Electrostatic field analysis is important in MEMS to determine both capacitance and electrostatic forces which are typically used to actuate devices such as comb drives. Coupling the electrostatics with the structural solution allows the actual electrostatic actuation of a MEMS device to be simulated, capturing the interdependencies of these these two physics. i.e. As a structure moves, the electrostatic field distribution will change, as will the force generated.
Six distinct methods for electrostatic -structural simulation are available in ANSYS Multiphysics, each method has its advantages and applications as follows:
Method |
Recommended Applications |
Physical Model Dimension |
Analysis Class |
Strengths |
Weaknesses |
| General purpose sequential coupled field tool. ectrostatic-structural-fluid and many others. Used to to compute load-deflection, pull-in, damping effects and hystersis. Large or small deformations | 2-D & 3-D |
Static (Load-deflection, Pull-in, hystersis) Time transient Pre-stress modal Pre-stress harmonic |
General tool for all geometry configurations, easy to use. |
Load vector coupled |
|
Electrostatic actuated devices with small delection, small gaps and large gap problems with small deformation. Applying pre-stress resulting from DC bias tuning etc. Time transient problems involving contact |
1D Functions with 2-D and 3-D FEA models |
Static (Load-deflection, Pull-in, hystersis) Time transient Pre-stress modal Pre-stress harmonic |
Easy to implement Fully coupled (matrix) solution Supports most MEMS analysis needs Can be used with other lumped elements , sub models or linked directly to FEA model. Uses EMTGEN macro auotmiates generation in 2-D and 3-D FEA models. |
Limited to small gap structures with known capacitance displacement relationship, or, for large gaps if the capacitance versus deflection charecteristic is first determined with CMATRIX etc. 1D only |
|
Electrostatic actuated devices such as comb drives, lateral resonators. Small and Large Deformation devices.
|
2-D |
Static (Load-deflection, Pull-in, hystersis)
Time transient Pre-stress modal Pre-stress harmonic |
Very accurate force calculations and structural coupling Fully coupled element formulation (matrix coupled) |
2-D only. Convergence is sensitive to the mesh descritization. less robust for devices that experience large deformation |
|
| Time-transient electrostatic-structural coupling. Sutiable for most electrostatic MEMS device applications. | 2-D & 3-D |
Static (Load-deflection, Pull-in, hystersis)
Time transient Pre-stress modal Pre-stress harmonic |
Modal basis functions used to create finite-element accurate analytic Reduced Order Macrmodel, may be exported in VHDL-A/MS format. Runs transient solutions in seconds. Can map full structural solution to original Finite Element mesh. |
Requires 3-D electrostatic-structural model. Computationally intensive to construct the macromodel |
|
Older / Obsolete Methods Still Supported |
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| General 3-d electrostatic-structural coupling to compute load-deflection, pull-in, and hystersis. | 2-D & 3-D |
Static (Load-deflection, Pull-in, hystersis) |
General tool for all geometry configurations, easy to use. Electrostatic and structural results are calculated and stored independently |
Replaced by Multi-field solver When using brick/hexa meshing, limited to small deflection geometry. Load vector coupled |
|
Easiest to apply to small deflection devices, but can certainly be applied to most electrostatic MEMS device applications. |
2-D & 3-D |
Static (Load-deflection, Pull-in, hystersis) Time transient Pre-stress modal Pre-stress harmonic |
Robust for large & small and gap/displacement devices Extremely flexible |
Requires advanced ANSYS knowled |
|
The Multi-field solver provides an easy-to-use framework to solve coupled field problems in many new markets and applications where previously there have been no solutions. It is a general purpose, automated sequential coupled physics solver applicable across all physics available in ANSYS Multiphysics. The Multi-field solver is an evolution of our successful fluid solid interaction (FSI) solver.
Key Features of the Multi-field Solver:
For MEMS applications the Multi-field solver supercedes ESSOLV. It can be used to perform coupled electrostatic-structural or electrostatic-structural-fluid analysis. It is applicable to large or small deformation, 2-D or 3-D, static or fully time transient classes of analysis.
ESSOLV is a sequential coupled electro-static structural macro. Is applicable for any 2-D, and smaller deformation 3-D analysis. Both structural & electrostatic domains are meshed. ESSOLV is an easy-to-use ANSYS command macro that automates a sequential coupled electrostatic structural 'static' simulation. ESSOLV is particularly useful for determining pull in voltages (structure snap through).
Structural (solid) and dielectric mesh of a deforming cantilever beam: Note how the electrostatic field mesh morphs to accommodate the deformed structure.
The following rollover image shows both the structural deformation and electro-static field changes computed by ESSOLV for a small rotation micromirror. The image shows a section through the mirror which is supported above two planar electrodes.
