Defects. Surfaces and grain boundaries. Phase diagrams.

From sand to silicon waferMetallurgical grade silicon (MGS)

Electronic grade silicon (EGS) Polycrystalline silicon (polysilicon)

25% of Earth surface is silicon

Single crystal Czochralski drawing

Single crystal Czochralski growth

Preparation of silicon wafers

(a) Perfect crystal withoutvacancies

(b) An energetic atom at the surface breaksbonds and jumps on to a new adjoining positionon the surface. This leaves behind a vacancy.

(c) An atom in the bulk diffusesto fill the vacancy therebydisplacing the vacancy towardsthe bulk.

(d) Atomic diffusions cause the vacancy todiffuse into the bulk.

Fig. 1.43: Generation of a vacancy by the diffusion of an atom to thesurface and the subsequent diffusion of the vacancy into the bulk.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Generation of vacancy in a perfect crystal

nv = N exp −Ev

kT⎛ ⎝ ⎜

⎞ ⎠ ⎟

nv = vacancy concentration,

N = number of atoms per unit volume,

Ev = vacancy formation energy,

k = Boltzmann constant,

T = absolute temperature(T,K = t,0C + 273.16)

Equilibriumconcentration of vacancies

In Si Ev =3.6 eV / vacancy

(a) A vacancy in the crystal. (b) A substitutional impurity in the crystal. Theimpurity atom is larger than the host atom.

(c) A substitutional impurity inthe crystal. The impurity atomis smaller than the host atom.

(d) An interstitial impurity in the crystal. Itoccupies an empty space between host atoms.

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Fig. 1.44: Point defects in the crystal structure. The regions aroundthe point defect become distorted; the lattice becomes strained.

Point defects in the crystal structure

Frenkel defect

(b) Two possible imperfections caused by ionized substitutionalimpurity atoms in an ionic crystal.

(a) Schottky and Frenkel defects in an ionic crystal.

Schottky defect

Substitutional impurity. Doublycharged

Fig. 1.45: Point defects in ionic crystalsFrom Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Point defects in the ionic crystals

Edge dislocation line

(a) Dislocation is a line defect. The dislocation shown runs into the paper.

CompressionTension

(b) Around the dislocation there is a strain field as the atomic bonds have beencompressed above and stretched below the islocation line

Fig. 1.46: Dislocation in a crystal is a line defect which is accompaniedby lattice distortion and hence a lattice strain around it.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

In SiED =100 eV / nm of dislocation

Compare withEv =3.6 eV / vacancy !!!

Edge dislocation

A

D

B

C

Atoms in theupper portion.

Atoms in thelower portion.

Dislocationline

(b) The screw dislocation in (a) as viewed from above.

(a) A screw dislocation in a crystal.

A

C

D

Dislocation line


Fig. 1.47: A screw dislocation involves shearing one portion of a perfectcrystal with respect to another portion on one side of a line (AB).

Screw dislocation

Photographs of real dislocations

Dislocation line

Fig. 1.48: A mixed dislocation.


Mixed dislocation

Growth of screw dislocation with the growth of crystal

In SiED =100 eV / nm of dislocation

Compare withEv =3.6 eV / vacancy !!!

Bulk crystal

SurfaceSurface atoms

Reconstructedsurface

OH

AbsorbedOxygen

H2O

OH2

Dangling bond

Fig. 1.52: At the surface of a hypothetical two dimensional crystal, theatoms cannot fulfill their bonding requirements and therefore havebroken, or dangling, bonds. Some of the surface atoms bond with eachother; the surface becomes reconstructed. The surface can havephysisorbed and chemisorbed atoms.


Surface of the hypothetical 2-D crystal

Bulk crystal

SurfaceSurface atoms

Reconstructedsurface

OH

AbsorbedOxygen

H2O

OH2

Dangling bond

Fig. 1.52: At the surface of a hypothetical two dimensional crystal, theatoms cannot fulfill their bonding requirements and therefore havebroken, or dangling, bonds. Some of the surface atoms bond with eachother; the surface becomes reconstructed. The surface can havephysisorbed and chemisorbed atoms.


