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Application of CAD Tools for Design and Simulation of Capacitive Microaccelerometers

Krzysztof Szaniawski, Piotr Podsiadly, Andrzej Napieralski Absfrocr - The paper demonstrates, how CAD design and

simulation tools can assist in developing MEMS devices in general, and capacitive accelerometers in particular. Two types of surface-micromachined accelerometers are presented and described. Advantages and disadvantages of particular tools are dincursed. The paper also includes sample simulation results, which prove that virtual simulations can provide the designer a lot of information with no need for device fabrication and measurements.

Keywords - CAD, MEMS, Accelerometers, Modeling

I. INTRODUCTION

CAD tools play a key role in development of integrated circuits, including design and simulation of MEMS (Micro- Elecho-Mechanical Systems) sensors and actuators. Obviously, in theory, the mask layouts of ICs can be designed 100% manually, without using a computer. That technique has been used extensively in the early stage of the IC era, including mask layouts of quite complex devices such as Intel 8086 microprocessor. The reason for that was that in those times there just were no computer systems powerful enough to run such complicated programs as mask layout editors or design nile checking tools. Since all layout had to be drawn manually, the design process was much more time-consuming than today and any, even minor modifications required the entire design or at least its large portion to be redrawn ftom the scratch. finally there was relatively high risk of errors in the designs, because the mask layouts had to be checked manually against violations of technological requirements. Also, the schematics of underlying electronics circuits could not be simulated to detect potential problems. Now, with CAD design tools, *e design time and risk has been reduced enormously. Mask layout can be easily edited and updated on a computer screen and.zoomed as necessary. Besides, the designer is assisted with various checking and simulations tools, such as designJelectrical rule checkers, layout verification tools, parameter extractors and circuit simulators. Finally, the mask layouts of some devices can be parameterized as necessary, which significantly improves their reusability. This applies mainly to fairly complicated geometrical shctures of MEMS sensors and actuators.

The assistance of CAD simulation tools seems to be even more significant. Obviously, the most reliable way to check if the designed device is working and to determine its parameters and properties is performing a thorough series of measurements after the device has been manufachmd. However, this approach will likely require at least a few consecutive fabrication runs, in which the design will be gradually improved until appropriate parameters are reached.

Krzysztof Szaniawski, Piotr Podsiadiy, Prof. Andrrej Napieralski - Department of Microelectronics and Computer Science, TeFhnical University of Lodz, Al. Politechniki 11, 93-590 Lodz, POLAND, E-mail: szaniaw@dmcs.p,lodz.pi

We must be aware that each of those runs is expensive and time-consuming and thus it is better to cany out all possible simulations before the device is manufactured. This lets the designer to roughly estimate the device operation, thereby reducing the number of test runs and saving precious time and money. Besides, the simulation allows the designer to test the device operation in a wide spectrum of operating conditions in a relatively short time, including situations that are difficult or even impossible to set up in a laboratory, hut can occur in real life though. Again, it is especially important in case of sensors and actuators

In the following sections we will show how the CAD tools are applied for design and simulation of capacitive, miniaturized silicon acceleration sensors.

11. THE DESIGNED SENSORS

We have designed a series of capacitive micro- accelerometers using the MUMPS surface micromachining process developed by CRONOS (USA) and now also available through CMP (France). All these devices use the same acceleration measurement scheme. The sensor contains a movable mass called seismic mass or proof mass, which displaces due to inertial force caused by the measured acceleration. In turn, the displacement of the seismic mass makes the capacitance between that mass and the silicon substrate change. The change of capacitance can be then converted to electrical signal using various conversion schemes, which are briefly discussed in [2,3]. So, to provide electrical output, a three-stage conversion is required.

The acceleration sensing elements (i.e. sensing capacitors) of particular sensors can differ from each other only by physical shape and direction of motion ofthe seismic mass, as shown in Figure 1 [I].

