Hybrid Numerical Simulation of Electrostatic Force Microscopes Considering Charge Distribution

Bala, Uzzal Binit; Greiff, M.; Mathis, Wolfgang

doi:10.2529/piers060908081435

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…In this context, the elements definitions and the solving of the system of equations are programmed in Matlab. In former studies the electrostatic and mechanical equations were considered to be weak coupled, which means that the mechanical and electrostatical forces are calculated separately (Helmich, 2007;Bala, 2008;Greiff, 2009). In this case convergence of the solution is not guaranteed.…”

Section: Approachmentioning

confidence: 99%

Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method

Freitag

Mathis

2010

Adv. Radio Sci.

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Abstract. In this contribution, an atomic force microscope is modelled and in this context, a non-linear coupled 3-D-boundary value problem is solved numerically using the finite element method. The coupling of this system is done by using the Maxwell stress tensor. In general, an iterative weak coupling is used, where the two physical problems are solved separately. However, this method does not necessarily guarantee convergence of the nonlinear computation. Hence, this contribution shows the possibility of solving the multiphysical problem by a strong coupling, which is also referred to as monolithic approach. The electrostatic field and the mechanical displacements are calculated simultaneously by solving only one system of equation. Since the Maxwell stress tensor depends nonlinearly on the potential, the solution is solved iteratively by the Newton method.

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Section: Approachmentioning

confidence: 99%

Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method

Freitag

Mathis

2010

Adv. Radio Sci.

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“…In the region Ω 2 linear FEM: Equation 4 is applied. Since, the approximation of equation (3) will be kept only near the tip and the approximation of equation (4) will be applied to the total region, the global approximation function for both ansatz functions becomes: Equation 5 where A ( ρ ) is applied to reduce the influence of equation (3) away from the tip which is shown in Figure 4 and defined by: Equation 6 Now applying equation (5) into equation (2) leads to a set of linear differential equations which can be represented in matrix form as: Equation 7 where M is the matrix resulting from the augmented FEM and F is the stiffness matrix expressed by: Equation 8 On the FEM‐BEM transmission interface (Bala et al , 2007) Γ T =Γ 3 ∩Γ 2 , u 2 = u 3 and: Equation 9 Using the Gauss theorem on the augmented finite element and finite element domain one obtains (Reddy, 1993): Equation 10 i.e. for all: Equation 11 Equation 12 where u 12 includes u 1 and u 2 .…”

Section: Numerical Formulationmentioning

confidence: 99%

Numerical modelling of electrostatic force microscopes considering charge and dielectric constant

Bala

Greiff

Preisner

et al. 2009

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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PurposeThe purpose of this paper is to present a hybrid numerical simulation approach for the calculation of potential and electric field distribution considering charge and dielectric constant.Design/methodology/approachEach numerical method has its own advantages and disadvantages. The idea is to overcome the disadvantages of the corresponding numerical method by coupling with other numerical methods. An augmented finite element method (FEM), linear FEM and boundary element method are used with an efficient coupling.FindingsThe simulation model of microstructured devices is not so simple. During the simulation various types of problems will occur. It is found that by using several numerical methods these problems can be overcome and the calculation can be performed efficiently.Research limitations/implicationsThe present approach can be applied in 2D cases. But, in 3D cases the calculation of augmented FEM in a spherical coordinate becomes quite elaborate.Practical implicationsThe proposed hybrid numerical simulation approach can be applied for the simulation of the electrostatic force microscope (EFM) which is a very high‐resolution measuring tool in nanotechnology. This approach can be applied also to other micro‐electro‐mechanical systems.Originality/valueSince the scanning process of the EFM is dynamic, it requires the updating of the FEM mesh in each calculation time step. In the present paper, the mesh updating is achieved by an arbitrary Lagrangian‐Eulerian (ALE) method. The proposed numerical approach can be applied for the simulation of the EFM including this remeshing algorithm ALE.

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Numerical Modelling and Simulation of Atomic Force Microscopes

Mathis

Preisner

Bala

2011

Modelling, Simulation and Software Concepts for Scientific-Technological Problems

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Hybrid Numerical Simulation of Electrostatic Force Microscopes Considering Charge Distribution

Cited by 3 publications

References 8 publications

Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method

Numerical modelling of nonlinear electromechanical coupling of an atomic force microscope with finite element method

Numerical modelling of electrostatic force microscopes considering charge and dielectric constant

Numerical Modelling and Simulation of Atomic Force Microscopes

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