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Semiconductors with Lattice DefectsAll 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 AcceptorP, As (5e-) B, Al, Ga (3e-)

within Si, Ge (4e-)Concentration of impurities 10-6

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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)

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Fermi Energy in Doped Semiconductors

At 0K the Fermi energy is located between the new energy band and E0.

At high temperatures, the Fermi energy approaches the value , as in intrinsic semiconductors.

Largest differences in electrical properties are expected at low temperatures (< 400K).

In p-type semiconductors, the temperature dependency is reversed

n-type semiconductor

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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

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The Hall EffectSemiconductor (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:

evBFBv

BveF

Hall force:

HEeF

Equilibrium:

vBEEeBve

H

H

0

Hall constant:

jBE

eNR

jBRBeNjE

Nvej

HH

HH

1The sign of Hall constant is different for n and p.

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The IV, III-V and II-VI Semiconductors

III-VGaAs: F-43m, a = 5,653 Å

GaAs: P63mc, a = 3,912 Å, c = 6,441 ÅInAs: F-43m, a = 6,056 Å

GaSb: F-43m, a = 6,095 ÅInSb: F-43m, a = 6,487 Å

GaN: P63mc, a = 3.189 Å, c = 5.185 ÅII-VI

CdTe: F-43m, a = 6,481 Å

IVSi: Fd3m, a = 5,430 ÅGe: Fd3m, a = 5,657 Å

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The IV, III-V and II-VI Semiconductors

GaAs: F-43m, a = 5.653 ÅInAs: F-43m, a = 6.056 ÅInSb: F-43m, a = 6.487 ÅGaP: F-43m, a = 5.450 Å

C: Fd3m, a = 3.567 ÅGe: Fd3m, a = 5.657 Å Si: Fd3m, a = 5.430 Å

-Sn: Fd3m, a = 6.489 Å

SiC: F-43m, a = 4.358 Å

ZnO: P63mc, a = 3.254 Å, c = 5.210 ÅCdSe: P63mc, a = 4.297 Å, c = 7.007 Å

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Energy gap vs. lattice parameter

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