Fig. I . Principles of capacitor-based acceleration sensing: horizontal comb-based (a,b) and vertical (c,d) [I]

In OUT work we have concenhated on the variant with a square-shaped seismic mass moving vertically, along the Z- axis (Fig. Id), although the approach based on comb-shaped sensing capacitors (Fig. la,b) has been investigated as well, but no relevant simulation results are available yet. The physical structure of one of the sensors is depicted in Figure 2.

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338 in the minimum setup, neither other MEMS devices nor any extemal circuitry are needed to provide the output signal.

Fig. 2. The 3-D view of thqsensing ca&citor designed in the MUMPs technology (double-poly version) [Z]

%e sensing capacitor consists of two square polysilicon electrodes, up to 400 microns wide, oriented horizontally (i.e. parallel to the silicon substrate), and separated by an air gap. The top electrode is formed of a 2 micron-thick polysilicon plate suspended 2 microns above the bonom electrode, which is deposited directly on the silicon substrate. The plate suspension consists of four folded-flexure springs, each one made of two or four elastic polysilicon beams. The suspended plate acts simultaneously as a proof mass. Under influence of the acceleration, the inertial force displaces the proof mass vertically (in Z-axis), thereby changing the distance between the capacitor electrodes, which in turn changes the capacitance. The proof mass moves until the inertial force is fully compensated by the elastic force generated by the deflected suspension beams, which (for relatively small deflections) is roughly proponional to the displacement of the proof mass. Consequently, the capacitance change is inversely proportional to the measured acceleration. For technological reasons, the proof mass must be perforated with a large number of little square holes, which are supposed to make it possible to effectively remove all silicon dioxide from the honom of the plate during the sacrificial layer etching process

The major drawback of the above solution is that to convert the variable capacitance into an electrical signal at the sensor output, either a voltage divider or bridge composed of multiple devices is needed [ I ] or an extemal electronic circuitry for capacitance-to-voltage conversion must he supplied [2,3]. Therefore, some triple-poly capacitive voltage dividers have been developed as well. The physical structure is shown in Figure 3. Now, the device consists of three polysilicon plates. While the top one and. the bonom one are fixed, the center plate can move vertically and plays the role of the seismic mass: These three plates form two air-gap capacitors - one between the honom and the center electrode and the other one between the top and the center electrode. What is more, when the capacitance of the top capacitor increases, the capacitance of the. bonom one decreases and vice versa. Despite different gap widths (bence different capacitances), the voltage divider composed of these two capacitors still works. To measure the acceleration, a HF sine voltage should be applied between the top and the bottom electrodes, and' the acceleration-dependent amplitude of the voltage at the center electrode should be acquired. This way,

PI.

Fig. 3. The 3-D view of the triple-poly capacitive voltage divide! designed in the MUMPs technology (springs outside)

111. APPLICATION OF DESIGN TOOLS All sensors have been designed using CADENCE IC

Package design environment. All devices are in a form of parameterized cells, which makes them fully scalable. The designer just specifies the width of the capacitor plates and all other dimensions are automatically adjusted, including spring length, the number of etch holes and their spacing. In the current versions, all other dimemions are fixed, but they also could be parameterized as necessaxy (e.g. beam width or etch hole width). Also, CADENCE tools assist in checking against violations of technological and design rules (Design Rule Checking). Figure 4 shows one of parameterized layout examples (along with stretch lines).

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Fig. 4. The parameterized mask layout of a lriple-poly sensing element (four-section springs, springs underneath 3rd poly)

w. APPLICATION OF SIMULATION TOOLS In case of sensors and actuators, simulation tools play even

more significant role than mask layout editors or design rule checkers. Particularly, in case of mechanical microstructures such as acceleration sensors, simulation tools allow estimation of mechanical properties crucial to device operation, such as steady-state suspension elasticity, natural fiequencies and the bequency response. Unfortunately, in this case the simulation task is very complicated, because the simulated.microsmcture is placed in gas rather than vacuum. Thus the pure mechanical

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result source

3-D simulation analytical estimation

simulation is insufficient and a coupled-field fluid-mechanical simulation must be carried out instead. A combined, multi- domain simulation is a great challenge to the simulation software and there are few tools that are capable of doing that. The worst problem however arises due to so called squeeze- effect caused by gas cushion that forms in narrow gaps between large electrodes. Compression and decompression of gas in the gap due to proof mass motion causes very strong, non-linear and frequency-dependent damping, which is very hard to calculate and simulate.