Reconstruction of the surface

Model of the surface

Grain

(c)

Grain boundary

(b)

CrystalliteNuclei

Liquid

(a)

Fig. 1.50: Solidification of a polycrystalline solid from the melt.(a) Nucleation. (b) Growth. (c) The solidified polycrystallinesolid. For simplicity, cubes represent atoms.


Growth of polycrystalline solid

B

A

A

B

Strained bond

Broken bond(dangling bond)

Grain boundary

Void, vacancySelf-interstitial type atomForeign impurity

Fig. 1.51: The grain boundaries have broken bonds, voids, vacancies,strained bonds and "interstitial" type atoms. The structure of the grainboundary is disordered and the atoms in the grain boundaries have higherenergies than those within the grains.


Model of the grain boundaries

(a) Stoichiometric ZnO crystal with equal number of anionsand cations and no free electrons.

(b) Non-Stoichiometric ZnO crystal with excess Zn ininterstitial sites as Zn2+ cations.

O2–

Zn2+

"Free" (or mobile)electron within the crystal.

Fig. 1.54: Stoichiometry and nonstoichiometry and the resultingdefect structure.


Non-stoichiometry

Silicon (or Arsenic) atomOxygen (or Selenium) atom

(a) A crystalline solidreminiscent to crystallineSiO2.(Density = 2.6 g cm-3)

(b) An amorphous solidreminiscent to vitreous silica(SiO2) cooled from the melt(Density = 2.2 g cm-3 )

Fig. 1.56: Crystalline and amorphous structures illustrated schematicallyin two dimensions.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Continuous Random Network

Crystalline vs. amorphous structure

(SiO2 )0.8 (Na2 O)0.2

SiO2 , GeO2

As2 S3

Ge-Ga-Se (S) : Er

Cu66 Zr33

Fe80 B20

Pd80 Si20

Quenching of amorphous metals

H H

H

H

H

H(c) Two dimensional schematicrepresentation of the structure ofhydrogenated amorphous silicon. Thenumber of hydrogen atoms shown isexaggerated.

(b) Two dimensional schematicrepresentation of the structure ofamorphous silicon. The structure hasvoids and dangling bonds and there is nolong range order.

(a) Two dimensional schematicrepresentation of a siliconcrystal


Fig. 1.58: Silicon can be grown as a semiconductor crystal or as anamorphous semiconductor film. Each line represents an electron in abond. A full covalent bond has two lines and a broken bond has one line.

Dangling bond

Crystalline (c-Si), amorphous (a-Si) and hydrogenated (a-Si:H) silicon

Silicon fordeposition

Evaporated Si atoms Electronbeam guidedby a magneticfield

Heated substrate

a-Si film

VACUUM

Electrongun

VACUUMPUMP

Depositionchamber

Crucible


Fig. 1.59: Amorphous silicon, a-Si, can be prepared by an electronbeam evaporation of silicon. Silicon has a high melting temperatureso that an energetic electron beam is used to melt the crystal in thecrucible locally and thereby vaporize Si atoms. Si atoms condenseon a substrate placed above the crucible to form a film of a-Si.

Heated substratea-Si:H film

Vacuum Pump

Electrode

Electrode

Silanegas(SiH4)

RF PowerGenerator

Vacuum

CVD Chamber

Plasma

Fig. 1.60: Hydrogenated amorphous silicon, a-Si:H, is generallyprepared by the decomposition of silane molecules in a radiofrequency (RF) plasma discharge. Si and H atoms condense ona substrate to form a film of a-Si:H.


