Materials Science and Engineering/Doctoral review questions/Daily Discussion Topics/January 5, 2008

(111) and (100) planes

The (111) plane is the lowest energy interface

(100) texture results from strain

• This plane is associated with the lowest Young modulus

If creating this interface by straining a material, apply thermal energy to allow the atoms to rearrange

Ohm's Law and Rectifying Behavior

SEM image of a failure caused by electromigration in a copper interconnect. The passivation has been removed by RIE and HF

What causes deviation of ohmic behavior of a light bulb?

Increase in resistivity due to increase of temperature

Change of conductivity due to impurity content

Scattering results from introduction of impurities into metal

Impurities in semiconductor can increase the number of charge carriers

What is the effect of electromigration?

Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in microelectronics and related structures. As the structure size in electronics such as integrated circuits (ICs) decreases, the practical significance of this effect increases.

Principles of statistical mechanics

Boltzmann's Law

Boltzmann's statistics provides a description of the spatial arrangement of molecules in a potential field (magnetic, electrical)

• up and down spins

Indistinguishable and Distinguishable Particles

• Indistinguishable particles: Boltzmann's statistics
• Distinguishable particles: Fermi-Dirac statistics

Heat Capacity

Contributions of each degree of freedom to energy

• $1/2kT$ per degree of freedom (per molecule)
  • Vibrations
• $1/2RT$ per degree of freedom (per mole)
  • $3/2RT$ when considering three dimensions

 $E_{tot}=E_{trans}+E_{vib}+E_{rot}+E_{elec}\;$

Total energy of a diatomic molecule

$E={\frac {1}{2}}k_{B}T[3+1+2]$

 $E=3k_{B}T\;$

• translational (x,y,z) freedom: $E=3/2k_{B}T$
• vibrational freedom: $E=1/2k_{B}T$
• rotational freedom: $E=1/2k_{B}T$

Definition of heat capacity

Per mole:

$C_{v}={\frac {d}{dT}}[E=3k_{B}T]N_{A}$

$C_{V}=3R\;$

Heat capacity in a metal

$C_{v}={\frac {d}{dT}}(E_{tot})$

$C_{v}={\frac {d}{dT}}(E_{pot}+E_{kin})$

$C_{v}={\frac {1}{2}}k_{B}T+{\frac {1}{2}}k_{B}T$

Five types of polarization

On application of an electric field, electron deviates from nucleus on a small time interval

In ionic materials, ions can move

Information Suggested to MEMORIZE

Mobilities of materials classes

• Metals ~ 10^8 S/m
• Semiconductors (doped) ~ 10^3
• Semiconductors (undoped) ~ 10^(-2)
• Holes in Si
• Electrons in Si
• Insulators ~ 10^(-14)

Young's Modulus of materials classes

• Metals ~ 100 GPa (10^11 Pa)
• Rubbers ~ 10 MPa (10^7 Pa)

Band gap of materials

• Si = 1.12 eV
• GaAs = 1.42 eV
• Ge = 0.7 eV
• Visible light = 1.77-3.10 eV

Structures of materials

• III-V compounds
• Wurtzite (combination HCP)
• Zinc blende (combination of FCC)

High-k materials

• Why are high k-materials needed?
  • Homeworks may be a helpful resource
• Fabrication of high k materials

Moore's Law

• Resource: paper by Megan and George

Most significant problems of the silicon industry

• Resistance of interconnects
  • Channel mobility will be very good

Modern channel width

• 45 nm gate: channel length
• 7 nm oxide thickness
  • Reduce tunneling effects

BJT

• Draw structure
• How to improve upon the device?
• Significance of heterojunctions

Examples of Major Material Classes

• Indirect semiconductor: Si
• Direct semiconductor: GaAs
• Ferroelectric: BaTiO3
• Superconductor: YBaCuO3, Nb-Ti
• Antiferromagnetic: Cr, Mn
• Soft ferromagnetic (refrigerator doors): defect-free Fe-Ni (permalloy)
• Hard ferromagnetic (refrigerator magnets): defect-full BaFeOx, rare-earth compounds, Alnico
• Anisotropic ferromagnets: Fe (BCC, [100] easy direction), Ni (FCC, [111]), Co (HCP, [0001])
• Diamagnetic: C2 (no net spin)
• Paramagnetic: B2 (net spin)
• Magnetoresistance:
• High-K Dielectric: HfO2
• Low-K dielectric:
• Polymer: Polyethylene
• Miscible system:
• Immiscible system:

List Of "Must Know" Trick Questions

• Write down Fick's first and second laws, as generally as possible. What is the origin of these equations?
• What happens to metals (such as Na) under extremely high pressures?
• Why does the electrical conductivity suddenly increase in metals at very low temperatures?
• What is k in Bloch's Theorem?
• What is so unique about diamond?
• Why is the sky blue? Why are sunsets red?
• What is the fundamental flaw in the regular solution model?
• Why do we use effective mass, rather than just mass, for mobility of electrons in a metal?
• What happens to the bandgap of a material under hydrostatic pressure?