COMSOL 6.4 - Aluminum Nitride Lamb Wave Resonator

Aluminum Nitride Lamb Wave Resonator — 3D

This tutorial demonstrates how to model an aluminum nitride Lamb wave resonator in 3D. The Lamb wave resonator (LWR) is an important building block in circuits used in mobile communication systems. Its operational characteristics are controlled by the piezoelectric material properties, the pattern of thin conducting layer on its surface, and its dimensions. Using the Piezoeletricity multiphysics interface and material models from the Piezoelectric Material Library, you can create a digital prototype of an LWR.

Model Definition

In this tutorial, the LWR is an aluminum nitride (piezoelectric ) block with an interdigitated electrode (IDE) on its surface as shown in Figure 1. Suspended from four anchor points, the 0.4 μm piezoelectric block responds to AC excitation through the platinum IDE (80 nm). The LWR is designed to resonate at 8 GHz. The thin platinum layer was specified using the Thin Film feature in the Solid Mechanics Interface.

The LWR geometric parameters are summarized in the first table in the Modeling Instructions section so the geometry can be easily modified for design optimization. The geometry is rebuilt automatically when geometric parameters are changed if the rules are followed. For example, n must be chosen so (n+1)/4 is an integer, or n = {3, 7, 11, …}. Also, the overlap parameter op should be smaller than the length of the finger l, that is, op < l. Keep in mind, however, that changes in the geometry will shift the resonant frequency. An outline of the steps in the fabrication of an actual LWR can be found in Ref. 1.

In this model, the fully coupled structural and electrostatic equations are solved in the piezoelectric domain. The model also includes mechanical loss through an isotropic structural loss factor of 0.002 for the piezoelectric and the platinum layers.

In this tutorial we are interested in the symmetric S0 mode, which, in typical applications, results in maximal electromechanical coupling efficiency. Because of the symmetry of the device structure and the symmetry of the S0 mode, only a half of the device needs to be modeled. This reduces computational time, which is important because this model requires a fine mesh (Figure 2) to compute accurate eigenmodes.

This tutorial shows you the setup of Eigenfrequency and Frequency Domain studies. In the Eigenfrequency study you investigate the eigenmodes of the structure to find the S0 mode. In the subsequent Frequency Domain study, a 1 V drive signal is applied to the Signal electrode and the resonator’s frequency response from 7.95 to 8.05 GHz is analyzed.

Figure 1: The geometric model of one half of the Lamb wave resonator. The interdigitated electrodes (IDE) are patterned from a thin layer of platinum (80 nm) on the top surface of the piezoelectric aluminum nitride block (0.4 μm).

Figure 2: The top surface of the LWR is meshed using Free Quad with maximum mesh size of 0.1 μm for accuracy and smooth surface plots.

Results and Discussion

Figure 3 shows the displacement in the z direction for the S0 mode at 7.993 GHz. In high-frequency resonant devices such as LWRs, the Eigenfrequency study returns many extraneous solutions very close to the mode of interest. Only through visual inspection can you identify the correct mode from among the spurious modes. Figure 4 shows the solid displacement across the XZ cut plane through the center of the resonator to verify the S0 mode.

Figure 3: 3D plot showing the pattern of the displacement along the z-axis for the S0 mode at 7.99 GHz.

Figure 4: Slice plot of solid displacement across the XZ cut plane through the center of the resonator for the S0 mode at 7.99 GHz.

Figure 5 is a log plot of the admittance magnitude versus frequency from 7.95 to 8.05 GHz. The plot is annotated with the positions of resonance and anti-resonance peaks for the calculation of the electromechanical coupling coefficient.

Figure 5: Admittance versus frequency.

The frequency response yields important information relating to device performance such as the effective electromechanical coupling coefficient given by

where fs and fp are the resonance and anti-resonance frequencies, respectively. With fs = 7.99 and fp = 8.04, kt2 = 1.5%. The effective electromechanical coupling coefficient is known to be a measure of transduction efficiency for conversion of electrical into mechanical energy.

Reference

1. J. Zou, C.M. Lin, A. Gao, and A.P. Pisano, “The Multi-Mode Resonance in AlN Lamb Wave Resonators,” J. Microelectromech. Syst., vol. 27, no. 6, pp. 973–84, 2018.

MEMS_Module/Piezoelectric_Devices/aln_lamb_wave_resonator_3d

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

Start by creating a new 3D model with a multiphysics interface.

In the tree, select > > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

Use microns as the geometry unit.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Define and specify the parameters of the model.

Global Definitions

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
tp	0.4[um]	4E-7 m	Thickness of piezoelectric layer
l	15[um]	1.5E-5 m	Length of finger
wf	0.2[um]	2E-7 m	Width of finger
op	14.6[um]	1.46E-5 m	Length of overlap, for op less than l
dy	(l-op)/2	2E-7 m	Electrode separation
n	11	11	Number of fingers, where (n+1)/4 = integer
we	0.2[um]	2E-7 m	Width of edge
la	0.4[um]	4E-7 m	Length of anchor
Vapp	1[V]	1 V	Applied voltage
eta0	2.0e-3	0.002	Loss factor for electrode layer
eta1	2.0e-3	0.002	Loss factor for piezoelectric layer

Create the geometry model for half of the lamb wave resonator.

Geometry 1

Work Plane 1 (wp1)

In the window, expand the > node.

Right-click and choose .

Work Plane 1 (wp1) > Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type wf.

In the text field, type l.

Locate the section. From the list, choose .

In the text field, type dy/2.

