Novel 3D modeling methods for virtual fabrication ... - Semantic Scholar

IOP PUBLISHING

JOURNAL OF MICROMECHANICS AND MICROENGINEERING

doi:10.1088/0960-1317/20/6/064003

J. Micromech. Microeng. 20 (2010) 064003 (15pp)

Novel 3D modeling methods for virtual fabrication and EDA compatible design of MEMS via parametric libraries Gerold Schröpfer1 , Gunar Lorenz1 , Stéphane Rouvillois1 and Stephen Breit2 1 2

Coventor Sarl, 3 Avenue du Quebec, 91140 Villebon sur Yvette, France Coventor Inc, 625 Mt. Auburn Street, Cambridge, MA 02138, USA

E-mail: [email protected]

Received 30 November 2009, in final form 13 April 2010 Published 1 June 2010 Online at stacks.iop.org/JMM/20/064003 Abstract This paper provides a brief summary of the state-of-the-art of MEMS-specific modeling techniques and describes the validation of new models for a parametric component library. Two recently developed 3D modeling tools are described in more detail. The first one captures a methodology for designing MEMS devices and simulating them together with integrated electronics within a standard electronic design automation (EDA) environment. The MEMS designer can construct the MEMS model directly in a 3D view. The resulting 3D model differs from a typical feature-based 3D CAD modeling tool in that there is an underlying behavioral model and parametric layout associated with each MEMS component. The model of the complete MEMS device that is shared with the standard EDA environment can be fully parameterized with respect to manufacturing- and design-dependent variables. Another recent innovation is a process modeling tool that allows accurate and highly realistic visualization of the step-by-step creation of 3D micro-fabricated devices. The novelty of the tool lies in its use of voxels (3D pixels) rather than conventional 3D CAD techniques to represent the 3D geometry. Case studies for experimental devices are presented showing how the examination of these virtual prototypes can reveal design errors before mask tape out, support process development before actual fabrication and also enable failure analysis after manufacturing. (Some figures in this article are in colour only in the electronic version)

tools and methodologies, but rather a short overview of the state-of-the-art and guide to several future trends.

1. Tools for MEMS design A MEMS designer is confronted with a number of challenges: complex, coupled, three-dimensional, multiphysics phenomena; unknown material property data; large variations in manufacturing processes; and interfacing with package and control electronics. To help the MEMS designer overcome these challenges, MEMS design tools must support four levels of design abstraction: system level, device level, physical level and process level [1, 2]. These abstraction levels provide a clear framework for categorizing MEMS design tools. Before discussing two recent design tool innovations in more detail, we summarize the existing approaches to addressing these four levels of abstraction. This summary is by no means a comprehensive review of all relevant design 0960-1317/10/064003+15$30.00

1.1. System level modeling The interactions of the MEMS component with its environment and control electronics can be modeled and simulated on the system level of abstraction. Models at this level can include not only MEMS and analog components, but also digital electronics and software. There are two main approaches to system level modeling: a model-based design method in which the design is described by a signal-flow diagram, or a hardware description language (HDL) in which the design is described by a circuit schematic (or netlist). MatLab SimulinkTM is an example of a signal1

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J. Micromech. Microeng. 20 (2010) 064003

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Figure 1. Network type schematic behavior model of a gyroscope with illustrations of the physical geometry represented by some of the schematic symbols [7].

flow design and simulation environment that supports the model-based design. Cadence VirtuosoTM is an example of an analog/mixed-signal circuit design and simulation environment that supports HDL-based design. The clear advantage of system level modeling is that the simulations run fast enough to allow modeling of complex, multi-physics systems. MEMS libraries for circuit simulators based on parameterized behavioral models and consisting of electromechanical building blocks such as beams, plates, comb structures and electrode models [3–5] are available commercially, and are now well established [7, 8] (see figure 1). Advanced versions include other physics such as RF, magnetics, thermodynamics, micro-fluidics and optics, turning traditional electronic simulators into multi-physics MEMS design environments. Over the past decade, ongoing development efforts have dramatically increased both the variety of MEMS library components and the sophistication of the underlying behavioral models, enabling system level simulation of a wide range of MEMS device types. In some cases, the library components are closely linked with the process technology, from which material properties and geometric parameters such as layer thickness are obtained. Recently, 3D visualization of the complex models and simulation results has been added [8]. One of the latest advancements allows designers to compose system-level designs in 3D [9], and is described in section 2.

suited to describing not only a complete system, but the detailed behavior of a single MEMS device as well. In cases where the available behavioral models are inadequate, it is possible to use so-called compact modeling or reduced order modeling (ROM) that allow the extraction of specialized behavioral models from detailed 3D numerical simulations with partial differential equation (PDE) solvers [10, 11]. Interfaces from ROM tools to widely used circuit simulators exist; however most commercially available ROM techniques produce only non-parametric, linear behavioral models. Consequently, recent research focuses on compact modeling algorithms for extracting parametric and nonlinear models [12, 13]. 1.3. Physical modeling MEMS devices have traditionally been modeled using 3D field solvers based on the finite element method (FEM) and boundary element method (BEM). These approaches, which can be generically described as physical modeling entail decomposing the device geometry into a collection of volume or surface elements, and then solving a system of partial differential equations for the field values at the element control points. Today, a variety of single-physics and multi-physics field solvers are available, ranging from general-purpose tools to those that address MEMS-specific physics such as electrostatic sensing and actuation, piezoelectric effects and gas damping [14, 15]. In the past decade, substantial improvements have been made in user-friendliness, automatic meshing algorithms, computational efficiency and results database management to link physical models with system level models [16]. Field solvers have the desirable property of being able to handle virtually any device geometry, making them the tools of choice for cases where behavioral modeling reaches its limits, and for design verification. However, field solvers

