1  Introduction of Varistor Ceramics 1 
1.1  ZnOVaristors 1 
1.2  FabricationofZnOVaristors 3 
1.2.1  PreparationofRawMaterials 4 
1.2.2  SinteringofZnOVaristors 5 
1.3  Microstructure 6 
1.4  TypicalParametersofZnOVaristors 7 
1.5  HistoryofZnOVaristors 9 
1.6  ApplicationsofZnOVaristors 12 
1.7  AlternativeVaristorCeramics 17 
1.8  Ceramic–PolymerCompositeVaristors 18 References 22 
2  Conduction Mechanisms of ZnO Varistors 31 
2.1  Introduction 31 
2.2  BasicConceptsinSolid-StatePhysics 33 
2.2.1  AtomicEnergyLevelandEnergyBandofCrystal 33 
2.2.2  Metal,Semiconductor,andInsulator 35 
2.2.3  CharacteristicsofFermi–DiracFunction 37 
2.2.4  ImpurityandDefectEnergyLevel 38 
2.3  EnergyBandStructureofaZnOVaristor 39 
2.3.1  EnergyBandStructureofaZnOGrain 39 
2.3.2  DSBofaZnOVaristor 40 
2.3.3  MicroscopicOriginofDSB 41 
2.3.4  Asymmetric I–V CharacteristicsoftheDSB 43 
2.4  ConductionMechanismofaZnOVaristor 45 
2.4.1  ConductionModelBasedonThermionicEmissionProcess 46 
2.4.2  MinorityCarrierGenerationProcess 49 
2.4.3  TheBypassE?ectModel 51 
2.5  DielectricCharacteristicsofaZnOVaristor 51 
2.5.1  ExplanationtoDielectricPropertiesofaZnOVaristor 52 
2.5.2  E?ectofInterfacialChargeRelaxationonConductingBehaviorofZnOVaristorsUnderTime-VaryingElectricFields 54 
2.5.3  DeterminationofBarrierHeightandRelatedParameters 58 
2.5.4  DeterminationofDeepDonorLevelintheZnOVaristor 59 
2.5.5  DeterminationofGrainandGrainBoundaryConductivity 60 References 62 
3  Tuning Electrical Characteristics of ZnO Varistors 67 
3.1  Introduction 67 
3.2  Liquid-PhaseFabrication 68 
3.2.1  MicrostructureofZnOVaristor 68 
3.2.2  PolymorphofBismuthOxide 71 
3.2.3  In?uenceofBi2O3Concentration 72 
3.2.4  VolatilizationofBismuthOxide 72 
3.3  PreparingandSinteringTechniques 74 
3.3.1  Fabrication 74 
3.3.2  FabricationStages 75 
3.3.3  E?ectofPores 76 
3.4  RoleofOxygenattheGrainBoundary 78 
3.5  DopantE?ects 79 
3.5.1  E?ectsofAdditives 79 
3.5.2  DonorDopants 82 
3.5.3  AcceptorDopants 86 
3.5.4  AmphotericDopants 87 
3.5.4.1  MonovalentDopants 88 
3.5.4.2  TrivalentDopants 89 
3.5.5  E?ectsofRareEarthOxides 92 
3.5.6  DopantsforImprovingtheStability 93 
3.5.7  EvidenceforHydrogenasaShallowDonor 95 
3.6  RoleofInversionBoundaries 95 
3.7  HighVoltageGradientZnOVaristor 98 
3.8  LowResidualVoltageZnOVaristor 101 
3.8.1  ResidualVoltageRatio 101 
3.8.2  LowResidualVoltageZnOVaristorsbyDopingAl 103 
3.8.3  LowResidualVoltageZnOVaristorsbyDopingGa 106 
3.8.4  LowResidualVoltageZnOVaristorswithHighVoltageGradient 108 References 110 
4  Microstructural Electrical Characteristics of ZnO Varistors 125 
4.1  Introduction 125 
4.2  MethodstoDetermineGrainBoundaryParameters 126 
