Modeling and simulation of the capacitive accelerometer

Diploma Thesis, 2005

80 Pages, Grade: Master 9.8/10



1.1 Overview of MEMS

Microelectromechanical systems (MEMS) are collection of microsensors and actuators that have the ability to sense its environment and react to changes in that environment with the use of a microcircuit control. They also include the conventional microelectronics packaging, integrating antenna structures for command signals into microelectromechanical structures for desired sensing and actuating functions. The system may also need micropower supply, microrelay, and microsignal processing units. Microcomponents make the system faster, more reliable, cheaper, and capable of incorporating more complex functions.

In the beginning of 1990s, MEMS appeared with the aid of the development of integrated circuit fabrication processes, in which sensors, actuators, and control functions are co-fabricated in silicon [1]. Since then, remarkable research progresses have been achieved in MEMS under the strong promotions from both government and industries. In addition to the commercialization of some less integrated MEMS devices, such as microaccelerometers, inkjet printer head, micromirrors for projection, etc., the concepts and feasibility of more complex MEMS devices have been proposed and demonstrated for the applications in such varied fields as microfluidics, aerospace, biomedical, chemical analysis, wireless communications, data storage, display, optics, etc. Some branches of MEMS, appearing as microoptoelectromechanical systems (MOEMS), micro total analysis systems, etc., have attracted a great research since their potential applications’ market.

At the end of 1990s, most of MEMS devices with various sensing or actuating mechanisms were fabricated using silicon bulk micromachining, surface micromachining, and lithography, galvanoforming, moulding (LIGA) processes [2]. Three-dimensional microfabrication processes incorporating more materials were presented for MEMS recently because of specific application requirements (e.g., biomedical devices) and higher output power microactuators.

Micromachining has become the fundamental technology for the fabrication of MEMS devices and, in particular, miniaturized sensors and actuators. Silicon micromachining is the most advanced of the micromachining technologies, and it allows for the fabrication of MEMS that have dimensions in the submillimeter range. It refers to fashioning microscopic mechanical parts out of silicon substrate or on a silicon substrate, making the structures three dimensional and bringing new principles to the designers. Employing materials such as crystalline silicon, polycrystalline silicon, silicon nitride, etc., a variety of mechanical microstructures including beams, diaphragms, grooves, orifices, springs, gears, suspensions, and a great diversity of other complex mechanical structures have been conceived.

In some applications, stresses and strains to which the structure is subjected to may pose a problem for conventional cabling. In others, environmental effects may affect system performance. Advances in ultra flat antenna technology coupled with MEMS sensors and actuators seem to be an efficient solution. The integration of micromachining and microelectronics on one chip results in so-called smart sensors [3]. In smart sensors, small sensor signals are amplified, conditioned, and transformed into a standard output format. They may include microcontroller, digital signal processor, application-specific integrated circuit (ASIC), self-test, self-calibration, and bus interface circuits simplifying their use and making them more accurate and reliable.

Silicon micromachining has been a key factor for the vast progress of MEMS in the last decade. This refers to the fashioning of microscopic mechanical parts out of silicon substrates and, more recently, other materials. It is used to fabricate such features as clamped beams, membranes, cantilevers, grooves, orifices, springs, gears, suspensions, etc. These can be assembled to create a variety of sensors. Bulk micromachining is the commonly used method, but it is being replaced by surface micromachining that offers the attractive possibility of integrating the machined device with microelectronics that can be patterned and assembled on the same wafer. Thus power supply circuitry and signal processing using ASICs can be incorporated. It is the efficiency of creating several such complete packages using existing technology that makes this an attractive approach.

1.2 Silicon Micro Accelerometers

Micromachined inertial sensors, consisting of acceleration and angular rate sensors are produced in large quantities mainly for automotive applications [4], where they are used to activate safety systems, including air bags, and to implement vehicle stability systems and electronic suspensions. Besides these automotive applications accelerometers are used in many other applications where low cost and small size are important, e.g. in biomedical applications for activity monitoring and in consumer applications such as the active stabilization of camcorder pictures. Miniaturized acceleration sensors are also of interest to the air and space industries and for many other applications.

