6. Give examples of point defects in a crystal. Explain what kind of defect is a dopant atom.

Defects in semiconductor crystals are:

  1. Point defects
  2. Line defects
  3. Surface defects
  4. Volume defects

Of point defects, there are native defects (happening without the addition of other atoms) and non-native defects due to contaminants. Native defects are vacancies and self-interstitials. Non-native point defects are substitutions or interstitials. Dopants must be substitution defects.

5. What is the behavior of the semiconductor energy gap Eg of direct-bandgap semiconductors vs. the lattice constant a?

For direct bandgap semiconductors, the bandgap is inversely proportional to the lattice constant. For ternary semiconductor compounds such as AlGaAs, varying the Al composition will change the bandgap of the compound, as well as the lattice constant. Ternary compounds vary the concentration of the metals, Al and Ga. As such this leads to a variation in Al concentration from AlAs with no Ga concentration to GaAs, with no Al concentration. AlAs and GaAs are lattice-matched and can therefore be grown together using conventional methods. AlGaAs is direct bandgap for Al concentrations below 0.45.

For a quarternary compound InGaAsP, the concentration varies between InAs, InP, GaAs, and GaP. These concentrations are not lattice matched to each other and vary significantly in bandgap.

The relationship between bandgap and lattice constant also enables an increased bandgap with compressive lattice strain and a reduced bandgap for tensile strain.

3. Explain why ferroelectric crystals already have, with zero applied electric field, a net dipole moment. What is the Curie temperature?

Ferroelectric materials possess a dielectric polarization without an applied electric field. Examples of ferroelectric materials include potassium dihydrogen phosphate (KH2PO4), barium titanate (BaTiO3) and Lithium niobate (LiNbO3).

Ferroelectric materials undergo a change based on temperature. Above a temperature called the Curie temperature, the crystal is cubic, but below the Cure temperature they are tetragonal. Undergoing the change to tetragonal, with an electric polarization.

Ferroelectric materials are also piezoelectric, meaning that they produce an electric charge under a mechanical load.

4. Quote at least one important ferroelectric material exploited in electrooptic modulators.

LiNbO3 is a highly attractive ferroelectric crystal used in electrooptic modulators, due to the strong electrooptic effect, or change in refractive index under an electric field.

2. What is the wurtzite crystal structure? Quote at least one important wurtzite semiconductor.

Wurtzite crystal structure is a hexagonal pattern found in some semiconductors. This differs from the cubic crystal structure of diamond and zinc-blende latttices.

While in the cubic semiconductor structures, the distance between points of the Bravais lattice are the same in three directions, which are separated each by 90 degrees. In the hexagonal structure, only the distance between two of the three points are the same. The two points that are the same distance from each other are separated by 90 degrees, while the third point is separated by 120 degrees.

Materials with a wurtzite crystal structure include GaN, AlN, InN, and ZnO.

1. Describe the crystal structure of Si and GaAs. Explain the difference between the diamond and zinc-blende lattice cells.

Both Silicon and GaAs are cubic semiconductors. Silicon is a diamond crystal, while GaAs is a zinc-blende crystal. Diamond differs from zinc-blende lattice in the composition of the atoms in the lattice.

Since Si is a pure substance, only Si atoms are present in the crystal lattice. A diamond crystal has 8 atoms, which include the corner atoms, atoms on faces, and internal atoms.

In the GaAs semiconductor compound, the corner and face atoms will be of a different atom than the internal atoms. For instance, the corner and face atoms can be the metal Gallium while the internal atoms are Arsenic.