Electrical material properties

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Gillian Pierce
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1 Electrical material properties U = I R Ohm s law R = ρ (l/a) ρ resistivity l length σ = 1/ρ σ conductivity A area σ = n q μ n conc. of charge carriers q their charge μ their mobility μ depends on T, defects, processing, anisotropy

2 Electrical conductivity e - -conductors σ / Ω -1 m -1 Bonding Insulators* ionic, covalent Semiconductors intermediate Metals metallic * Ionic salts conduct ions at high T

3 Resistivity of metals ρ = ρ T + ρ d ρ T increases almost linerarly with T because of the interaction of e - and lattice vibrations ρ d depends on the concentration of defects: impurity atoms, vacancies, dislocations, grain boundries (thus not on T)

4 Superconductivity Below the critical temperature the resistivity ρ goes to zero T c Superconductors also have: Critical magnetic fields Critical current densities H c J c The higher - the better

5 Superconductors Type I (low H c ) T c /K Coolants T b /K W 0.01 He(l) 4 Al 1 H 2 (l) 20 Sn 4 N 2 (l) 77 Type II (high H c ) Nb 9 V 3 Ga 17 Nb 3 Sn 18 Ceramic Material problems? (La,Sr) 2 CuO 4+x 40 YBa 2 Cu 3 O 7 93 YBa 2 Cu 3 O 6 semiconductor TlBa 2 Ca 3 Cu 4 O

6 Inorganic solid electrolytes σ = n Zq μ Z charge of mobile ion at high T μ = (ZqD)/kT but D = D o exp (-Q/RT) and k = R/N a σ/ω -1 m -1 Cu 10 8 metal Ge 10 0 semiconductor NaCl(aq) 10-1 electrolyte LiCl(l) 10 electrolyte, high T RbAg 4 I solid electrolyte, high T Organic conductors (e -, ions) in separate lecture

7 Intrinsic semiconductors Conduction band E e - electron e - h + hole Valence band E g band gap ev (visible light: ev)

8 Intrinsic semiconductors Conduction band σ = n e q (μ e + μ h ) E e - n e = n h = n o exp (-E g /2kT) E g σ = n o exp (-E g /2kT)q(μ e + μ h ) e - h + Ge: σ increases with T (n e &n h increase) Al: σ decreases with T (μ decreases) Valence band

9 Extrinsic semiconductors Conduction band E e Ed _ e - h + Donor level : n-type doping, e.g. P in Si Eg = ev E(doping) = ev e - Acceptor level: p-type doping, e.g. Ga in Si Ea e - h Valence band

10 Extrinsic semiconductors n-type: n total = n e (extrinsic)+ n e (intrinsic) + n h (intrinsic) = n od exp (-E d /kt) + 2n o exp (-E g /2kT) Extrinsic e - dominate at low temperature, while intrinsic e - dominate at high temperature σ(t) exhibits a plateau due to exhaustion of e -

11 Semiconducting compounds E g varied III V GaAs, GaP, GaSb, AlP, InSb II VI CdS, CdSe, ZnSe, ZnTe IV IV SiC Non-stoichiometric oxides n-type: Zn 1+x O Zn (interstitial) Zn e - p-type: Fe 1-x O 3Fe 2+ replaced by 2Fe 3+ Fe 2+ + Fe 3+ Fe 3+ + Fe 2+ h +

12 Semiconductor applications Thermistor: σ(t) gives T Pressure transducer: E g decreases with increasing P and σ increases Diode (p-n junction): AC rectifier, high-voltage protection, LED Transistor (n-p-n or p-n-p junction): Amplifier

13 Dielectric properties Metals E g = 0 ev Intrinsic semiconductors E g = ev Insulators E g > 3 ev P = Zqd P polarization (dipole moment per unit volume) Z number of displaced charge centers per unit volume q charge of an electron d distance between positive and negative end of dipole

14 Polarization mechanisms Electronic polarisation Ionic polarisation Molecular Space charges (charges at grainboundries between different phases)

15 Capacitor A Q = CU Q stored charge C capacitance d U electrical potential C = ε(a/d) = κε o (A/d) ε ε o κ = ε/ε o permittivity of material permittivity of vacuum dielectric constant (relative permittivity)

16 Capacitor P = (κ-1)ε o ξ ξ electric field strength [Vm -1 ] The maximum electric field that can be maintained without breakdown ξ max = (U/d) max Storing of large charge Q requires: (i) High C and κ, (ii) high ξ max, and (iii) high ρ Materials: clays, ceramics, glass, polymers, impregnated paper, polar liquids

17 Dimensional changes Electrostriction: Any material may show a change of dimensions in an applied electric field Piezoelectricity: A much larger effect, only found for non-centrosymmetric crystals Electric field ξ produced by stress σ: ξ = g σ Strain ε produced by electric field ξ: ε = d ξ

18 Piezoelectricity Hooke s law: E = σ/ε = 1/(gd) Please do not confuse σ(stress) with σ(el. conductivity) or ε(strain) with ε (permittivity) Transducers convert acoustical waves to electric fields and vice verca. Quartz SiO 2 oscillators are used in watches. Piezocrystals are used for nanomoving. PZT Pb(Zr,Ti)O 3 is used in gas lighters and BaTiO 3 is another common piezoceramic.

19 Pyro- and ferroelectricity Pyroelectricity: A change in temperature generates a polarization and an electric field Material: iron-poor tourmaline Ferroelectricity: Ferroelectric materials are both piezoand pyroelectric. They have a net polarisation in the absence of an electric field. The polarization can be reversed by an applied field. Material: BaTiO 3

20 Ferroelectricity The polarization is lost above the critical temperature A hysteresis loop is observed in the P- ξ diagram because the reversal of domains (μm-size) requires energy The hysteresis loop is described by: P s (the saturation polarisation), P r (the remanent polarisation), and ξ c (the coercive field)

Electrical Properties

Electrical Properties Electrical Conduction R Ohm s law V = IR I l Area, A V where I is current (Ampere), V is voltage (Volts) and R is the resistance (Ohms or ) of the conductor Resistivity Resistivity,