1.2. Device level modeling MEMS devices are often large and complex compared to IC devices (transistors). It is sometimes difficult to capture specific physics or behavior in terms of ordinary differential equations. This is the case, for example, with details of mechanical anchors and energy loss via gas damping. Nevertheless, state-of-the-art behavioral model libraries are 2


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studies the number of finite elements can be controlled and adjusted to ensure a sufficient accuracy of the model. When developing new library components of network-type models, the model accuracy is usually compared to analytical solutions and FEM simulations, for example for mechanical beams [6]. A detailed comparative study of different methods for calculating the pull-in voltage of electrostatically actuated fixed–fixed beam actuators has been presented in [17, 18]. Five different pull-in voltage calculation methods are compared to simulations based on FEM and parametric MEMS behavior library in detail. It has been observed that many closedform methods did not sufficiently consider the modeling of the fringing field capacitances and the stress-induced nonlinear spring hardening effects. Detailed comparisons between measurements and simulation results, both for FEM and behavior library components, are provided for MEMS resonators in [19, 20]. The validation of a newly developed piezoelectric (PZE) beam model is described in detail in [22, 23]. The new PZE beam model used in the tool ARCHITECT3DTM [8] consists of a purely mechanical element and an electro-mechanical element describing the coupling as well as the electrical behavior of the piezo-electric layer. It has been employed in piezoMEMS devices, such as energy harvesters [22, 23], as shown in figure 2. This model also includes a power transfer circuit composed of a bridge rectifier with storage capacitor and resistive load. The mechanical element uses the Bernoulli beam theory. The nonlinear behavior of this beam is obtained by computing the element matrices at runtime on the deformed structure. The electro-mechanical component’s active part describes the effect of a potential difference on the forces: the stress tensor is obtained from the electric field and the piezo-electric coefficients are to be integrated over the beam. The sensing part describes the effect of displacements on charge and is modeled as a charge source whose value is a linear function of the strain. The difference between the behavior model and the finite element model is less than 1% in terms of simulated resonance frequency. This level of accuracy for ARCHITECT3DTM models is very typical and was multiple times observed for other types of models in the mentioned studies [6, 17–23]. The agreement between measurements and simulated results for the piezoelectric energy harvester is within 2%, for both the ARCHITECTTM and the finite element model. In this case, the mismatch between the simulated resonance frequencies and the measured values is likely due to a difference in material properties [23]. The slight difference between the ARCHITECT3DTM and the finite element results can be attributed to the length (1.3 mm) to width (3 mm) ratio of the cantilever. The low value of 2.3 indicates that the cantilever tends to show plate behavior rather than beam characteristics. One of the advantages of parametric behavior models is the short simulation time and with this the ability to carry out statistical analysis. Tolerances of the technology layer properties such as thickness, stress and stress gradients will give in practice a range of pull-in voltages for a number of devices. Based on the material and process characterization,

Table 1. Relative advantages of behavioral modeling and FEM/BEM-based modeling. Behavioral modeling

FEM/BEM modeling

• System level design • Enables easier design automation and integration with EDA • Short simulation time enables ◦ Transient analysis ◦ Rapid optimization ◦ Statistical analysis, such as yield or sensitivity analysis

• Geometric flexibility • Captures field details such as stress distribution • Addresses physics not amenable to behavioral modeling such as gas damping • Arbitrarily accurate via mesh refinement

Table 2. A selection of recent developments in MEMS CAD. • 3D geometry and result visualization of MEMS behavior models • 3D environment for assembling behavioral models of MEMS devices • Integration MEMS behavioral modeling with standard EDA tools • Enhanced techniques for extracting compact models (ROM) from FEM/BEM models for incorporation in system level design • Improved algorithms for physical modeling of various damping phenomena (low gas pressure, anchor damping and thermo-elastic damping) • Enhanced process emulation techniques

require substantial computational effort in the form of memory and simulation time, making it infeasible to directly include FEM/BEM-based models in incompatible with system level simulations. A comparison between behavioral modeling and PDEbased solvers is provided in table 1. In addition to physical modeling of a device, physical design in the form of 2D layout must be considered. Typically, layout editors from EDA suppliers and general-purpose mechanical 2D CAD tools such as AutoCADTM are employed for MEMS design. MEMS-specific layout generators have been added to these tools to ease the task of creating complex MEMS device design. However, until now, MEMS layout parameterization has been disconnected from the other levels of modeling, and especially from system level modeling. This stands in contrast to electronic design automation (EDA), for IC design, which makes extensive use of parameterized layout cells. A new approach, described later in this paper, makes it possible to generate complex, fully parameterized MEMS layout cells from system-level device designs. An overview over recent developments in the area of CAD tools for MEMS is given in table 2. 1.4. Model validation Different methods are applied to validate modeling results: firstly, comparison with simple analytical formula, also called closed-forms; secondly, comparison with other modeling techniques; and thirdly, with measurement results. A large number of articles have been published comparing different modeling tools using the above-mentioned validation schemes [6, 17–23], to name just a few. FEM techniques are well accepted and used across for applications. Via mesh 3


