3.155J/6.152J Lecture 13: MEMS Lab Testing

Prof. Martin A. SchmidtMassachusetts Institute of

Technology

10/31/2005

Outline

� Review of the Process and Testing � Mechanics

� Cantilever � Fixed-Fixed Beam � Second-order effects

� Residual stress � Support compliance

� References � Senturia, Microsystems Design, Kluwer

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 2

The Process – Lab 1

� Grow 1.0µm of Si-Rich Silicon Nitride (SiNx) � LPCVD Process (details to follow) � Characterize (UV1280)

� Thickness

� Refractive index

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 3

The Process – Lab 1

� Pattern Transfer � Deposit photoresist � Expose on contact aligner � Plasma etch using SF6 chemistry � Strip resist

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 4

The Process – Lab 2

� KOH Undercut Etch � 20%, 80C

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 5

The Process – Lab 3

� Break the wafer into die � Mount the die on a metal plate � Test using the Hysitron Nanoindenter

F

w

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 6

Testing

� Cantilever � Young’s Modulus

� Fixed-Fixed Beams � Young’s Modulus � Residual Stress

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 7

The Mask

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 8

The Mask - Cantilevers

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 9

The Mask – Fixed-Fixed Beams

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 10

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 11

Cantilever Data

0

2

4

6

8

10

12

0 100 200 300 400 500 600

Displacement (nanometers)

Forc

e (m

icro

New

tons

)

F = k x

Force on a Beam

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 12

Uniaxial Stress

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 13

Material Properties: Elastic/Plastic

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 14

Figure removed for copyright reasons.

Material Properties: Brittle

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 15

Figure removed for copyright reasons.

Differential Equation of Bending

H = thicknessW = width

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 16

I = WH3( (112

d2w =dx2

M-EI

z

w(x)

xx dx

θ(x)

dθ

ds

Figure by MIT OCW.

Reference: Senturia, S.D. Microsystems Design. Norwell, MA: Kluwer Academic Publisher, 2001.

FPOINT LOAD

FR

MR

Lx0

Figure by MIT OCW.

3L

Deflection of a Cantilever - 2

Ref: Senturia (Kluwer) C.V. Thompson – 6.778J

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 18

Deflection of a Cantilever - 3

W = width H = thickness L = length

Ref: Senturia (Kluwer) C.V. Thompson – 6.778J

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 19

Deflection of a Plate - 1

Ref: Senturia (Kluwer) C.V. Thompson – 6.778J

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 20

ρ/ν

ρ

Given axial strain

Poission effect leads to transverse strain εy given by εy=-νεx where ν is Poisson's ratio (unitless and about 1/3 for most materials)

More important as W L(beams approach plates)

( (zρ=εx

Original cross-section

ANTICLASTIC CURVATURE

So z( (νρ=εy

Figure by MIT OCW.

Deflection of a Plate - 2

σ − νσx yε = x E But ε zero be to d constraine isy

σ − νσy x⇒ 0 ε = = y E ⇓

σ x = ⎜⎛ E

2 ⎟⎞ε x

Replace Modulus(E) with Plate Modulus⎝ 41 3 421 ν − ⎠

Modulus Plate Ref: Senturia (Kluwer)

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 21

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 22

Fixed-Fixed Beam

0200400600800

10001200140016001800

0 500 1000 1500 2000 2500 3000 3500

Displacement (nanometers)

Load

(mic

roN

ewto

ns)

Fixed-Fixed Beam: Large Displacement

� Beam stretches under large displacement � Becomes ‘stiffer’

� Solved by Energy Methods � c = w

Ref: Senturia (Kluwer)

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 23

Residual Axial Stress in Beams

� Residual axial stress in a beam contributes to it bending stiffness

2ρ WP0 = 2σ 0WH

� Leads to the Euler beam equation ⇒ P0 =σ 0 H ρ

to equivalent is which load ddistribute a 2d w q = W P σ = 0WH0 0 2dx

: equation beam into load added as Insert d 4 wEI dx4 = q q + 0

d 4 w d 2 wEI dx4 σ − 0WH

dx2 = q

Ref: Senturia (6.777)

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 24

Effect of stress on stiffness

Ref: Senturia (6.777)

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 25

Graph found in Senturia, S.D. Microsystems Design. Norwell, MA: Kluwer Academic Publisher, 2001.

Figure removed for copyright reasons.

Effect of Residual Stress

� Not an issue in cantilevers � For a point load, F, in the center of a bridge

� Important when

Ref: Senturia (Kluwer)

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 26

Compliant Supports

C.V. Thompson – 6.778J Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 27

MEMS Lab Report

� Report Young’s Modulus extracted from� Cantilevers� Fixed-Fixed Beams

� Explain differences from ideal theory� Compare to literature values for mechanical

properties� Assess the effects of:

� Residual stress� Estimate from measurements

� Experimental error� Compliant supports� Beam versus Plate� Others….

Fall 2005 – M.A. Schmidt 3.155J/6.152J – Lecture 13 – Slide 28