Breaking Invisible Specimens with Zero Force

Roberto BallariniUniversity of Minnesota

Collaborators:

Arthur Heuer, Hal Kahn

Sponsors:

NSF, DARPA, ARO, NASA

Strength and FractureStandards at the Micro and

Nano Scales1/27/08

Surface Micromachining

Si wafersacrificial SiO2 (4 μm)

undoped polysilicon (5.7 μm)masking SiO2 (1 μm)

Plasma etch

Pd sputter (17 nm)

B diffusion dopeHF release

HF release

Two types of on-chip specimenshave been developed:

•Loading through electrostatic actuation•Loading through fabrication-induced residual stress

100 μm

100 μm

specimen

electrostatic actuator notch

notch

500 μm

Fatigue Testing

1438 pairs of comb fingers; 0.8 mN at 150 V

ADVANTAGES OF THIS “ON-CHIP” SPECIMEN

•No need for external loading device.•Resonance loading can be used to study very high cycle fatigue.

•Uncracked ligament size of the same order as dimensions of typical MEMS components.

•Can adjust mean stress and alternating stress.

Stre

ss

Schematic Bend Strength Tests

Monotonic Increasing Amplitude Fatigue

1 Comp/Mono Fixed Δσ

Fatigue/Mono High T Hold/Mono

Time

Stre

ss

0

σm Δσσcr

10 min.= 6x106cycles

TimeSt

ress

0

σcrσhold

10 min.

Δσ=(σmax -σmin )

Time

Stre

ss

0σmax = σcr

σmin

σm

~1 min.(6x105cycles)

Time

0

σcr

σmin

Time

Stre

ss

0

σcr

Dynamic Fatigue of Polysilicon

Bagdahn and Sharpe, Sensors and Actuators A, 2003

1.0

0.8

0.6

0.4

(Pea

k S

tress

/Mea

n Te

nsile

Stre

ngth

)

100 103 106 109 1012

Cycles to Failure, N

10 kHz 1 Hz 40 kHz 50, 200, 1000, 6000 Hz

Nor

mal

ized

Fat

igue

Stre

ss

Bagdahn and Sharpe

No frequency dependence of fatigue life, only on total number of cycles

Sharpe et al., Bagdahn and Sharpe, and

Muhlstein et al.used the MUMPSfoundry

Dynamic Fatigue Resultslow-cycle fatigue

1

2

3

4

5

6

-4 -3 -2 -1 0 1

Load Ratio, RLow

-Cyc

le F

atig

ue S

tren

gth,

σm

ax(G

Pa)

PolySi thickness Test Ambient3.5 μm air (105 Pa)5.7 μm air (105 Pa)5.7 μm vacuum (10 Pa)

Monotonic Bend Strength after cycling with a fixed mean stress

Time

Stre

ss

0

σcrit

Time

Stre

ss

0

σm Δσσcrit

σa = Δσ/2

Mon

oton

ic S

tren

gth,

σcr

it(G

Pa)

Fatigue Amplitude, σa (GPa)

Mean Stress, σm = -2.2 GPa

2

2.5

3

3.5

4

0 0.5 1 1.5 2

Monotonic Bend Strength after cycling with a fixed (low) amplitude

2

2.5

3

3.5

4

4.5

-5 -4 -3 -2 -1 0 1 2 3

Mean Stress, σm (GPa)

Mon

oton

ic S

tren

gth,

σcr

it(G

Pa)

σa = 1.0 GPa

Time

Stre

ss

0

σcrit

Time

Stre

ss

0

σm Δσσcrit

10 min.= 6x106cycles

σa = Δσ/2

polysilicon

indent

2h = 500 μm

w=60 μmaA

silicon substrate

polysilicon

SiO2 anchors

B pre-crack

Stress Intensity and Stress vs. Crack Length

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.0 5 9 13 17 21 25 29 33 37 41 45 49 53 57

Crack Length [um]

Str

ess

Inte

nsi

ty

[MP

a m

1/2 ]

0.05.010.015.020.025.030.035.040.045.050.0

Str

ess

[MP

a]

Stress Intensity Stress*

)(* απσ FaK =

σ* = σresidual /(1+4aV(α)/2h)

PASSIVE DEVICE ASSOCIATEDWITH CONSTANT TENSION

(Science 298, 1215-1218, 2002)

5 um

indent

substrate

pre-crack

beam

residual tensile stressbeam anchor (to substrate)

crack tip

1 um

INDENTATION CRACK

CWRU

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25 30 35 40 45 50 55 60

Crack Length [μm]

Stre

ss In

tens

ity [M

Pa m

1/2 ]

= no propagation = propagation to failure

45 MPa

56 MPa

69 MPa

FINE-GRAINED POLYSILICONFRACTURE TOUGHNESS

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25 30 35 40 45 50 55 60

Crack Length [μm]

Stre

ss In

tens

ity [M

Pa m

1/2 ]

= no propagation = propagation to failure

69 MPa

FINE-GRAINED SILICONSTATIC FATIGUE STUDY

90% RH

K between 0.62- 0.86 MPa-m1/2

No growth in 30 daysV< 3.9 x10-14 m/s

Same results for eight multipoly specimens

Static Fatigue ExperimentNotched Tensile BeamsUndoped LPCVD Polysilicon

deposited at 570°C, annealed at 615°C → 318 MPa (Tensile)500 μm

20 μm

a

20 μm

a

a(μm) σmax (GPa) broken5.2 2.3 0/146.2 2.8 0/147.2 3.4 0/148.2 3.9 11/149.2 4.5 14/1410.2 5.0 14/14

After 200 hrs in 90% humidity → no additional beams broke

20 μm

Small Residual TensionSputtered Aluminum

Anchor

Anchor Anchor

Anchor

Anchor Anchor

200 μm

20 μm 20 μm

10 μm

Large Residual TensionSilicon Nitride

Residual CompressionColumnar Polysilicon

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5

1st test2nd test3rd test4th test

with fibril

1st test2nd test

without fibril

Displacement (μm)

Appl

ied

Vol

tage

(V)

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Strain (%)S

tress

(MP

a)

200 μm

5 μmA

B D

C

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

with fibrilwithout fibril

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

with fibrilwithout fibril

F

E

fixed fingers

overlap

movablefingers

tether beams

anchor

anchoranchor anchor

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5

1st test2nd test3rd test4th test

with fibril

1st test2nd test

without fibril

Displacement (μm)

Appl

ied

Vol

tage

(V)

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Strain (%)S

tress

(MP

a)

200 μm

5 μmA

B D

C

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

with fibrilwithout fibril

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

0

10

20

30

40

50

60

0 1 2 3 4 5

Displacement (μm)

Forc

e (μ

N)

extra force needed to strain fibril

with fibrilwithout fibril

F

E

fixed fingers

overlap

movablefingers

fixed fingers

overlap

movablefingers

tether beams

anchor

anchoranchor anchor