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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.
2
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
3
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
+-
4
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
5
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 ,
6
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
7
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)
8
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)
9
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