Download Lab 4: Design of RF MEMS switches using ANSYS multiphysics

Lab 4: Design of RF MEMS switches using ANSYS Multiphysics
1. Introduction
Verizon recently launched the first 3G, or third generation, wireless network in the
United States. Sprint and AT&T are rolling out similar broadband wireless services in
2002. But as wireless networks advance, so too are challenges for mobile phone
designers. RF (radio frequency) MEMS may help engineers add new capabilities and
improved power efficiency while keeping wireless devices small and affordable.
Micro-Electro-Mechanical System (MEMS) is a technology that enables the batch
fabrication of miniature mechanical structures, devices, and systems. The technology
leverages existing state-of-the-art integrated circuit (IC) fabrication technologies and
hence, also exhibits many advantages indigenous to IC technologies. A few of these
advantages include cost reduction through batch fabrication, device-to-device consistency
from advanced lithography and etching techniques, tremendous size, weight and thus
power reduction from general dimensional downscaling, and improved performance and
reliability by hermetic packaging. The above advantages demonstrate the great potential
of MEMS for the quickly growing RF applications.
Fig. 1. MEMS components inside a mobile handset on the drawing boards.
A number of fundamental building blocks have been manufactured successfully by
microfabrication techniques, including RF switches, tunable capacitors, high-Q inductors,
high-Q mechanical resonators and filters, and some representative microwave and
millimeter-wave components, as shown in Figure 1. The common characteristic of all
these devices is that electrical and mechanical domains are coupled. The device
performance and reliability has to be well designed and optimized before a batch
fabrication is started. FEA analysis offers a powerful tool for design and optimization.
ANSYS/Mulitphysics is newly released package from ANSYS dedicated to MEMS
devices and other coupled-field problems. ANSYS/Multiphysics has an extremely broad
physics capability directly applicable to many areas of microsystem design. Coupling
between these physics enables accurate, real world simulation of devices such as
electrostatic driven comb drives. For example, the ability to compute fluid structural
damping effects is critical in determining the switching response time of devices such as
micromirrors. A number of the features included in ANSYS/Multiphysics are listed
below and Figure 2 shows a sample result for the comb drive.
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Structural static, modal, harmonic, transient mechanical deformation.
Large deformation structural non-linearities.
Full contact with friction and thermal contact.
Linear & non-linear materials.
Buckling, creep.
Material properties: Temperature dependent, isotropic, orthotropic, anisotropic.
Tabular, polynomial and function of a function loads.
Plasticity, viscoplasticity, phase change.
Electrostatics & Magnetostatics.
Low and High Frequency Electromagnetics.
Circuit coupling - voltage & current driven.
Acoustic - Structural coupling.
Electrostatic-structural coupling.
Capacitance and electrostatic force extraction.
Fluid-Structural capability to evaluate damping effects on device response time.
Microfluidics: Newtonian & non Newtonian continuum flow
Free Surface VOF with temperature dependent surface tension.
Charged particle tracing in electrostatic and magnetostatic fields.
Electro-thermal-structural coupling.
Piezoelectric transducers: Direct coupled structural-electric physics. Full
isotropic, orthotropic parameters.
Fig. 2. Voltage distribution of a comb drive pair simulated by ANSYS/Multiphysics.
In this lab, the objective is to simulate the electrostatic and structural behaviors of RF
MEMS switches, and extract useful information for the purpose of MEMS switch design.
We’ll achieve this objective in the following activities.
1. Learn the general procedure of ANSYS, with a static analysis example.
2. Know the concept of sequentially coupled method used in the coupled-field problems,
in our case, the electrostatic-structural analysis, with a 2D analysis example.
3. Study the electrostatic behavior of a parallel-plate capacitor and compare with the
theoretical analysis.
4. Model the MEMS RF switch and predict the pull-in voltage.
Activity 1. ANSYS Basic Analysis Procedure
The ANSYS program has many finite element analysis capabilities, ranging from a
simple, linear, static analysis to a complex, nonlinear, transient dynamic analysis.
Activity 1 in this lab describes the basic analysis procedure by going through a sample
static analysis. Both GUI (Graphical User Interface) method and command method,
which are equivalent to each other, are demonstrated.
A typical ANSYS analysis has three distinct steps:
1. Build the model.
2. Apply loads and obtain the solution.
3. Review the results.
Fig3. Drawing of the example used in the analysis.