Amorphous silicon (a-Si) and amorphous hydrogenated silicon (a-Si:H)

Covalentlybonded networkof atoms

Cubic crystal

(a) Diamond unit cell

Covalently bonded layer

Layers bonded by van derWaals bonding

Hexagonal unit cell

Covalently bondedlayer

(b) Graphite

Buckminsterfullerene (C60) molecule (the"buckyball" molecule)

The FCC unit cell of theBuckminsterfullerene crystal. Each latticepoint has a C60 molecule

(c) Buckminsterfullerene

Fig. 1.42: The three allotropes of carbon.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Polymorphism or allotropy = the ability to create more than one crystal structure

Allotropy

(a) DisorderedSubstitutional SolidSolution. Example: Cu-Nialloys ({100} planes)

(c) Interstitial Solid Solution.Example: Small number of Catoms in FCC Fe (austenite).({100} planes)

(b) Ordered SubstitutionalSolid Solution. Example: Cu-Zn alloy of composition50%Cu-50%Zn. ({110}planes).

Fig. 1.61: Solid solutions can be disordered substitutional, orderedsubstitutional and interstitial substitutional. There is only one phasewithin the alloy which has the same composition, structure andproperties everywhere.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Solid solutions ∈

alloys

majority atoms = solventminority atoms = solute

Solidification of pure Cu

L0

S0

heat of fusion

Solidification of pure Cu and Ni

1453 0C

Pure NiL100 S100

Solidification of 80% Cu + 20% Ni

1453 0C

Pure Ni

1195 0C

1130 0C

L20

S20

L0

S0

L100 S100

1000

1100

1200

1300

1400

1500

0 20 40 60 80 100Ni Content (wt.%)

Pure Cu Pure Ni

LIQUID

SOLID

L100S100

L 0 S 0

L20

S20

(b)

1000

1100

1200

1300

1400

1500

1130 °C

1195 °C

L0S0

L20

S20

Time

Pure Cu 80%Cu-20%Ni

1083 °C

Solid

Liquid

SolidCrystal grains

Liquid

(a)TE

MPE

RATU

RE (°

C)

LIQUID + SOLIDLIQUIDUS

SOLIDUS

TEM

PERA

TURE

(°C)

Heterogeneous mixtureof liquid and solid.

Formation of first solid

Fig. 1.62: Solidification of an isomorphous alloy such as Cu-Ni.(a) Typical cooling curves. (b) The phase diagram marking theregions of existence for the phases.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

1000

1100

1200

1300

0 20 40 60

LIQUID

SOLID(α-PHASE)

S2

S1

S3

L2

L3

C0wt.% Ni

L0

L1

X

Pure Cu

S4

L(20%Ni)

L(20%Ni)S(36%Ni)

L(13%Ni)S(28%Ni)

S(20%Ni)

Liquid

Fig. 1.63: Cooling of a 80%Cu-20%Ni alloy from the melt to thesolid state.

LIQUID

US

SOLID

US

TEM

PER

ATU

RE

(°C

)

What is the composition of solid phase?

Lever Rules

WL = weight fraction of liquidWs = weight fraction of solid

WL + WS = 1 (1)

C0 = total concentration of Ni CL = concentration of Ni in liquid CS = concentration of Ni in solid

CL WL + CS WS = C0 (2)

CS

CL

WL =CS − CO

CS − CL

WS =CO − CL

CS − CL

andCSCL

TX

Lever Rules

WL = the weight fraction of the liquid phase, WS = the weight fraction of the solid phase, CS = composition of the solid phase, CL = composition of the liquid phase, CO = overall composition.

WL =CS − CO

CS − CL

and WS =CO − CL

CS − CL

1000

1100

1200

1300

0 20 40 60

LIQUID

SOLID(α-PHASE)

S2

S1

S3

L2

L3

C0wt.% Ni

L0

L1

X

Pure Cu

S4

L(20%Ni)

L(20%Ni)S(36%Ni)

L(13%Ni)S(28%Ni)

S(20%Ni)

Liquid

Fig. 1.63: Cooling of a 80%Cu-20%Ni alloy from the melt to thesolid state.

LIQUID

US

SOLID

US

TEM

PER

ATU

RE

(°C

)

What is the influence of fast cooling?