4.2.1  TheIndirectMethod 126 
4.2.2  TheDirectMicrocontactMethods 126 
4.3  StatisticalCharacteristicsofGrainBoundaryParameters 129 
4.3.1  NonuniformityofBarrierVoltages 129 
4.3.2  DistributionofBarrierVoltage 131 
4.3.3  DistributionofNonlinearCoe?cient 132 
Contents 
4.3.4  DistributionofLeakageCurrentThroughGrainBoundary 133 
4.3.5  DiscussiononMicrocontactMeasurement 133 
4.4  Classi?cationofGrainBoundaries 134 
4.5  OtherTechniquestoDetectMicrostructurallyElectricalPropertiesofZnOVaristors 137 
4.5.1  ScanningProbeMicroscopy-BasedTechniques 137 
4.5.2  GalvanicDeterminationofConductiveAreasonaVaristor Surface 139 
4.5.3  LineScanDeterminationofDi?erencesinBreakdownVoltageWithinaVaristor 141 
4.5.4  CurrentImagesinSEM 141 
4.6  TestonFabricatedIndividualGrainBoundary 142 
4.6.1  ThinFilmApproach 143 
4.6.2  SurfaceIn-Di?usionApproach 143 
4.6.3  BicrystalApproach 143 References 145 
5  Simulation on Varistor Ceramics 149 
5.1  Introduction 149 
5.2  GrainBoundaryModel 151 
5.2.1  I–V CharacteristicModelofGrainBoundary 151 
5.2.2  GBModelConsideringConductionMechanism 154 
5.3  SimulationModelof I–V Characteristics 159 
5.3.1  Simple2DSimulationModel 159 
5.3.2  2DSimulationModelsBasedontheVoronoiNetwork 161 
5.3.3  ConsiderationonPoresandSpinels 164 
5.3.4  AlgorithmtoSolveEquivalentCircuit 165 
5.3.5  ModelVeri?cation 169 
5.4  SimulationModelforThermalCharacteristics 170 
5.4.1  ThermalConductionAnalysis 171 
5.4.2  Pulse-InducedFractureAnalysis 173 
5.5  SimulationsonDi?erentPhenomena 174 
5.5.1  SimulationonMicrostructuralNonuniformity 174 
5.5.2  SimulationonCurrentLocalizationPhenomenon 175 
5.5.3  In?uenceofMicrostructuralParametersonBulkCharacteristics 179 
5.5.3.1  In?uenceofZnOGrainParameters 180 
5.5.3.2  In?uenceofGrainBoundaryParameters 183 
5.5.4  In?uentialFactorsonResidualVoltageRatio 186 References 188 
6  Breakdown Mechanism and Energy Absorption Capability of ZnO Varistor 193 
6.1  Introduction 193 
6.2  ImpulseFailureModesofZnOVaristors 194 
6.3  MechanismsofPunctureandFractureFailures 197 
6.3.1  MechanismsofPunctureFailure 197 
6.3.2  MechanismofFractureFailure 201 
6.4  SimulationofPunctureandFractureFailures 204 
6.4.1  PunctureDestructionSimulation 204 
6.4.1.1  PunctureSimulationinMicrostructure 206 
6.4.2  CrackingFailureSimulationinMicrostructure 208 
6.5  Thermal Runaway 209 
6.5.1  PowerLossofZnOVaristor 210 
6.5.2  ThermalRunawayMechanism 210 
6.5.3  TeststoEnsuretheThermalStabilityCharacteristics 213 
6.6  In?uencesofDi?erentFactorsonFailuresofZnOVaristors 213 
6.6.1  In?uenceofMicrostructuralNonuniformity 213 
6.6.2  In?uenceofElectricalNonuniformityinMicrostructure 216 
