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Investigation of the structural resistance of Silicon membranes

for microfluidic applications in High

Energy PhysicsC. Gabry

A. Mapelli, G. Romagnoli, D. Alvarez, P. Renaud,

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Summary1 – Objectives of the project

2 – Literature review

3 – Single-Edge V-Notch Beam (SEVNB) tests 3.1 – SEVNB specimens 3.2 – Experiments 3.3 – Results 3.4 – Discussion

4 – Channel geometry beam specimens under bending stress 4.1 – Specimens 4.2 – Experiments 4.3 – Results 4.4 – Discussion

5 – Conclusion

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ContextAim : reduce material budget of SCSi micro-

devices

Minimize of thickness of SCSi membranes

Insure sufficient resistance to internal pressures=> Need of fracture prediction tool to optimize

structures

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1 – Objectives

Main goal : provide fracture data for the implementation of a fracture prediction tool

Requirements : simple situation to allow CERN’s Engineering Office to make reliable models

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1 – Objectives2 testing rounds :

Fracture toughness test => to set parameters of FEA model

Test with slightly more complex geometry to validate those parameters

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2 – Literature review

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Fracture ToughnessDefinition : Fracture toughness (Kc) is the ability

of a material to resist against propagation of a pre-existing crack.

Fracture toughness = critical stress intensity

Unit : Pa√m

High fracture toughness : Ductile fracture

Low fracture toughness : Brittle fracture

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Fracture modes3 different fracture modes :

tensile (mode I), -typically the weakest- shear (mode II), tear (mode III)

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Fracture toughness testTo perform a fracture toughness determination

test, one need :

Sample with pre-existing crack of known geometry

Tool able to apply and measure load & displacement

The load at fracture to allow for fracture toughness calculation

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3 – Single-Edge V-Notched Beam (SEVNB) in three point bending

tests

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3.1 – SEVNB Specimens

Easy to manufactureExisting standards

(ASTM C1421-10 for ex.)Possible to perform FEAEasy to testNo tensile stress (except at crack tip)

Reasons of the choice

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3.1 – SEVNB Specimens

1st step : Alignment to crystalline structure

2nd step : Photolithography

3rd step : Notch etching (KOH)

4th step : Dicing

Fabrication process

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3.1 – SEVNB Specimens

Mask for SEVNB specimens fabrication

Fabrication process

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3.1 – SEVNB SpecimensObtained specimens

Obtained notches :

Picture of full specimen ?

Mask ?

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3.1 – SEVNB SpecimensDimensions of specimens

Standard sizes are too large (e.g. W=3mm)

ASTM standards gives two main ratios to respect :W/B = 0.75 0.35 < a/W < 0.6 Fabricated specimens :

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3.1 – SEVNB SpecimensAnalytical formula for fracture toughness

FEA Comparison between Sharp and V-Shaped crack

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3.1 – SEVNB SpecimensAnalytical formula for fracture toughness

Comparison between various analytical formulas for fracture toughness

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3.2 – SEVNB ExperimentsExperimental setup – Overview

1 actuator

1 load cell

Mechanical support to link & align parts

Removable chuck to adapt to every test

Transportable & adaptable system

Taken from “In-situ MEMS Testing”, A. Schifferle, A. Dommann, A. Neels and E. Mazza

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3.2 – SEVNB ExperimentsExperimental setup – Chucks

Vertical pins (1mm spacing)

Available chucks :S0=5mm

S0=10mm

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3.2 – SEVNB ExperimentsCompliance calibration

Extremely stiff sample (1mm diameter steel rod) in place of specimen

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3.2 – SEVNB ExperimentsData analysis

Initial slack correction by linear fit

Tool compliance correction on measured deformation

δb : Deformation of the beam P : Load δt (=P*Ct) : Deformation of the toolδm : Measured deformation Ct : Compliance of the tool,

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3.3 – SEVNB ResultsCompliance

Analytical compliance : 1.55*10-6 m.N-1

Mean experimental compliance : 1.27*10-6

± 0.39*10-6 m.N-1

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3.3 – SEVNB ResultsFracture Load

Fracture toughness from literature (for (110) plane)* :1.23±0.18 MPa.√m-1

Experimental fracture toughness : 1.50±0.09 MPa.√m-1

*T. Ando, X. Li, S. Nakao, T. Kasai, M. Shikida and K. Sato, “Effect of crystal orientation on fracture strength and fracture toughness of single crystal silicon”, Micro Electro Mechanical Systems, 17th IEEE International Conference on MEMS, pp. 177-180 (2004)

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3.3 – SEVNB ResultsScatter in results

No correlation between fracture load and compliance

Higher scatter for compliance than fracture toughness

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3.4 – Sources of scatterSharpness of notch

Notch sharpness :

22.89nm radius for this measurement

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3.4 – Sources of scatterDepth of notch (a)

Notch depth conform to what was planned

(143um for the measured sample, 2um bigger than expected)

Make more measurements to see standard deviation

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3.4 – Sources of scatterMisalignment of sample

500um misalignment=> 5.8% compliance variation

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3.4 – Sources of scatterThickness of sample (B)

10um variation of B=> 1.1% variation of compliance

B fixed by dicing=> low variability expected

Actual measurements of B with standard deviation !!

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3.4 – Sources of scatterMisalignment of tool

Multiple types of possible misalignments

(In plane, out of plane…)

Not possible to estimate without changing boundary conditions of FEA model

Source of global error ? (same misalignment for a batch)

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3.4 – Sources of scatterCompliance of tool too high

Tool compliance higher than sample compliance… Not ideal !

