An investigation into the applicability of perturbation techniques to solve the boundary integral equations for a parallel-plate capacitor with a rough electrode

Abstract

We derive a system of integral equations for the surface charge distribution on the electrodes of a parallel-plate capacitor for which the profile of one electrode is rough. We show that the solution to this system of equations is tractable using a perturbation technique assuming small surface heights compared with the mean plate separation. The accuracies of the first- and second-order perturbative approximations and of the local height approximation are evaluated for a few examples with a one-dimensional rough surface by comparing them with exact numerical results obtained by solving the boundary integral equations directly using a numerical procedure. Some general guidelines for when the first- and second-order approximations will be accurate are given. It is shown that the perturbative formulation provides approximations with a regime of validity that may extend over a larger region than the regime of validity of the local height approximation. These results could be useful for capacitive-sensor design purposes or in modelling solid-state electronic devices.

The lateral resolution limit for imaging periodic conducting surfaces in capacitive microscopy

“…We present the values of the normalized capacitance per unit length, C, which corresponds to the ratio of the capacitance due to the central section of length L (see figure 1), which coincides with an integer number of periods The local-height (LH) approximation [1] to the normalized capacitance per unit length for the central half of the surface is calculated using the local separation between the plates at each value of x:…”

“…In previous papers [1,2] we investigated the problem of the capacitance of a capacitor with one plane surface and one rough (about a mean plane) surface. We showed that a perturbative solution was valid in a wider range of parameters of the rough surface than a simple 'local-height' solution and that it is possible to find approximate equations which fit the capacitance values over a wide range of parameter values and surface shapes for the rough surface.…”

The influence of surface topography on the electromechanical characteristics of parallel-plate MEMS capacitors

“…When surface topography on the electrodes is taken into account, analysing the capacitance and electric field becomes a non-trivial undertaking which requires cumbersome numerical calculations [18,19] or approximate analytical solutions by considering limit cases of the surface topography [14][15][16][17]. A common approach taken with problems involving rough surfaces is to replace the original rough surfaces with an equivalent rough surface and a flat [25].…”

“…It has been shown that roughness has an adverse effect on a variety of electrical characteristics of those devices including conductivity of semiconducting and metallic thin films [11], gate oxide leakage currents in metal-oxide-semiconductor devices [12], and dielectric breakdown of triple-layer films used in dynamic random access memories [13]. Moreover, it has been shown that the capacitance, electric field and leakage currents [14][15][16][17][18][19] of microelectronic capacitors are affected by surface topography on the electrodes. These findings imply a possible influence of surface topography on the electromechanical characteristics of parallel-plate MEMS capacitors, which has not been studied thoroughly yet.…”

Self-affine roughness influence on redox reaction charge admittance

“…[8,9]. The frequency response of rough interface depends on the regime under consideration such as for example (i) the capacitive behavior of rough electrodes [24][25][26][27][28][29][30][31][32][33][34][35][36], and (ii) diffusion controlled charge transfer on rough interfaces [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”