Silicon acceleration sensors generally consist of a proof mass which is suspended to a reference frame by a spring element. Accelerations cause a displacement of the proof mass, which is proportional to the acceleration. This displacement can be measured in several ways, e.g. capacitively by measuring a change in capacitance between the proof mass and an additional electrode or piezoresistively by integrating strain gauges in the spring element [3]. To obtain large sensitivity and low noise a large proof mass is needed, which suggests the use of bulk micromachined techniques. For less demanding applications surface micromachined devices seem to be more attractive because of the easy integration with electronic circuits and the fact that bulk micromachining requires the use of wafer bonding step [5]. Recently, some designs have been presented which combine bulk and surface micromachining to realize a large proof mass in a single wafer process.

The technology can be classified in a number of ways, such as mechanical or electrical, active or passive, deflection or null-balance accelerometers, etc.

This thesis reviewed following type of the accelerometers:

- Electromechanical
- Piezoelectric
- Piezoresistive
- Capacitive and electrostatic force balance
- Resonant accelerometer

Depending on the principles of operations, these accelerometers have their own subclasses.

1.2.1 Electromechanical Accelerometers

Electromechanical accelerometers [6], essentially servo or null-balance types, rely on the principle of feedback. In these instruments, an acceleration-sensitive mass is kept very close to a neutral position or zero displacement point by sensing the displacement and feeding back the effect of this displacement. A proportional magnetic force is generated to oppose the motion of the mass displaced from the neutral position, thus restoring this position just as a mechanical spring in a conventional accelerometer would do. The advantages of this approach are better linearity and elimination of hysteresis effects, as compared to the mechanical springs. Also, in some cases, electrical damping can be provided, which is much less sensitive to temperature variations. One very important feature of electromechanical accelerometers is the capability of testing the static and dynamic performances of the devices by introducing electrically excited test forces into the system. This remote self-checking feature can be quite convenient in complex and expensive tests where accuracy is essential. These instruments are also useful in acceleration control systems, since the reference value of acceleration can be introduced by means of a proportional current from an external source. They are used for general-purpose motion measurements and monitoring low-frequency vibrations. There are a number of different electromechanical accelerometers: coil-and-magnetic types, induction types, etc.

1.2.2 Piezoelectric Accelerometers

Piezoelectric accelerometers are widely used for general-purpose acceleration, shock, and vibration measurements. They are basically motion transducers with large output signals and comparatively small sizes and they are self generators not requiring external power sources. They are available with very high natural frequencies and are therefore suitable for high-frequency applications and shock measurements. These devices utilize a mass in direct contact with the piezoelectric component or crystal as shown in Fig. 1.1. When a varying motion is applied to the accelerometer, the crystal experiences a varying force excitation (F = ma), causing a proportional electric charge q to be developed across it. So,

illustration not visible in this excerpt

Where q is the charge developed and dij is the piezoelectric coefficient of the material.

As this equation shows, the output from the piezoelectric material is dependent on its mechanical properties, dij. Two commonly used piezoelectric crystals are lead- zirconate titanate ceramic (PZT) and crystalline quartz. They are both self-generating materials and produce a large electric charge for their size. The piezoelectric strain constant of PZT is about 150 times that of quartz. As a result, PZTs are much more sensitive and smaller in size than quartz counterparts. These accelerometers are useful for high-frequency applications. These active devices have no DC response. Since piezoelectric accelerometers have comparatively low mechanical impedances, their effect on the motion of most structures is negligible.

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Figure 1.1 A compression type piezoelectric accelerometer arrangement.

The low-frequency response is limited by the piezoelectric characteristic, while the high frequency response is related to mechanical response. The damping factor is very small and it is usually less than 0.01 or near zero. Accurate low-frequency response requires large damping factor, which is usually achieved by use of high-impedance voltage amplifiers. At very low frequencies thermal effects can have severe influences on the operation characteristics. Piezoelectric accelerometers are available in a wide range of specifications and are offered by a large number of manufacturers.

