Doping and Crystal Growth Techniques
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Transcript Doping and Crystal Growth Techniques
Impurity Segregation
CS
ko
CL
CS Co ko (1 f )
k o 1
Where Co is the initial concentration of th impurity in the melt
Float Zone
www.mrsemicon.com
/crystalgrowth.htm
www.tms.org/pubs/journals/JOM/9802/Li/
Impurity Segregation
C S ( x) Co 1 (1 ko )e
ko x
L
Where Co is the initial concentration of the impurity in the
solid and L is the width of the melted region within RF coil
Impurity Segregation
Atom
ko
Atom
ko
Cu
Ag
Au
C
Ge
Sn
As
4 · 10–4
10–6
2.5 · 10–5
7 · 10–2
3.3 · 10–2
1.6 · 10–2
0.3
O
B
Ga
Fe
Co
Ni
Sb
0.5
0.8
8 · 10–3
8 · 10–6
8 · 10–6
4 · 10–4
2.3 · 10–2
Bridgeman
Used for some compound semiconductors
– Particularly those that have a high vapor
pressure
– Produced “D” shaped boules
Crystalline Defects
Point Defects
– Vacancies
– Impurities
– Antisite Defects
Line Defects
– Dislocations
Edge
Loop
Volume Defects
– Voids
– Screw Dislocations
Edge Dislocation
http://courses.eas.ualberta.ca/eas421/lecturepages/mylonite.html
Screw Dislocation
http://focus.aps.org/story/v20/st3
Strain induced Dislocations
The temperature profile across the
diameter of a boule is not constant as the
boule cools
– the outer surface of the boule contracts at a
different rate than the internal region
– Thermal expansion differences produces edge
dislocations within the boule
Typical pattern is a “W”
Strain due to Impurities
An impurity induces strain in the crystal
because of differences in
– ionic radius as compared to the atom it
replaced
Compressive strain if the ionic radius is larger
Tensile strain if the ionic radius is smaller
– local distortions because of Coulombic
interactions
Both cause local modifications to Eg
Dislocation Count
When you purchase a wafer, one of the
specifications is the EPD, Etch Pit Density
– Dislocations etch more rapidly in acid than
crystalline material
– Values for EPD can run from essentially zero
(FZ grown under microgravity conditions) to
106 cm-2 for some materials that are
extremely difficult to grow.
Note that EPD of 106 cm-2 means that there is a
dislocation approximately every 10mms.
Wafer Manufacturing
Boules are polished into cylinders
Aligned using an x-ray diffraction system
Cut into slices using a diamond edged saw
– Slices are then polished smooth using a
colloidal grit
Mechanical damage from sawing causes point
defects that can coalesce into edge dislocations if
not removed
http://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_6/backbone/r6_1_2.html#_dum_1
Epitaxial Material Growth
Liquid Phase Epitaxy (LPE)
Vapor Phase Epitaxy (VPE)
Molecular Beam Epitaxy (MBE)
Atomic Layer Deposition (ALD) or Atomic
Layer Epitaxy (ALE)
Metal Organic Chemical Vapor Deposition
(MOCVD) or Organometallic Vapor Phase
Epitaxy (OMVPE)
MBE
Wafer is moved into the chamber using a
magnetically coupled transfer rod
Evaporation and sublimation of source material
under ultralow pressure conditions (10-10 torr)
– Shutters in front of evaporation ovens allow vapor to
enter chamber, temperature of oven determines vapor
pressure
Condensation of material on to a heated wafer
– Heat allows the atoms to move to appropriate sites to
form a crystal
Schematic View
http://web.tiscali.it/decartes/phd_html/III-Vms-mbe.png
http://ssel-front.eecs.umich.edu/Projects/proj00630002.jpg
http://www.mse.engin.umich.edu/research/facilities/132/photo
Advantages
Slow growth rates
In-situ monitoring of growth
Extremely easy to prevent introduction of
impurities
Disadvantages
Slow growth rates
Difficult to evaporate/sublimate some
materials and hard to prevent the
evaporation/sublimation of others
Hard to scale up for multiple wafers
Expensive
MOCVD
Growths are performed at room pressure or low
pressure (10 mtorr-100 torr)
Wafers may rotate or be placed at a slant to the
direction of gas flow
– Inductive heating (RF coil) or conductive heating
Reactants are gases carried by N2 or H2 into
chamber
– If original source was a liquid, the carrier gas is
bubbled through it to pick up vapor
– Flow rates determines ratio of gas at wafer surface
Schematic of MOCVD System
http://nsr.mij.mrs.org/1/24/figure1.gif
http://www.semiconductor-today.com/news_items/2008/FEB/VEECOe450.jpg
Advantages
Less expensive to operate
– Growth rates are fast
– Gas sources are inexpensive
Easy to scale up to multiple wafers
Disadvantages
Gas sources pose a potential health and
safety hazard
– A number are pyrophoric and AsH3 and PH3
are highly toxic
Difficult to grow hyperabrupt layers
– Residual gases in chamber
Higher background impurity
concentrations in grown layers
Misfit Dislocations
Occur when the difference between the
lattice constant of the substrate and the
epitaxial layers is larger than the critical
thickness.
