Transcript Doping and Crystal Growth Techniques

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
Drift Currents
Va
Va
I

R

L 
1

A  q m n no  m p po  
Va
I
Aqm n no  m p po 
L
Va
E
L
I  Aqm n no  m p po E
Four Point Probe

Probe tips must make
an Ohmic contact
– Useful for Si
– Not most compound
semiconductors
V
  2S when t  S
I
t V

when t  S
ln 2 I
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
 qDnno  qDn
dx
 J diffp
dpo
 qD p po   qD p
dx
 J diffn  J diffp  q Dnno  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
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.
N vs. P doping
The sign of the Hall voltage, VH, and on
 R13,24 in the Van der Pauw measurement
provide information on doping.
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.
http://www.iue.tuwien.ac.at/phd/smirnov/node68.html
Critical Thickness, tC
where
b is the magnitude of the lattice distortion caused by a
dislocation (Burger vector)
f is the mismatch between the lattice constants of film
and the substrate
n is Poisson’s ratio (transverse strain divided by the axial
strain).