The most basic mechanical properties such as steady-state response or natural frequencies can be roughly estimated without taking gas influence into account, i.e. through a pure mechanical simulation. To do so we were using ANSYS, which is a powerful, multi-physics 3-D simulator that features excellent accuracy and performance, especially for very complex structures. Fortunately, due to very small deformations of accelerometer microstructures compared to their size, the deflection of suspension beams is roughly proportional to the acceleration. Therefore, linear simulation is sufficient in this case, which both simplifies modeling and substantially reduces simulation time. Steady-state analysis allows the designer to estimate (quite accurately) the displacement of the proof mass caused by steady-state acceleration. We can examine not only the impact of vertical acceleration, but also the impact of horizontal acceleration components, as well as angular accelerations. In tum, modal analysis allows us to extract main vibration modes and corresponding resonant frequencies, including horizontal and rotational modes as well. The Figure 5 shows the main vibration mode of one of the sensors, which we obtained through the modal analysis with ANSYS (the deformation is scaled in order to make it noticeable). 4

S: SY SP fi [nmilgl [nmilgl [ndlgl [ Hz]

62,s 0.2 0,4 2022 65,5 nia d a 1950

Fig. 5 . Sample results of 3-D modal analysis - main vibration mode (double-poly sensing capacitor, two-section springs) [41

TABLE 1

SAMPLE STEADY-STATE SENSITIVITIES AND THE NATURAL FREQUENCY COMPARED TO ANALYTICAL ESTIMATIONS

where r is the horizontal axis oriented 45Oto axes X and Y.

To give another example, Table I provides steady-state sensitivities in various directions and the dominant natural

frequency for another sensor (double-poly version and four- section suspension springs).

ANSYS can be used to cany out any kmd of mechanical simulation and determine any mechanical parameter, as long as gas damping is not involved. Otherwise, the problem becomes extremely hard to overcome, because although a coupled-field fluid-mechanical simulation is theoretically possible with ANSYS, in practice coupling these two simulation domains is a very difficult and tedious task. The only available approach is so-called sequential coupling via physics environments and no direct coupling between these two domains is possible. Sequential coupling consists in performing iteratively a series of alternate fluid and mechanical simulations and passing partial results (grid deformation, gas pressure and velocity) between them, until given accuracy level is reached. Unfortunately, with ANSYS the coupling process is not automated and must be done manually via custom scripts. Also, two compatible mesh grids (with corresponding node numbers) composed of different kind of elements (mechanical and fluid) and two independent sets of physical properties must be defmed in order to run a sequentially coupled fluid-mechanical, simulation. For most users, this technique is too complicated and time-consuming to deal with.

Therefore we are using another simulation tool for coupled- field fluid-mechanical simulations, which take gas-damping phenomenon into account - CFD-ACE+ released by CFDRC. Unlike ANSYS, ’ CFD-ACE+ couples multiple simulation domains automatically, without user’s activity. The domains are coupled sequentially as in ANSYS, but the user only selects the simulation domains and defines just a single property set, containing all physical properties - both fluid (such as fluid density) and mechanical (e.g. Young’s modulus). The simulator automatically carries out altemate fluid and mechanical simulations and manages transferring partial results from one simulation to another. Besides, the CFDRC package includes MicroMESH tool, which automatically generates mesh grids from mask layouts in CIF format, which can be exported e.g. from CADENCE via Design Framework 11. This feature is another significant advantage over ANSYS, because it makes creating models easier and faster.

