In Search of a Better MEMS Switch How nanostructured dielectrics soften

landing, increase travel Range, and reduce Energy dissipation

Muhammad A. Alam

Ankit Jain, and Sambit Palit alam@purdue.edu

Landau

2

copyright 2012

This material is copyrighted by M. A. Alam under the following Creative Commons license. Conditions for using these materials is described at http://creativecommons.org/licenses/by-nc-sa/2.5/

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‘More than Moore’ Technologies

MOSFET, MEMS, and ISFET

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Gate S D

Gate

Fluid Gate

Beats thermo- dynamic limit of 60 mV/dec

Beats Nernst limit of 60 mV/pH

A classical MOSFET switch

Applications of MEMS Switches

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1. Communication

RF-MEMS Switch

2. Computation

NEMFET

4. Biosensor

Resonator / Mass Sensor

3. Optics

Deformable Mirrors

Mirasol Display

Active and Passive Displays

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Kindle

IPAD Newton/Hooke

P. Vukusik, PW, 2004

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MEMS and Mirasol Display

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h1

h2

h2

Physics of switch closing Tunability of the physical spacing MEMS as a Landau switch

Outline

• Introduction to More than Moore Technology • Elementary Physics of MEMS • Theory of Soft Landing • Physics of Travel Range • Hysteresis-Free Switching • Conclusions

8 Taylor, PRS, 1968

Mechanical model for cantilever movement

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= − − −2

( 02 ) ( )elec down

d y dym k y y b

dtF

dt

damping Spring force

Net force

MATLAB simulation

( )ε ε

ε=

+(

2 20

2)2

relec dow

r

n

d

AV

y yF

Why does it snap?

Gate

Many Puzzles of MEMS C-V

Pull-In

Pull-Out

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Source of instability Point of instability Geometry of instability Energy dissipation

y y0

Fs, FE

Asymmetry in Pull-in and Pull-out Voltages

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E

ε

2A

2A

0

1E = V

2dE 1

F = =

C

dCdy

Vy

C

d 2A

=y

2y0/3

y0

VA

22pif

dissf

1 εV A ky2E = -y 2

Energy Landscape of MEMS Transition

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Order parameter y, …in other system M or P are order parameter Sub kT transition is fundamentally related to absence of states in the gap

MW = W +WT E

y

( ) 22M 0W = k y - y

( )( ) 2E 0W = 1 2 y Vε

MEMS, 1st order Phase Transition, Cusp Catastrophe

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Q (Cal)

T

water to ice

Gate

V2

C(y)

Is there a 2st order Phase Transition in MEMS? Physics of Bows and Arrows

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Q. Wang, J. Colloid and Itf. Sci. v. 458(2), 491, 2011

P

F:T,V

1st order

2nd order

Euler Buckling, 2st order Phase Transition, Fold Catastrophe

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y

T MθW = W +W

( )( )22θ µ θW = 2

2 4

2! 4!Mθ θβ

× × ≈ −

W = 2 F z

z

L=1

( ) ( )2 4T µ θ θ× + ×W = 2 - F L F L /12

LµcF = 2

y

F Fc

Symmetry breaking, power-law expansion of the order parameter …

Outline

• Introduction to More than Moore Technology • Elementary Physics of MEMS • Theory of Soft Landing • Physics of Travel Range • Hysteresis-Free Switching • Conclusions

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Reliability: The problem of Hard Landing

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0

dm = k(y - y )- F - b

dtυ υelec

( )2elec

1 dF = CV

2 dy

The hard landing damages the surface and can lead to stiction …

A. Jain et.al., APL, 98, 234104 (2011)

Soft Landing by Resistive Braking

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elecυ υ

×

0

cc

dm = k(y - y )- F - b

dtd(C )

I = ; V = I R+dtV

V

( )2

2 2 celec c c

VV V

d 1 d 1 dC 1F = C = +

2 dy 2 dy 2 dyC

Reduction in impact velocity and reduced variability

A. Jain et.al. Patent 61/483225

Operation: Geometry and Capacitance

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( )2 2elec c

1 d 1 dCF = CV = V

2 dy 2 dy

1C = Ay−up

C = A(y) y Cα× down up

Before Pull-in Close to contact

Soft Landing by Capacitive Braking

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( )2elec

2c

1 dF = CV

2 dy1 dC

= V2 dy

1 (< PI)

(near contact)

C = Ay

C = A(y) yα

−

×

A. Jain et.al., APL, 98, 234104 (2011)

Patterning is Widely used …

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Outline

• Introduction to More than Moore Technology • Elementary Physics of MEMs • Theory of Soft Landing • Physics of Travel Range • Hysteresis-Free Switching • Conclusions

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Charge Controlled Arbitrary Travel Range

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0y

… depositing precise amount of charge could be difficult?!

