*Product Feature*

*An EM Simulator for MEMS and Real Life MMICs *

*MEM Research Spoltore, Pescara, Italy *

Generally speaking, there are two large families of commercially available electromagnetic (EM) solvers. The first one is a general-purpose set, covering the analysis of arbitrarily shaped structures and using finite elements or differences, either in the frequency- or time-domains, or some variations of these principles. The second one, based on the method of moments (MoM), and generally developed in a spectral domain (SD) formulation, includes programs expressly designed for the efficient analysis of printed planar structures. While the first solver family is in principle able to address virtually any problem, it is faced with severe difficulties whenever the structure under analysis has a critical aspect-ratio, that is, the ratio between the largest and smallest dimensions involved. This condition is often encountered when addressing planar multilayer structures. Such limitation stems from the need of discretizing, that is, dividing in sub-domains (mesh), the whole space surrounding the structure. Smaller objects impose a constraint on the sub-domain dimensions. This is true even when graded meshes are allowed.

While the second family solver lacks such generality, it provides instead unpaired performance when addressing planar structures - according to the underlying technique, only surface electric currents over infinitely thin conductors (or magnetic currents over gaps) have to be subdivided. Information about the surrounding space is embedded within an operator known as the Green function. The Green function is by definition an operator linking an arbitrary current distribution to the electric and magnetic fields. While obtaining such an operator requires additional preprocessing, the efficiency and accuracy are excellent, as the number of unknowns in the final system is greatly reduced. A drawback is that only infinitely thin conductors are normally handled (hence they are indicated as 2.5D methods), even though this limitation is partially circumvented by some devices.

**Fig. 1 The shunt RF MEM switch reported by Pacheco, et al.**

**Real Life Problems **

The two software families seem to cover the entire set of EM problems. However, monolithic microwave integrated circuits (MMIC) and microelectromechanical systems (MEMS) are generally a challenge for both families, lying between the two classes of problems each of them addresses. They are on the one hand not completely planar, in the sense that conductor (and dielectric) thickness is often of the same order of magnitude as other dimensions, while on the other hand, having definite critical aspect-ratios. A couple of examples will clarify the scenario. A coplanar waveguide (CPW) on a modulation-doped substrate (MOD), such as the ones involved in field effect transistors (MOD-FET), may be engineered on a bulk substrate several hundred microns thick. At the same time the structure may support a thin so-called two-dimensional electron gas (2DEG) that acts as a lossy layer with thickness in the order of 0.1 micron, while conductors may be a few microns spaced and thick. More generally, MMICs feature complex multilayer structures - hence critical aspect-ratios - while not being reasonably planar.

An equally interesting example is that of a capacitive MEM shunt switch. In its simpler configuration, it is basically a CPW with a bridge, so that an electrostatic potential may snap down to create a high shunt capacitance able to reflect an incoming RF signal. In order to avoid a static short-circuit in this condition, a passivation dielectric area, with thickness ranging around 0.1 mm, is grown under the bridge. At the same time conductors may be a few microns thick.

MEMS are attracting more and more attention, as witnessed by the number of technical papers dedicated to them and the investment in MEMS R&D. According to MEMS Clearing House (www.memsnet.org): "...MEMS is destined to become a hallmark 21st-century manufacturing technology with numerous and diverse applications having a dramatic impact on everything from aerospace technology to biotechnology." They appear to be a virtual panacea in high frequency design, providing significant reductions in power consumption and signal loss, as needed in order to shrink devices. In spite of this, advanced RF simulation and modeling tools for MEMS design are still needed.

**Fig. 2 An EM3DS model of the MEM switch.**

**EM3DS Foundations **

In this context EM3DS is a novel EM simulator, conceived to address those problems lying to some extent between the capabilities of the two aforementioned families. Its underlying principle, the generalized transverse resonance-diffraction (GTRD) approach, was developed to address the EM modeling of active linear devices. Generally speaking, its EM engine may be classified as a 3D MoM approach specifically developed in order to take advantage of the peculiarities of multilayer quasi-planar structures.

EM3DS uses volume currents to model conductors and dielectric discontinuities^{1} rather than surface currents. Using volume currents involves an additional computational load, with respect to traditional 2.5D MoM simulators, but several analytical techniques, including its asymptotic accelerator, are implemented so as to reduce the required resources to those normally required by 2.5D methods.

** Figure 1 ** shows the shunt RF MEM switch reported by Pacheco, et al.,

^{2}while

**shows its model in EM3DS.**

*Figure 2*Results are shown in ** Figure 3 ** for the transmitting position (switch unactuated) and the reflecting state, including the comparison with the measurements.

^{2}

**shows the current distributions over the underlying CPW at 1 and 40 GHz, where the effect of the high bridge capacitance is visually evident.**

*Figure 4*

**Fig. 3 Calculated and measured S-parameters for the (a) transmitting and (b) reflecting states.**

**Performances and Features **

This kind of agreement is almost typical for EM3DS in MEMS analysis. The simulation takes only a few minutes on a desktop computer. The same analysis could require hours, if not days, to be performed by a space-discretizing technique. The best performance of EM3DS is obtained for 3D structures involving complex substrates, those structures known to be a challenge to available commercial software packages. Its frequency-domain formulation ensures reliable results even for strongly resonant structures that usually prove to be very difficult for time-domain approaches. At the same time a new algorithm, an asymptotic estimator, guarantees reduced computational time for broadband simulations.

