SUZANA: A 3D CAD Tool for Anisotropically Etched Silicon Microstructures S. Büttgenbach and O. Than Institute for Microtechnology, Technical University of Braunschweig, D-38106 Braunschweig, Germany

Abstract This paper reports on a workstation-based simulation module for silicon anisotropic etching using a cellular automata model. Starting from 2D mask data, the program delivers a 3D solid geometric model of the etched structure, which can be transferred to other modeling tools like FEM. The capabilities of the CAD tool are demonstrated by comparing simulation results to realized microstructures.

1. Introduction The three-dimensional nature of microsystems implies that the required CAD tools are different from those used for the design of integrated circuits. The most important requirement for a microsystem CAD tool is that it should be able to derive 3D solid geometric models of microstructures from the process description and 2D mask data. With such a tool, the process parameters as well as the mask layouts can be verified before the beginning of the time- and cost-consuming microfabrication process. Furthermore, the 3D models can be used with other tools like finite element modeling (FEM) packages to analyze the mechanical, thermal, and electromechanical behaviour of the microstructures. Since 1989, several groups have reported on microsystem-specific CAD frameworks. The 3D structural simulator OYSTER [1] creates a 3D solid geometric model from an integrated-circuit process description and 2D mask data. It can be applied to microsystems manufactured using lithography-based planar processes. The MEMCAD system [2] comprises several functions: the layout and process editing, the model construction, and the mechanical and electrical analysis. The 3D solid model construction program of MEMCAD concentrates on simple deposit and etch processes and has been applied successfully to both surface-micromachined and

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wafer-bonded processes [3]. The system CAEMEMS [4] provides an overall user interface for the integration of microsystem-specific CAD and CAE programs. Since anisotropic and selective deep etching of singlecrystal silicon is one of the key technologies for the fabrication of microsystems, the integration of an etch simulator within a microsystem CAD architecture is essential. Most of the etch simulation tools reported so far are based on geometrical models ([5]-[11]). They start from complete etching diagrams which have been obtained experimentally and use the Wulff-Jaccodine [12] or a similar method to calculate the etching shape. Other geometrical models like the etch simulator ASEP [5], which has been successfully integrated within the CAEMEMS framework and applied to the design of silicon micromachined resonators [13], reduce the crystal to a few important planes and the corresponding set of etch rates. The approaches reported in [10] and [11] make first attempts to extend the algorithm to the true 3D case. Geometrical models permit rapid calculation of the etching shapes. On the other hand, the adaption to etch stop techniques is difficult and only simple shapes can be simulated with high precision. The outstanding features of etch simulators based on atomic models are high precision, easy adaption to etch stop techniques, and the possibility to allow for broken planes. However, they are time-consuming and require large storage capacity. The atomic model of Camon et al. [14] classifies the surface atoms by the number of free chemical bonds and assumes that the removal probability directly depends on the number of effective bonds of an atom to its neighbours. This paper reports on the etch simulation tool SUZANA which is able to model a wide range of 3D shapes. The method simulates the etch process at an atomic level by cell removal in a cellular automaton. Experimental etch rate ratios, the influence of temperature and concentration of the echant as well as the influence of dopants on the etch rate are taken into account. SUZA-

NA is intended to play a key role in the CAD system for etched silicon microstructures which is currently under development in our laboratory (Fig. 1).

cell, - the transition rules. In the present case we chose the silicon crystal structure as the lattice of the cellular automaton, that is each silicon atom corresponds to a cell. Because the etching process is primarily a stepwise removal of silicon atoms from the surface, this choice suggest itself. This approach leads to the maximum possible resolution of the simulation process. However, in order to reduce the large amount of data that has to be handled in the case of real micromechanical devices with total dimensions in the millimeter range, it is necessary to define macrocells consisting of a cluster of atoms. Of course, the resolution is lower depending on the number of atoms in a macro-cell.

Fig. 1. Schematic block diagram of the CAD architecture for etched silicon microstructures

2. Modeling of chemical etching of silicon using cellular automata Cellular automata may be considered as discrete systems containing large numbers of simple identical components with local interactions. They consist of a lattice of "cells", each with a finite number of possible states. The cells evolve synchronously in discrete time steps according to identical transition rules. The rules can be regarded as a function whose arguments are the states of the cell under consideration and of the neighboring cells and whose value is the new state of the considered cell [15]. Therefore, a cellular automaton can be defined by the following characteristics: - the lattice of cells, - the possible states of a cell, - the neighborhood, that influences the behaviour of a

Fig. 2. Schematic of the crystal structure of silicon Each cell corresponding to an etch front atom, i.e. an atom that is attacked by the etchant, assumes one of the two states "removed" or "not removed". In the silicon crystal each atom is bonded to its four nearest neighbors, which are located at the edges of a tetrahedron (Fig. 2). In our model we assume that the four cells that correspond to the four nearest neighbors of an atom form the neighborhood that influences the behaviour of the cell.

