# Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment

## Abstract

Electric Force-Distance Curves (EFDC) is one of the ways whereby electrical charges trapped at the surface of dielectric materials can be probed. To reach a quantitative analysis of stored charge quantities, measurements using an Atomic Force Microscope (AFM) must go with an appropriate simulation of electrostatic forces at play in the method. This is the objective of this work, where simulation results for the electrostatic force between an AFM sensor and the dielectric surface are presented for different bias voltages on the tip. The aim is to analyse force-distance curves modification induced by electrostatic charges. The sensor is composed by a cantilever supporting a pyramidal tip terminated by a spherical apex. The contribution to force from cantilever is neglected here. A model of force curve has been developed using the Finite Volume Method. The scheme is based on the Polynomial Reconstruction Operator—PRO-scheme. First results of the computation of electrostatic force for different tip–sample distances (from 0 to 600 nm) and for different DC voltages applied to the tip (6 to 20 V) are shown and compared with experimental data in order to validate our approach.

- Authors:

- LAPLACE (Laboratoire Plasma et Conversion d'Energie), Université de Toulouse, UPS, INPT, 118 route de Narbonne, 31062 Toulouse cedex 9 (France)
- Universidade do Minho, Centro de Matemática, Campus de Gualtar, 4710 - 057 Braga (Portugal)
- (France)

- Publication Date:

- OSTI Identifier:
- 22314683

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 116; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMIC FORCE MICROSCOPY; COMPARATIVE EVALUATIONS; DIAGRAMS; DIELECTRIC MATERIALS; DISTANCE; ELECTRIC POTENTIAL; POLYNOMIALS; SENSORS; SIMULATION; SPHERICAL CONFIGURATION; SURFACES

### Citation Formats

```
Boularas, A., E-mail: boularas@laplace.univ-tlse.fr, Baudoin, F., Villeneuve-Faure, C., Clain, S., Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, Teyssedre, G., and CNRS, LAPLACE, F-31071 Toulouse.
```*Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment*. United States: N. p., 2014.
Web. doi:10.1063/1.4894147.

```
Boularas, A., E-mail: boularas@laplace.univ-tlse.fr, Baudoin, F., Villeneuve-Faure, C., Clain, S., Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, Teyssedre, G., & CNRS, LAPLACE, F-31071 Toulouse.
```*Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment*. United States. doi:10.1063/1.4894147.

```
Boularas, A., E-mail: boularas@laplace.univ-tlse.fr, Baudoin, F., Villeneuve-Faure, C., Clain, S., Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, Teyssedre, G., and CNRS, LAPLACE, F-31071 Toulouse. Thu .
"Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment". United States.
doi:10.1063/1.4894147.
```

```
@article{osti_22314683,
```

title = {Multi-dimensional modelling of electrostatic force distance curve over dielectric surface: Influence of tip geometry and correlation with experiment},

author = {Boularas, A., E-mail: boularas@laplace.univ-tlse.fr and Baudoin, F. and Villeneuve-Faure, C. and Clain, S. and Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse and Teyssedre, G. and CNRS, LAPLACE, F-31071 Toulouse},

abstractNote = {Electric Force-Distance Curves (EFDC) is one of the ways whereby electrical charges trapped at the surface of dielectric materials can be probed. To reach a quantitative analysis of stored charge quantities, measurements using an Atomic Force Microscope (AFM) must go with an appropriate simulation of electrostatic forces at play in the method. This is the objective of this work, where simulation results for the electrostatic force between an AFM sensor and the dielectric surface are presented for different bias voltages on the tip. The aim is to analyse force-distance curves modification induced by electrostatic charges. The sensor is composed by a cantilever supporting a pyramidal tip terminated by a spherical apex. The contribution to force from cantilever is neglected here. A model of force curve has been developed using the Finite Volume Method. The scheme is based on the Polynomial Reconstruction Operator—PRO-scheme. First results of the computation of electrostatic force for different tip–sample distances (from 0 to 600 nm) and for different DC voltages applied to the tip (6 to 20 V) are shown and compared with experimental data in order to validate our approach.},

doi = {10.1063/1.4894147},

journal = {Journal of Applied Physics},

number = 8,

volume = 116,

place = {United States},

year = {Thu Aug 28 00:00:00 EDT 2014},

month = {Thu Aug 28 00:00:00 EDT 2014}

}