Work Plane 1 (wp1) > Array 1 (arr1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type (n+1)/4.

Locate the section. In the text field, type 4*wf.

Work Plane 1 (wp1) > Move 1 (mov1)

In the toolbar, click

and choose .

Click the

button in the toolbar.

In the window for , locate the section.

Select the checkbox.

Locate the section. In the text field, type 2*wf.

In the text field, type -dy.

Work Plane 1 (wp1) > Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type (n-1/2)*wf+we.

In the text field, type 2*wf.

Locate the section. In the text field, type (l+dy)/2.

Work Plane 1 (wp1) > Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2*we.

In the text field, type la.

Locate the section. In the text field, type (n-1/2)*wf-we.

In the text field, type (l+dy)/2+2*wf.

Work Plane 1 (wp1) > Mirror 1 (mir1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Select the checkbox.

Locate the section. In the text field, type 0.

In the text field, type -1.

Work Plane 1 (wp1) > Rectangle 4 (r4)

In the toolbar, click

In the window for , locate the section.

In the text field, type (n+1/2)*wf.

In the text field, type l+dy.

Locate the section. From the list, choose .

In the text field, type (n+1/2)*wf/2.

Work Plane 1 (wp1) > Partition Objects 1 (par1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Click to select the

toggle button for .

Select the object only.

Select the checkbox.

Work Plane 1 (wp1) > Delete Entities 1 (del1)

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

On the object , select Domain 1 only.

Extrude 1 (ext1)

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (µm)
tp

Click

Click the

button in the toolbar.

Define selections for the electrodes and other boundaries. This will make specifying the material models and physics interface settings easier.

Definitions

Signal

In the window, expand the > node.

Right-click and choose > .

In the window for , type Signal in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type -l/2.

In the text field, type tp-0.01.

Locate the section. From the list, choose .

Ground

Right-click and choose .

In the window for , type Ground in the text field.

Locate the section. In the text field, type -Inf.

In the text field, type l/2.

Electrodes

In the toolbar, click

In the window for , type Electrodes in the text field.

Locate the section. From the list, choose .

Locate the section. Under , click

In the dialog, in the list, choose and .

Click .

Symmetry

In the toolbar, click

In the window for , type Symmetry in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type 0.

Locate the section. From the list, choose .

Top Surface

In the toolbar, click

In the window for , type Top Surface in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type tp-0.01.

Locate the section. From the list, choose .

Device

In the toolbar, click

In the window for , type Device in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type -((l+dy)/2+2*wf+la)+0.01.

In the text field, type (l+dy)/2+2*wf+la-0.01.

Fixed Constraints

In the toolbar, click

In the window for , type Fixed Constraints in the text field.

Locate the section. From the list, choose .

Locate the section. Under , click

In the dialog, select in the list.

Click .

Specify the settings for the interface.

Electrostatics (es)

Boundary Terminal 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the V0 text field, type Vapp.

Ground 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Symmetry Plane 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Specify the settings for the interface.

Solid Mechanics (solid)

Piezoelectric Material 1

In the window, under > click .

Mechanical Damping 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Thin Layer 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Lth text field, type 80[nm].

Linear Elastic Material 1

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

Damping 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Fixed Constraint 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Add materials to the model and specify the regions they belong to.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > > .

Click the button in the window toolbar.

Materials

Pt - Platinum (mat1)

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Isotropic structural loss factor	eta_s	eta0	1	Basic

Add Material

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Aluminum Nitride (mat2)

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Isotropic structural loss factor	eta_s	eta1	1	Basic

Create the mesh for the model.

Mesh 1

Free Quad 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Size 1

Right-click and choose .

In the window for , locate the section.

Click the button.

Locate the section.

Select the checkbox. In the associated text field, type 0.1.

Click

Swept 1

In the toolbar, click

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 3.

Click

Set up an study to search for an eigenfrequency around 8 GHz.

Eigenfrequency

In the window, click .

In the window for , type Eigenfrequency in the text field.

Locate the section. Clear the checkbox.

Step 1: Eigenfrequency

In the window, under click .

In the window for , locate the section.

Select the checkbox. In the associated text field, type 20.

From the list, choose .

In the text field, type 8.

In the toolbar, click

Add a dataset to complete the device structure. This dataset will be used to plot the result of the study.

Results

Mirror 3D 1

In the window, expand the node.

Right-click > and choose > .

In the window for , click

With the solution from the study, create a 3D plot to display the shape of the eigenmode at 8 GHz. Use the dataset previously created.

Mode Shape

In the toolbar, click

In the window for , type Mode Shape in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Clear the checkbox.

Surface 1

Right-click and choose .

In the window for , locate the section.

In the text field, type w.

Select the checkbox.

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

Click the

button in the toolbar.

With the solution from the study, create a plot to display the eigenmode in the xz cut plane through the center.

Mode Shape

In the window, click .

Mode Shape, Center XZ Plane

In the toolbar, click

In the window for , type Mode Shape, Center XZ Plane in the text field.

Locate the section. From the list, choose .

From the list, choose .

Slice 1

Right-click and choose .

In the window for , locate the section.

In the text field, type solid.disp.

Select the checkbox.

Locate the section. From the list, choose .

In the text field, type 1.

Locate the section. From the list, choose .

In the text field, type 15.

Mode Shape, Center XZ Plane

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Click the

button in the toolbar.

Set up a study with a range that includes the features of interest, for example, resonance and anti-resonance peaks. Disable the option to generate default plots from this study.

Add Study

In the toolbar, click