The example discusses the deformation of a steel cantilever beam under a vertical force
as shown in Figure 3. The ANSYS 2D beam element 'beam3' is used for modeling. The
ten-inch long beam is represented by ten beam3 elements connecting 11 nodes along the
global X-axis. Displacement boundary conditions at the left end restrain axial, vertical
and ThetaZ movement shown in Figure 4.
Fig. 4. FEM model of the cantilever beam.
From now on, let’s go through this sample analysis in two methods: GUI and command,
one by one.
GUI Method
You can launch ANSYS GUI in four easy steps: click Start Menu>All
Programs>Ansys 6.1>Run Interactive Now. And ANSYS GUI pops up like following.
---------------------------------BELOW IS ANSYS GUI STEPS---------------------------------Step 1: Set the analysis title
1. Choose menu path Utility Menu>File>Change Title.
2. Type the text "1d beam sample" and click on OK.
Step 2: Define parameters
1. Choose menu path Utility Menu>Parameters>Scalar Parameters. The Scalar
Parameters dialog box appears.
2. Type the following parameters and their values in the Selection field. Click on
Accept after you define each parameter. For example, first type “length=2000” in
the Selection field and then click on Accept. Continue entering the remaining
parameters and values in the same way.
length=10
depth=.375
width=.5
xsect=depth*width
inertiaz=(width*depth**3)/12
3. Click on Close.
4. Click on SAVE_DB on the ANSYS Toolbar.
Step 3: Define element types
1. Choose menu path Main Menu>Preprocessor>Element Type>
Add/Edit/Delete.
2.
3.
4.
5.
Click on Add. The Library of Element Types dialog box appears.
In the scroll box on the left, click once on "Structural Mass>Beam."
In the scroll box on the right, click once on "2D elastic 3."
Click on Close in the Element Types dialog box.
Step 4: Define Material Properties
1. Choose menu path Main Menu>Preprocessor>Material Props>Material
Models. The Define Material Model Behavior dialog box appears.
2. In the Material Models Available window, double-click on the following options:
Structural, Linear, Elastic, Isotropic. A dialog box appears.
3. Type the text 3.e7 in the EX field (for Young's modulus), and 0.0 for PRXY.
Click on OK. This sets Young's modulus and Poisson ratio.
4. Choose menu path Material>Exit to remove the Define Material Model Behavior
dialog box.
Step 5: Define Real Constants
1. Choose menu path Main Menu>Preprocessor>Real Constants>
Add/Edit/Delete.
2. Click on Add. The Element Type for Real Constants box appears.
3. Click on OK. The Real Constants for BEAM3 appears.
4. Type in the cross-sectional area, area moment of inertia and total beam height.
Leave the others blank or type zeros.
5. Click on Close in the Real Constants box.
Step 6: Create the model including key points, lines
1. Choose menu path Main Menu>Preprocessor>Modeling>
Create>Keypoints>In Active CS.
2. Type the text 1 in the Keypoint number field, 0, 0 ,0 in the X, Y, Z location.
3. Click on Apply, and type text 2 in keypoint number field, text length (parameters
defined above), 0, 0 in the X, Y, Z location.
4. Click on OK. Choose menu path Main Menu>Preprocessor>Modeling>
Create>Lines>Lines>Straight Line.
5. Create Straight Line window pops up. Select the two keypoints by mouse and a
straight line is made.
6. Click on OK.
Step 7: Mesh the model
1. Choose menu path Main Menu>Preprocessor>Meshing>Mesh Tool.
2. MeshTool window pops up. Click on Set button beside Lines. Element Size on
Picked Lines window pops up.
3. Highlight the line by mouse and click on OK. Element Size on Picked Lines box
appears. Type the text 10 in the No. of element divisions field.
4. Click on OK. Click Mesh button in MeshTool window. Mesh Lines window pops
up. Highlight the line and click OK.
5. Click on Close in MeshTool window.
Step 8: Apply Displacement Boundary Conditions
1. Choose menu path Main Menu>Preprocessor>Loads>Define
Loads>Apply>Structural>Displacement>on Nodes.
2. Pick Node 1 at x = 0, and click on OK.
3. Apply U, ROT on Nodes window appears. Select UX, UY, and ROTZ, type the
text 0 in the Displacement value field.
4. Click on OK.
Step 9: Apply Force Load
1. Choose menu path Main Menu>Preprocessor>Loads>Define
Loads>Apply>Structural>Force/Moment>On Nodes.
2. Pick Node 2 at x = length, and click on OK.
3. Apply F/M on Nodes window appears. Select FY in Direction of force/mom field,
type the text -50 in the force/moment value field.