The most significant limitation of CFD-ACE+ is that unlike ANSYS, it does not provide harmonic analysis, which basically is required to determine dynamic properties of the modeled accelerometer, particularly its frequency response. Obviously, the term “frequency response” applies to linear models only. Although, due to non-linear nature of the squeeze-film damping effect, our model is basically non-linear too, the model in CFD-ACE+ is linearized however. Thus determining the frequency response still makes sense in this case, Since the software cannot perform the harmonic analysis, the frequency response must be determined indirectly, that is extracted from transient simulation results. The most straightfonvard way to do that would be to carry on a series of transient analyses for sinusoidal excitation, one for each frequency to be covered. However, since a single transient

0

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340 simulation takes up a few days, this approach is completely impractical and useless. Fortunately, there is a better way to determine the frequency response, as it can be calculated by dividing the Fourier transform of the transient response by the Fourier transform of the .excitation function, as far as both functions are periodical. This way, we need only one transient simulation rather than multiple simulations. This method has been described in detail in [4] and it is beyond the scope of this paper.

Another considerable drawback of the CFD-ACE+ is that it yields ANSYS in accuracy and performance. Also, often there are convergence problems, especially in multi-domain simulations or in extreme physical conditions. In such case, the mesh grid, boundary conditions or simulation parameters must be modified using a try-by-experiment approach method.

The 3-D mechanical model of one of the acceleration sensors (double-poly version) developed for CFD-ACE+ simulator is shown in figure 6. To make the picture more readable, the air mesh ,is not shown and the microstructure mesh density is reduced. Since the modeled microstructure has two planes of symmetry, the model covers only the quarter of the suucture, which is sufficient in this case. Consequently, the mesh complexity has been reduced four times, which both speeds up the computations and reduces the utilization of the computer memory [4].

Fig. 6. The 3-D physical model of double-poly acceleration sensing capacitar far CFD-ACE+ (air mesh not shown) [4]

We were able ‘to extract frequency response from transient, simulation results, using the procedure described in [4]. Once we have done it, we made attempts to reduce the model, i.e. develop a very simple model, which still provides quite accurate frequency response in Z-axis. One of such reduced models is discussed in detail in [4]. Figure 7 shows sample eeequency response extracted from 3-D simulation in CFD- ACE+ compared to results obtained from the reduced model. Please notice that due to very strong damping caused by the squeeze-film effect, the microstructure is no more a resonator. The small peak visible on both curves is the resonance related to spring oscillations (independent on proof mass motion), which is not significant though.

,

I 1 0 , I , o I , ,* ,, .* I. ....... ,.*.,

~. I..”‘.,...., , , - I . O ” . . . I

Fig. 7. The fiequency response of double-poly accelerometer compared to reduced model results [4]

111. CONCLUSIONS CAD applications assist IC designers in developing MEMS

sensors and actuators in many ways. Mask layout editors allow fast and convenient design. One can create parameterized and scalable designs and reuse components designed earlier, which reduces design effort even more. In tum, simulation tools let the designer estimate important static and dynamic parameters, such as steady-state sensitivity or fiequency response. Although today’s simulators are quite advanced and are constantly enhanced and improved, there is still a lot of work to be done, particularly adding more features, improving computational algorithms and simplifying modeling process.

ACKNOWLEDGEMENTS This work was supported by tbe grant of Polish State

Committee for Scientific Research No. 8 TI 1B 021 19.

REFERENCES e [ I ] K. Szaniawski, A. Napieralski, “An Approach to Design a

Silicon, Low-g Microaccelerometer for Turbogenerator Vibration Measurement”, Proceedings of 8th MLYDES Conference, Zakopane. Poland, Jun 2001, pp. 99-104

[2] K. Szaniawski, A. Rominski, “A Capacitive Low-g Surface- Micromachined Microaccelerometer with Frequency Modulation and Digital Readout”, Proceedings of 9th Mu?)= Conference, Wroclaw, Poland, Jun 2002, pp. 213-216

[31 A. Pawlowski, K. Szaniawski, A. Napieralski, “Design of Mixed-Signal Microsystems for Measurement and Processing”, Ppoceedings of 9th A4IXDES Confirence, Wroclaw, Poland, lun 2002, pp. 261-264

[4] K. Szaniawski, P. Podsiadly, G. Jablonski, “A Methodology of Developing Reduced Linear Mechanical Models for MEMS Microstructures”. Proceedinm of 91h MLYDES Conhrence. Wroclaw, Poland, Iun 2002, ip. 467-412

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