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Sensores Integrados em Silício IE325 EE824

Professor Fabiano Fruett

UNICAMP – FEEC - DSIFSala 207

www.dsif.fee.unicamp.br/~fabiano

Propriedades mecânicas do silício

Referências

F. Fruet and G. C. M. Meijer, "The piezojunction effect in silicon integrated circuits and sensors", Kluwer, 2002

http://www.ioffe.rssi.ru/SVA/NSM/Semicond/Si/

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Classificação dos sólidos

• Cristais: apresentam uma estrutura altamente ordenada chamada de rede cristalina. Exemplos: wafer de Si, diamante

• Policristalinos: apresentam uma ordem intermediária, com pequenas regiões chamadas de grãos, tendo cada estrutura cristalina unida pelos limites dos grãos. Exemplos: silício policristalino, algumas rochas

• Amorfos: estrutura sem ordem definida.

Estrutura dos sólidos

Amorfo Policristalino Cristal

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Silicon as a basic material for the production of integrated sensors• Excellent mechanical properties• Many transduction effects available• Small size• Possible co-integration of sensors and

interface electronics• Low unit costs in mass production• Silicon microelectronic infrastructure

already available

Mechanical properties of crystalline silicon

Density

[103 Kg/m3]

Knoop Hardness

[109 Kg/m2]

Young’s modulus [1011 Pa]

Yield Strenght [109 Pa]

Thermal Conduct. [W/m oC]

Thermal Expans. [10-6/oC]

2.3 0.85 1.9* 7.0 157 2.33 * average in the isotropic approximation

Fonte K.E. Peterson, Silicon as a mechanical material, Proc. IEEE, 70, pp. 420-457, 1982.S. Johansson, Micromechanical properties of silicon, PhD Thesis, Uppasala University, Uppsala, Sweden, 1988.

Low density High modulus of elasticity

High fracture strength

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The “size effect”

In theory, there are essentially no crystal defects present in a micromachinedcomponents, and the surface might be close to atomic smoothness.

Fonte: H.H. Bau, N.F. de Rooij and B. Kloeck (ed.), Mechanical sensors, Sensors , A Comprehensive Survey, VCH Verlagsgesellschaft mbH, Weinheim, 1994.

Mechanical stressSecond-rank stress tensor σij in a cubic volume element of a solid

=

zzzyzx

yzyyyx

xzxyxx

ij

σσσσσσσσσ

σ

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If F is the force and A is the area, the stress components are given by:

j

iij A

F∂∂

=σ

yxxy σσ = zxxz σσ = zyyz σσ =

(a) Force F acting on its associated area A. The forces Fn and Ft are the normal and tangent components of F, respectively.

(b) Definition of the normal and shear stress

Fn

n n

F

t tFt

A A

σn

σt(a) (b)

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General state of stress of an infinitesimal cubic volume element

y

x

z σzz

σzyσzx

σyy

σyz

σyx

σxx

σxy

σxz

only six independent components

Strain

Strain is a dimensionless quantity which represents the state of deformation in a solid body.

=

zzzyzx

yzyyyx

xzxyxx

ij

εεεεεεεεε

ε

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Normal and shear strain

a) Normal strain εxx b) Normal strain εyy c) Shear strain εxy

dx

dy

εxxdxεyydy

x x x

y y y

εxy

εxy

( /2)-2π εxy

Hooke’s lawIf the stress is below a certain value (the elastic limit), the strain is recoverable, and the body returns to its original shape when the stress is removed.

klijklij C εσ = ,klijklij S σε =

Cijkl are the stiffness constants and Sijkl are the compliances

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Deflexão de uma viga de silício durante um teste mecânico

Fonte: T. Yi and C.J. Kim

Análise FEM (Método dos Elementos Finitos)

Fonte: T. Yi and C.J. Kim

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Simplification of indexes in reduction notation

r, s=1, 2, 3, 4, 5 and 6,

xx yy zz yz=zy xz=zx xy=yx1 2 3 4 5 6

srsr S σε =

=

6

5

4

3

2

1

44

44

44

111212

121112

211211

6

5

4

3

2

1

000000000000000000000000

σσσσσσ

εεεεεε

SS

SSSSSSSSSS

Hooke´s law:

Stiffness and compliance coefficients of silicon

S11 [10-11 /Pa]

S12 [10-11 /Pa]

S44 [10-11 /Pa]

C11 [1011 Pa]

C12 [1011 Pa]

C44 [1011 Pa]

0.768 -0.214 1.26 1.657 0.639 0.796

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Cristal de silício

Silicon has the same crystal structure as diamond.

