Three-dimensional electrostatic potential, and potential-energy barrier, near a tip-base junction

Pan, Li-Hong; Sullivan, T. E.; Peridier, Vallorie J.; Cutler, P.H.; Miskovsky, N. M.

doi:10.1063/1.112775

Cited by 45 publications

(33 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most suitable of the models for our purpose is the hyperboloid or semi-ellipsoid model in which a solution for the potential and the field can be obtained in the prolate-spheroidal coordinate system. [24][25][26][27][28][29] A simpler derivation of the same result can be obtained by considering the field that is generated by a linear distribution of charges, whose density increases linearly along its length. 24,30 The electron-optical phase shift can also be calculated easily in this case.…”

Section: Theoretical Modelmentioning

confidence: 90%

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

Beleggia

Kasama

Larson

et al. 2014

Journal of Applied Physics

View full text Add to dashboard Cite

We apply off-axis electron holography and Lorentz microscopy in the transmission electron microscope to map the electric field generated by a sharp biased metallic tip. A combination of experimental data and modelling provides quantitative information about the potential and the field around the tip. Close to the tip apex, we measure a maximum field intensity of 82 MV/m, corresponding to a field k factor of 2.5, in excellent agreement with theory. In order to verify the validity of the measurements, we use the inferred charge density distribution in the tip region to generate simulated phase maps and Fresnel (out-of-focus) images for comparison with experimental measurements. While the overall agreement is excellent, the simulations also highlight the presence of an unexpected astigmatic contribution to the intensity in a highly defocused Fresnel image, which is thought to result from the geometry of the applied field.

show abstract

Section: Theoretical Modelmentioning

confidence: 90%

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

Beleggia

Kasama

Larson

et al. 2014

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…However, simplifying assumptions with respect to the tip geometry have been made. For example, Terris et al [1] restricted the mathematical formulation to a tip; Pan et al [2] assumed a tip geometry in the shape of a hyperboloid; Hudlet et al [3] limited the analytical formulation to an axisymmetric but otherwise arbitrary shaped AFM tip; Strassburg et al [4] suggested a numerical model based on the boundary integral equation method. Unfortunately, the use of the boundary integral equation method is possible only for domains with C 2 -smooth boundaries, i.e.…”

Section: Introductionmentioning

confidence: 99%

Variational treatment of electrostatic interaction force in atomic force microscopy

Shmoylova

Dorfmann

Potapenko

2007

Z. angew. Math. Phys.

View full text Add to dashboard Cite

In this paper we introduce the mathematical model for the electrostatic interaction force between an atomic force microscope (AFM) tip and a sample surface. We formulate the electrostatic potential problem in Sobolev spaces and find the corresponding weak solution in terms of the integral potential, which can be approximated numerically by generalized Fourier series and used to find the interaction force between an AFM tip and a sample surface. The formulation of the problem in a weak (Sobolev) space setting allows us to determine the force for AFM tips of arbitrary shape. Efficiency of the method is illustrated using numerical examples for the spherical and tetrahedral AFM tips. (2000). 35J05, 42C15, 31B05, 31B10. Mathematics Subject Classification

show abstract

“…Various simplified models for the AFM tip shape have been proposed that obtain an expression for the electrostatic interaction, and hence capacitance, between an AFM tip and a molecularly smooth substrate. A few of the older models proposed are: a sphere model, 6 a uniformly charged line model, 7 a knife edge model, 8 a single charge model, 9 a perfect cone model, 10 a hyperboloid model, 11 and a plane surface model. 5 Belaidi et al 8 analyzed these models in detail and found that no single model describes accurately the capacitance between the AFM tip and sample.…”

Section: Historical Developmentmentioning

confidence: 99%

Nanoscale dielectric measurements from electrostatic force microscopy

Kumar

Crittenden

2014

Mod. Phys. Lett. B

View full text Add to dashboard Cite

Electrostatic force microscopy has evolved as a standard tool for electrical characterization of surfaces with high lateral resolution. Key to its success is an accurate and informative model of the cantilever capacitance. In this brief review, we summarize the progress made in the dielectric characterization of surfaces using electrostatic force microscopy and discuss the development of various models to analytically describe the capacitive forces between the cantilever tip and sample. We include a discussion of the recent extension of these measurements to the liquid environment.

show abstract

Three-dimensional electrostatic potential, and potential-energy barrier, near a tip-base junction

Cited by 45 publications

References 4 publications

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle

Variational treatment of electrostatic interaction force in atomic force microscopy

Nanoscale dielectric measurements from electrostatic force microscopy

Contact Info

Product

Resources

About