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EE C245 – ME C218 Fall 2003 Lecture 11

EE C245 - ME C218Introduction to MEMS Design

Fall 2003

Roger Howe and Thara SrinivasanLecture 11

Electrostatic Actuators II

2EE C245 – ME C218 Fall 2003 Lecture 11

Today’s Lecture• Linear (vs. displacement) electrostatic actuation:

vary overlap area: electrostatic comb drive• Electrostatic springs: positive (comb levitation)• Second-order effects in electrostatic actuators:

charged dielectrics, work functions, depletion, and Casimir

• Reading:1. W. C. Tang, M. G. Lim, and R. T. Howe, “Electrostatic comb drive

levitation and control method,” Journal of MicroelectromechanicalSystems, 1, 170-178 (1992).

2. B. D. Jensen, S. Mutlu, S. Miller, K. Kurabayashi, and J. J. Allen, “Shaped comb fingers for tailored electromechanical restoring force,” Journal of Microelectromechanical Systems, 12, 373-383 (2003).

3. Kudrle, T. D., et al, “Pull-in suppression and torque magnification in parallel plate electrostatic actuators with side electrodes,” 12th Int. Conf. on Solid-State Sensors, Actuators, and Microsystems (Transducers ’03), Boston, Mass., June 8-12, 2003, pp. 360-363.

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3EE C245 – ME C218 Fall 2003 Lecture 11

Interdigitated Comb Drive

William Tang, Ph.D. EECS Dept., 1990(this device by Clark Nguyen, Ph.D. 1994)

Common bias:DC offset VP connectedto shuttle through poly0“ground plane”

4EE C245 – ME C218 Fall 2003 Lecture 11

Electrostatic Force: a First Pass*

W. C. Tang, Ph.D. EECS Dept., 1990

stator (fixed electrode)

rotor (not … but moving)

gap = g, thickness = tL = finger lengthx = overlap length

t g

L x

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5EE C245 – ME C218 Fall 2003 Lecture 11

First-Pass Electrostatic Force (Cont.)

• Neglect fringing fields• Parallel-plate capacitance between stator and rotor

=∂

′∂=x

WFe

=′′=′ ∫ VdVxqVxWrsV

rs0

),(),(

6EE C245 – ME C218 Fall 2003 Lecture 11

Comb Drive Force: a Second Pass • Energy must include capacitance between the stator

and rotor and the underlying ground plane, which is typically biased at the stator voltage Vs … why?

L x

t g

zo

+- VrVs

+-

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7EE C245 – ME C218 Fall 2003 Lecture 11

Comb-Drive Force with Ground Plane Correction

• Finger displacement changes capacitances from stator and rotor to the ground plane à modifies the electrostatic energy

( )222, 2

121

21

rsrs

rrp

ssp

xe VVdx

dCV

dx

dCV

dx

dC

xW

F −++=∂

′∂=

Gary Fedder, Ph.D., pp. 119-122, 1994

8EE C245 – ME C218 Fall 2003 Lecture 11

Capacitance Expressions

• Consider case where Vr = Vp = 0 V• Csp depends on whether or not fingers are engaged

Gary Fedder, Ph.D., pp. 119-122, 1994

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9EE C245 – ME C218 Fall 2003 Lecture 11

Simulation (2D Finite Element)

Gary Fedder, Ph.D., p. 123, 1994

10EE C245 – ME C218 Fall 2003 Lecture 11

Vertical Force (Levitation)

W. C. Tang, JMEMS , 1992 (reader)

=∂

′∂=

zW

F ze ,

Consider Vr = 0 V as shown: =zeF ,

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11EE C245 – ME C218 Fall 2003 Lecture 11

Levitation Force

Gary Fedder, Ph.D., p. 122, 1994

)(, zzkF eeze ∆−∆≅

constant

“electrical spring const.”

Levitation force adds to themechanical spring constant inthe z direction à increases the resonant frequency

12EE C245 – ME C218 Fall 2003 Lecture 11

Vertical Resonant Frequency

W. C. Tang, JMEMS , 1992 (reader)

Must account for electricalsprings in finding MEMSresonant frequencies

comb (x-axis) à ke = 0comb (z-axis) à ke > 0parallel plate à ke < 0

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13EE C245 – ME C218 Fall 2003 Lecture 11

Relative Forces for Surface Microstructures

L x

x

y

gap = g = 1 µm,thickness = t = 2 µmfinger length = L =100 µmoverlap length x = 75 µm

Comb drive (x-direction)(V1 = V2 = Vs = 1V)

V1 V2

Vr = 0 V =xeF ,

Differential || plate (y-direction)(V1 = 0 V, V2 = 1V)

=yeF ,

14EE C245 – ME C218 Fall 2003 Lecture 11

Levitation Suppression

Pattern Poly0 into differentially biased electrodes to minimizefield lines terminating on top of combPenalty: x-axis force is reduced

W. C. Tang, JMEMS , 1992 (reader)

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15EE C245 – ME C218 Fall 2003 Lecture 11

Experimental Measurements

Shuttle is pulled down(toward the substrate)with zero applied voltage

Why?

W. C. Tang, JMEMS , 1992 (reader)

16EE C245 – ME C218 Fall 2003 Lecture 11

Charged Dielectrics:No Applied Voltage Needed!

Nitride charge inferred from deflection and simulated field distribution isconsistent with typical values

Minimizeexposeddielectrics!

W. C. Tang, JMEMS , 1992 (reader)

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17EE C245 – ME C218 Fall 2003 Lecture 11

Work Function DifferencesExample: p+ structure over n+ poly0 electrode

n+ poly-Si

p+ poly-Si

Equilibrium band diagram

+ + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - -

z

How is chargeexchanged toreach equilibrium?

Answer:

18EE C245 – ME C218 Fall 2003 Lecture 11

Depletion Effects in Silicon

+ + + + + + + + + + + + + + + + + + + +

--

--

--

--

--

--

--

--

--

--

n type silicon (SOI structure)

+ -

V

x

x

ρ(x)

+qNd

-Xd g

E(x)

-Xd gx