1Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering1Electrical PropertiesIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering2Goals of this topic:• Understand how electrons move in materials: electrical conduction• How many moveable electrons are there in a material (carrier density), how easily do they move (mobility)• Metals, semiconductors and insulators• Electrons and holes• Intrinsic and Extrinsic Carriers• Semiconductor devices: p-n junctions and transistors• Ionic conduction• Electronic Properties of Ceramics: Dielectrics, Ferroelectrics and PiezoelectricsIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering3Outline of this Topic• 1. Basic laws and electrical properties of metals• 2. Band theory of solids: metals, semiconductors and insulators• 3. Electrical properties of semiconductors• 4. Electrical properties of ceramics and polymers• 5. Semiconductor devicesIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering4• Ohm’s LawV = IRE = V / Lwhere E is electric field intensityµ = / E where µ = the mobility• Resistivityρ = RA / L (Ω.m)• Conductivityσ = 1 / ρ (Ω.m)-1νν = the drift velocity1. Basic laws and electrical properties of metals2Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering5• Electrical conductivity between different materials varies by over 27 orders of magnitude, the greatest variation of any physical propertyMetals: σ > 105(Ω.m)-1Semiconductors: 10-6 < σ < 105(Ω.m)-1Insulators: σ < 10-6(Ω.m)-1Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering6Conductivity / Resistivity of Metals• High number of free (valence) electrons → high σ• Defects scatter electrons, therefore they increase ρ (lower σ). ρtotal= ρthermal+ρimpurity+ρdeformationρthermalfrom thermal vibrationsρimpurityfrom impuritiesρdeformationfrom deformation-induced point defects• Resistivity increases with temperature (increased thermal vibrations and point defect densities)ρT= ρo+ aT• Additions of impurities that form solid sol:ρI = Aci(1-ci) (increases ρ)• Two phases, α, β:ρi = ραVα+ ρβV βIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering7Materials Choices for Metal Conductors• Most widely used conductor is copper: inexpensive, abundant, very high σ• Silver has highest σof metals, but use restricted due to cost• Aluminum main material for electronic circuits, transition to electrodeposited Cu (main problem was chemical etching, now done by “Chemical-Mechanical Polishing”)• Remember deformation reduces conductivity, so high strength generally means lower σ: trade-off. Precipitation hardening may be best choice: e.g. Cu-Be.• Heating elements require low σ(high R), and resistance to high temperature oxidation: nichrome.Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering8• Electric field causes electrons to accelerate in direction opposite to field• Velocity very quickly reaches average value, and then remains constant• Electron motion is not impeded by periodic crystal lattice• Scattering occurs from defects, surfaces, and atomic thermal vibrations• These scattering events constitute a “frictional force” that causes the velocity to maintain a constant mean value: vd, the electron drift velocity• The drift velocity is proportional to the electric field, the constant of proportionality is the mobility, µ. This is a measure of how easily the electron moves in response to an electric field.• The conductivity depends on how many free electrons there are, n, and how easily they move3Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering9vd= µeEσ = n|e|µen : number of “free” or conduction electrons per unit volumeEScattering eventsNet electron motionIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering10(m) = Metal (s) = Semicon Mobility (RT) µ (m2V-1s-1) Carrier DensityNe (m-3) Na (m) 0.0053 2.6 x 1028 Ag (m) 0.0057 5.9 x 1028 Al (m) 0.0013 1.8 x 1029 Si (s) 0.15 1.5 x 1010 GaAs (s) 0.85 1.8 x 106 InSb (s) 8.00 σmetal >> σsemiIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering11Band Theory of Solids• Schroedinger’s eqn (quantum mechanical equation for behavior of an electron)• Solve it for a periodic crystal potential, and you will find that electrons have allowed ranges of energy (energy bands) and forbidden ranges of energy (band-gaps).δ2 ψδx2δ ψδtKψ + V ψ = E ψ(-h’2/2m) + V ψ = ih’2. Band theory of solids: metals, semiconductors and insulatorsIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering12Electrons in an Isolated atom (Bohr Model)Electron orbits defined by requirement that they contain integral number of wavelengths:quantizeangular momentum, energy, radius of orbit4Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering13• When N atoms in a solid are relatively far apart, they do not interact, so electrons in a given shell in different atoms have same energy• As atoms come closer together, they interact, perturbing electron energy levels• Electrons from each atom then have slightly different energies, producing a “band” of allowed energies Introduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials Science and Engineering14MetalsSemiconductors Eg < 2 eVInsulators Eg > 2 eVEmpty bandEmpty conduction bandEmpty bandBand gapEmpty statesFilled statesFilledbandFilled valencebandEmpty conduction bandEfEfEfEfBand gapBand gapFilled valencebandIntroduction To Materials Science FOR ENGINEERS, Ch. 19University of Tennessee, Dept. of Materials