Electronic and ionic conductivity in metal oxides

1 1 PAUL SCHERRER INSTITUTPAUL SCHERRER INSTITUTE lectronic and ionic conductivity in metal oxidesKazimierz ConderLaboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, >1023 CuPbGraphiteGeSiGlassInsulatorsSemicondu ctorsMetalsConductivity [ -1cm-1]Temperature [K]Electrical conductivityConductivity of metals decreases with temperature. Increased interaction of electrons with lattice!Superconductivity: by cooling resistivity drops to zeroConductivity of insulators and semiconductors increases with temperature. Concentration of carriers increases!3 Electrical resistivity of ceramic (oxide) materials over 20 orders of magnitude 10-1310-810-3102107 conductivity , -1m-1 InsulatorsSemiconductorsConductorsSuperc onductors418+18-18+18-18+18-18+18-18+18- 18+18-Molecular: Ar19+18-17+18-19+18-17+18-19+18-17+18-19 +18-17+18-19+19+19+19+19+19+19+19+4+4+4+ 4+4+4+ ionic : KClCovalent: C (diamond)Metallic: KElectronic charge distribution in the basic solid types(chemical bond point of view)After Ashcroft, Mermin, Solid State Physics , Philadephia, 1976 KClDelocalized electrons5 Metals, semiconductors , insulators1/TLog MetalSemiconductor:intrinsicextrinsicIns ulatorTSemiconductors: electrons are excited over the band gap and occupy energy levels in conductivity band.

2 Holes are created in valence band. The process is thermally activated- conductivity increase with material with an energy gap > eV is an can be increased by a doping. Through the doping energy levels within band gap will be of an electron: E = = ( k)2/2mk=2 / wave vectorEkE ~ k2 Electrons with >>a (lattice parameter)can travel freely through a crystalFor more energetic electrons when a ???? wavelengthof the electronElectron in a (1D) solid 7 EkE ~ k2a 2~ sin2( x/a) higher energyDistribution of the electron densities: 2~cos2( x/a) lower energy =2aElectrons which have a wavelength commensurate with the lattice are scattered on the periodic potentialE- /a /aForbidden bandElectron in a (1D) solidPotential energy of an electron in a periodic array of positive ionsWave functions for =2a 8 Band (Bloch-Wilson)insulatorsSPartially filled energy band metalFilled energy band insulatorsplitted d orbitals(trigonal prism coordination)dxz, dyzdxy, dx2-y2dz2insulatormetalNb4+ 4d1Mo4+ 4d29No carriers no conductivityMgOMg2+2p63s0O2-2p6insulator Na2 ONa+2p63s0O2-2p6 Noble gas configuration.

3 InsulatorTiO2O2-2p6Ti4+3d04s0insulatorFr ee d-electrons:metalTiOTi2+3d24s0O2-2p6 NiONi2+3d84s0O2-2p6 InsulatorBut why???Free carriers?10 TiO- rutileTiOTi 3d24s0metalNiO- NaCl structureNi 3d84s0Is insulator!Why not a metal ?NiO11 CuOCu2+3d94s0 CoOCo2+3d74s0 MnOMn2+3d54s0Cr2O3Cr3+3d34s0 Odd number of d electrons-all this oxides should bemetals but areinsulatorsWhatever is the crystal field splitting the orbitalsare not fully occupied!!! Why not metal ?3d74s23d54s23d94s23d44s2 Electron configurationsof elements12 The d-levels in most of the transition metal oxides are partially filled, therefore, the band theory predicts electron delocalization and metallic properties. According to band structure calculations half of the known binary compounds should be conducting.

4 In reality, many oxides show insulating behavior, implying that the d-electrons are localized. Short-range Coulomb repulsion of electrons can prevent formation of band states, stabilizing localized electron states. Mott-Hubbard insulatorsThe Nobel Prize in Physics 1977: Philip Warren Anderson, Sir NevillFrancis Mottand John Hasbrouck van Vleck"for their fundamental theoretical investigations of the Electronic structure of magnetic and disordered systems".13 Mott considered the idealized metal -insulator transition for Na crystal by changing the interatomic : Feng Duan, Jin Guojun, Introduction to Condensed Matter Physics , , World Scientific 2005 Hubbard U - energy penalty for transferring an electron between two adjacent sites -assumed to be independent on aNa + Na Na++ Na-UBandwidth or band dispersion: energy difference between the highest and lowest level.

5 Bandwidth increases with better orbital overlap. Localization of electrons narrow hopping between atoms during conduction1/aa conductivityEUNa Na Na NaNa+Na-14U ~I -Aionization energy(a few eV)electronaffinityCoulomb repulsion is described in terms of a correlation energy, Hubbard-U,which is the energy penalty for transferring an electron between two adjacent ++ Ni2+ Ni3++ Ni+d8+ d8 d7+ d9 Mott-Hubbard insulatorsU15At the point where W~ U, the bands overlap. Beyond this point, there is no energy gap andthe material is U> W, the d band of the transition metal is splitted into sub-bands. For an electron transfer an energy barrier Umust be overcome and the material is insulating. Mott-Hubbard (MH) (B1+B2)Bandwidth WEfUpper Hubbard bandLower Hubbard bandThe effect of the electron repulsion makes even the half-filled band insulating when the interaction between atoms (band width W) is small.

