Doping and Crystal Doping and Crystal Growth TechniquesGrowth Techniques

Types of ImpuritiesTypes of Impurities

Substitutional ImpuritiesSubstitutional Impurities– Donors and acceptorsDonors and acceptors– Isoelectronic DefectsIsoelectronic Defects

VacanciesVacancies– Charged VacanciesCharged Vacancies

Color centers in solids (alkali halides)Color centers in solids (alkali halides) Interstitial AtomsInterstitial Atoms

– Mid Gap TrapMid Gap Trap Antisite DefectsAntisite Defects

Back to the Periodic TableBack to the Periodic Table

Column V AtomsColumn V Atoms

Have 5 outer shell electronsHave 5 outer shell electrons

The extra electron on the phosphorous atom is easily removed and becomes a free electron without generating a hole.

The phosphorous atom becomes positively charged (ionized).

Back to the Periodic Table Back to the Periodic Table (again)(again)

Column III AtomsColumn III Atoms

Have 3 outer shell electronsHave 3 outer shell electrons

The boron atom ‘steals’ an electron from a neighboring Si atom to complete the four bonds with the surrounding Si atoms, generating a hole at the neighboring Si atom. The boron atom becomes negatively charged (ionized).

n-type Semiconductorsn-type Semiconductors

Are doped with donor atoms, which have Are doped with donor atoms, which have an extra electron that they donate to the an extra electron that they donate to the crystalcrystal– When the concentration of donor atoms is When the concentration of donor atoms is

much greater than the intrinsic carrier much greater than the intrinsic carrier concentration, the electron concentration is concentration, the electron concentration is composed of these donated electrons.composed of these donated electrons.

dNn

p-type Semiconductorsp-type Semiconductors

Are doped with acceptor atoms, which Are doped with acceptor atoms, which generate holes in the crystalgenerate holes in the crystal– When the concentration of acceptor atoms is When the concentration of acceptor atoms is

much greater than the intrinsic carrier much greater than the intrinsic carrier concentration, the hole concentration is concentration, the hole concentration is composed of the holes generated by the composed of the holes generated by the acceptors.acceptors.

aNp

Carrier ConcentrationsCarrier Concentrations

n-type n-type semiconductorsemiconductor

p-type p-type semiconductorsemiconductor

a

i

a

i

N

nn

Np

pnn

2

2

d

i

d

i

N

np

Nn

pnn

2

2

Bohr model for Hydrogen Bohr model for Hydrogen atomatom

nm 053.04

6.13

)4(2

24

22

2222

4

nqm

nr

n

eVE

n

qmEE

o

on

vaco

ovacn

Translation to Donor AtomTranslation to Donor Atom

Include relative dielectric constantInclude relative dielectric constant Extra electron has a effective mass Extra electron has a effective mass

equal to the conduction band electronsequal to the conduction band electrons

nm 053.04

6.13

)4(2

2*4*

22

2

*

2222

4*

nmqmm

nr

m

nE

n

qmmEE

n

r

on

ron

r

nC

ro

onCn

Translation to Acceptor Translation to Acceptor AtomAtom

nm 053.04

6.13

)4(2

2*4*

22

2

*

2222

4*

nmqmm

nr

m

nE

n

qmmEE

p

r

op

ron

r

pV

ro

opVn

Include relative dielectric constantInclude relative dielectric constant Missing electron has a effective mass Missing electron has a effective mass

equal to the valence band electronsequal to the valence band electrons

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

In quantum mechanics, we talk In quantum mechanics, we talk about the probability of finding a about the probability of finding a particle in a certain place.particle in a certain place.

xxp p ≥ħ/2≥ħ/2

tt ≥1/4≥1/4ttE E ≥ħ/2≥ħ/2

Impurity LevelImpurity Level

2

1

kx

kp DeBroglie’s relation

The deeper the impurity level from either Ec or Ev, the smaller rn is – i.e, the electron or hole is more tightly bound to the impurity.

http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm

GaP LEDs have a low concentration of N impurities in them. The impurity energy level has a large k that extends from the X minima to the minima, allowing the trapped electrons to radiative recombine with holes.

