Semiconductors with Lattice Defects All defects in the

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 Ø Non-stoichiometric composition Ø Substitutional defects (impurities on lattice sites) Ø Vacancies Ø Substoichiometric Ø Schottky defects (migration of atoms to the crystal surface) Ø Interstitial defects Ø Hyperstoichiometric Ø Frenkel defects (atoms leaves their lattice site, creating vacancies and becoming interstitials in the immediate environment, Frenkel pair = vacancy + interstitial) Ø Crystal and crystallite boundaries Ø Dislocations Ø Incomplete ordering of the crystal Donator Acceptor P, As (5 e-) B, Al, Ga (3 e-) within Si, Ge (4 e-) Concentration of impurities 10 -6 1

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) 2

Fermi Energy in Doped Semiconductors n-type semiconductor In p-type semiconductors, the temperature dependency is reversed 3

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

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: The sign of Hall constant is different for n and p. Hall constant: 5

The IV, III-V and II-VI Semiconductors IV Si: Fd 3 m, a = 5, 430 Å Ge: Fd 3 m, a = 5, 657 Å III-V Ga. As: F-43 m, a = 5, 653 Å Ga. As: P 63 mc, a = 3, 912 Å, c = 6, 441 Å In. As: F-43 m, a = 6, 056 Å Ga. Sb: F-43 m, a = 6, 095 Å In. Sb: F-43 m, a = 6, 487 Å Ga. N: P 63 mc, a = 3. 189 Å, c = 5. 185 Å II-VI Cd. Te: F-43 m, a = 6, 481 Å 6

The IV, III-V and II-VI Semiconductors C: Fd 3 m, a = 3. 567 Å Ge: Fd 3 m, a = 5. 657 Å Si: Fd 3 m, a = 5. 430 Å -Sn: Fd 3 m, a = 6. 489 Å Ga. As: F-43 m, a = 5. 653 Å In. As: F-43 m, a = 6. 056 Å In. Sb: F-43 m, a = 6. 487 Å Ga. P: F-43 m, a = 5. 450 Å Si. C: F-43 m, a = 4. 358 Å Zn. O: P 63 mc, a = 3. 254 Å, c = 5. 210 Å Cd. Se: P 63 mc, a = 4. 297 Å, c = 7. 007 Å 7

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Energy gap vs. lattice parameter 9