1. Semiconductors with Lattice Defects
All defects in the perfect crystal structure (i.e. real structure phenomena) produce additional energy levels for electrons, which are often located in the energy gap
Non-stoichiometric composition
Substitutional defects (impurities on lattice sites)
Vacancies
Substoichiometric
Schottky defects (migration of atoms to the crystal surface)
Interstitial defects
Hyperstoichiometric
Frenkel defects (atoms leaves their lattice site, creating vacancies and becoming interstitials in the immediate environment, Frenkel pair = vacancy + interstitial)
Crystal and crystallite boundaries
Dislocations
Incomplete ordering of the crystal
Donator Acceptor
P, As (5e-) B, Al, Ga (3e-)
within Si, Ge (4e-)
Concentration of impurities  10-6

2. Doped (extrinsic) Semiconductors
Additional „conduction electrons“ (with P, As)
Additional holes (with Ba, Al, Ga)
n-type semiconductor with electron donors (P, As)
p-type semiconductors with electron acceptors (B, Al, Ga)

3. Fermi Energy in Doped Semiconductors
n-type semiconductor
At 0K the Fermi energy is located between the new energy band and E0.
At high temperatures, the Fermi energy approaches the value 𝑬𝐠/𝟐, as in intrinsic semiconductors.
Largest differences in electrical properties are expected at low temperatures (< 400K).
In p-type semiconductors, the temperature dependency is reversed

4. Small concentration of impurities
Number of Charge Carriers (per units of volume) and Electrical Conductivity
Small concentration of impurities
Large concentration of impurities
(b) Small concentration of impurities

5. The Hall Effect
Semiconductor (or metal) within an external magnetic field
Without magnetic field:
The concentration of electrons along the y-direction is homogeneous
Within a magnetic field:
The movement of electrons is affected by the Lorentz force, causing a non homogeneous distribution of electrons along the y-direction and the formation of an electric field
Lorentz force:
Hall force:
Equilibrium:
Hall constant:
The sign of Hall constant is different for n and p.

6. The IV, III-V and II-VI Semiconductors
Si: Fd3m, a = 5,430 Å
Ge: Fd3m, a = 5,657 Å
III-V
GaAs: F-43m, a = 5,653 Å
GaAs: P63mc, a = 3,912 Å, c = 6,441 Å
InAs: F-43m, a = 6,056 Å
GaSb: F-43m, a = 6,095 Å
InSb: F-43m, a = 6,487 Å
GaN: P63mc, a = Å, c = Å
II-VI
CdTe: F-43m, a = 6,481 Å

7. The IV, III-V and II-VI Semiconductors
C: Fd3m, a = Å Ge: Fd3m, a = Å Si: Fd3m, a = Å -Sn: Fd3m, a = Å
GaAs: F-43m, a = Å
InAs: F-43m, a = Å
InSb: F-43m, a = Å GaP: F-43m, a = Å
SiC: F-43m, a = Å
ZnO: P63mc, a = Å, c = Å CdSe: P63mc, a = Å, c = Å

9. Energy gap vs. lattice parameter