TRANS126 is a lumped or reduced order macro element that converts energy from an electrostatic domain into a structural domain (and vice versa), while also allowing for energy storage. e.g. It can be used as a variable capacitor with a user programmable capacitance versus displacement function. TRANS126 fully couples the structural and electrical domains, and is correctly referred to as an electromechanical transducer element (EMT). The element has up to two degrees of freedom at each node: translation in the nodal x, y, or z direction and electric potential (VOLT), and can solve for static or time transient behavior of electrostatic-structural devices. The TRANS126 element also employs a node-to-node gap feature so you can perform contact-type simulations where the structure contacts a plane (such as a ground plane). The TRANS126 is one of four lumped or Reduced Order Macro Model Elements that can be effectively used to reduce problems sizes and efficiently simulate relatively complex systems. The element is suitable for simulating the electromechanical response of devices such as electrostatic comb drive resonators / actuators, capacitive transducers, and RF switches. TRANS126 is commonly used to apply an electrostatic pre-stress to a structure in a pre-stressed modal analysis.
For example, the following linear comb drive resonator has two electrostatic comb drives:
By performing an electrostatic analysis on one comb drive, (or even one tooth pair of one comb drive)an electrostatic versus displacement function can be extracted (using CMATRIX) and associated with the TRANS126 element. The following diagram show the process schematically:
In our example, the end result being that a pair of TRANS126 transducer elements (labeled EMT1 and EMT2 in ANSYS) can replace the two comb drives in the original solid model, as shown in the following image:
The EMTGEN command is an ANSYS Macro that automatically generates a set of "distributed" TRANS126 elements between the surfaces of a pair of electrodes in a users model. One surface is typically the surface of a moving electrode (e.g .the undersifde of a mirco mirro), the other surface is a plane of nodes, typically representing an electrode on the substrate. Each TRANS126 element attaches to a surface node and to a corresponding node representing the plane. each generated TRANS126 element is assumed to be a parallel plate capacitor. The number of TRANS126 elements created is controlled by the mesh denisty on the selected surfaces.
With a distributed set of TRANS126 elements attached directly to the structure and a plane (such as a ground plane), you can perform a full range of coupled electrostatic-structural simulations, including:
TRANS109 is a triangular element used in fully coupled electromechanical analysis. It has three degrees of freedom at each node: translation in the nodal x and y directions (UX and UY) and electric potential (VOLT). This element is useful for simulating the electromechanical response of micro-electromechanical systems (MEMS) such as electrostatic comb drives and optical switches. TRANS109 is applicable to large signal static and transient analyses, but not to small signal modal or harmonic analyses (prestressed).
Voltage contours for a TRANS109 analysis of "three fingers" of a lateral comb drive resonator. The "white" regions are the solid comb fingers.
Only isotropic permittivity, independent of temperature, is allowed.The element works with 2-D mechanical elements assuming negligible strain in the thickness direction (plane strain). TRANS109 is not intended for use with with TRANS126, PLANE121, INFIN110, CIRCU94, CIRCU124, or CIRCU125.
Further details about TRANS109 can be found in our TRANS109 technical paper.
The ROM144 element is a 2-D or 3-D reduced order model of a coupled electrostatic-structural system. The element fully couples the electro-mechanical domains and represents a reduced order model suitable for use in finite element analysis as well as electromechanical circuit simulations. The element has ten modal degrees of freedom relating modal forces and modal displacements (EMF), ten voltage degrees of freedom relating electrical current and potential (VOLT) and, optionally, ten master nodes relating nodal forces to nodal displacements (UX).
The element is suitable for simulating the electromechanical response of micro-electromechanical devices (MEMS) such as clamped beams, micromirror actuators, and RF switches.The element is derived from a series of uncoupled structural and electrostatic domain simulations. The ROM144 element represents a complicated flexible structure whose nodes move mainly in one direction either X, Y or Z referred to the global Cartesian axes. For instance, torsional systems with angles less than ten degree or flexible bending of cantilevers or membranes obey those restrictions (pressure sensors, cantilever for AF microscopy, RF filter). Geometrical nonlinearities caused by stress stiffening or initial prestress are considered as well as multiple conductor systems.
Further details about ROM144 can be found on our seperate ROM144 feature page.
The soft air approach is the techinque used to model a field around a structure simply by setting the elastic modulus of the field material to a suitably low value. This technique was used by experienced ANSYS users before ANSYS Inc has introduced the more advanced and easier to use techinques described above (ESSOLV, TRANS126, TRAN109, ROM144). It has largely been replaced by these other techniques mainly because it is difficult to apply. When a structure undergoes large deformation, the user needs to control how the mesh in the field domain responds by using constraint equations. Another difficulty was establishing a suitable value of the field (air) elastic modulus. Arbitrarily low values could cause ill-conditioned matrices, but if the user makes the field (air) too stiff, its presence will produce erroneous results. Our in house experts recommend starting with a field elastic modulus that is about 8 orders smaller than the elastic moduli of structure. Although difficult to implement, once a model is set up using approach is is relativley robust.