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Figure 2. Finite element model of a piezoelectric energy harvester showing the mesh structure (a) and corresponding parameterized MEMS library component model, which features two beam components for the cantilever and mass sections as well as a power transfer circuit (b). Measured and simulated output voltage of the harvester (c).

A number of devices have been fabricated and their pull-in voltages were measured between 6.6 and 7.8 V. The measurement results for 20 devices are compared to the performed Monte Carlo analysis, as shown in figure 3. Average values as well as three sigma deviations are presented for both measurements and simulations. The thickness tolerance is a combination of the error in the nominal thickness and the process uniformity. Thus in a given batch, a shift in the nominal thickness would appear systematic and hence account

statistical analysis (Monte Carlo simulation) can be performed to calculate the distribution of certain performance parameters, for example the pull-in voltage of a variable capacitor. In [24] such a variable capacitor is described. Figure 3 shows the solid and schematic model of a variable capacitor using beam, rigid plate and electrode components of the parametric MEMS library ARCHITECT3DTM . To simplify the design, the schematic includes a hierarchical component that represents the folded suspensions of the device. 4


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Figure 3. Solid and corresponding schematic model of a variable capacitor (a). Measured pull-in voltages for 20 suspended plate variable capacitors in comparison to simulation results (b).

and specific etch conditions (type of etchant, and etchant concentration and temperature). An alternative approach is to employ an atomistic model, which takes the binding energy between atoms into account and provides the etching rate as a simulation output instead of an input [25]. Reference [25] provides validation of etching simulation via comparison to experimental samples. The existing etch simulation tools have the disadvantages of capturing only one type of processing step, and requiring prodigious computational resources. To address these limitations, MEMS CAD tools such as CoventorWareTM have favored a process emulation approach, in which the 2D layout and a description of the fabrication process sequence are used to create an idealized 3D solid model of the MEMS device. These geometric models can be built rather quickly and are well suited as input to subsequent physical modeling tools. The restriction of idealized geometry

for the slight difference of 0.49% in the mean value of the measured data compared with the simulated data. 1.5. Process modeling Process simulation involves 3D numerical simulation of process chemistry and physics with the result being the accurate 3D device geometry after material addition and/or subtraction. While a variety of tools are available for simulating typical semiconductor processing steps (such as implantation and diffusion), the offerings for MEMS-specific process simulation are more limited. Available tools have focused on simulating wet chemical anisotropic etching of single-crystal silicon and, more recently, deep reactive ion etching (DRIE). Wet etch simulators require accurate measurement of etch rates for many crystal silicon planes 5


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mentioned methods aim toward establishing extended libraries of flexible models allowing better component and system design [28]. With the growth of independent MEMS foundries and the corresponding emergence of fabless product companies [29], one can expect that the exchange of information between manufacturers and designers will be facilitated by MEMSspecific process design kits (PDKs), and that such MEMS PDKs will be increasingly important to the industry. These PDKs will include the necessary process and material data to allow MEMS designers to access foundry processes. Future versions may even provide complete libraries of MEMS devices or parts. On a device level, the technological influences will be better modeled—especially in early design phases [28]. In section 2, we describe a methodology that enables designers to create fully parameterized behavioral models of MEMS devices in a system-level environment. Process modeling will be increasingly used by both captive MEMS fabs and independent MEMS foundries to establish better communication between process engineers and device designers [28, 30]. Improvements for process modeling will take place in the empirical 3D model extraction for process steps and sequences [28]. With all these developments virtual manufacturing will be used more and more; we describe two different use cases in section 3. One can expect standardization of the formats for exchanging technology and geometrical data [28]. The MEMS design and process modeling tools will increasingly become part of an integrated and complete software eco-system for MEMS product development [30]. Finally, with better understanding of reliability issues and phenomena, future MEMS design tools will include more accurate reliability modeling and thereby increase the predictability of components and MEMS-based systems [31, 32]. A summary of trends in MEMS CAD tool development is provided in table 3.

