1. 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

2. Drift Currents

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

4. 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.

5. Diffusion Currents

6. Relationship between Diffusivity and Mobility

7. Mobility vs. Dopant Concentration in Silicon

8. 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

9. 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.

10. Hall Measurement
See for a more complete explanation

11. 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.

12. 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.

13. 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)

14. 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

15. Schematic View

17. Advantages Slow growth rates In-situ monitoring of growth
Extremely easy to prevent introduction of impurities

18. 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

19. 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

20. Schematic of MOCVD System

22. Advantages Less expensive to operate
Growth rates are fast
Gas sources are inexpensive
Easy to scale up to multiple wafers

23. 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

24. Misfit Dislocations
Occur when the difference between the lattice constant of the substrate and the epitaxial layers is larger than the critical thickness.

25. 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).