Q

2A

1E = CV2

=

=

2

0

2

y0

1 Q2 C

ε AC =

ydE 1 QF = = const.dy 2ε A

y y0

Fs,FE

Fs=k(y0-y)

FE=(1/2ε0 Α)Q2

yy0

Fs,FE

Fs=k(y0-y)

FE=1/2ε0 V2/y2

Manipulating stability point: Sculpting the Electrode

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FE=FM dFE/dy= dFM/dy y~y0/2

y0

( )

2

2y

0

1E = CV

2dE 1 dC

F = = Vdy 2 dy

2πεC =

ln a + y a

2y0/3

Shaping the 2D e-field …

y0/2

Geometry allows tailoring of the critical gap !

Manipulating stability point: Fractal Sculpting of the Electrode

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( 1)

2 ( 1)0

1( )2

12 1

α α

α

− −−

− +

=

− = =

+= =

+ +

FDn

nelec

Fc

F

k y y F V y

Dnyn D

C(y) = y y

yc=2/3 for planar electrode yc=1/2 for cylindrical electrode yc=0! for spherical electrode

Taylor, soup bubble and cloud formation

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Below pull-in Above pull-in

Travel range > 0.5 !

… when he was 82 years old!

Outline

• Introduction to More than Moore Technology • Elementary Physics of MEMs • Theory of Soft Landing • Physics of Travel Range • Hysteresis-Free Switching • Conclusions

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?

Hysteresis and Power Dissipation

Is hysteresis free MEMS operation possible?

yPOp

yPIn

yPOn yPIp -50 0 50-4000

-2000

0

2000

4000

6000

8000

x

U

4 2U cx ax= +

a− ↑

Origin of Hysteresis Loss

-100 -50 0 50 100-30

-20

-10

0

10

20

30

ε

x

0

-100 -50 0 50 100-40

-20

0

20

40

ε

x

-1

-100 -50 0 50 100-50

0

50

ε

x

-2

Landau theory suggests optimum landscape ..

100 101 102 1030

5

10

15

20

G/R

V (V

)

VPIVPO

yPOp

yPIn

yPOn yPIp

yPOp

yPIn

yPOn yPIp

yPIn =yPOp

yPIp=yPOn

g=2R g=100R g=120R

g=2R g=100R g=120R

There is always a hysteresis-free geometry with minimum dissipation

Conclusions: MEMS & Nanostructured Electrodes

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-50 0 50-4000

-2000

0

2000

4000

6000

8000

x

U

4 2U cx ax= +

a− ↑

1F

cF

DyD

=+

Impact velocity Travel Range Hysteresis free

Geometrization of Electronic Devices: www.ncn.purdue.edu/workshops/2009summerschool

Conclusions: Future of CMOS+ Technology

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Bio Sensors

Carbon NanoNet

OPV

GateS DFET (logic) Negative C

RRAM PCM FeRAM

Gate

SRAM (Memory)

vin

vo

Boltzmann Switch Landau Switch

References • H. Torun, APL, 91, 253113, 2007. Spring constant tuning of active atomic force

microscope. G. Taylor, The coalescence of closely space drops" Proc. Roy. Soc. A, 306, 423, 1968. As a model for spherical electrodes in the MEMs configuration. http://www.memtronics.com/page.aspx?page_id=15 (Goldsmith dimpled structure) http://www.memtronics.com/files /Understanding%20and%20Improving%20Longevity%20in%20RF%20MEMS%20SPIE%206884-1.pdf http://www.google.com/patents?hl=en&lr=&vid=USPATAPP11092462&id=BEeZAAAAEBAJ&oi=fnd&dq=muldavin+switch+dimpled&printsec=abstract#v=onepage&q&f=false (corrugated top electrode).

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