01.introduction integrated circuit

7/30/2019 01.Introduction Integrated Circuit

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Moores Law and material processing Defects in crystals Eutectic phase diagram Solid solubility Homogeneous nucleation

Heterogeneous Nucleation Growth processes

INTRODUCTION


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High

Low

FailureRate

Co

st

1 mm

1-5 nm High

Low

Minim

um

FeatureSize

Comp

lexity

1930-

1950s

1960s

1970-90

VACUUM TUBES

SEMI CONDUCTOR BASEDTRANSI STORS

PLANAR TRANSI STORS

I Cs LSI , VLSI

SMART STRUCTURES1995-

NANO STRUCTURES

2010-


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Intel Roadmap for VLSI/ULSI

300300300200/

300

200200Wafer (mm)


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Moores LawProcessor power will keep doubling every two years.

Aft er I ntel CorpAft er I ntel Corp


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Aft er I ntel CorpAft er I nt el Corp

Moores Law


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Aft er I ntel CorpAft er I nt el Corp

Moores Law


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Aft er I ntel CorpAft er I ntel Corp

Moores Law


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Processed Silicon Wafer in 2000


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EUV Lithography


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Silicon Crystal

Crystal Structure :

Diamond cubicTwo interpenetrating FCC latticesa = 0.543 nmd = distance between atoms

= 3a/4Atomic density = 8 / a3

Closed packed plane (111)

http://jas.eng.buffalo.edu/education/solid/unitCell/home.html


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Silicon Crystal


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Silicon Crystal

100 = 6.8 x 1018 at/m2

111 = 9.6 x 1018 at/m2


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Silicon Crystal


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Silicon Crystal

K300atSiform/10n

eVT10x6.321.1)T(Ewhere

m/)Tk2

)T(Eexp(T10x9.3n

316i

4g

3

B

g2/322i


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Silicon CrystalCharge Carriers in Doped Si


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Silicon Crystal

SinforEvvelocityDrift

pqnq

nd

pn

Conductivity and Mobility :

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

1E+19 1E+21 1E+23 1E+25 1E+27at/m3

m2/V-sec

n

p1E+19

1E+21

1E+23

1E+25

1E-05 1E-03 1E-01 1E+01

Resistivity, ohm-m

at/m3 p-type

n-type


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Mobility in Silicon

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

1.E+19 1.E+21 1.E+23 1.E+25 1.E+27

at/m3

m2/V-sec

n

p


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1E+19

1E+21

1E+23

1E+25

1E-05 1E-03 1E-01 1E+01

Resistivity, ohm-m

at/m

3

p-type

n-type

Resistivity in Silicon


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Defects in CrystalsTypes of Defects:

Point Defects vacancy, interstitial, V-I pairs, clusters Line Defects Dislocations edge & screw Planar Defects stacking fault, twin, grain boundary

Point Defects:

Interstitial

Impurity Vacancy


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20

Defects in CrystalsDislocations:

Extra planeof atoms

Edge

dislocation Screwdislocation

Screw Dislocation:b ||le to l

Edge Dislocation:Extra plane of atom is

present.b r to l


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Defects in Crystals

Screw Dislocation


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Defects in CrystalsPlanar Defects: Stacking Faults Twins

Grain Boundaries

Layer ordering in silicon:A B C A B C along (111) plane.

Stacking fault:A B C B C A B C A B C

Twin :A B C A B A C B A

Grain Boundary:

Twin plane

C

A

B


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Phase ChangeLiquid state : High entropy and High enthalpySolid state : Low entropy and low enthalpy

A phase change, say liquid to solid, occurs, if

F = H - T S is negative

where F = free energy change for solidificationH = enthalpy change for solidification = latent heat of fusionS = entropy change during solidification

Above melting point (Tm), F > 0At melting point, F = 0 gives H = Tm SBelow melting point, F = S(Tm-T) < 0


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Phase DiagramComplete Solid Solution:Liquid of composition x onsolidifying at temp T gives solid of

composition xs and liquid ofcomposition xl.

s

l

xx

xx

os

ol

liquidofVol

solidofVol

Eutectic :At TeutecticA + B = L

or + = L

Temp

compA B

L

L+S

Sxs xl

s o l

x

T

TmA

TmB

Temp

compA B

L

A+L

A+B

Teutectic

B+L

TmA TmB

Eutectic with nosolid solubility

Temp

compA B

L

+L

+

Teutectic

+L

TmBTm

A

Eutectic withlimited solid

solubility

Gibbs Phase Rule :F + P = C + 2

P no. of phasesC no. of componentsF degree of freedom


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SegregationWhen a liquid having composition xlfreezes, the solid that first freezes has

composition xs.

This gives a purification onsolidification since xs < xl.

Segregation coefficient = ko

0citliminc

ck l

l

so

= ratio of slopes of solidus and

liquidus at origin

ko < 1 purificationko > 1 no purification

Temp

Comp(%B)

L

L+S

S

clcs

liquidus

solidus

ks1


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Solid SolubilitySolubility of B in A depend on the bond energies of A-A, B-B and A-B bondsand the entropy of the mixture of A and B atoms.

