Modeling of Surface Forces between Micron-Sized Objects in Dry Condition

Capillary, van der Walls (vdW) and electrostatic forces, which usually termed as surface forces, can significantly affect the behavior and performance of Micro Electro Mechanical Systems (MEMS) containing surfaces that can contact each other. Here, we are concerned with vdW force, which is the dominant surface force between conducting surfaces in the dry condition. In this study, we first review existing roughness models described by stochastic processes of Gaussian and Fractal type. Then, the vdW force is formulated using two methods by considering the first and second order probability density function (pdf) of the height distribution of rough surfaces. The resulting formulae are functions of the correlation ( ñ) between successive sampling points. By analyzing these formulae based on the correlation and other parameters, the upper and lower bound of vdW force are identified and a numericalbased closed-form formula for the upper bound is derived. Finally, various situations are discussed based on the developed equations and data from a surface micro machining process.