arises from limitations in conventional solid modeling kernels, and manifest themselves in the ability to conveniently ensure geometry details as well as occasional failure to produce a model at all (due to lack of robustness in heuristics that are inherent to this approach). Voxel-based 3D modeling is an alternative approach which produces more realistic geometry and has proven more robust in practice [24, 26]. A voxel is a cube and is, in essence, the 3D equivalent of a pixel in a 2D image (volumetric pixel). The user is able to specify the resolution of the voxel model in microns or nanometers. The smaller the resolution, the more voxels are required to represent the geometry. Voxel-based 3D modeling would require intensive computing resources in the form of memory and CPU time if all voxels were generated and stored. To overcome this potential limitation a very efficient compression algorithms was developed that enable users to create models with 100 s of billions of voxels in a few hours on a typical desktop workstation [26]. 1.6. Trends Future MEMS design platforms must seamlessly support both a top-down approach, based on parametric behavioral models, and a bottom-up approach based on FEM/BEM modeling in order to strike an ideal balance between the multi-domain coupling and efficiency of system-level design and the ability to capture the detailed physics of almost any device geometry provided by physical modeling with field solvers. Such integrated platforms will enable a design methodology that is more effective and significantly less time consuming. One way to combine the virtues of behavioral and physical modeling is via compact model extraction, as briefly mentioned in section 1.2. Another way to achieve this goal is to incorporate advanced, higher-order finite elements directly in the behavioral modeling environment. This approach is embodied in a new generation of flexible-plate models that have been added to a MEMS behavioral model library [8]. These new flexible-plate models are built around state-of-the-art, nonlinear, shell elements that employ mixed interpolation of tonsorial components (MITC) [27]. The new plate models significantly expand the geometric flexibility of existing behavioral model libraries and can be used to simulate polygon-shaped membranes, tapered beams, various switch geometries, stress stiffening and buckling. Another example of the trend toward convergence of behavioral and physical modeling is a novel mixed modeling approach known as hybrid modeling [16]. It combines field solver analysis (FEM) with system-level modeling in a circuit simulation environment and relies on a new class of parameterized behavioral models that can automatically access and use field solver solutions that are stored in a relational database. This hybrid approach exploits the complementary strengths of each of these modeling techniques, namely the ability of field solvers to analyze arbitrarily complex geometric shapes, and the optimized computational performance of behavioral models. Possible applications to MEMS design range from designing piezoresistive sensors to thermal codesign of a MEMS device and its package. Overall, these

2. Novel EDA-compatible MEMS design methodology MEMS engineers and IC engineers frequently express the need to co-simulate their MEMS and IC designs in a common simulation environment. Co-simulation is required to verify the IC design and to predict yield sensitivity to manufacturing variations. The most obvious path is to do the co-simulation in the environment used by the IC designers. This requires that the MEMS designers deliver a behavioral model of the MEMS devices expressed in a HDL. Today, MEMS engineers have very limited ability to deliver behavioral models in these formats. In practice, the employed methods are to hand craft a model, usually in the form of a lookup table, or generate a reduced-order model from finite element analysis. Both of these options result in non-parametric models, i.e. point designs, that are not useful for yield analysis and are not reusable. In this section we present a new integrated methodology to be used in MEMS+IC design, simulation and product development. This new methodology allows the MEMS 6


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the indirect approach presented in section 1.1. The resulting 3D view differs from a traditional 3D CAD modeling tool in that there is an underlying behavioral model associated with each MEMS building block that rivals the accuracy of FEM models, as described in section 1.4.

Table 3. Future trends in MEMS CAD tools, partly from [28]. System design • Extended libraries of 3D flexible behavioral models • Technology influences considered in early design phases • Tight integration between process, physical and system level design • Integration with analog/mixed-signal IC design flow • Support for widely used EDA platforms • Process design kits compatible with EDA flows • Standard interfaces such as SystemC-AMS for connecting behavioral models with signal-flow and circuit simulators

2.2. Parameterization Another new and unique aspect of this methodology is the parameterization over the complete design space—including the 3D model, its HDL representation, and the 2D layout. There are two categories of parameters that are relevant for MEMS design. The first category consists of the material properties and geometric parameters that are determined by the manufacturing process. The second category consists of the dimensional parameters of the MEMS building blocks (such as length, width, number of comb fingers, etc) that are determined by the MEMS engineer. While MEMS and IC design share aspects related to manufacturing, they differ in the impact manufacturing has on their design flows. Conventional IC design tools do not offer the flexibility to change the location of a component within the various layers created during the fabrication process. Thus the impact of the chosen fabrication process on an IC design is fixed from the beginning and does not change from one design iteration to the next. In comparison, the MEMS fabrication processes are much less standardized. In reality, the fabrication process is to some extent a ‘free parameter’ in MEMS design that often needs to be refined as the development progresses. The flexibility to change the description of the fabrication process is missing from conventional IC design environments. In addition, behavioral models of electrical IC components cannot be parameterized in terms of the process parameters. In MEMS design, the parameters of the process description can be varied as part of the design; thus, the models must be parameterized with respect to the process parameters. The new environment addresses the specific needs of MEMS designers by providing two editors that are used to specify all relevant fab-specific data. A material property editor is used to create a material database that contains all relevant physical as well as visual properties. All material properties can be defined as absolute values, variables or algebraic equations. A combination of variables and algebraic equations allows for properties to be dependent on other properties, environmental variables (e.g. temperature and humidity) or even entirely abstract variables such as the equipment settings of a given fabrication process. The MEMS engineer can choose which variables are to be exposed in the model, and in the corresponding MEMS schematic symbol and layout. A second editor is used to define the sequence of MEMS fabrication steps. The underlying process data include all relevant information about the layer stack, such as the layer order, material type, thickness and sidewall profile. The process data are dependent on a material database: each of the layers in the process data specifies a material type that must exist in the corresponding material database.

