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Variable Capacitance and Pull-in Voltage Analysis of
Electrically Actuated Meander-Suspended Superconducting
MEMS
∞∞∞∞∞∞∞∞
Nouha ALCHEIKH
Pascal XAVIER
Jean Marc DUCHAMP
Project funded by the Rhône-Alpes Region(France)
COMSOL conference 201018/11/2010
Presented at the COMSOL Conference 2010 Paris
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Filtre
Passepass
Filtre
Sélectif
Context
� Use of superconducting MEMS for tuneable RF devices
� Behavioral multi physic model of a MEMS:
� IRAM process : Niobium on quartz
� Influence of the sacrificial layer
Electro-
Mechanical
Thermics
(superconducting)
Microwaves
COMSOL conference 201018/11/2010 1
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
2COMSOL conference 201018/11/2010
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g
Presentation of suspended-meander MEMS
18/11/2010 COMSOL conference 2010 3
� Variation of the capacitance : � Cg
LbC
××=
0ε
� Deformation of the meanders
� C(V) depends on the meanders
� Optimal ∆C/C
� Electrostatic force � reduction of the air gap “g”
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
4COMSOL conference 201018/11/2010
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g
LW
Experimental characterization
� L=160µm , W=100µm, g=2.6µm
� Q1 : Interferometric measurements shows that the
MEMS bridge is initially slightly deflected.
18/11/2010 COMSOL conference 2010 5
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Experimental characterization
Cap
acit
ance
(fF
)
105
125
145
165
185
205
225
245
Vpi =27.6 V and ∆C(V)/C(0) is 33%.
Q2 : C(0)measure =79fF & C(0)Calculated =67fF
18/11/2010 COMSOL conference 2010 6
Can COMSOL help us to answer these questions ?
Voltage (V)C
apac
itan
ce (
fF)
45
65
85
105
0 10 20 30 40Vpi
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
7COMSOL conference 201018/11/2010
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COMSOL multiphysic simulation
Objectives
� Mechanical simulation to explain the deflection of the bridge
� Coupled simulation to find extra capacitance origin.� Coupled simulation to find extra capacitance origin.
� Multiphysics electromechanical simulation to describe C(V) measured for suspended –meanders MEMS
18/11/2010 COMSOL conference 2010 8
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
9COMSOL conference 201018/11/2010
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Mechanical simulation
Fixed
Fixed
� Assumption: Observed deflection result from intrinsic
stress gradient in the beam (sacrificial layer).
18/11/2010 COMSOL conference 2010 10
Fixed
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X1X2
Mechanical simulation
18/11/2010 COMSOL conference 2010 11
Measure deflection ≈simulated
deflection
For σ0 =85 Mpa
Should be confirmed by X ray
measurement
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
12COMSOL conference 201018/11/2010
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The value of the capacitance is
C(0) =e2W
2
∆V
Coupled simulation without electrostatic force
18/11/2010 COMSOL conference 2010 14
C(0)=70 fF with air substrate
C(0)=81.6 fF with quartz
Extra capacitance : 11.6 fF as shown on
measure
Ground
Port:Enegy
method
C(0) =e2W ∆V
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Outline
� Presentation of suspended-meander MEMS
� Experimental characterization
� Multiphysics simulation� Multiphysics simulation
� Mechanical simulation
� Coupled Simulation without electrostatic force
� Coupled Simulation with electrostatic force
� Conclusions & Perspectives
14COMSOL conference 201018/11/2010
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Coupled simulation with electrostatic force
C(V) measure ≈ C(V) simulation
15COMSOL conference 201018/11/2010
Vpi
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� C(V) is validated by an Electromechanical 3D simulation and predict the pull-in voltage
� The deflection of the bridges can be explained by an intrinsic stress gradient in the beam
Conclusions &Perspectives
� Extra capacitance is due to the quartz substrate
� Explain the effect of hysteresis by a simple simulation usingCOMSOL
� Superconducting modeling
18/11/2010 COMSOL conference 2010 16
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