ksjp

, 7/0

1

MEMS Design & Fab

Overview

• Integrating multiple steps of a single actuator

• Simple beam theory

• Mechanical Digital to Analog Converter

ksjp

, 7/0

1

MEMS Design & Fab

Limits to electrostatics• Residual stress (limits size)

• Pull-in• Gap-closing• Comb drive• Tooth (for comb and gap-closing)

• Thermal noise

ksjp

, 7/0

1

MEMS Design & Fab

Force/Area

n

L

W

2

max

/4.0

30VV m,50 tm,3 If

7.1ax when

mmmNA

F

nM

ksjp

, 7/0

1

MEMS Design & Fab

Energy-Area Ratio

n

L

W

2

22

/4.9

30VV m,50 tm,3 If2

1

2

1

mmnJA

U

VW

tV

WL

C

A

U

ksjp

, 7/0

1

MEMS Design & Fab

Inchworm Motor Design

F

F

shoe

F

F

shoe

shut

tle

Vs1

Va2

Vs2

Va1

shoe

shut

tle

F

F

shoe

Add ShoeActuators

ksjp

, 7/0

1

MEMS Design & Fab

guides

MUMPs Inchworm Motors

Gap Stop

Shoe Actuators Shuttle

Large Force Large Structures Residual Stress Stiction

shoes

ksjp

, 7/0

1

MEMS Design & Fab

Silicon Inchworm Motors

1mm

ksjp

, 7/0

1

MEMS Design & Fab

Power Dissipation of the Actuator

WPKhzfVV

fCVP

pFCmNFV

FCVCF

pFC

mmmA

mmA

gge

parasitic

paths

pads

6.271,30For

7.61For

2

2

1

24

102.71035412

108.4100412

2

22

253

2522

ksjp

, 7/0

1

MEMS Design & Fab

Springs

• Linear beam theory leads to• Ka = Ea3b / (4L3)

• Kb = Eab3 / (4L3)

L

b

a

Fa

Fb

ksjp

, 7/0

1

MEMS Design & Fab

Springs

• Linear beam theory leads to• Ka = Ea3b / (12L)

• Kz = Ea3b / (3(1+2) L)

• Note that Tz results in pure torsion,

whereas Ta results in bending as well.Ta

Tz

ksjp

, 7/0

1

MEMS Design & Fab

Spring constant worksheet• Assume that you have a silicon beam that is 100 microns long,

and 2um wide by 20um tall. Calculate the various spring constants.

• Esi ~ 150 GPa; Gsi = Esi / (1+ 2) = 80 GPa

a3b=Ka=Kb=Ka =Kz =

ksjp

, 7/0

1

MEMS Design & Fab

Damping• Two kinds of viscous (fluid) damping

• Couette: b = A/g ; = 1.8x10-5 Ns/m2 • Squeeze-film: b ~ W3L/g3 • proportional to pressure

• Dynamics:• m a + b v +k x = Fext

• If x(t) = xo sin(t) then

• v(t) = xo cos(t)

• a(t) = - 2xo sin(t)

• -m2xosin(t) + bxocos(t) +kxosin(t) = Fext

ksjp

, 7/0

1

MEMS Design & Fab

Dynamic forces, fixed amplitude xo

• -m2xosin(t) + bxocos(t) +kxosin(t) = Fext

frequency

Force

n

Low dampingQ~10

High damping~10

ksjp

, 7/0

1

MEMS Design & Fab

Dynamic forces, fixed amplitude xo

• -m2xosin(t) + bxocos(t) +kxosin(t) = Fext

frequency

Force

n

increase k

Increasing k raises n but at costof more force or less deflection

n’

ksjp

, 7/0

1

MEMS Design & Fab

Dynamic forces, fixed amplitude xo

• -m2xosin(t) + bxocos(t) +kxosin(t) = Fext

frequency

Force

n n’Decreasing m raises n atno cost in force or deflection

decrease m

ksjp

, 7/0

1

MEMS Design & Fab

Dynamic forces, fixed amplitude o

• -J2osin(t) + bocos(t) +kosin(t) = Fext

frequency

Torque

n n’Identical result for angular systems withJ (angular momentum) instead of m

decrease m

ksjp

, 7/0

1

MEMS Design & Fab

Mechanical Digital to Analog Converter

ksjp

, 7/0

1

MEMS Design & Fab

Basic Lever Arm Design

Stops

6m6m

Folded spring support

Input Beam (digital) Input Beam (analog)

Output Beam (analog)

ksjp

, 7/0

1

MEMS Design & Fab

6-bit DAC Implementation

(Courtesy of Matthew Last)

ksjp

, 7/0

1

MEMS Design & Fab

Output of a 6-bit DAC

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

DNL = 1.4 LSB

INL = 6.3 LSB

Digital input

Nor

mal

ized

bea

m p

ositi

on19 cycles