Device design • Tighter integration of behavioral and physical modeling as well as physical design (2D layout) within one environment • Compatible multi-domain libraries of MEMS building blocks • A delivery methodology for multi-domain IP • Automatic generation of compact models via new algorithms for parametric and nonlinear model order reduction • Standard interchange format for technology and geometry data • Improved reliability models Process modeling • Improved methodology for extracting empirical values of process parameters for process modeling • Libraries of standard process sequences and steps • Routine modeling of complete MEMS processes

designer to work in a 3D environment that suits his needs and yet easily deliver parameterized behavioral models that are compatible with IC design and simulation environments. The IC designer, meanwhile, will see no difference between including a MEMS device and any other analog or digital component. The parameters in the MEMS behavioral model may include manufacturing variables, such as material properties and dimensional variations, as well as geometric properties of the design. It is expected that the sophistication and accuracy of these models will enable optimization of the MEMS+IC design, both for performance and yield. 2.1. MEMS behavior model in 3D The first step in the new methodology is to create a MEMS design by selecting MEMS building blocks from a parameterized 3D MEMS component library and assemble them into a MEMS device. As part of this process, the MEMS designer can specify which parameters will be exposed in the IC design environment. The graphical user interface, shown in figure 4, is similar to that of a feature-based 3D mechanical CAD tool. One unique innovation of this methodology is that the MEMS designer can construct the behavioral model in a 3D view. Heretofore, as described in [8], the user first created a schematic (i.e. wiring diagram) and then generated a 3D view. In the new tool, the user selects a component from the library, enters values for its parameters, and the 3D view is then immediately updated. This direct creation of a MEMS device in a 3D view is expected to be more natural for MEMS engineers, and therefore will save time in contrast to 7


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Figure 4. MEMS design environment that allows direct creation and simulation in 3D (center) of a parameterized behavioral model that includes mechanical and electrostatic components. The designer can choose which parameters to expose for further system modeling (–top right). The lower panes contain editors for material and process parameters.

On completion of a simulation, the designer can view the simulation results in the MEMS 3D viewer, which can animate the motion of the MEMS device. At any time, but especially when the MEMS and IC designers are satisfied with the MEMS design, they can export a parameterized layout cell (p-cell) that can generate a layout of the MEMS device. Thus, one MEMS design is represented in the following different ways that all share the same set of parameters:

The separation of the materials and process data from the MEMS design and simulation environment allows the model to have process-related parameters whose specification is not fixed, but rather is tied by reference to the manufacturing process data. 2.3. Integration into EDA Upon completing the design of the device in the 3D MEMS design environment, the MEMS designer can share the design with the IC design environment in the form of a netlist and a schematic symbol. The number and names of the pins on the schematic symbol are controlled by the MEMS engineer and represent electrical connections to the MEMS device. The MEMS symbol can be placed in a schematic in the IC schematic editor. For the MEMS designer who wants to simulate the behavior of the MEMS device alone, it may be necessary to connect only a few other components to the MEMS symbol to provide electrical excitation, or electrical sensing of the output signal. For the IC designer, however, the schematic will include the complete IC design. Simulations can now be run in the circuit simulator. The simulator will connect with the MEMS component library to evaluate the MEMS behavioral model at each simulation point, i.e. time step or frequency.

• • • •

3D model, schematic symbol, netlist written in HDL, layout p-cell.

The IC engineer, on the other hand, will work only within the EDA platform (right-hand side of figure 5). That is, the IC designer will be provided with a MEMS behavioral model in the form of a symbol and netlist and then need to only incorporate that symbol in a schematic and run MEMS+IC simulations, viewing the results only at the electrical level. The different views of the MEMS component provide a customizable environment to transfer MEMS component intellectual property (IP) between various actors in MEMS development [30]. 8


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Figure 5. Novel MEMS-IC design flow that combines 3D MEMS design with standard EDA tools.

Cadence. CoventorWare 2010 was used to run simulations with Saber (version 2009.06.1.0). Cadence reference times were measured using Spectre 7.1.1 with the MEMS+ 2.0 model library. The complete transient simulation of the gyro model took 654 s with the circuit simulator Saber and 76.9 s with the circuit simulator Spectre. The second simulation example is a RF MEMS switch. The device model is shown in figure 5. The switch cycle is illustrated in figure 7. The simulation time under CoventorWare and Saber was 5.1 s and under Spectre and MEMS+ 17.1 s. Using the Cadence simulator Ultrasim instead of Spectre decreases the simulation time to 5.9 s. While the gyroscope transient simulation despite a fully nonlinear mechanical MEMS model does not include major nonlinear effects, the RF switch modeling need considers a major discontinuity, which is the contact between the moving MEMS structure and the underlying fixed electrode. All simulations for the gyroscope and the RF MEMS switch were run on a standard computer (CPU: Intel xeon W3520, quad core, 2.67 GHz, memory: 8 GB).

