Lecture 5 Analysis and design of electro-thermally actuated MEMS

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Lecture 5Analysis and design of
electro-thermally actuated MEMS

• Solving three sets of coupled partial
  differential equations and its implications in
  design.

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Contents

• Overview of thermal actuators
• Principle of electro-thermal-compliant (ETC)
  actuation
• Analysis issues
• Thermal modeling
• Design issues
• Examples

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Bimorph effect is used widely
Heating is easily achieved in MEMS with Joule
heating.
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Electro-thermal actuation using a single material
structure
Guckel, H., Klein, J., Christenson, T., Skrobis,
K., Laudon, M., and Lovell, E.G., 1992,
Thermomagnetic Metal Flexure Actuators,
Technical Digest of Solid State Sensors and
Actuators Workshop, Hilton-Head Island, SC, 1992,
p 73. Comtois, J. and Bright, V, 1996, Surface
Micromachined Polysilicon Thermal Actuator Arrays
and Applications, Technical Digest of
Solid-State Sensor and Actuator Workshop, Hilton
Head Island, SC, June 1996, pp. 174-177. Lerch,
P, Slimane, C.K., Romanwicz, B., and Renaud, P,
1996, Modelization and characterization of
asymmetrical thermal micro-actuators, J.
Micromechanics and Microengineering, Vol. 6,
1996, pp. 134-137 Moulton, T., 1997, Analysis
and design of Electro-Thermal-Compliant micro
devices Center for Sensor Technologies at the
university of Pennsylvania technical report
TR-CST31DEC97, pp.13-26. Keller, C.G. and Howe,
R.T., 1997, Hexsil Tweezers for Teleoperated
Micro-Assembly, Proc. 10th Annual International
Workshop on Micro-Electro-Mechanical Systems
(MEMS '97), Nagoya, Japan, January 26-30, 1997,
pp. 72-77. Pan, C. S. and Hsu, W., 1997, An
electro-thermally and laterally driven
polysilicon microactuator, J. Micromechanics and
Microengineering, 7 (1997), pp. 7-13. Sigmund,
O., Topology Optimization in Multiphysics
Problems, Proceedings of the 7th
AIAA/USAF/NASA/ISSMO Symposium, Vol. 3, St Louis,
August 1998, pp. 1492-1500. Cragun, R. and
Howell, L.L., A Constrained Thermal Expansion
Micro-Actuator, Proceedings of the
Micro-Electro-Mechanical Systems (MEMS) Symposium
at the International Mechanical Engineering
Congress and Exhibition, DSC-Vol. 66, pp.
365-371. Huang, Q. and Lee, N., Analysis and
Design of Polysilicon Thermal Flexure Actuator,
J. Micromechics and Microengineering., Vol. 9,
1998, pp. 64-70. Comtois, J. H., Michalicek,
M.A., and Barron, C.C., Electrothermal
actuators fabricated in four-level planarized
surface micromachined polycrystalline silicon.
Sensors and Actuators A Physical, Vol. 70, 1998,
pp 23-31.
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Electro-Thermal-Compliant MEMS
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Actuator and mechanism are together.
Embedded ETC actuation
Moulton, T. and Ananthasuresh, G.K., Design and
Manufacture of Electro-Thermal-Compliant Micro
Devices, Sensors and Actuators, Physical, 90
(2001), pp. 38-48.
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In series connection
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In parallel connection
(Moulton and Ananthasuresh, 1997)
Bends down
V
Temperature
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Prototype in the series mode
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Prototype in the parallel mode
25 um diameter gold wire
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Changing electrical resistivity with doping (if
made with silicon)
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Changing the length of the flexure
Bends downwards
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ETC expansion building block
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Parallel micro manipulator
With three degrees of freedom Made using MUMPs,
polysilcon.
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Analysis of ETC devices
Thermal flux
Specified voltage
Fixed
V
Traction force
Specified temperature
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Three analyses
Electrical
Voltage and current
The equations are coupled because -- almost all
properties are temperature-dependent --
deformation can effect thermal boundary
conditions (e.g., convection and radiation)
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Electrical analysis steady-state equilibrium
equations
Strong form
Weak form
voltage
virtual voltage
electrical conductivity
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Thermal analysisSteady-state equilibrium
equations
Joule heating
Strong form
? Fixed temperature
? Convection and radiation
Weak form
Temperature
virtual temperature
thermal conductivity
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Thermo-elastic analysisstatic equilibrium
equations
Strong form
Weak form
stress
stress
deformation
virtual deformation
elastic constitutive properties
thermal strain
thermal expansion coefficient
ambient temperature
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Issues in thermal modeling