3. Transition rules for anisotropic and selective etching From extensive studies of the anisotropic etching behaviour of single-crystal silicon in aqueous alkaline solutions (see e.g. [16]) it is known that the etch rates of (100) and (110) crystal planes are of the same order of magnitude, whereas the etch rate of (111) planes is smaller by a factor of about 100. In order to model this

etching behaviour one has to classify the etch front atoms with respect to their neighborhood. In the present approach we analyze the bonding situations for the three main low index crystal planes (100), (110), and (111) only (Fig. 3) and derive transition rules from the results of this analysis. This simplification is based on the assumption that complex crystal planes are composed of low index planes. The terraced structure of etched silicon surfaces which has been detected by scanning tunneling microscopy [17] supports this assumption.

bonds to the crystal and one free bond. However, two of the neighboring atoms are located in the etch front and are attacked by the etchant as well. Consequently the strength of the bonds to the crystal is reduced. The etch rates R(hkl) depend on the temperature T and the concentration c of the etchant. They can be expressed as [16] R(hkl)(T, c) R0 (hkl)(c) exp ( Ea (hkl) / kT ) where both the factor R0 and the activation energy Ea depend on the particular crystal plane (hkl). They are usually derived from numerical fits of experimental etch rates. From the etch rates the etching probabilities Phkl can be evaluated Phkl f (R(100) , R(110) , R(111)). They are normalized such that max (P100 , P110 , P111)

1.

From these considerations we derive the following transition rules: (1) A cell located in the etch front will be removed if it has (a) two neighbors and if a random number from the range [0,1] lies in the interval [0, P100 ], or (b) three neighbors, of which at least one is located in the etch front, and if a random number from the range [0,1] lies in the interval [0, P110 ], or (c) three neighbors, of which no one is located in the etch front, and if a random number from the range [0,1] lies in the interval [0, P111 ]. (2) A cell that fulfills none of the rules (1a), (1b), (1c) will be removed.

Fig. 3. Bonding situation of (100), (110), and (111) surface atoms In the case of a (100) plane the attacked atom has two neighboring atoms below the etch front and two free bonds due to the two neighbors above the etch front, which have been removed in a previous etch step. That means, two bonds have to be broken in order to remove such an atom from the surface. An atom located in a (111) etch front is characterized by three neighbors below the etch front and only one free bond. Therefore, three bonds have to be broken to remove an atom from a (111) surface. (110) surface atoms also exhibit three

From the theory of crystal growth it is well known that for the explanation of the equilibrium form the second nearest atoms have to be included into the model. Therefore second next neighbors should also be taken into account in the analysis of the etching shapes. Since the present model takes into account not only the number of existing next neighbors but also their location with respect to the etch front, some of the effects of second next neighbors are included implicitly.

4. The structure of the simulation tool As shown in Fig. 1 SUZANA accepts input in the form of 2D mask layout data and process data, then performs automatic derivation of the 3D model. Double-

TMAH (c = 10 - 40 %, T = 60 - 90 °C), for KOH (c = 10 - 60 %, T = 20 - 100 °C), and for KOH (20 %) and isopropanol (250 g/l). In order to implement the selectivity of the etching process, predetermined etch rates can be related to well-defined layers within the crystal, thus allowing for doped zones acting as etch stop or disordered zones exhibiting isotropic etch behaviour. The predetermined etch rates may vary over the thickness of the layers. For visualization of the 3D geometry of the etched microstructure, the 3D solid model is translated into a 3D surface model [18], which is imported into SHADER. SHADER calculates photo-realistic pictures of the simulation results and exports the data for display on the terminal screen and for hard copy output.

5. Demonstration examples A concave corner of a properly oriented mask will not be underetched since two etch limiting (111) planes meet each other, and the resulting etch shape is welldefined. On the contrary, convex corners will be underetched due to the fast etching crystal planes developing at convex mask corners. In order to obtain well-defined shapes in this case, mask compensation techniques are usually applied [19]. Well-defined corners emerge from compensating elements, which are removed along the etch limiting (111) planes. At a certain number of steps the additional mask element is completely under-etched. Fig. 4 demonstrates how a comb-like compensation element is removed along the etch limiting (111) planes. The pictures on the left-hand side show the simulation results after 5 min., 10 min., 15 min., 20 min., and 25 min. of etching using KOH (30%) at 80 °C. The pictures on the right-hand side are SEM micrographs. From Fig. 4 it can be seen that the agreement between the simulation results and the etched structures is very good. Fig. 5 shows the etch simulation of a capacitive acceleration sensor consisting of a silicon proof mass suspended by two highly boron doped silicon beams. The structure can be fabricated by double-sided anisotropic and selective etching using corner compensation with squares. Fig. 4. Comb-like mask compensation element in anisotropic etching of (100)-silicon

sided etching of both (100)- and (110)-oriented silicon can be simulated. Presently the process data base, which can easily be expanded, contains the etch rates for

6. Conclusion We have developed a 3D CAD tool for anisotropic and selective etching of silicon which relies on a cellular automaton model. Starting from a 2D mask layout, SUZANA allows full 3D automated derivation of solid geometric models. This etch simulator will play a key role in a forthcoming CAD system for silicon microsy-

Fig. 5. Etch simulation of the proof mass of a capacitive acceleration sensor

stems, which is in the development stage in our laboratory. In addition, the implementation of further crystalline materials such as GaAs and quartz is in progress.

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