First solidification(S1) Ni rich

Grain boundary

Last solidification(S3) Ni defficient

Fig. 1.64: Segregation in a grain due to rapid cooling (non-equilibrium cooling)


HEATDirection of travel

ImpureSolid

Purifiedregion

AB

Melt

C0

ImpureSolidA'B' C0

(b) As the torch travels towards theright, the refrozen solid at B' has CB'where CB < CB' < C0. The impurityconcentration in the melt is now evengreater than CL'

x

C0

CB

CB'

Zone refined region

(a) Heat is applied locally starting at oneend. The impurity concentration in the re-frozen solid at B is CB < C0. Theimpurity concentration in the melt is CL' >C0.

(c) The impurity concentration profile inthe refrozen solid after one pass.

x

C0

Zone refined regionC0

106

(d) Typical impurity concentrationprofile after many passes.

Impu

rity

conc

entra

tion

Fig. 1.66: The principle of zone refiningFrom Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Impu

rity

conc

entra

tion

Impurity content

Temperature

LIQUID

L + S

1 4 1 2 ° C CLB

TB CL'

B'TB'

SOLID

CB CB' C0

Fig. 1.65: The phase diagram of Si with impurities near the lowconcentration region.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

SOLIDUS

LIQUIDUS

Zone refining principles

X

Isomorphous alloys


TEM

PER

ATU

RE

Wt.% Salt

Brine

XsX1 X3

BrineSalt

Brine + SaltBrine

Fig. 1.67: We can only dissolve so much salt in brine (solution ofsalt in water). Eventually we reach the solubility limit at Xs whichdepends on the temperature. If we add more salt then the excesssalt does not dissolve and coexists with the brine. Past Xs wehave two phases, brine (solution) and salt (solid).

Solvus

Pure Pb100

SOLIDUS

LIQUID

α + L

α + β

α

β61.9%183°C 97.5%

80604020Composition in wt.% Sn

100

200

300

400

0

19.2%

0

LL

MNO

P

Q

R

αL

α

αβ

R'

Q'

R''

Pure Sn

SOLIDUS SOLIDUSL+βE

A

B

C D

Fig. 1.68: The equilibrium phase diagram of the Pb-Sn alloy. Themicrostructures on the left show the observations at various pointsduring the cooling of a 90%Pb-10%Sn from the melt along the dashedline (the overall alloy composition remains constant at 10 %Sn)From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Tem

pera

ture

(oC

) LIQUIDUS

LIQUIDUS

SOLV

US SO

LVUS

SOLIDUS

Non-isomorphous alloys

SOLID

T

t

L+αL

β+α

L+β+αMO P

Q

N

Cooling of a 60%Pb-40%Sn alloy T

t

L

Cooling of 38.1%Pb-61.9%Sn alloy

E FG

α (light)and β (dark)

L (61.9%Sn)Eutectic

Eutectic

Sn

L (61.9%Sn)

SOLIDUS

LIQUID

α+L

α + β

α

βL+β

61.9%183°C

80604020

100

200

300

400

0Pb

NO

P

Primary α

L

Lα

α (19%Sn)L (61.9%Sn)

Eutectic

Eutectic Q

E

L

M

L

F

G

A

C

BD

Composition in wt.% Sn

Fig. 1.69: The alloy with the eutectic composition cools like a pure element exhibiting asingle solidification temperature at 183°C. The solid has the special eutectic structure.The alloy with the composition 60%Pb-40%Sn when solidified is a mixture of primaryα and eutectic solid.From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Tem

pera

ture

(o C

) LIQUIDUS

LIQUIDUS

SOLV

US SO

L VUS

SOLIDUS

L + Eutectic solid (β+α)

Eutectic solid (β+α)183 °C

235°C183°C

Eutectic Transformation

L = liquid phase

α = Pb-rich solid phase of PbSn

β = Sn-rich solid phase of PbSn

L61.9% Sn → α19.2% Sn + β97.5% Sn

Defects. Surfaces and grain boundaries. Phase diagrams.

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Transcript of Defects. Surfaces and grain boundaries. Phase diagrams.