6.6.3  SimulationAnalysisonBreakdownModes 217 
6.7  In?uentialFactorsonEnergyAbsorptionCapability 218 
6.7.1  In?uenceoftheAppliedCurrent 218 
6.7.2  In?uenceofVaristorCross-sectionalArea 221 
6.7.3  SimulationAnalysisonSurgeEnergyAbsorptionCapability 221 
6.8  DiscussionsonEnergyAbsorptionCapability 225 
6.8.1  EnergyAbsorptionCapabilityDeterminedbyFractureFailure 225 
6.8.2  EnergyAbsorptionCapabilityDeterminedbyPunctureFailure 226 
6.8.3  DiscussiononNonuniformityofEnergyAbsorptionCapability 228 
6.8.4  AdditivesE?ectonEnergyAbsorptionCapability 229 
6.8.5  OtherMeasurestoImproveEnergyAbsorptionCapability 230 References 230 
7  Electrical Degradation of ZnO Varistors 235 
7.1  Introduction 235 
7.2  DegradationPhenomenaofZnOVaristors 237 
7.2.1  DegradationPhenomenaoftheVaristorBulk 237 
7.2.2  DegradationofGrainBoundary 242 
7.2.3  PulseDegradationCharacteristics 245 
7.2.4  TopographicInformationforDegradationAnalysis 247 
7.3  MigrationIonsfortheDegradationofZnOVaristors 249 
7.3.1  GrainBoundaryDefectModel 249 
7.3.2  ExperimentalProofofIonMigration 251 
7.3.3  Identi?cationofDominantMobileIons 252 
7.3.4  Three-DimensionalExtension 256 
7.4  DegradationMechanismofZnOVaristors 257 
7.4.1  DCDegradationMechanism 258 
7.4.2  ACDegradationMechanism 258 
7.4.3  NonuniformDegradationMechanism 260 
7.4.4  PulseDegradationofZnOVaristors 262 
7.4.4.1  DegradationMechanismUnderImpulseCurrent 263 
7.4.4.2  SuperimposingDegradation 264 
7.5  RoleofInteriorMicrocracksonDegradation 266 
7.6  AntidegradationMeasures 267 
7.6.1  Speci?cPreparationProcedures 268 
7.6.2  OptimizationofFormula 269 
Contents 
7.6.2.1  DopantE?ectsonImprovingACDegradationCharacteristics 270 
7.6.2.2  DopantE?ectsonImprovingImpulseDegradationProperty 271 References 272 
8  Praseodymium/Vanadium/Barium-Based ZnO Varistor Systems 281 
8.1  PraseodymiumSystem 281 
8.1.1  DopingE?ects 281 
8.1.2  E?ectofSinteringProcesses 285 
8.1.3  High-VoltageApplications 288 
8.1.4  Low-VoltageApplications 288 
8.2  VanadiumSystem 289 
8.2.1  DopingE?ects 290 
8.2.2  ElectricalCharacteristics 291 
8.2.3  MicrostructuralCharacteristics 292 
8.2.4  E?ectsofVanadiumOxideonGrainGrowth 294 
8.3  BariumSystem 295 
8.3.1  PreparationandElectricalCharacteristics 295 
8.3.2  MicrostructuralCharacteristics 296 
8.3.3  ImprovingStabilityAgainstMoisture 298 
8.4  ZnO–GlassVaristor 298 References 300 
9  Fabrications of Low-Voltage ZnO Varistors 307 
9.1  Introduction 307 
9.2  ExaggeratingGrainGrowthbySeedGrains 308 
9.3  SynthesisofNanocrystallineZnOVaristorPowders 309 
9.3.1  Gas-PhaseProcessingMethods 309 
9.3.2  CombustionSynthesis 311 
9.3.3  Sol–GelMethods 311 