)]x1ln()x1(xlnx[Tk)x1(zxNN

ABBBBBBB

BA

where

NA no. of A atoms & NB no. of B atomsxB = NB/ (NA + NB)9uhg

= AB (AA + BB)/2AA, BB, AB are energies of A-A, B-B and A-B bonds respectivelyz = no. of nearest neighbours of A

A = Helmholtz Free energy of forming solid solution of B in A = E - TS

Slope ( A/ xB) near xB=0 is - . It is impossible to purify silicon to100%.

We have to spend more and more

energy to purify as material gets purer.Solubility limit

xBA >0


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TkEexpxx,1xIf

]Tk

)x21(zexp[

x1

x

0x1

x

lnTk)x21(z

.itlimilitylubsogives0x

])NN/[A(

B

BoBB

B

B

B

B

B

B

bB

B

BASolid Solubility

This equation applies to solutes, vacancies, interstitials and allother thermal defects present in solids.

exampleforerstitialsintforTk

Eexpxx

exampleforvacanciesforTk

Eexpxx

B

IIoI

B

VVoV


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nucliicriticalinmoleculesof.no)gg(3

n2n

nucliiofradiuscritical)gg(

v2r

0r8v

)gg(r4gives0

r

G

area/energysurfacewhere,n)v(36)gg(n

)areasurface(G)volchemcial(Gr4

v

gr

3

4G

,growingis'r'radiusofnucleisphericalaSince

)p

pln(TkT)ss()TT)(ss()ss(Thhggg

ioncondensat0G,TTAt

ioncondensatno0G,TTAt

3

vlc

vl

l

c

cl

vl2c

r

32

3 2lvl

sv2

l

lv3

iBs

vlv

vlvlvlvllv

v

v

c

Homogeneous NucleationCondensation of Liquid from Vapour Phase:r

rc r

G

Gc

Gv ~r3

Gs ~r2


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29

2s

3

2c3

2

vl

lc

T

K

energysurfaceofrd3/13

r4

gg

v

3

16G

Homogeneous NucleationCondensation of Liquid from Vapour Phase:For r < rc, the nuclei will reduce in size.For r > rc, the nuclei will grow.

An energy barrier of Gc has to be overcome for nucleation toproceed.

rc

where, Ts is the supersaturation, i.e., (Tv -T)

2sB

2

o

B

co

)T(TkKexpI

TkGexpIInucleationofRate

Rate of nucleation increases with supersaturation.


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Homogeneous NucleationNucleation of Solid from Vapour : = f(orientation of the crystal plane) = anisotropic

Singular surface, is minimum

Non-singular surface consists

of steps of singular surface

2

3s

c

s

s

32

3 2svs

ib

vsc

)T(

)(KG

area/energysurfaceaveragewheren)v(36)gg(nG

,growingismolecules'n'containingofnucleiaSince

)p

pln(TkggG


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Homogeneous NucleationNucleation of Solid from Liquid :

Tk

g

)T(T

KKlnIln

Tk

)gG(expIIrateNucleation

)T(

1

)gg(

1G

)ss(T)ss)(TT(

)ss(T)ss(T)ss(Thhgg

B

#

2

21

B

#c

o

22lsc

lslsm

lslsm

lslsls

where g# = energy required to break bonds in liquid

Below a temperature, nucleation rate reduces so that glassformation takes place at that point.

Tm

I

glassformation

T


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32

Heterogeneous Nucleation

4

CosCos32

gg

v

3

16

)gg(

v)(27

4

G

)(rv

ggrG

anglecontactwhere,Cos

32

vl

l3lv

2vll

2l

3

lssvlslvlv

c

lssvlslvlv2

l

vl

3l

lvslsv

Gc

=0

Gc decreases with smaller contact angle.

Hence nucleation rate increases if there isheterogeneous nucleation.

Nucleation is still easier inside a cavity.

lv

sv

sl surface

Condensation of Liquid on a Surface :


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Nucleation will proceed by arrival ofmolecule on the surface and then itsmovement to the nucleating site bysurface diffusion.If surface diffusion is slow,nucleation rate, I, will become

dependent on surface diffusion.

Heterogeneous Nucleation

Tk

gGexp

Tk3

GANI

B

sdc

B

3c

cs

surface

surfacediffusion

I = Nucleation rate for heterogeneous nucleationgsd = activation energy for surface diffusion.

Condensation of Liquid on a Surface :


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Heterogeneous NucleationNucleation of a Solid inside Another Solid : Phase is growing inside phase.

2

3c

gg

v4G

Cos2

Cos

Gc

GcH

0

1 boundary

edge

cornerStrain :

gs = strain energyIf g

s

is small, surface energydominates.

If gs is large, nucleation takesplace to minimize the strain energy.

bsn A)ggg(nG

1

y/RE(y/R)

sphere

needle

platelet

0

R

y

01.introduction integrated circuit

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