Fonte: M. Madou, Fundamentals of microfabrication

Si crystal orientation and Miller indices

y

[001]

[100]

(001)

[010]

y

[001]

[100]

(011)

[010]

y

[001]

[100]

(111)

[010]

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• The crystallographic orientation of the silicon wafer is determined in the sawing process during the wafer fabrication.

• Some process-related defects such as the oxide-fixed charge density and interface trap level density are less on a (001) surface than on a (011) or (111) surface.

Fonte:E.H. Nicolian and J.R. Brews, MOS (Metal Oxide Semiconductor) physics and technology, John Wiley & Sons, 1982.D. Lambrichts, private communication, IMEC, Leuven, Belgium, Jun. 1999.

Orientação do wafer

Fonte: WTPRocessS – CCS Unicamp

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Cristalografia do silício

Fonte: Wolf and Tauber

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Planos e direções

Planos(001)=(010)=(100) => {100}

Direções[100]=[010]=[001] => <100>

Main crystal axes of an (001) wafer plane

[100] [010]

[001]

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Elastic properties of silicon

• Young’s modulus Y• Shear modulus ν• Poisson’s ratio G

Stress orientation

Y [GPa]

ν G [GPa]

<100> 130.4 0.280 79.6 <011> 170.7 0.057 51.3

Temperature dependence of the silicon stiffness coefficients

dTdC

C11

11

1

[10-5 K-1] dT

dCC

12

12

1

[10-5 K-1] dT

dCC

44

44

1

[10-5 K-1] -9.4 [18] -9.3 [19]

-9.8 [18]

-8.3 [18] -7.3 [19]

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Temperature dependences of elastic constants

Pontilhados – Skimim [1953]Circulos – Nikanorov et al. [1971]

Propriedade mecânica dos filmes finos

• Características desejáveis:– Excelente adesão– Baixo stress residual– Boa resistência mecânica– Resistência química

• Essas características dependem do:– Processo de deposição e crescimento– substrato

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Propriedade mecânica dos filmes finos

Para aplicações em micromáquinas, estruturas com reduzido stress são necessárias.

Exemplo: polisilício

Origin of mechanical stress in a silicon die

• Stress from silicon wafer processing

• Stress from packaging

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Mechanical properties of some materials used in

electronic packaging

Material Thermal Expansion [10-6 /oC]

Young’smodulus[109 Pa]

Silicon 2.6 130-190Attachment 40-60 1-5 Substrate 4-17 12-15

Plastic 13-20 10-15

Etapas de fabricação

Wafer Die ElectronicPackaging

1 2 3

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Die attachment

Silicon dieAttachmentSubstrate

+ εmax

- εmax

Normal strain distribution

Electronic devices

(b)

(c) (d)

(a)

σxxσyy

σzz

Simulação do stress com FEM

[Mpa]

Substrato metálico

Silicio

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Stress from packaging

• Moderated level of stress, up to 200 MPa.• The stress can both be compressive and

tensile.• Dominant-normal stress in any orientation

parallel to the wafer plane.

Aparato mecânico para teste

Silicon Beam

Switch Control

Current andVoltageSources

Instruments Computer LabView

Virtual Instruments

Driver

Stepper

Mechanical Apparatus

Position Interface

Micrometer Gear

ClampDUT in/out

DUT Temp. Ref.

Thermoset

DriverStepperEncoder

Oven

36 mm teflon

Pt 100

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Cantilever technique

L

x=0

y

L

yLoadSilicom beam

[100] [010]

[001] Plane

sawlanes