carrier mobility and velocity
DESCRIPTION
Carrier Mobility and Velocity. Mobility - the ease at which a carrier (electron or hole) moves in a semiconductor Symbol: m n for electrons and m p for holes Drift velocity – the speed at which a carrier moves in a crystal when an electric field is present - PowerPoint PPT PresentationTRANSCRIPT
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
Drift CurrentsDrift Currents
EpnAqIL
VE
pnAqL
VI
pnqAL
V
R
VI
opon
a
opona
opon
aa
1
Four Point ProbeFour Point Probe
Probe tips must Probe tips must make an Ohmic make an Ohmic contactcontact– Useful for SiUseful for Si– Not most compound Not most compound
semiconductorssemiconductors
S when t 2ln
S when t 2
I
VtI
VS
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
Mobility vs. Dopant Mobility vs. Dopant Concentration in SiliconConcentration in Silicon
http://www.ioffe.ru/SVA/NSM/Semicond/Si/electric.html#Hall
Van der PauwVan der Pauw
Four equidistant Four equidistant Ohmic contactsOhmic contacts
Contacts are small Contacts are small in areain area
Current is injected Current is injected across the diagonalacross the diagonal
Voltage is measured Voltage is measured across the other across the other diagonaldiagonal Top view of Van der Pauw sample
http://www.eeel.nist.gov/812/meas.htm#geom
CalculationCalculation
Resistance is determined with and Resistance is determined with and without a magnetic field applied without a magnetic field applied perpendicular to the sample.perpendicular to the sample.
FRRt
R
B
tH
22ln14,2334,12
24,13
F is a correction factor that F is a correction factor that takes into account the takes into account the geometric shape of the geometric shape of the sample.sample.
Hall MeasurementHall Measurement
See See http://www.eeel.nist.gov/812/hall.html for a more complete explanationfor a more complete explanation
http://www.sp.phy.cam.ac.uk/SPWeb/research/QHE.htmlhttp://www.sp.phy.cam.ac.uk/SPWeb/research/QHE.html
CalculationCalculation
Measurement of resistance is made while Measurement of resistance is made while a magnetic field is applied perpendicular a magnetic field is applied perpendicular to the surface of the Hall sample.to the surface of the Hall sample.– The force applied causes a build-up of carriers The force applied causes a build-up of carriers
along the sidewall of the samplealong the sidewall of the sample The magnitude of this buildup is also a function of The magnitude of this buildup is also a function of
the mobility of the carriersthe mobility of the carriers
where A is the cross-sectional area.where A is the cross-sectional area.
L
A
R
RR
L
HHH
N vs. P dopingN vs. P doping
The sign of the Hall voltage, VThe sign of the Hall voltage, VHH, and , and on on
RR13,2413,24 in the Van der Pauw in the Van der Pauw measurement provide information on measurement provide information on doping.doping.
Epitaxial Material GrowthEpitaxial Material Growth
Liquid Phase Epitaxy (LPE)Liquid Phase Epitaxy (LPE) Vapor Phase Epitaxy (VPE)Vapor Phase Epitaxy (VPE) Molecular Beam Epitaxy (MBE)Molecular Beam Epitaxy (MBE) Atomic Layer Deposition (ALD) or Atomic Layer Deposition (ALD) or
Atomic Layer Epitaxy (ALE)Atomic Layer Epitaxy (ALE) Metal Organic Chemical Vapor Metal Organic Chemical Vapor
Deposition (MOCVD) or Organometallic Deposition (MOCVD) or Organometallic Vapor Phase Epitaxy (OMVPE)Vapor Phase Epitaxy (OMVPE)
MBEMBE
Wafer is moved into the chamber using a Wafer is moved into the chamber using a magnetically coupled transfer rodmagnetically coupled transfer rod
Evaporation and sublimation of source Evaporation and sublimation of source material under ultralow pressure conditions material under ultralow pressure conditions (10(10-10-10 torr) torr)– Shutters in front of evaporation ovens allow vapor Shutters in front of evaporation ovens allow vapor
to enter chamber, temperature of oven determines to enter chamber, temperature of oven determines vapor pressurevapor pressure
Condensation of material on to a heated waferCondensation of material on to a heated wafer– Heat allows the atoms to move to appropriate sites Heat allows the atoms to move to appropriate sites
to form a crystalto form a crystal
Schematic ViewSchematic View
http://web.tiscali.it/decartes/phd_html/III-Vms-mbe.png
http://www.mse.engin.umich.edu/research/facilities/132/photo
http://ssel-front.eecs.umich.edu/Projects/proj00630002.jpg
AdvantagesAdvantages
Slow growth ratesSlow growth rates In-situ monitoring of growthIn-situ monitoring of growth Extremely easy to prevent Extremely easy to prevent
introduction of impuritiesintroduction of impurities
DisadvantagesDisadvantages
Slow growth ratesSlow growth rates Difficult to evaporate/sublimate some Difficult to evaporate/sublimate some
materials and hard to prevent the materials and hard to prevent the evaporation/sublimation of othersevaporation/sublimation of others
Hard to scale up for multiple wafersHard to scale up for multiple wafers ExpensiveExpensive
MOCVDMOCVD Growths are performed at room pressure or Growths are performed at room pressure or
low pressure (10 mtorr-100 torr)low pressure (10 mtorr-100 torr) Wafers may rotate or be placed at a slant Wafers may rotate or be placed at a slant
to the direction of gas flowto the direction of gas flow– Inductive heating (RF coil) or conductive heatingInductive heating (RF coil) or conductive heating
Reactants are gases carried by NReactants are gases carried by N22 or H or H22 into into chamberchamber– If original source was a liquid, the carrier gas is If original source was a liquid, the carrier gas is
bubbled through it to pick up vaporbubbled through it to pick up vapor– Flow rates determines ratio of gas at wafer Flow rates determines ratio of gas at wafer
surfacesurface
Schematic of MOCVD Schematic of MOCVD SystemSystem
http://nsr.mij.mrs.org/1/24/figure1.gif
http://www.semiconductor-today.com/news_items/2008/FEB/VEECOe450.jpg
AdvantagesAdvantages
Less expensive to operateLess expensive to operate– Growth rates are fastGrowth rates are fast– Gas sources are inexpensiveGas sources are inexpensive
Easy to scale up to multiple wafersEasy to scale up to multiple wafers
DisadvantagesDisadvantages
Gas sources pose a potential health Gas sources pose a potential health and safety hazardand safety hazard– A number are pyrophoric and AsHA number are pyrophoric and AsH33 and and
PHPH33 are highly toxic are highly toxic
Difficult to grow hyperabrupt layersDifficult to grow hyperabrupt layers– Residual gases in chamberResidual gases in chamber
Higher background impurity Higher background impurity concentrations in grown layersconcentrations in grown layers
Misfit DislocationsMisfit Dislocations
Occur when the difference between Occur when the difference between the lattice constant of the substrate the lattice constant of the substrate and the epitaxial layers is larger than and the epitaxial layers is larger than the critical thickness. the critical thickness.
http://www.iue.tuwien.ac.at/phd/smirnov/node68.html
Critical Thickness, tCritical Thickness, tCC
where where
b is the magnitude of the lattice distortion caused b is the magnitude of the lattice distortion caused by a dislocation (Burger vector)by a dislocation (Burger vector)
f is the mismatch between the lattice constants of f is the mismatch between the lattice constants of film and the substratefilm and the substrate
is Poisson’s ratio (transverse strain divided by the is Poisson’s ratio (transverse strain divided by the axial strain).axial strain).