal circumstances, any two graphene layers in a graphite stack will be Bernal-stacked with respect to one another. However, when examining layers more than one apart, there can be multiple nearly-degenerate stacking configurations (2 (n−2) such configurations for n layers) [1]. For example, in the simplest case of trilayer graphene, the top layer may lie directly above the bottom layer (denoted Bernal-or ABA-stacked), or may instead be configured such that one sublattice of the top layer lies above the center of the hexagon of the bottom layer (denoted rhombohedrally-or ABC-stacked). Applying a perpendicular electric field breaks the sublattice symmetry differently depending on the stacking configuration, and thus is capable of re-ordering the energy hierarchy of the stacking configurations [1][2][3][4][5][6][7][8][9][10][11]. As a consequence, multilayer graphene exhibits the rare behavior of crystal structure modification, and hence modification of electronic properties, via the application of an external electric field.To examine this effect, we perform scanning tunneling topography (STM) and scanning tunneling spectroscopy (STS) measur...

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“…In fact, we believe the electrostatic attraction to the STM tip helps stabilize this configuration. 25,26 An STM image of the surface is shown as an inset in Fig. 2(a).…”

mentioning

confidence: 99%

A pathway between Bernal and rhombohedral stacked graphene layers with scanning tunneling microscopy

Yang

et al. 2012

Applied Physics Letters

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Horizontal shifts in the top layer of highly oriented pyrolytic graphite, induced by a scanning tunneling microscope (STM) tip, are presented. Excellent agreement is found between STM images and those simulated using density functional theory. First-principle calculations identify that the low-energy barrier direction of the top layer displacement is toward a structure where none of the carbon p z orbitals overlap, while the high-energy barrier direction is toward AA stacking. Each directional shift yields a real-space surface charge density similar to graphene; however the low-energy barrier direction requires only one bond length to convert ABA (Bernal) to ABC (rhombohedral).

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Solution for the electric potential distribution produced by sphere-plane electrodes using the method of images

Cited by 15 publications

References 1 publication

New scanning tunneling microscopy technique enables systematic study of the unique electronic transition from graphite to graphene

New scanning tunneling microscopy technique enables systematic study of the unique electronic transition from graphite to graphene

Electric field control of soliton motion and stacking in trilayer graphene

A pathway between Bernal and rhombohedral stacked graphene layers with scanning tunneling microscopy

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