Refined selleckbio control of etched profiles is one of the most important tasks of M(N)EMS manufacturing process. In spite of its wide use, the simulation of Inhibitors,Modulators,Libraries etching for Gemcitabine mw Inhibitors,Modulators,Libraries M(N)EMS applications Inhibitors,Modulators,Libraries has been so far a partial success only, although a great number of commercial and academic research tools dedicated to this problem are developed.Actually, two types of simulations exist [2]: the first category includes simulators describing etching process on the atomistic level, usually including the description of etched surface morphologies. The second type deals with the prediction of the etching profile evolution in engineering applications, typically including the combination of etching with other MEMS manufacturing techniques.
The so called atomistic simulators based on cellular automata and Monte Carlo methods [2�C7] belong to the former group.
In this methods, a silicon substrate is represented by a large number of cells Inhibitors,Modulators,Libraries that reside in a crystalline lattice. During the etching Inhibitors,Modulators,Libraries process, the state of each individual cell, i.e., whether Inhibitors,Modulators,Libraries it is removed from or remains within the lattice, is determined by the strength of chemical bounds and link status of its lattice neighbors. Also, the step-flow aspect [8] of wet etching process fits well into cellular automata method [7].The most common type of the engineering simulators are so called geometrical simulators [9]. The etching profile is viewed as a set of planes propagating along their normal directions with the velocities obtained experimentally.
The earlier Inhibitors,Modulators,Libraries geometric approaches implicitly assume that the etching is (quasi) equilibrium process AV-951 Inhibitors,Modulators,Libraries that can be regarded as the reversal of crystal growth in saturated solutions, and that for every intermediate state Wulff theorem holds (a relatively new and mathematically rigorous exposition of the Wulff problem can be found in reference [10]). That means that the etched crystal is always in the minimum energy state with the shape determined by the Legendre transformation of the surface tension (Wulff shape). Within each time step, each plane forming a part of the surface evolves along its normal direction, experiencing a displacement according to the known etch rate for that particular plane.
The change in Carfilzomib geometry at the intersecting lines between adjacent crystallographic planes or at the edge of a masked region is determined using the Wulff-Jaccodine method [9], in order to avoid the problem of the missing values of the surface tensions. These simulators require the knowledge of complete etch rate diagrams, 17-DMAG manufacturer to be obtained somehow (experimentally, or in another calculations). Since only a finite set of etch rates Nutlin-3a FDA can be obtained from experiment, it is particularly complicated to describe the evolution of curved non-crystallographic surfaces.