6 16 Pressure and temperature dependence Every material under high pressure will have metallic properties Insulator- metal transition can be achieved increasing temperature (thermally induced carriers) or doping1/a metalinsulator1/ac17 Phase diagram of McWhan et al., PRL, 23 (1969) 1384 Mixed oxides (chemical pressure)Ti3+ ;V3+ ;Cr3+ Pressure experiments for V2O3and ( )2O318V2O3metal-insulator McWhan et al., PRL, 23 (1969) 1384J. Feinleib and W. Paul, Phys. Rev. 155(1967) 841~145 Kconductivity (ohm cm)-11/T, 103/K19 Larger d orbitals low oxidation state (more electrons) for early TM (good M-M overlap) high oxidation state for late TM (good M-O-M overlap: covalent bond) for covalent bonds: low electronegativity anions halides, O, S, Se, Te, W W U U electron configuration Mn2+3d5has half-filled shell other cations in the structure (as in perovskites ABO3) General rulesNiS, CoS and CuS-metalsNiO, CoO and CuO-(MH) insulatorsTransition metals TM20 Mott-Hubbard models assumes that the band gap is within d-band.

7 In many cases one has to consider ligands- oxide anions in oxides . Additionally to W and U a third parameter has to be considered: gap. Oxygen p bandsMetal d bands is a gap between 2poxygen band and the d-bandof the a metalCu 3d-band and O 2p-band overlap. oxygen p bandmetal d bandsEgap U is large(Semi)MetalCharge-transfer-insulato r (semiconductor)Mott-Hubbard-insulatorEga p Different /Uratio! conductivity via holes in O 2p-band22 Oxygen p bandMetal bandsU< Mott-Hubbard insulatorNiO, NiPS3, Ti2O3, V2O3, Cr2O3 <UCharge transfer insulatorCuCl2, CuO <WSemimetalLaCuO3, CuS,CuSeU<WMetalHigh temp. mod. of TiO, CrO2 Examples23 Oxygen p bandmetal d bands24 CoOFe2O3 NiOCr2O3Mn3O4 FeOVO2 MoO2Ti2O3 ReO3 TiOCrO2V2O3 VOFe3O4 NbOReO2 MnO210-1410-1010-610-2102106 conductivity , -1m-11000800 333 250200167149125T, K1000/T, K-112345678Cu 107 at RTmetallicAfter: Schaumberg, Keramik25after I.

8 H. Inoue, Semicond. Sci. Technol., 20 (2005) S112 Perovskites26d1 perovskitesSrVO3 metalCaVO3 metalLaTiO3 insulatorgap insulatorgap eV2727 Oxygen nonstoichiometric3d oxidesDoes the electrical conductivity depend on oxygen content and cationdoping? 2828 Lattice defectsSchottky- und Frenkel-defects in crystalsSchottky-defekts:The volume of the crystal will increaseFrenkel-defekts:The volume of the crystal stays constantTemperature L/LDilatometerSchottky-defects2929 Defect concentration n/N0 Temperature[oC]Activation Energy eV1 2 81003 10-141 10-271 10-1085003 10-71 10-138 10-5310001 10-41 10-82 10-3215001 10-32 10-62 10-2320006 10-34 10-52 10-18 kTENnVexp03030Fe1-xO (FeO1+x) semiconductor type pF( )EnergyEfVBCBA cceptor level4 FexFe+ O2 FeO4Fe Fe+ 2 OxO + 2V,,FeFeOFe FeFexFe+ h Fe Feion can trap an electron from the valence band.

9 In VB a hole is created. h 3131 TiO2-xsemiconductor type nF( )EnergyEfVBCBD onor level2 TixTi+ OxOTiO22Ti Ti + V O + O2Ti TiTiO2 TixTi+ e Ti4+Donor level is situated close to the conductive donor cation Ti Ti(Ti3+) can inject an electron into conducting semiconductor. Ni1- OIn NiO nickel vacancies are created when oxidized with oxygen. The charge of the additional oxygen sites is compensated by oxidation of some nickel sites to Ni3+. Through the oxidation the volume of the material increases. p ++ + + hNiNiNiNiONi + ++hNiheNiNiNiONi/Ni3+sites are electron acceptors:3333 Application ceramic semiconductorsNTC-thermistors(Negative Temperature Coefficient- thermal resistor)( ) =TBTexp0 kEBA/ =-60 -40 -20 0 20 40 60 80 100 12010010110210310410510610710850 500 500 k 50 k 5 k Resistivity [ ]Temperature [oC] conductivity is thermally activatedTill 300oC spinels:Mn3O4 NiMn2O4 CoFe2O4 Till ca.

10 1000oC rare earth oxides eg.:70%Sm2O330%Tb2O334 Extrinsic ionic conductors1/TLog DopingintrinsicextrinsicConductivity increase by a with fluorite structure (ZrO2, ThO2, CeO2) doped with CaO, MgO, Y2O3, Sc2O3and La2O3Y2O3 ZrO22Y,Ce + 3 OxO + V OFluorite structure (CaF2-type)ZrO3535 Intrinsic superionic conductor. -aluminum oxide-Na+ ionic conductor -aluminum oxide Na2O 11Al2O3 AlONaLayered structure of -aluminum oxide3636 -AluminiumoxidIIHexagonal unit cell. For larger cations (K+, Tl+) lower conductivity is [ -1cm-1]Temperature [K]Leitf higkeit37 High energy density, high efficiency of charge/discharge (89 92%) and long cycle life, and is fabricated from inexpensive materials. The sodium is separated by a beta-alumina solid electrolyte (BASE) cylinder from the container of molten Sulfur Cell ++ eNaNal222)()(52)(252llSNaeSNa ++ ++ Cathode -Anode )(52)()(52lllSNaSNa +DischargingCharging)()()(5252lllSNaSNa+ High operating temperatures of 300 to 350 C and the highly corrosive sodium polysulfides and sodium.