ANSYS Microsystem Analysis Key Feature

Automated Capacitance Matrix Extraction

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. The capacitance change as a function of device displacement is important in designing both sensing and actuation circuitry.

CMATRIX is a macro automates the computation of a systems capacitance matrix. Is is applicable to any number of conductors, with any number of dielectric materials present. CMATRIX computes the self and mutual capacitance of each conductor and derives the system ground and lumped matrices. CMATRIX is useful for extracting lumped capacitance for use in a MEMS system level simulation. Consider the following MEMS comb drive:

The following image show the electric field contour plots for an analysis on a small section of the above comb drive resonator (two teeth of the comb are analyzed). The image shows a cross section through the teeth, which in this example includes a thin dielectric oxide layer coating. The animated contour plots alternate between the electric field used to compute the self and mutual capacitance.

The ground matrix is computed directly from the finite element analysis, for a two conductor system it is:

The lumped matrix is derived from the ground matrix, so for our two conductor system we have:

CMATRIX Procedure:

Create electrostatic finite element model of conductors and surrounding dielectric.
Conductors are assumed to be “perfect” conductors and therefore represent a constant potential surface. The solid interior of the conductor does not require a mesh.
Group the nodes (use ANSYS selection logic) on the surface of the conductors into individual node components. The node component names must share a common prefix, and the suffix should be a numbered sequentially, ascending. e.g. For three conductor system, conductor components names could be cond001,cond002, cond003.
Issue the SOLVE command.

The CMATRIX macro will run a series of Finite element simulations with alternating voltage loads to the conductors. From the stored electrostatic energy, the macro computes the Ground Matrix. From this matrix, the macro derives the Lumped Matrix which provides the self and mutual capacitance between conductors. These lumped values (Pmn) can be used as capacitors in a SPICE circuit simulation, or as input to the ANSYS TRANS126 electromechanical transducer element. The results can be listed on screen, output to a file, or accessed by the ANSYS APDL macro language.