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

Four Point Probe Probe tips must make an Ohmic contact Useful for Si Not most compound semiconductors

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

Relationship between Diffusivity and Mobility

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 diagonal Top view of Van der Pauw sample http://www.eeel.nist.gov/812/meas.htm#geom

Calculation Resistance is determined with and without a magnetic field applied perpendicular to the sample. F is a correction factor that takes into account the geometric shape of the sample.

Hall Measurement See http://www.eeel.nist.gov/812/hall.html for a more complete explanation http://www.sp.phy.cam.ac.uk/SPWeb/research/QHE.html

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 where A is the cross-sectional area.

N vs. P doping The sign of the Hall voltage, VH, and on D 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).