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).