Carrier Mobility and Velocity
Mobility - the ease at which a carrier
(electron or hole) moves in a
semiconductor
– Symbol: mn for electrons and mp for holes
Drift velocity – the speed at which a
carrier moves in a crystal when an electric
field is present
– For electrons: vd = mn E
– For holes:
vd = mp E
L
H
W
Va
Va
Resistance
L
L
R
WH
A
Resistivity and Conductivity
Fundamental material properties
1
1
q m n no m p po q m n m p ni
1
Resistivity
n-type semiconductor
1
q m n no m p po
1
ni
q m n N d m p
N
d
1
qm n N d
2
p-type semiconductor
1
qm n no m p po
1
ni 2
q m n
m p N a
Na
1
qm p N a
Drift Currents
Va
Va
I
R
L
1
A q m n no m p po
Va
I
Aqm n no m p po
L
Va
E
L
I Aqm n no m p po E
Diffusion
When there are changes in the
concentration of electrons and/or holes
along a piece of semiconductor
– the Coulombic repulsion of the carriers force
the carriers to flow towards the region with a
lower concentration.
Diffusion Currents
I diffn
A
I diff p
A
I diff
A
J diffn
dno
qDnno qDn
dx
J diffp
dpo
qD p po qD p
dx
J diffn J diffp q Dnno D p po
Relationship between Diffusivity
and Mobility
Dn
kT
mn
q
Dp
kT
mp
q
Mobility vs. Dopant Concentration
in Silicon
http://www.ioffe.ru/SVA/NSM/Semicond/Si/electric.html#Hall
Wafer Characterization
X-ray Diffraction
– Crystal Orientation
Van der Pauw or Hall Measurements
– Resistivity
– Mobility
Four Point Probe
– Resisitivity
Hot Point Probe
– n or p-type material
Van der Pauw
Four equidistant Ohmic
contacts
Contacts are small in
area
Current is injected
across the diagonal
Voltage is measured
across the other
Top view of Van der Pauw sample
diagonal
http://www.eeel.nist.gov/812/meas.htm#geom
Calculation
Resistance is determined with and without a
magnetic field applied perpendicular to the
sample.
t R13, 24
mH
B
t R12,34 R23,14
F
ln 2
2
F is a correction factor that takes
into account the geometric shape
of the sample.
Hall Measurement
http://www.sp.phy.cam.ac.uk/SPWeb/research/QHE.html
See http://www.eeel.nist.gov/812/hall.html for a
more complete explanation
Calculation
Measurement of resistance is made while a
magnetic field is applied perpendicular to the
surface of the Hall sample.
– The force applied causes a build-up of carriers along
the sidewall of the sample
The magnitude of this buildup is also a function of the
mobility of the carriers
RH
RH A
mH
RL L
where A is the cross-sectional area.
Four Point Probe
Probe tips must make
an Ohmic contact
– Useful for Si
– Not most compound
semiconductors
V
2S when t S
I
t V
when t S
ln 2 I
Hot Point Probe
Simple method to determine whether
material is n-type or p-type
– Note that the sign of the Hall voltage, VH, and
on R13,24 in the Van der Pauw measurement
also provide information on doping.