A theoretical study on the electrostatic interaction between the dissimilarly charged membranes in a salt-free solution has been presented in this paper. The results show that the electric double-layer force is always repulsive for positively charged planar surfaces regardless of surface charge density (or potential) and separation; however, a long-range attraction is observed between surfaces with unequally opposite charge densities. Such attractive force also exists and is independent of the separation when both surfaces carry unequally opposite potential.
A three-dimensional lattice model is constructed to theoretically study the size effects on the elastic properties of ultrathin films with face-center-cubic crystal structure. The lattice model directly takes the discrete nature in the thickness direction into account and treats the deformations along the film plane with continuum mechanics. Only the interactions between the nearest and second nearest atoms are considered in this model and represented as harmonic springs. The constitutive relation of the ultrathin film is then derived using the energy approach and the analytical expressions of the elastic moduli of ultrathin films, including in-plane, out-plane Young's modulus and Poisson's ratio, are obtained. Moreover, the analytical expressions of ultrathin films with different crystal orientations are also formulated. It is shown that the ultrathin film along in-plane directions may be stiffer or softer than its bulk counterpart, but it is always softer along the out-plane direction.
This paper presents a numerical comparison between the differential transform method and the modified Adomian decomposition method for solving the boundary layer problems arising in hydrodynamics. The results show that the differential transform method and modified Adomian decomposition method are easier and more reliable to use in solving this type of problem and provides accurate data as compared with those obtained by other numerical methods.
It is well known that dishing occurring in chemical mechanical polishing of plug structures leads to considerable wafer surface non-planarity and reduces the current/charge conduction. Thus, a closed-form solution for quantitative prediction of dishing is needed. A contact-mechanics-based approach to describe the steady-state dishing occurring in chemical mechanical polishing of plug structures is presented. The model is then applied to investigate the effect of pattern geometry on dishing in details. It was shown that plug dishing strongly depends on plug size, but minimally on pattern density. In addition, the maximum value of dishing occurs at a critical pattern density for fixed pitch.
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