Compact Modelling of Electrical, Mechanical and Thermal Behaviour for MEMS with SPICE
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Compact Modelling of Electrical, Mechanical and Thermal Behaviour for MEMS with SPICE Andreas Frank1, J.-P. Zoellner1, Y. Sarov1, Tz. Ivanov1, I. Kuhnholz1, St. Klett1, I. W. Rangelow1, M. Swiatkowski2, T. Gotszalk2, and N. Nikolov3 1 Micro- and nanoelectronic systems, TU-Ilmenau, Gustav-Kirchoff-Str. 1, Ilmenau, 98693, Germany 2 Wroclaw Technical University, Wroclaw, 50372, Poland 3 Microsystems Ltd., Varna, 9010 P.O. Box 147, Bulgaria ABSTRACT In this paper we present a novel method of nonlinear macro model of a cantilever for mixed domain simulation only with SPICE. Based on lumped elements of equivalent circuits a model is developed, which realizes a coupled electro-thermal-mechanical simulation including crosstalk effects. The model is verified with measurement and helps to class and solve crosstalk. With SPICE as electrical circuit simulator the cantilever array could be simulate in conjunction with the excitations and analysis electronics more detailed like the system level models and faster like FEM-simulation. INTRODUCTION For surface imaging, manipulation and bottom up synthesis of large areas with scanning probe microscopy cantilever arrays are promising candidates. In the frame of the EU funded PRONANO-project a 2-dimensional massively parallel self-actuated piezoresistive sensor array with several hundred independently controlled cantilevers has been fabricated with up to 128 probes and larger arrays are in progress. The principle of actuation is the bimorph effect where tips are resistively heated which occurs bending due to the different thermal expansion of the two materials. Tips are operated in non-contact mode, ideal for limiting tip wear, and closed–loop height positioning is achieved using piezoresistive sensors instead of optical detection [1]. For such an array as multi physical system the mixed domain simulation together with the ASIC is required. Typical for MEMS are the use of FEM-based simulations with ANSYS to investigate coupled electro-thermal-mechanical behaviour the so called physical modelling. To focus more at system level models for simulators like for example SPICE [2], VDHLAMS [3], VerilogA [4] and MATLAB/SIMULINK have been developed [5, 6]. So the simulation together with the electrical circuit is enabling. Since the development of such a model is very time consuming and has to be done for every new device again more automatable solutions are applied. Micro-mechanical and electro-mechanical components may be partitioned hierarchically into low-level reusable elements, the so called macro elements [7], or a model order reduction based on the FEM-model enables fast simulations and link to the ASIC design flow [8, 9, 10]. Both methods have the disadvantage that crosstalk effect are not sufficient regarded. For example electrical coupling through parasitic devices or thermal effects on devices are not included. Typical for system level model the complete function is of interest which does not illustrate and exemplify the operation principle in detail. Diener et. al [11]
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