COMSOL 6.4 - Normal Modes of a Biased Resonator

Normal Modes of a Biased Resonator — 3D Geometry from a GDS-File

When modeling a MEMS or semiconductor device with complex 3D structure, the geometry buildup can be time consuming, tedious, and error-prone. Buildup can require numerous primitive shapes in an assembly that does not correspond to how such a device would be fabricated, that is, through sequence of processes that deposit and pattern the distinct materials one layer at a time. This tutorial demonstrates how, with the ECAD Import, and Design Modules, we can emulate semiconductor fabrication processes to build 3D geometry more efficiently and in a way that reflects actual semiconductor or MEMS fabrication.

This tutorial recreates from a GDS file the device structure modeled in the Stationary Analysis of a Biased Resonator — 3D using operations available in the ECAD Import, and Design Modules. The original model was created from 15 rectangles specified by 60 parameters. In contrast, this tutorial builds the geometry layer-by-layer and requires only 6 parameters for specifying thicknesses of the layers which greatly simplifies future optimization studies.

After the geometry model is completed, the tutorial solves for the eigenmodes of the structure which can be compared to the results in the Normal Modes of a Biased Resonator — 3D.

Model Definition

The following is an outline of the steps that you can use to emulate basic MEMS or semiconductor fabrication processes using geometry operations. For the detailed instructions see the Modeling Instructions section.

Deposition of a Layer of Material over a Flat Surface

To create the geometry for a layer deposited over a flat surface, use an operation. Depending on the mask in GDS file, the resulting layer could be patterned or unpatterned. During the import the layer is extruded according to the specified thickness and elevation values. The substrate layer imported in this way is shown in Figure 1.

Figure 1: First imported layer: substrate.

The unpatterned nitride layer, imported as the second layer in the structure is shown Figure 2.

Figure 2: Second imported layer: nitride.

Deposition and Patterning of a Layer of Material over a Flat Surface

When a patterned layer is deposited over a flat surface, and the GDS file contains the mask for the layer when using positive photoresist, the imported layer can be directly extruded by the Import operation. The import then replicates the sequence of processes that include material deposition, photoresist coating and exposure, etching of the material, and the photoresist stripping. In the model, this is illustrated by importing layer 3 and layer 4 that correspond to polysilicon base layer and bottom electrode layer, respectively, as shown in Figure 3 and Figure 4

Figure 3: Third imported layer: patterned polysilicon base.

Figure 4: Fourth imported layer: patterned bottom electrode.

Conformal deposition of a layer of material over nonflat surface

Two layers in this structure are deposited over a nonflat surface: the sacrificial layer and the polysilicon layer for the beam. You can follow the same procedure for creating both layers. The following is an overview for how to create the sacrificial layer which covers the patterned polysilicon base, bottom electrode, and the exposed areas of the nitride layer. This layer is thus to be created over a nonflat surface, so the import operation cannot be used to extrude the layer mask. Instead, a sequence of geometry operations that includes , , , and should be used to emulate the deposition of the material.

First, use to select previously imported layers (geometry objects) for use in the following operation. Second, use to unite previously imported layers (geometry objects) so its faces (outer surfaces) could be selected in the following operation. Next, use to select the boundaries of the geometry to be used in the following as the faces to offset. Finally, use to ‘grow’ the layer over the selected boundaries. The result of these operations is shown in Figure 5.

Figure 5: Sacrificial layer. This layer is conformal to the underlying polysilicon base and bottom electrode.

Coating and patterning of virtual photoresist

The patterning of the conformal sacrificial layer can be done in two steps. First, create a virtual photoresist by importing the mask layer. This is equivalent to photoresist coating and lithographic patterning, as shown in Figure 6. In the subsequent step, use the Intersection operation to transfer the pattern of the virtual photoresist to the target layer. The virtual photoresist layer must penetrate the entire depth of the target layer, so this determines the elevation and thickness of the imported mask layer.

Figure 6: Patterned virtual photoresist layer.

Patterning of a layer of material over nonflat surface

By using the Intersection operation, you can transfer the photoresist pattern to the target sacrificial layer. This step is equivalent to an etch process followed by a photoresist strip. What remains is the patterned sacrificial layer, as seen in Figure 7.

Figure 7: Patterned sacrificial layer.

To obtain the patterned polysilicon beam deposited over the sacrificial layer and the exposed faces of the polysilicon base and nitride layers, follow the same steps for creating the sacrificial layer. The result is shown in Figure 8.

Figure 8: Patterned polysilicon beam.

Removal of a layer of material

To remove the sacrificial layer seen in Figure 9 use the Delete Entities operation. This step is equivalent to an isotropic etch process for releasing the structure. The completed half structure is shown in Figure 10.

Figure 9: The patterned sacrificial layer under the polysilicon beam is selected for removal.

Figure 10: Completed half of the geometry.

For this tutorial it is not enough to model half of the geometry using symmetry boundary conditions, because doing so excludes all the antisymmetric vibrational modes. The geometry is therefore mirrored prior to performing the eigenfrequency analysis.

Results and Discussion

Figure 11, Figure 12, and Figure 13 show the normal modes of the device, together with the eigenfrequencies, in the unbiased state. The lowest three normal modes are symmetric and anti-symmetric bending modes and a torsional mode. These results are similar to those in Normal Modes of a Biased Resonator — 3D.

Figure 11: Symmetric bending mode, fo = 8.4 MHz.

Figure 12: Antisymmetric bending mode, fo = 22.3 MHz.

Figure 13: Torsional mode, fo = 27.2 MHz.

MEMS_Module/Actuators/biased_resonator_3d_ecad_design

Modeling Instructions

Create a 3D model with a interface.

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Enter the parameters used for creating the geometry.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
t_sub	0.75[um]	7.5E-7 m	Thickness of substrate
t_nitride	0.15[um]	1.5E-7 m	Thickness of nitride layer
t_base	0.3[um]	3E-7 m	Thickness of polysilicon base layer
t_sl	0.2[um]	2E-7 m	Thickness of sacrificial layer
t_poly	1.9[um]	1.9E-6 m	Thickness of polysilicon layer
w_box	38.9[um]	3.89E-5 m	Width of box

Geometry 1

While it is possible to import all layers at the same time, it is easier to view the resulting 3D geometry if you import and build the layers one at a time.

In the window, expand the > node, then click .

In the window for , locate the section.

From the list, choose .

In addition to the ECAD Import Module functionality, the operation, which is available in the Design Module, is used to create the geometry. Make sure that the CAD kernel is used.

Locate the section. From the list, choose .

Import 1 = L1, Substrate

Start with importing the substrate.

In the toolbar, click