Types of ImpuritiesTypes of Impurities

Substitutional ImpuritiesSubstitutional Impurities– Donors and acceptorsDonors and acceptors– Isoelectronic DefectsIsoelectronic Defects

VacanciesVacancies– Charged VacanciesCharged Vacancies

Color centers in solids (alkali halides)Color centers in solids (alkali halides) Interstitial AtomsInterstitial Atoms

– Mid Gap TrapMid Gap Trap Antisite DefectsAntisite Defects

Types of Crystal GrowthTypes of Crystal Growth

Product is a boule from which wafers Product is a boule from which wafers are then cutare then cut– Czochralski (CZ)Czochralski (CZ)– Float Zone (FZ)Float Zone (FZ)– BridgemanBridgeman

CzochralskCzochralskii

http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/illustr/i6_1_1.html

www.qahill.com/tz/silicon/silicon.html

http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1

Impurity SegregationImpurity Segregation

1)1(

okooS

L

So

fkCC

C

Ck

Where Co is the initial concentration of th impurity in the melt

Impurity SegregationImpurity Segregation

Atom Cu Ag Au C Ge Sn As

ko 4 · 10–4 10–6 2.5 · 10–5 7 · 10–2 3.3 · 10–2 1.6 · 10–2 0.3

Atom O B Ga Fe Co Ni Sb

ko 0.5 0.8 8 · 10–3 8 · 10–6 8 · 10–6 4 · 10–4 2.3 · 10–2

Float ZoneFloat Zone

www.tms.org/pubs/journals/JOM/9802/Li/

www.mrsemicon.com/crystalgrowth.htm

Impurity SegregationImpurity Segregation

L

xk

ooS

o

ekCxC )1(1)(

Where Co is the initial concentration of the impurity in the solid and L is the width of the melted region within RF coil

BridgemanBridgeman

Used for some compound Used for some compound semiconductorssemiconductors– Particularly those that have a high vapor Particularly those that have a high vapor

pressurepressure– Produced “D” shaped boulesProduced “D” shaped boules

Crystalline DefectsCrystalline Defects

Point DefectsPoint Defects– VacanciesVacancies– ImpuritiesImpurities– Antisite DefectsAntisite Defects

Line DefectsLine Defects– DislocationsDislocations

EdgeEdge LoopLoop

Volume DefectsVolume Defects– VoidsVoids– Screw DislocationsScrew Dislocations

Edge DislocationEdge Dislocation

http://courses.eas.ualberta.ca/eas421/lecturepages/mylonite.html

Screw DislocationScrew Dislocation

http://focus.aps.org/story/v20/st3

Strain induced DislocationsStrain induced Dislocations

The temperature profile across the The temperature profile across the diameter of a boule is not constant diameter of a boule is not constant as the boule cools as the boule cools – the outer surface of the boule contracts the outer surface of the boule contracts

at a different rate than the internal at a different rate than the internal regionregion

– Thermal expansion differences produces Thermal expansion differences produces edge dislocations within the bouleedge dislocations within the boule Typical pattern is a “W”Typical pattern is a “W”

Strain due to ImpuritiesStrain due to Impurities

An impurity induces strain in the An impurity induces strain in the crystal because of differences incrystal because of differences in– ionic radius as compared to the atom it ionic radius as compared to the atom it

replacedreplaced Compressive strain if the ionic radius is largerCompressive strain if the ionic radius is larger Tensile strain if the ionic radius is smallerTensile strain if the ionic radius is smaller

– local distortions because of Coulombic local distortions because of Coulombic interactionsinteractions

