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

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)

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

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

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.

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 = 3.189 Å, c = 5.185 Å II-VI CdTe: F-43m, a = 6,481 Å

The IV, III-V and II-VI Semiconductors C: Fd3m, a = 3.567 Å Ge: Fd3m, a = 5.657 Å Si: Fd3m, a = 5.430 Å -Sn: Fd3m, a = 6.489 Å GaAs: F-43m, a = 5.653 Å InAs: F-43m, a = 6.056 Å InSb: F-43m, a = 6.487 Å GaP: F-43m, a = 5.450 Å SiC: F-43m, a = 4.358 Å ZnO: P63mc, a = 3.254 Å, c = 5.210 Å CdSe: P63mc, a = 4.297 Å, c = 7.007 Å

Energy gap vs. lattice parameter