2.4. MEMS simulation examples In this section we describe two simulation examples using the tool described above. The first example is a transient simulation of a MEMS gyroscope. The second example is a simulation of a RF MEMS switch cycle including high nonlinear effects due to contact issues. In the case of the gyroscope, we are interested in the complete transient simulation starting from steady-state oscillations. This simple gyroscope is designed to sense rotation only while the perforated mass is oscillating steadily in the y-direction. When a fabricated gyroscope is first powered up, there is a short delay due to inertial and damping effects until the mass is steadily oscillating at its full stroke. Similarly for this simulated gyroscope, the steady state must be achieved before attempting to sense. The simplest approach to achieve this steady state would be to run the transient analysis for an initial quiet period that is long enough to reach the steady state. But this initial start-up time can be on the order of hundreds of milliseconds, while one only needs to simulate the sensing response for tens of milliseconds. The simulation starts with steady-state oscillations of the gyroscope in the y-direction. The reference frame is then rotated at 1 rad s−1 and stopped. The image in figure 6(a) shows (from top to bottom) the steady-state oscillation of the gyroscope in its driving mode; the angular velocity of the reference frame and the response of the gyroscope to the angular motion of the reference frame. The MEMS models are implemented into CoventorWare and MEMS+, both commercially available tools. The circuit simulator was either Saber from Synopsis or Spectre from

3. Virtual manufacturing of MEMS As described in section 1.5, process modeling, in contrast to process simulation, is efficient enough to capture the complete process sequence for a complete MEMS device. When the individual process step parameters are empirically calibrated, the resulting device model can be silicon accurate. Thus process modeling is, in effect, a method of virtual 9


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Figure 6. Transient simulation of a MEMS gyroscope. The 3D illustrations of the model (not to scale) show the device after 0.01 ms, 0.02 ms and 0.03 ms, respectively.

manufacturing [24, 33]. A conceptual diagram of process modeling is shown in figure 8. Virtual fabrication starts with 2D layout and a description of the fabrication process and produces a virtual 3D geometric model of a sub-region of a wafer (such as a die or sub-region of a die). The resulting 3D model is similar to a 3D CAD model of a macro-scale mechanical device or system—it can be visualized, animated or serve as input to numerical simulation tools. Visualization has proven valuable in its own right, as will be demonstrated by several use cases described in subsequent sections based on the tool SEMulator3DTM [33, 34]. The input consists of the actual 2D layout together with a technology description. The layout can be provided in the widely used GDSII format or transmitted via a bridge from a layout tool such as Cadence VirtuosoTM . The technology description, in the form of a process file, is prepared with a graphical process editor. The user inputs information about the fabrication sequence and for each step in the sequence, specifies geometric parameters. The process step parameters for an isotropic etch step, for instance, would

include the mask name, the materials being etched, the depth of the etch, and an eccentricity ratio that defines the sidewall profile. The geometry related parameters are usually obtained by experimental metrology or TCAD simulations of single process steps. The layout and process file are supplied to a modeling engine, which builds a 3D model. The modeling engine uses voxels rather than traditional solid modeling techniques, which was described in section 1.5. In this section, process modeling by a voxel-based approach will be described more in detail with the help of typical examples that explain how it is used by MEMS manufacturers. 3.1. Virtual process development Process engineers often know what to expect from a specific well-characterized process step, such as deposition or etching, and thus can predict its geometrical effects. But it is much more difficult to anticipate the geometry that will be created when a new process flow is created by a novel combination 10


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Figure 7. Transient simulation of a RF switch representing the switching cycle. The corresponding 3D MEMS model is illustrated in figure 5.

of existing process steps, or when a specific physical design is subjected to the process flow. One example occurs when multiple etches are performed sequentially, using multiple mask layers; each etch depends strongly on the outcome of the previous one. Virtual manufacturing enables process engineers to quickly test a large number of process step combinations and novel process flows using multiple physical design patterns in a way that would not be possible in a real manufacturing environment, due to excessive time and cost. If the parameters for each process step can be calibrated through experimental measurements, process modeling results can be sufficiently accurate for performing trade-off studies. Moreover, each variation can be modeled in a few hours or less, allowing exploration of a wide process and design space. Our first example shows how DALSA Semiconductor used virtual fabrication before actual fabrication of a MEMSintegrated microphone (see figure 9). As input, DALSA used a process description in which all steps had been well characterized experimentally and a preliminary product design in the form of 2D layout that was supplied by their customer. The design required a large cavity in the sensing area. DALSA used process modeling software not only to evaluate the impact of various etch methods on the final die size, but also to show the impact of each choice on the previous and following process steps. This proved to be important because there were material stacks, which needed to be exposed to chemicals in different ways (i.e. dry or wet etch) and at different etch rates.

Figure 8. Conceptual diagram of voxel-based process modeling. 2D layout and parameterized process description are supplied to a modeling engine that builds a 3D voxel model for visualization and exports a surface mesh for use in other tools. 11


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Figure 9. Actual SEM images (a) versus 3D rendering produced by process modeling (b) of DRIE etched polysilicon edges. Pictures courtesy of DALSA [33].