Both cause local modifications to EgBoth cause local modifications to Eg

Dislocation CountDislocation Count

When you purchase a wafer, one of When you purchase a wafer, one of the specifications is the EPD, Etch Pit the specifications is the EPD, Etch Pit DensityDensity– Dislocations etch more rapidly in acid Dislocations etch more rapidly in acid

than crystalline materialthan crystalline material– Values for EPD can run from essentially Values for EPD can run from essentially

zero (FZ grown under microgravity zero (FZ grown under microgravity conditions) to 10conditions) to 1066 cm cm-2-2 for some materials for some materials that are extremely difficult to grow.that are extremely difficult to grow. Note that EPD of 10Note that EPD of 1066 cm cm-2-2 means that there is means that there is

a dislocation approximately every 10a dislocation approximately every 10ms.ms.

Wafer ManufacturingWafer Manufacturing

Boules are polished into cylindersBoules are polished into cylinders Aligned using an x-ray diffraction Aligned using an x-ray diffraction

systemsystem Cut into slices using a diamond edged Cut into slices using a diamond edged

sawsaw– Slices are then polished smooth using a Slices are then polished smooth using a

colloidal gritcolloidal grit Mechanical damage from sawing causes point Mechanical damage from sawing causes point

defects that can coalesce into edge defects that can coalesce into edge dislocations if not removed dislocations if not removed

http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1

SCS ManufacturingSCS Manufacturing• After some processing steps

such as dicing, lapping, etching, and polishing, silicon wafers will be ready to be used.

• For wafers <200mm, the flats are used to determine the crystal orientation and the impurity type of the wafer.

Carrier Mobility and VelocityCarrier Mobility and Velocity

MobilityMobility - the ease at which a carrier - the ease at which a carrier (electron or hole) moves in a (electron or hole) moves in a semiconductorsemiconductor– Symbol: Symbol: nn for electrons and for electrons and pp for holes for holes

Drift velocityDrift velocity – the speed at which a – the speed at which a carrier moves in a crystal when an carrier moves in a crystal when an electric field is presentelectric field is present– For electrons: vFor electrons: vdd = = n n EE

– For holes: For holes: v vdd = = p p EE

H

L

W

Va

Va

ResistanceResistance

A

L

WH

LR

Resistivity and ConductivityResistivity and Conductivity

Fundamental material propertiesFundamental material properties

1

11

ipnopon nqpnq

Current FlowCurrent Flow

EpnAqIL

VE

pnAqL

VI

pnqAL

V

R

VI

opon

a

opona

opon

aa

1

ResistivityResistivity

dn

d

ipdn

opon

Nq

N

nNq

pnq

1

1

1

2

n-type n-type semiconductorsemiconductor

p-type p-type semiconductorsemiconductor

ap

apa

in

opon

Nq

NNn

q

pnq

1

1

1

2

DiffusionDiffusion

When there are changes in the When there are changes in the concentration of electrons and/or concentration of electrons and/or holes along a piece of semiconductorholes along a piece of semiconductor– the Coulombic repulsion of the carriers the Coulombic repulsion of the carriers

force the carriers to flow towards the force the carriers to flow towards the region with a lower concentration.region with a lower concentration.

Diffusion CurrentsDiffusion Currents

opondiffdiffdiff

opopdiff

diff

onondiff

diff

pDnDqJJA

Idx

dpqDpqDJ

A

Idx

dnqDnqDJ

A

I

pn

p

p

n

n

Relationship between Relationship between Diffusivity and MobilityDiffusivity and Mobility

q

kTD

q

kTD

p

p

n

n

Wafer CharacterizationWafer Characterization

X-ray DiffractionX-ray Diffraction– Crystal Orientation Crystal Orientation

Van der Pauw or Hall MeasurementsVan der Pauw or Hall Measurements– ResistivityResistivity– MobilityMobility

Four Point ProbeFour Point Probe– ResisitivityResisitivity

Hot Point ProbeHot Point Probe– n or p-type materialn or p-type material