1.2.3 Piezoresistive Accelerometers

Piezoresistive accelerometers (see Fig. 1.2) are essentially semiconductor strain gauges with large gauge factors. High gauge factors are obtained since the material resistivity is dependent primarily on the stress, not only on the dimensions. The sensitivity of a piezoresistive sensor comes from the elastic response of its structure and resistivity of the material. Wire and thick or thin film resistors have low gauge factors, that is, the resistance change due to strain is small. Piezoresistive accelerometers are useful for acquiring vibration information at low frequencies, for example, below 1 Hz. In fact, they are inherently true non-vibrational acceleration sensors. They generally have wider bandwidth, smaller nonlinearities and zero shifting, and better hysteresis characteristics compared to piezoelectric counterparts. They are suitable to measure shocks well above 100,000g. Typical characteristics of piezoresistive accelerometers may be listed: 100 mV/g as the sensitivity, 0–750 Hz as the frequency range, 2500 Hz in resonance frequency, 25g as the amplitude range, 2000g as the shock rating, and 0–95°C as the temperature range. The total mass is about 25 g. Most contemporary piezoresistive sensors are manufactured from a single piece of silicon. This gives better stability and less thermal mismatch between parts. In a typical monolithic sensing element a 1-mm silicon chip incorporates the spring, mass and four-arm bridge assembly. The elements are formed by a pattern of dopant in the originally flat silicon. Subsequent etching of channels frees the gauges and simultaneously defines the masses as regions of silicon of original thickness.

illustration not visible in this excerpt

Figure 1.2: Piezoresistive acceleration sensor.

1.2.4 Electrostatic Accelerometers

Electrostatic accelerometers are based on Coulomb’s law between two charged electrodes; therefore, they are capacitive types. Depending on the operation principles and external circuits they can be broadly classified as (a) electrostatic-force-feedback accelerometers, and (b) differential-capacitance accelerometers. Electrostatic-Force-Feedback Accelerometers

An electrostatic-force-feedback accelerometer consists of an electrode, with mass m and area S, mounted on a light pivoted arm that moves relative to some fixed electrodes. The nominal gap h between the pivoted and fixed electrodes is maintained by means of a force-balancing servo system, which is capable of varying the electrode potential in response to signals from a pickoff mechanism that senses relative changes in the gap.

Hence, if the bias potential is held constant and the gain of the control loop is high so that variations in the gap are negligible, the acceleration becomes a linear function of the controller output voltage. The principal difficulty in mechanizing the electrostatic force accelerometer is the relatively high electric field intensity required to obtain an adequate force. Damping can be provided electrically or by viscosity of the gaseous atmosphere in the inter-electrode space if the gap h is sufficiently small. The scheme works best in micromachined instruments. Nonlinearity in the voltage break down phenomenon permits larger gradients in very small gaps. The main advantages of electrostatic accelerometers are their extreme mechanical simplicity, low power requirements, absence of inherent sources of hysteresis errors, zero temperature coefficients, and ease of shielding from stray fields. Differential -Capacitance Accelerometers

illustration not visible in this excerpt

Figure 1.3 Capacitive measurement of acceleration.

Differential-capacitance accelerometers are based on the principle of the change of capacitance in proportion to applied acceleration. In one type, the seismic mass of the accelerometer is made as the movable element of an electrical oscillator. The seismic mass is supported by a resilient parallel-motion beam arrangement from the base. The system is set to have a certain defined nominal frequency when undisturbed. If the instrument is accelerated, the frequency varies above and below the nominal value depending on the direction of acceleration. The seismic mass carries an electrode located in opposition to a number of base-fixed electrodes that define variable capacitors. The base-fixed electrodes are resistances coupled in the feedback path of a wideband, phase-inverting amplifier.

1.2.5 Resonant Accelerometers

Resonant accelerometers are attractive for their high sensitivity and frequency output. Most of the conventional, high precision accelerometers are of this type. The structure of resonant accelerometers is quite different from other sensors, as shown in Fig. 1.4. The proof mass is suspended by relatively stiff suspension to prevent large displacement due to acceleration. Unlike other types of accelerometers, resonators are attached to the proof mass. Upon acceleration, the proof mass changes the strain in the attached resonators, which causes a shift in those resonant frequencies. The frequency shift is then detected by the electronics and the output can be measured easily by digital counters. Resonant accelerometers are still in the early stages of research and development. Nevertheless, the use of resonant strain gauges is a competitive approach for high precision sensing and can be developed into a key technology for inertial grade accelerometers.