But in theory possible to correct

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3.4 – Sources of scatterConclusion

Most sources did not have a big enough impact to explain all the scatter

Misalignment inside the tool was not estimated, but is probably the main source of mismatch (not scatter)

Brittle materials typically have a random behaviour

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4 – Channel geometry beam under bending

stress

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4.1 – Introduction & goals

Sample with channel-like notch

Goals :1 – validate simulation

parameters establishedduring SEVNB tests

2 – study influence of manufacturing method on overall strength of sample

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4.2 – Specimens

1st step : Alignment to crystalline structure

2nd step : Photolithography

3rd step : Notch etching (KOH or DRIE)

4th step : Dicing

Fabrication process

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4.2 – SpecimensObtained specimens

4 types of specimen :

DRIE90° KOH

DRIE80° DRIE60°

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4.2 – SpecimensDimensions of specimens

Optical measurements performed on 5 samples for each type

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4.3 – ExperimentsExperimental process

3 point bending :

Chuck just under channel

Precise alignment

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4.3 – ExperimentsExperimental process

Tests both in three– and four point bending

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4.4 – Results3 point bending

DRIE 60° DRIE80°

DRIE 90° KOH

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4.4 – Results4 point bending

DRIE 60° DRIE80°

DRIE 90° KOH

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4.4 – ResultsFracture loads

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4.4 – ResultsCompliance

Much higher mismatch for 3 point bending than for 4 !

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4.4 – ResultsCompliance – Summary

Much higher mismatch for 3 point bending than for 4 !

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4.4 – Parametric analysis

FEA estimation of influence of notch depth on compliance

Estimation of measurement errors through FEA model

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4.4 – Parametric analysis

Measurement errors have more impact for 3 point bending tests than for 4 point ones

Estimation of measurement errors through FEA model

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5 – ConclusionGathering of fracture data with SEVNB specimens to

allow setting parameters of fracture prediction tool

Validation of parameters through second testing batch

Essays on tensile-test machine for micro-scale specimens

Observation of sensitive aspects in fracture tests (scatter sources)

Observation of impact of manufacturing methods on fracture strength

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Backup slides

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Energy based approach

Elastic energy released = surface energy created

Energy release rate (G = πσ2a/E) : speed at which the energy is released by growth of the crack

GIc= KIc2*(1-ν2)/E[hkl]

(E : Young’s modulus, a : half crack length, σ : stress ; ν : Poisson’s coefficient ; [hkl] : Miller indexes)

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Possible test methodsA – Micro-indentation

B – Double Cantilever Beam

C – Compact Tests

D – Compression Loaded Double Cantilever Beam

E – Three/four point bending

F – Other (cantilever bending, On-chip tensile test device)

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A – Micro-indentationEasy to implement

Possible to test several crystalline orientations

Machinery quite common

Measuring the crack length

Residual stress after indentation

Hard to simulate with FEA

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B – Double Cantilever Beam

Theoretically possible to measure propagation values

Plastic deformation in arms

Direction of crack growth

Tensile load applied

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C – Compact TestsLess plastic deformation in thick arms

Short arms => crack growth direction more controllable

Plastic deformation & parasitic crack growth at load pins

Only initiation

Tensile load applied

D – Compression-Loaded Double Cantilever Beam

No tensile stress applied

Side groove to help crack grow in the intended direction

Stable crack growth

Crack growth monitored with thin film resistance

Wrong direction of crack growth

Hard to test such specimens (need a frame to hold them)

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E – Three/four point bending of notched

specimenASTM standard procedures available

Test under bending conditions

Easy modeling and manufacturing

Standard not adapted to our needs (scale)

No propagation measurements

F – Other

On chip tensile test device :

Complicated analysis

Sharpness of notch

Complicated fabrication process

Easy to apply the load

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Wet etching for vertical sidewalls

45° orientation of specimens relative to primary flat can lead to vertical sidewalls with KOH etch

%wt of KOH and temperature have an influence on the obtained slope of the walls

Ex : 60%wt & 60°C

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Alignment to crystalline planes

Anisotropic KOH etching step results in squares under the circle openings

Squares which are the most alligned give the cristalline orientation

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Support of the beams

Beam should be free to rotate around the rollers

Diameter : 0.5 – 1 mm

Supports considered :Razor bladesSteel wires

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3 points bendingmanufactured wafer

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3.2 – Compression Loaded Double

Cantilever Beam

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Reasons of the choiceCL-DCB has been chosen

as second specimen :

Easy to manufacture Possible to perform

FEA No tensile stress

(except at crack tip) Eventually possible to

measure both initiation & propagation values

Stable crack growth Easy to monitor crack growth (metal

gage)

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Dimensions of specimensb defined by wafer

thickness

Other dimensions set to keep ratios of previous experiments with this specimen

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Fabrication process

1st step : Alignment to crystalline structure

2nd step : DRIE with specimen shape

3rd step : Smoothing (RCA cleaning, SiO2 oxidation, etching of SiO2 layer)

4th step : Releasing of specimens by grinding of back side

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Required machinery

Possible to estimate fracture load P and displacement by assuming KIc = 1Pa√m

For B=1mm, W=525μm, L=10mm, a=300μm : Fc = 450 mN

yc = 23 μm

=>Resolution required : ≈ 10mN & 1μm

(Tensile test machine at CERN has 8mN and 1μm resolution)

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Tools available