# Semiconductors: Arrhenius plot of - Wits Structural Chemistry

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Semiconductors: Arrhenius plot of - Wits Structural Chemistry

Semiconductors• Conductivity (σ)() increases (exponentially)with temperature; compare to metalsSemiconductors• Calculate the fraction of Si atoms thatprovide a conduction e - at roomtemperature and compare this to thevalue obtained for Cu.• [density (Si) = 2.33g/cm 3 ; M(Si) ) = 28.09 g/mol; carrier density n e =14 x 10 15 m - 3 ]• Ans: : fraction = 2.8 x 10 -13cf 1.23• Exercise: convert 1eV and 6eV to kJ/molSemiconductors:change in the Fermi function (f(E((E) with temperature1f ( E)=[exp( E − E ) / kT]+ 1FSemiconductors1f ( E)=[exp( E − E ) / kT]+ 1Calculate the probability of an e - beingthermally promoted to the conductionband of Si (E(g = 1.07eV) at 25 °CFAns: f(E) ) = 4.39 x 10 -10SemiconductorsBand gaps, E g (eV)Semiconductors: Arrhenius plotof electrical conductivity• conductivity is proportional to the density of charge carrierssinceandσ = nq( μ + μh)en ∝ exp( −Eg/ 2kT)from f(E)E g 1∴ln( σ ) = ln( σ0)−2kT1

Semiconductors: Arrhenius plotof electrical conductivityE g 1∴ln( σ ) = ln( σ0)−2kT• Note: althoughconductivity will decreaseas T increases in allmaterials due to thermalvibration, but this is onlysignificant in metals• see exampleSemiconductorsTo characterize a new semiconductor one can find theband gap by measuring conductivity at differenttemperatures (Note: this can also be donespectroscopically).Example: The conductivity of a new material is 250Ω -1 m -1 at 20°C C and at 100°C C it is 1100 Ω -1 m -1 . What isits band gap, E g ?Ans: : 0.349 eVIntrinsic semiconductors• conductivity in an intrinsic (pure) semiconductor depends on the bandgap energy and temperature.• Examples of intrinsic semiconductors are Si, Ge, , Se, GaAs, CdSIntrinsic semiconductorsrange of band gaps• electrons can also be excited into theconduction band by light of the correctenergy: E=hc/hc/λ. . Conversely, light can beemitted (tunable(LED’s).• Ex: Calculate the photon wavelength (nm)needed to promote an e - to the conductionband in Si.p- and n-doped nsemiconductors• small amounts of dopants (from 0.01 atom% to less than 1 atom in 10 9 )can be added to modify the conductivity (“extrinsic(semiconductors”)and subsequently to make electronic devices.• (see periodic table to decide on p-por n-dopants)p- and n-doped nsemiconductorsband structure• p- and n-dopantsmodify the band structure of a semiconductor;effectively adding either ‘donor’ or ‘acceptor’ bands.p-dopant2

p- and n-doped nsemiconductors:band structure• n-dopantExtrinsic semiconductors• Extrinsic semiconductors exhibit an ‘exhaustion range’ at a certaintemperature when all “extra electrons” have been promoted to theconduction band.The p-n p n junction• The p-n juction is one of the simplest and most common applicationsusing semiconductors in a variety of devices (transistors, siliconchips, photocells, LED’s,thermistors)Current flow in a p-n p n junction• The p-n junction acts as a solid-state state rectifier, allowing current toflow only in one direction• Nano-CdSeCdSe: : optical properties vary withparticle sizeRadius (nm)0.9 1.4 1.9 2.4• Nano-CdSeCdSe: : synthesis by organometallicmethods3

• Nano-CdSesemiconductorInsulators• Band gaps; range of conductivity; examplesInsulators• Piezoelectric and pyroelectric effects(see text books: AR West)Insulators• Barium titanate structure and the Piezoelectric effect(see text books)Insulators• Other perovskite structures (solid solutions)Electrical properties of solids:Summary• Conductors can be classified according to their response to temperature:erature:conductors, semiconductors & superconductors.• The electronic properties of solids can be rationalised using band theory• For metallic conductors, resistivity is proportional to temperature.• For semiconductors, conductivity increases exponentially withtemperature. The population of the conduction band as a function oftemperature is given by the Fermic-Dirac distribution.• Radiation of the correct energy can also excite electrons into the tconduction band. Conversely light of different wavelengths (Eg(Eg) ) can beemitted.• Extrinsic semiconductors have a higher conductivity than similar intrinsicones at low temperature.• The conductivity of extrinsic semiconductors is accurately controlled olled bythe concentration of the dopant; ; wide temperature range possible.• Superconductivity phenomena can be explained in terms of ‘Cooper pairsof electrons’, , which can conduct electricity with zero resistance4

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