4. Click on OK.
Step 10: Solve
1. Choose menu path Main Menu>Solution>Analysis Type>New Analysis.
2. New analysis window appears. Pick Static, click OK.
3. Choose menu path Main Menu>Solution>Solve>Current LS.
4. Choose File>Close to close the STATUS command window.
5. Click on OK on Solve Current Load Step window.
6. Yellow window with “Solution is done!” appears. Click on Close.
Step 11: Display Displacement Contour
1. Choose menu path Main Menu>General Postproc>Read Results>Last Set.
2. Choose menu path Main Menu>General Postproc>Plot Results>Contour
Plot>Nodal Solu.
3. Contour Nodal Solution Data window appears.
4. In the scroll box on the left, click once on "DOF solution"
5. In the scroll box on the right, click once on "Translation UY."
6. Click on OK.
--------------------------GUI method stops/Command method starts----------------------------Command or Batch Method
There are two ways to run command method. One uses the graphical interface. You can
type the text in the ANSYS Command Prompt in GUI or type in any text editor such as
notepad then copy into ANSYS Command Prompt. The other way is to launch batch
interface, similar to launch GUI. You simply click Start Menu>All Programs>Ansys
6.1>Batch. And ANSYS batch interface pops up like following. You need to type Ansys
command in text editor and save a file. You can select this file in Input File Source in
batch interface.
------------------------------------BELOW IS ANSYS COMMAND-----------------------------/title, 1d beam sample
!------------------parameters---------------length=10
depth=.375
width=.5
xsect=depth*width
!cross-sectional area
inertiaz=(width*depth**3)/12 !moment of inertia in z axis
!------preprocessor
/prep7
/com,------------element type-----------------et,1,beam3
/com,-----------material properties-----------mp, ex, 1, 3.e7
! Elastic modulus for material number 1 in psi
mp, prxy, 1, 0.
/com,-------------real constant----------------r, 1, xsect, inertiaz, depth
/com,----------------key point-----------------k,1,0,0
k,2,length,0
/com,---------------line and mesh--------------l,1,2
lsel,all
lesize,all,,,10
lmesh,all
/com,-----Displacement Boundary Conditions-----d, 1, ux, 0.0
! Displacement at node 1 in x-dir is zero
d, 1, uy, 0.0
! Displacement at node 1 in y-dir is zero
d, 1, rotz, 0.0
! Rotation about z axis at node 1 is zero
/com,----------------force load----------------f,2,fy,-50
!-------solution
/solu
! Select static load solution
antype, static
solve
save
finish
!-------post processor
/post1
set,last
plnsol,u,y,0,1
fini
Assignment:
Plot the deflection of the cantilever beam and compare with the analytical value.
Activity 2. Coupled-Field Analyses
A coupled-field analysis is an analysis that takes into account the interaction (coupling)
between two or more disciplines (fields) of engineering. An electrostatic-structural
analysis, for example, solves the interaction between the electric and structural fields.
There are two distinct methods for coupled-field analysis: sequential and direct. The
sequential method involves two or more sequential analyses, each belonging to a
different field. The direct method usually involves just one analysis that uses a coupledfield element type containing all necessary degrees of freedom. An example is MEMS
analysis with the TRANS126 element. In this lab, we’ll mainly discuss sequential
method.
Fig. 5. Data Flow for a Sequentially Coupled Physics Analysis (Using Physics
Environments)
The ANSYS program performs sequentially coupled physics analyses using the concept
of a physics environment. Physics environment file is an ASCII file, in which a lot of
analysis information is stored, such as element types and material properties. You can
perform a sequential coupled-field analysis using either an indirect method or the physics
environments. In this lab, the physics environments method is discussed. Figure 5 shows
a typical data flow for a sequential coupled-field analysis.
For many applications, a command macro can customize for the sequentially coupled
analyses. For instance, ESSOLV is the macro customized for the electrostatic-structural
analysis. It uses a sequential analysis using the physics environment approach. The macro
will automatically iterate between an electrostatic field solution and a structural solution,
transferring the electric load to the structure, until the field and the structure are in
equilibrium. The macro automatically updates the electrostatic field mesh to conform to
the structural displacements.
The procedure for preparing the problem for the ESSOLV command macro is as follows.
·
Build a solid model encompassing the entire electrostatic and structural domains.
Mesh both the structural and electrostatic domains.
·
Create the electrostatics physics environment by assigning appropriate element
types to the meshed region, defining material properties, defining solid model boundary
conditions and excitation, selecting the equation solver, etc. For the structural region, set
the element type to the “null” element (ET,,0). Write the electrostatics physics to a
physics file (PHYSICS,WRITE).