EM3DS is designed to be run on a PC under the Microsoft Windows platform, with an advanced and professional graphical user interface (GUI). A key feature is that the user interface guarantees simple understanding and access to the program capabilities. Developed "ab initio" as an object-oriented tool, the time required to properly use EM3DS is usually very short.

**Fig. 4 Current distributed on the switch CPW at (a) 1 and (b) 40 GHz.**

The structure to be modelled is entered by using a highly intuitive editor - the user defines a dielectric stack by selecting a set of layers with desired properties. Each dielectric layer is accessed by the editor. The user selects a layer and enters the items that it should contain. The material constituting each item may be arbitrarly defined, allowing thick lossy conductors as well as dielectric discontinuities to be modeled. In the previous MEM example, a dielectric brick is defined in order to model the silicon nitride region preventing the bridge from sticking over the CPW in its actuated position.

The object thickness is the same of the embedding layer - every object, unlike in 2.5D approaches, has its finite thickness. A 3D view, one that the user can rotate, zoom and handle as desired, is updated in real-time. A set of tools are also available in order to simplify entering complex structures (circular spirals, rings and circles, for example).

EM3DS also includes GDSII and DXF translators allowing the simulator to reuse the design of other sources, or simply using external editors. There is no grid constraining the user design. This feature eases matching real dimensions of the structure being imported.

Once the desired structure is completed, the user has only to select a set of excitation points (ports) and the frequency range, and then to press a Go button. S-parameters, as well as a number of additional measurements (Z and Y parameters, quality factor and characteristic parameters of the feeding lines), are available. Parameters may be updated in real-time, and the user can see results during computation. Raw and calibrated results are always available.

A powerful post-processor enables the simulator to display network parameters in multiple charts, either rectangular or Smith plots. Network parameters may be exported and imported as Touchstone text files, while each view may be copied into the clipboard so as to be used by other applications, as well as exported in standard graphical formats (BMP, EMF). At the end of a simulation, the volume current distribution may be displayed, animated in time or frequency, and animations may be saved in standard formats (AVI, GIF). An intuitive Data Browser allows simple access to the multiple graphs and external data.

Post-processing includes a quick Spice-model extractor for electrically short devices, a linear circuit solver allowing lumped and distributed elements to be connected to the EM simulation, and TRL numerical de-embedding for rectangular waveguide structures.

**Fig. 5 A double MEM switch with tuning line.**

**Some Examples**

** Figure 5 ** shows one more MEM example - a double MEM capacitive switch.

^{3}It includes two membranes and a high impedance line selected in order to lower reflections over the band of the switch.

**shows a comparison between EM3DS results and experimental ones in the transmitting position. These simulations take advantage of several features of EM3DS, such as the ability to deal with conductors having finite thickness and losses, and to handle dielectric blocks, along with an effective built-in de-embedding algorithm.**

*Figure 6*

**Fig. 6 S-parameter results for the double MEM switch in the transmitting position.**

The capabilities of EM3DS may also be successfully used to address other quasi-planar and planar structures. ** Figure 7 ** depicts a three-pole low pass filter obtained using a photonic band-gap structure.

^{4}It is an interesting structure since it involves slots in the ground plane, a microstrip structure and radiation losses. The comparison with the experimental results is reported in

**, showing a satisfactory agreement even in this case.**

*Figure 8*

**Fig. 7 A low pass PBG filter.**

Coplanar waveguides with very thick conductors (if compared to the interelectrode spacing), as encountered in electro-optical modulators, are a natural test-bed for EM3DS. In this case, neglecting the conductor thickness as in 2.5D approaches results in errors ranging near 50 percent (or more). On the other hand, using space-discretizing-based tools require large computational time, owing to the complex substrates involved.

As a final note, due to its 3D nature and to a new calibration technique, EM3DS is also able to handle a class of two-port waveguide components.

**Fig. 8 S-parameters for the low pass PBG filter.**

**Conclusion **

A new, low cost software package, implementing cutting-edge theory and addressing the 3D EM analysis of structures involving complex substrates, as usually encountered in common MMIC design, has been introduced.

Additional details about EM3DS may be found at the company's Web site at www.memresearch.com, where a complete version (including manuals and examples) may be downloaded and activated for a 60-day trial period. Moreover, a completely free companion of EM3DS, Free EM3DS (no time-limitation but functionally limited), is also available.

**References**

1. M. Farina and T. Rozzi, "A 3D Integral Equation-based Approach to Analysis of Real Life MMICs: Application to Microelectromechanical Systems,"* IEEE Transactions on Microwave Theory and Techniques* , Vol. 49, No. 12, December 2001, pp. 2235-2240.

2. S.P. Pacheco, L.P.B. Katehi and C.T.C. Nguyen, "Design of Low Actuation Voltage RF MEMS Switch,"* IEEE 2000 International Microwave Symposium Proceedings* , Boston, MA, June 11-16, 2000.

3. J.B. Muldavin and G.M. Rebeiz, "High Isolation CPW MEMS Shunt Switches - Part II: Design," *IEEE Transactions on Microwave Theory and Techniques* , Vol. 48. No. 6, June 2000, pp. 1053-1056.

4. D. Ahn, et al., "A Design of the Low Pass Filter Using the Novel Microstrip Defected Ground Structure," *IEEE Transactions on Microwave Theory and Techniques* , Vol. 49, No. 1, January 2001, pp. 86-96.

*MEM Research, Spoltore, Pescara, Italy +39 347 8279009. *

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