illustration not visible in this excerpt

Figure 1.4 Resonant accelerometer

1.3 MEMS Modeling and Simulation

Accurate modeling and efficient simulation, in support of greatly reduced development cycle time and cost, are well established techniques in the miniaturized world of integrated circuits (ICs) [7-9]. Simulation accuracies of 5% or less for parameters of interest are achieved fairly regularly, although even much less accurate simulations (25–30%, e.g.) can still be used to obtain valuable information. In the IC world, simulation can be used to predict the performance of a design, to analyze an already existing component, or to support automated synthesis of a design. Eventually, MEMS simulation environments should also be capable of these three modes of operation. The MEMS developer is, of course, most interested in quick access to particular techniques and tools to support the system currently under development. In the long run, however, consistently achieving acceptably accurate MEMS simulations will depend both on the ability of the CAD (computer-aided design) community to develop robust, efficient, user-friendly tools which will be widely available both to cutting-edge researchers and to production engineers and on the existence of readily accessible standardized processes.

We need to look specifically at the tools and techniques the MEMS designer has available for the modeling and simulation tasks because all models are not created equal. The developer must be very clear about what parameters are of greatest interest and then must choose the models and simulation techniques (including implementation in a tool or tools) that are most likely to give the most accurate values for those parameters in the least amount of simulation time.

Let us look at a simple example that combines electrical and mechanical parts. The cantilever beam in Fig. 1.5(a), fabricated in metal, polysilicon, or a combination, may be combined with an electrically isolated plate to form a parallel plate capacitor. If a mechanical force or a varying voltage is applied to the beam (Fig. 1.5(b1)), an accelerometer or a switch can be obtained.

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Figure.1.5 Cantilever beam and beam - capacitor options (a) cantilever dimension

(b) Basic – capacitor designs

To obtain an accurate model of the beam we can use the method of nodal analysis that treats the beam as a graph consisting of a set of edges or “devices”, linked together at “nodes” [10]. Nodal analysis assumes that at equilibrium the sum of all values around each closed loop (the “across” quantities) will be zero, as will the sum of all values entering or leaving a given node (the “through” quantities). Thus, for example, the sum of all forces and moments on each node must be zero, as must the sum of all currents flowing into or out of a given node. This type of modeling is sometimes referred to as “lumped parameter,” since quantities such as resistance and capacitance, which are in fact distributed along a graph edge, are modeled as discrete components. In the electrical domain Kirchhoff’s laws are examples of these rules.

Since nodal analysis is based on linear elements represented as the edges in the underlying graph, it cannot be used to model many complex structures and phenomena such as fluid flow or piezoelectricity. Even for the cantilever beam, if the beam is composed of layers of two different materials (e.g., polysilicon and metal), it cannot be adequately modeled using nodal analysis. The technique of finite element analysis (FEA) must be used instead [11-12]. Finite element analysis for the beam begins with the identification of sub elements, as in Fig. 1.5(a), but each element is treated as a true three-dimensional object. Elements need not all have the same shape, for example, tetrahedral and cubic “brick” elements could be mixed together, as appropriate. In FEA, one cubic element now has eight nodes, rather than two (Fig. 1.6), so computational complexity is increased. Thus, developing efficient computer software to carry out FEA for a given structure can be a difficult task in itself. But this general method can take into account many features that cannot be adequately addressed using nodal analysis, including, for example, unaligned beam sections, and surface texture (Fig. 1.7).

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Figure 1.6 Nodal analysis and finite elements analysis

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Figure. 1.7 Ideal and actual cantilever beams (side view).

In the past fifteen years, much progress has been made in providing MEMS designers with simulators and other tools which will give them the ability to make MEMS as useful and ubiquitous. While there is still much to be done, the future is bright for this flexible and powerful technology. Table 1 listed several simulation tools and their supported levels:

Table1.1. Available MEMS simulation tools, by level and view

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In this thesis I used SUGAR tool which applies modified nodal method to implement simulation programs. More details of this tool will be discussed in chapter 3.


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Modeling and simulation of the capacitive accelerometer
Master 9.8/10
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Msc Tan Tran Duc (Author), 2005, Modeling and simulation of the capacitive accelerometer, Munich, GRIN Verlag,


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