• Convection
• Temperature dependence of heat transfer
  properties.
• Size dependence of heat transfer properties.
• Radiation
• View / Shape factors.
• Radiation heat transfer between parts of the
  same device which are at different temperatures.
• Boundary Conditions
• Essential Boundary conditions at the device
  anchor.
• Natural Boundary conditions at the device anchor.
• Conduction through trapped air volume
• Conduction between parts of the same device at
  different temperature with an intervening
  trapped air volume.
• Conduction from the underside of the device to
  the substrate through the air trapped between
  them.
• Temperature dependence of thermo-physical
  Properties

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Why is convection so important?
Thermal Expansion Device (TED), Cragun Howell
(1998)
Without convection or radiation
With convection and radiation
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Essential vs. natural boundray conditions
Essential boundary conditions Thermally Grounded
Natural boundary conditions Not Thermally
Grounded
Having one or the other makes a big difference.
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Scaling effects are quite significant
20 node, 3-D Continuum finite elements in ABAQUS
Fully Coupled Electro-Thermal Analysis Sequentiall
y Coupled Thermo-Elastic Analysis With
temperature dependent material properties and
heat transfer coefficients.
Mankame, N. and Ananthasuresh, G. K.,
Comprehensive Thermal Modelling and
Characterization of an Electro-Thermal-Compliant
Microactuator, J. Micromechanics and
Microengineering, Vol. 11, 2001, pp. 452-462.
For the same maximum temperature, meso (up to a
cm) scale device provides more deflection.
Meso
Micro
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Experimental validation of temperature
distribution
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Dealing with more complicated geometryline
element modeling
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Electro-thermal-compliant design
Three types of problems
Objective Output disp. Outdisp
temp. Outdisp., temp. current
Uniform temperature rise Non-uniform
temperature with external heating Non-uniform
heating with voltage (Joule heating)
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With multiple materials
V
Output displacement
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Design parameterization
Material properties
Convection
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Interpolation of convection
h convection heat transfer coefficient
Heat flux
Output displacement
e
Hole created during optimization
convection
fixed
Weak form of the thermal equilibrium equation
Convection through element surfaces only if the
neighboring elements are empty
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Optimization problem
Minimize
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Optimality criteria
First Variation of the Lagrangian 0 ?
Adjoint volt.
Adjoint temp.
Adjoint disp.
Solve from bottom to top
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Variable update scheme
Lagrangian multiplier for volume constraint
Solved in an inner loop
k is iteration number
Step length
Move limit
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Uniform heating with one material
Intuitive
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Uniform heating with two materials

• Red color stiffer material
• Blue color flexible material
• only the top portion of the square design domain
  is utilized
• Since the objective is to maximize the downward
  displacement, it helps if the middle bar expands
  less

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Non-uniform heating with heat flux input
Intermediate material to prevent heat flow to the
output port
Optimal topology
specifications
Initial temp. profile
final temp. profile
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Effect of convection
Side surface as well as top and bottom convection
Only top and bottom convection
No convection
Temperature profiles
Side convection has two effects on the topology
optimization to make boundary smoother to
preserve heatto make boundary rougher to
dissipate heat.
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ETC design example 1
Single material
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ETC design example 2
Single material
Two materials
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ETC design example 3
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Eliminating the intermediate material
Penalty to be added to the objective to run
optimization again
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ETC design example 4
Single material
Two materials
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Microfabrication of structures with in-plane
heterogeneity
Micro-structure with in-plane heterogeneity
Electroplated metal
Thin deposited metal (seed layer)
Silicon
Subtrate silicon
Gold
After shallow maskless etching of metal and deep
etching of the substrate from underneath
Side views
First trial with Si and gold
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Main points

• Three analyses need to be done to simulate ETC
  devices
• Thermal modeling is not trivial
• Ideas from design in single energy domain easily
  extend to multiple energy domains
• Adjoint method is powerful