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