·
Clear the electrostatics physics (PHYSICS,CLEAR) and set up the physics for the
structural analysis by selecting the appropriate element type, defining material properties,
defining solid model boundary conditions and loads, selecting the equation solver and
options, etc. Write the structural physics to a physics file (PHYSICS,WRITE).
·
Prepare a solid model or element component for morphing (this step is optional).
For a 2-D analysis you may wish to group the areas of the electrostatic region that will
undergo mesh morphing into an area component. For 3-D you would group volumes into
a volume component.
·
If initial stress in the structure exists, prepare an initial stress file. In addition,
create a component of elements that are contained in the initial stress file. The format of
the initial stress file is documented in Initial Stress Loading in the ANSYS Basic
Analysis Guide.
·
Issue the ESSOLV command macro.
Fig. 6. A silicon beam above grounded gate. Voltage is applied across the beam and
ground.
In this example problem, a beam is positioned above a gate as shown in Figure 6. A
voltage is applied to the beam while the gate is grounded. The beam is deflected down to
the ground. The objective of the problem is to compute the total force on the beam and
the beam deflection.
Below is the input file.
!------------------parameters---------------bl=150
! Beam length (µm)
bh=2.0
! Beam height
glc=bl/2
! Center location of ground
gl=90
! Ground conductor length
gh=1.5
! Ground conductor thickness
gap=4.5
vltg=120
! Air gap
! Applied voltage
!------preprocessor
/prep7, Silicon beam deflection from an applied voltage
/com,------------element type and material properties-----------------et,1,121
et,2,121
emunit,epzro,8.854e-6
mp,perx,2,1
!
!
!
!
Temporary element for beam region
PLANE121 element for air region
Free-space permittivity, µMKSV units
Relative permittivity for air
/com,-------------create the model-------------------rectng,0,bl,gap,bh+gap
! Create model
rectng,glc-gl/2,glc+gl/2,-gh,0
rectng,-10,170,-20,30
aovlap,all
/com,--------assign the material type and mesh--------asel,s,area,,1
! Area for beam
aatt,1,,1
asel,s,area,,4
cm,air,area
aatt,2,,2
allsel,all
! Area for air elements
! Group air area into component
smrtsiz,2
amesh,1
mshape,1
amesh,4
! Mesh beam
! Mesh air with triangles
/com,---------apply electric boundary condition-------asel,s,area,,1
lsla,s
dl,all,,volt,vltg
! Apply voltage to beam
asel,s,area,,2
lsla,s
dl,all,,volt,0
! Ground conductor (not meshed)
/com,-----write the ELECTRIC physics environment-----allsel,all
et,1,0
! Set structure to null element type
physics,write,ELECTROS
! Write electrostatic physics file
physics,clear
! Clear Physics
/com,-----write the STRUCTURE physics environment-----et,1,82,,,2
! Define beam element type, 2 plane strain
et,2,0
! Set air to null element type
mp,ex,1,170e3
mp,nuxy,1,0.34
! Set Modulus
dl,4,,ux,0
dl,4,,uy,0
! Apply beam constraints
allsel,all
physics,write,STRUCTURE
finish
µN/(µm)**2
! Write structural physics file
!-------solution
/solu
ESSOLV,'ELECTROS','STRUCTURE',2,0,'air',,,,10
finish
! Solve coupled problem
!-------post processor
/post1
physics,read,ELECTROS
set,last
esel,s,mat,,2
etable,fx,fmag,x
etable,fy,fmag,y
ssum
finish
!
!
!
!
Read electrostatic physics file
Retrieve results
Select air elements
Retrieve electrostatic forces
! Sum forces
Assignment:
Change the voltage and remain other parameters, plot the deflection vs. voltage.
Activity 3. Parallel-Plate Capacitor
Before going ahead to work on the electromechanical behavior of the MEMS RF switch,
we need to verify the accuracy of the model. Parallel-plate capacitor is good sample. A
general model for the analytical description of electrostatically deflectable actuators is a
parallel-plate capacitor with the upper plate suspended by a spring as sketched in Figure
7.
k
x=d
x=0
Fig. 7. Model of a parallel-plate capacitor. K is the stiffness of the spring, d is the plate
separation without electrostatic interaction.
Increasing voltage attracts the upper plate down. At a critical point, the upper plate
collapses down to the fixed plate. This collapse is called pull-in. The formula between
voltage and corresponding gap is given as
U ( x) 
2k 2
x ( d  x)
0 A
(1)
where A is the plate area (2500 m2), k stiffness (2N/m), d initial gap (2.3 m), and 
vacuum permittivity (8.8510-12 F/m).
