Accuracy Issues in a High-Level Model for MEMS Varactors Janakiram G. Sankaranarayanan, Manas Behera Narayan Aluru Kartikeya Mayaram School of Electrical Engineering & Beckman Institute for Advanced School of Electrical Engineering Computer Science Science and Technology Computer Science Oregon State University University of Illinois at Urbana- Oregon State University Corvallis, OR-97331, USA Champaign Corvallis, OR-97331,USA sankaraj@ece.orst.edu, behera@ece.orst.edu Urbana, IL-61801, USA karti@ece.orst.edu aluru@uiuc.edu Abstract This paper presents accuracy issues for an equivalent circuit model and an AHDL model (high-level models) of MEMS varactors. Simulations of different MEMS varactor structures were done using the high-level models and an electrostatic/mechanical solver EM8.9. The limitations of the varactor high-level models are presented in the context of a RF MEMS VCO operating at 1.6 GHz in a TSMC 0.35 たm CMOS technology. Keywords- High-level model, MEMS varactors, electrostatic/mechanical solver, RF MEMS VCO I Introduction Recent developments in micromachining technology have made possible the implementation of MEMS-based varactors. Compared with solid-state varactors, MEMS- based varactors have the advantages of lower loss and potentially greater tuning range. In addition to having a high Q factor and a wide tuning range, these devices can also withstand large voltage swings, thus making them suitable for low phase noise VCO applications [1]. The design of a MEMS VCO requires the combination of the MEMS varactors with conventional integrated circuit technology. Such mixed-technologies can lead to highly efficient, low cost systems with a wide range of applications. A crucial part in the design phase of such mixed-technology systems is the verification of their behavior by simulation. Therefore, accurate macromodels for the MEMS varactors are necessary in simulating the performance of RF MEMS VCOs. In this paper, we compare two different methods for modeling the MEMS varactor structures. An equivalent circuit model [2] and a behavioral model are compared with numerical simulations from an electrostatic/mechanical solver EM8.9 [3]. Accuracy issues of the high-level models are identified in the context of RF MEMS VCOs. The equivalent circuit model and the behavioral model are described in Section II and a brief description of the electrostatic/mechanical solver EM8.9 is provided in Section III. The different MEMS varactor structures are described in Section IV. Simulation results of these MEMS varactor structures and the effects of different materials and different dimensions on their tuning characteristics are illustrated in Section V. Comparisons between the simulation results obtained from the high-level model and the electrostatic/mechanical solver are discussed and conclusions are drawn in Section VI. II High-Level Model for MEMS Capacitor A. Working Principle The functional model of an electro-mechanically tunable capacitor shown in Fig. 1 consists of two parallel plates. The top plate of the capacitor is suspended by a spring with spring constant k, while the bottom plate of the capacitor is fixed. When a bias voltage is applied across the capacitor plates, the suspended plate is attracted towards the bottom plate due to the resultant electrostatic force. The suspended plate moves towards the fixed plate until equilibrium between the electrostatic and the spring forces is reached. i(t) Spring k Suspended plate Fixed plate d1 + x(t) Cd V(t) Fig. 1. Functional model of an electro-mechanically tunable parallel-plate capacitor with two parallel plates. At equilibrium, the electrostatic force and the spring force can be equated as given below [2] kx = - ． 0 AV 2 / 2(d 1 + x) 2 (1) where, ． 0 = 8.85415 x 10 -12 F/m, A = area of the capacitor plates, d 1 = separation of the capacitor plates for no applied bias voltage, x = displacement of the suspended plate, k= spring constant, This work is supported in part by NSF grant CCR – 0121616.