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Figure 10. Result of a virtual and real manufacturing run in comparison. The SEM picture (a) shows the details of a SOI comb device with a pad versus its corresponding 3D virtual device (b). The manufacturing process is described in [35].

3.2. Design validation before mask tape-out One challenge for a designer to create a correct MEMS design is to understand the correlation between the 2D layout and the final 3D micromechanical structure. This requires more than a basic knowledge of the MEMS technology; the designer must understand how the 2D layout design is translated, step by step, into silicon by the fixed sequence of processing steps defined by the technology. A virtual manufacturing run allows the designer (or foundry) to check a new design before actual fabrication starts. Using this approach, the designer gains a better understanding of the technology and is able to discover design flaws in advance of mask tapeout. For example, X-FAB Semiconductor Foundries AG now routinely builds a virtual prototype for each new design [34]. The first masks are fabricated only after the virtual prototype has been visually examined and found acceptable, as shown in figure 10. This saves mask costs and avoids the time and expense of actual fab runs that would have ended with undesired results. Visual examination of a virtual prototype can reveal design flaws that can be corrected before masks are taped out. An example of a design flaw uncovered by examining a

Figure 11. Example of a design flaw in the DRIE mask for a mechanical structure discovered by using a virtual wafer processing run. The picture shows the affected location [34].

virtual prototype of an accelerometer built with X-FAB’s SOI technology is shown in figure 11. A crucial step in this SOI process is the shaping of the mechanical structure by a deep dry etch (DRIE). Prior to the 12


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(a)

(b)

Figure 12. SEM image (a) of a cross section of completely processed mechanical structure with eroded trenches at the wafer surface. Clearly visible are the gaps in the protection oxide and the resulting pocket-like cavities in the silicon of the mechanical structure. The virtual prototype image (b) shows the same process status, with the undesirable pocket-like cavity in the silicon.

DRIE step, an oxide mask is deposited on the wafer surface. The visible location is in the vicinity of an isolation trench. It can be seen that directly above the isolation trench contour there is no oxide cover and the metal (red) is exposed; see figure 11. This is not correct—the structure should have been completely covered by oxide. A direct comparison of a top view of the virtual prototype and the applied DRIE mask layout revealed that the cause is a misplaced polygon on the oxide mask. This errant polygon satisfied the 2D design rules; it only became apparent on visual inspection of the 3D virtual prototype. This design failure was found before the start of the real wafer processing and the design was corrected in time.

4. Conclusions This paper provided an overview of different modeling levels of abstraction and the CAD tools that are relevant to each of these levels. Multiple publications describe the validation of the mentioned MEMS behavioral models via other modeling techniques or measurement. Recent developments have been described and future trends for MEMS CAD tools are suggested, with the aim of addressing the challenging requirements for MEMS development. Among the recent innovations in the area of MEMS design tools, the paper then described two new tools in more detail. The first one provides a new MEMS+IC design methodology that enables MEMS and IC engineers to design and simulate in the same environment. This new methodology is expected to have substantial advantages over the traditional approach of transferring handcrafted or reducedorder behavioral models from the MEMS engineers to the IC engineers. First, the behavioral models of the MEMS device are sufficiently sophisticated to fully represent the MEMS behavior, capturing, for example, cross-coupling between the mechanical degrees of freedom. These behavioral models are more accurate than reduced-order models or look-up tables and have been validated via other modeling techniques and measurements. Second, the behavioral models and layout p-cells are fully parameterized both with respect to manufacturing-dependent variations and geometric attributes of the design, enabling design and yield optimization studies in the EDA environment. And third, the automatic hand-off a cross-linking between the MEMS and IC design environments eliminates inevitable human errors that arise in any manual hand-off process. The second tool is related to process modeling based on a voxel-based algorithm that is quite different from the solid modeling kernels employed in traditional CAD tools. This approach allows highly accurate virtual manufacturing. Although the process modeling approach is based strictly on geometric parameters and geometric operations, which are calibrated through empirical data, it has proven to

3.3. Virtual failure analysis At the beginning of the process development of its surfacemicromachining technology, X-FAB found irregularly eroded edges at the interface between the top surface of the mechanical structures and the DRIE trenches (figure 12(a)). A failure analysis showed that these irregular structures developed during the release etch step for the moveable mechanical structures. This isotropic etch step releases the moveable structures by etching into the handle wafer. During this step, the mechanical structure must be completely covered by protective oxide. Only the bottoms of the DRIE trenches can be exposed to the etchant. In practice, the thickness of the protective oxide is variable. In the worst case, it may become locally absent, exposing the silicon of the mechanical structure during the release etch. The weakest point with the thinnest oxide cover is at the intersection of the trench sidewalls and the wafer surface. At these edges, the release etch can remove the thin cover oxide, thus exposing the silicon of the mechanical structure to attack by the isotropic etch process. The presented failure model was verified by process emulation that took into account a more detailed deposition/etch geometry of the protective oxide. At exactly the experimentally observed locations, the same pocket-like etched cavity can be seen in the silicon in the virtual prototype (figure 12(b)). 13


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have significant advantages over conventional TCAD process simulation when it comes to modeling complete MEMS devices and process sequences in their entirety. Three application examples have been discussed. The first example described how the tool is used during process flow development. The second example showed how visualization of a virtual prototype uncovered a design flaw before mask tape out. The third showed how virtual prototyping confirmed the suspected cause of a process failure during process development. Virtual manufacturing can be employed during the complete product development cycle and not only improves efficiency and reduces cost, but supports ‘green IT’ strategy by reducing use of fabrication resources. Both tools represent a new generation of CAD tools to address the challenges of developing ever more sophisticated MEMS enabled systems.