Assignment:
1. Derive the equation (1).
2. Predict the pull-in voltage and explain why.
3. Plot the displacement as a function of applied voltage.
Below is the ANSYS input file.
/prep7
/com,-----define the model geometry--------w_plate=50
h_plate=1
x0=0
y0=0
z0=0
z1=z0+1
z2=z1+2.3
z3=z2+1
z4=z3+5
vltg=10
/com,---define key point, line, area--------k,1,-w_plate/2,w_plate/2,z4
k,2,w_plate/2,w_plate/2,z4
k,3,w_plate/2,-w_plate/2,z4
k,4,-w_plate/2,-w_plate/2,z4
k,5,-w_plate/2,w_plate/2,z3
k,6,w_plate/2,w_plate/2,z3
k,7,w_plate/2,-w_plate/2,z3
k,8,-w_plate/2,-w_plate/2,z3
k,9,-w_plate/2,w_plate/2,z2
k,10,-w_plate/2,w_plate/2,z1
k,11,-w_plate/2,w_plate/2,z0
l,1,5
l,2,6
l,3,7
l,4,8
l,5,9
l,9,10
l,10,11
a,5,6,7,8
asel,s,,,1
vdrag,1,,,,,,5,6,7
!extrude into volumes
nummrg,all,1e-6
numcmp,all
lsel,s,loc,z,z1+1e-6,z2-1e-6
lesize,all,,,8
lsel,s,loc,z,z2+1e-6,z3-1e-6
lesize,all,,,2
lsel,s,loc,z,z3+1e-6,z4-1e-6
lesize,all,,,1
alls
/com,--------------meshing------------------et,1,solid95
et,2,solid122
et,3,combin14
emunit,epzro,8.854e-6
mp,ex,1,170e3
mp,nuxy,1,0.34
mp,perx,2,1
r,3,.5
vsel,s,loc,z,z2+1e-6,z3-1e-6
vatt,1,,1
vmesh,all
vsel,s,loc,z,z1+1e-6,z2-1e-6
cm,air,volu
vatt,2,,2
vmesh,all
lsel,s,line,,1,4
keyopt,3,3,0
latt,3,3
lmesh,all
allsel,all
/com,-------------boundary condition-------!vsel,s,loc,z,z2+1e-6,z3-1e-6
!vsel,s,,,1
!aslv,s
asel,s,area,,6
da,all,volt,vltg
asel,s,area,,11
da,all,volt,0
/com,---------ESSOLV macro------------------
!use macro ESSOLV
shpp,off
allsel,all
et,1,0
! Set structure to null element type
et,3,0
physics,write,ELECTROS
! Write electrostatic physics file
physics,clear
! Clear Physics
et,1,solid95
et,3,combin14
et,2,0
! Define beam elementy type
! Set air to null element type
mp,ex,1,170e3
mp,nuxy,1,0.34
! Set Modulus µN/(µm)**2
dk,1,all,0
dk,2,all,0
dk,3,all,0
dk,4,all,0
asel,s,area,,2,5
da,all,ux,0,1
da,all,uy,0,1
allsel,all
finish
physics,write,STRUCTURE
! Write structural physics file
ESSOLV,'ELECTROS','STRUCTURE',3,0,'air',,,,100 ! Solve coupled-field problem
finish
/post1
zmax=uz(467)
/output,test,dat,,append
*msg,info,vltg,zmax
%g %g
/out
finish
Assignment:
Change the voltage and remain other parameters, plot the deflection vs. voltage.
Activity 4. MEMS RF Switch
You should feel now you are able to model a real device and conduct the ANSYS/
Multiphysics analysis. A good application is MEMS RF switch, which is similar to the
2D analysis we did in Activity 2 but is 3D. But 3D analysis is not strange to us now. We
have done the 3D analysis of parallel-plate capacitor in Activity 3. In this activity, the
geometrical parameters of the switch are given, and you need to generate the model and
start the analysis. You need to submit the input file with the plot of deflection against
voltage and predicted pull-in voltage.
Reference:
[1] Small Times News
(http://www.smalltimes.com/document_display.cfm?document_id=3053)
[2] J. J. Yao, “RF MEMS from a device perspective”, J. Micromech. Microeng., Vol. 10,
pp. R9-R38, 2000.
[3] ANSYS MEMS Initiative (http://www.ansys.com/ansys/mems/)