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

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

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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

g

Presentation of suspended-meander MEMS

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� 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”

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

g

LW

Experimental characterization

� L=160µm , W=100µm, g=2.6µm

� Q1 : Interferometric measurements shows that the

MEMS bridge is initially slightly deflected.

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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

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Can COMSOL help us to answer these questions ?

Voltage (V)C

apac

itan

ce (

fF)

45

65

85

105

0 10 20 30 40Vpi

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

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

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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

Mechanical simulation

Fixed

Fixed

� Assumption: Observed deflection result from intrinsic

stress gradient in the beam (sacrificial layer).

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Fixed

X1X2

Mechanical simulation

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Measure deflection ≈simulated

deflection

For σ0 =85 Mpa

Should be confirmed by X ray

measurement

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

The value of the capacitance is

C(0) =e2W

2

∆V

Coupled simulation without electrostatic force

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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

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

Coupled simulation with electrostatic force

C(V) measure ≈ C(V) simulation

15COMSOL conference 201018/11/2010

Vpi

� 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

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