[9] Schröpfer G et al 2009 A novel EDA-compatible methodology for design and simulation of MEMS with IC 7th GI/GMM/ITG-Workshop on Multi-Nature Systems (Ulm, Germany, 3 February 2009) [10] Schneider P, Reitz S, Bastian J and Schwarz P 2005 Combination of analytical models and order reduction methods for system level modeling of gyroscopes Nanotech 2005, MSM (Anaheim, CA, 8–12 May 2005) [11] Bechtold T 2005 Model order reduction of electro-thermal MEMS PhD Thesis University of Freiburg, Germany [12] Li X, Li P and Pileggi L T 2005 Parameterized interconnect order reduction with explicit-and-implicit multi-parameter moment matching for inter/intra-die variations Proc. ICCAD pp 806–12 [13] Kolchuzhin V, Mehner J, Gessner T and Dötzel W 2007 Application of higher order derivatives method to parametric simulation of MEMS Proc. EuroSimE (London, UK, 16–18 April 2007) pp 588–93 [14] Frangi A, Spinola G and Vigna B 2006 On the evaluation of damping in MEMS in the slip-flow regime Int. J. Numer. Methods Eng. 68 1031–51 [15] Frangi A 2005 A fast multipole implementation of the qualocation mixed-velocity–traction approach for exterior Stokes flows J. Eng. Anal. Bound. Elem. 29 1039–46 [16] Lorenz G, Greiner K and Breit S 2006 A hybrid modeling approach for multi-physics systems Proc. IMSTW 2006 (Edinburgh, UK, 22 June 2006) [17] Chowdhury S, Ahmadi M and Miller W C 2005 A comparison of pull-in voltage calculation methods for MEMS-based electrostatic actuator design 1st Int. Conf. on Sensing Technology (Palmerston North, New Zealand, 21–23 November 2005) pp 112–7 [18] Chowdhury S, Ahmadi M and Miller W C 2005 A closed-form model for the pull-in voltage of electrostatically actuated cantilever beams J. Micromech. Microeng. 15 756–63 [19] Zine-El-Abidine I and Yang P 2009 A tunable mechanical resonator J. Micromech. Microeng. 19 125004 [20] Casset F, Welham C, Durand C, Ollier E, Carpentier J F, Ancey P and A¨ıd M 2008 In-plane RF MEMS resonator simulation Proc. MEMSWAVE 2008 (Heraklion, Greece, 30 June–3 July 2008) [21] Judy M 2002 Computer-aided design (CAD) for integrated, microelectromechanical (MEMS) devices DARPA AFRL-IF-RS-TR-2002-176 Final Technical Report, approved for public release [22] Matova S, Elfrink R, van Schaijk R and Renaud M 2008 Modeling and validation of AlN piezoelectric harvesters Proc. Eurosensors 22th Conf. (Dresden, Germany, 7–10 September 2008) [23] Matova S, Hohlfeld D, van Schaijk R, Welham C J and Rouvillois S 2009 Experimental validation of aluminum nitride energy harvester model with power transfer circuit Proc. Eurosensors 23rd Conf. (Lausanne, Switzerland, 6–9 September 2009) pp 1443–6 [24] Schröpfer G, King D, Kennedy C and McNie M 2005 Advanced process emulation and circuit simulation for co-design of MEMS and CMOS devices Proc. DTIP (Montreux, Switzerland, 1–3 June 2005) [25] Gosálvez M A et al 2001 Anisotropic wet chemical etching of crystalline silicon: atomistic Monte Carlo simulations and experiments Appl. Surf. Sci. 178 7–26 [26] Parker E and Udeshi T 2003 Exploiting self-similarity in geometry for voxel based solid modeling Proc. 8th ACM Symp. on Solid Modeling and Applications (Seattle, WA, USA, June 2003) [27] Chapelle D and Bathe K J 2000 The mathematical shell model underlying general shell elements Int. J. Numer. Methods Eng. 48 289–313

Acknowledgments The authors acknowledge the help of Dennis Hohlfeld of IMTEK HOLST and Mark McNie of QinetiQ for providing measured samples for the validation of parametric behavior models, as well as Gisbert Hölzer of X-FAB Semiconductor and Maurice Delavosse of DALSA Semiconductor for providing the real-life examples of virtual manufacturing. This work was partially supported by the European Commission Framework 7 project CORONA.

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