9.3.4  Solution-CoatingMethod 315 
9.4  Nano?llersinZnOVaristorCeramics 320 
9.5  SinteringTechniquestoControlGrainGrowth 321 
9.5.1  Step-sinteringApproach 321 
9.5.2  MicrowaveSinteringMethod 322 
9.5.3  SparkPlasmaSinteringTechnique 324 References 327 
10  Titanium-Based Dual-function Varistor Ceramics 335 
10.1  SrTiO3 Varistors 335 
10.1.1  Introduction 335 
10.1.2  MicrostructureofSrTiO3Varistors 336 
10.1.3  PreparationofSrTiO3Varistors 336 
10.1.4  PerformanceofSrTiO3 338 
10.1.5  ConductionMechanismofSrTiO3 339 
10.2  TiO2-BasedVaristors 341 
10.2.1 Introduction 341 
10.2.2  PreparationofTiO2-BasedVaristors 342 
10.2.3  MechanismofTiO2Capacitor–VaristorCeramics 342 
10.2.4  DopingofTiO2-BasedVaristors 343 
10.2.4.1 Acceptor-DopedTiO2-BasedVaristors 343 
10.2.4.2 Donor-DopedTiO2-BasedVaristors 344 
10.2.4.3 CodopingE?ectsofAcceptorandDonorDopants 345 
10.2.4.4 SinteringAdditivesinTiO2-BasedVaristors 347 
10.2.5  DevelopmentofTiO2-BasedVaristors 348 
10.3  CaCu3Ti4O12 Ceramics 348 
10.3.1  Introduction 348 
10.3.2  StructureofCCTO 349 
10.3.2.1 CrystalStructure 349 
10.3.2.2 PhaseandMicrostructure 350 
10.3.3  PerformancesofCCTOCeramics 352 
10.3.3.1 NonohmicCurrent–VoltageCharacteristic 352 
10.3.3.2 ColossalPermittivity 354 
10.3.3.3 DielectricLoss 357 
10.3.4  Mechanism 358 
10.3.4.1 IBLCModel 358 
10.3.4.2 ConductingMechanism 362 
10.3.4.3 PolarizationMechanismofGrains 364 
10.3.4.4 APolaronicStackingFaultDefectModel 365 
10.3.5  RoleofDopants 366 
10.3.5.1 RoleofDopingCuO 366 
10.3.5.2 DopingMechanismstoTuneCCTOPerformances 368 
10.4  BaTiO3VaristorsofPTCRE?ect 375 
10.4.1  Introduction 375 
10.4.2  DopingE?ects 377 
10.4.3  PreparationofBaTiO3Ceramics 379 
10.4.4  PTCRE?ectofBaTiO3Ceramics 381 
10.4.5  VaristorCharacteristicsofBaTiO3Ceramics 384 References 386 
11  Tin Oxide Varistor Ceramics of High Thermal Conductivity 407 
11.1  PreparationofSnO2-BasedVaristors 407 
11.2  ElectricalPerformancesofSnO2-BasedVaristors 410 
11.3  MechanismofSnO2-BasedVaristors 414 
11.3.1  FormationofGrainBoundaryPotentialBarrier 414 
11.3.2  AtomicDefectModel 415 
11.3.3  AdmittanceSpectroscopyAnalysis 417 
11.3.4  Capacitance–VoltageAnalysis 420 
11.3.5  E?ectofThermalTreatment 421 
11.4  RoleofDopantsinTuningSnO2-BasedVaristors 423 
11.4.1  DopantsforDensifyingSnO2-BasedVaristors 423 
11.4.2  AcceptorDoping 424 
Contents 
11.4.3  DonorDoping 427 
11.5  ThermalPerformances 429 
11.6  DegradationBehaviors 431 
11.7  DevelopmentofSnO2-BasedVaristors 432 References 434 
12  WO3-Based Varistor Ceramics of Low Breakdown Voltage 441 
12.1  Introduction 441 
12.2  TungstenOxide 442 
12.3  PreparationofWO3-BasedVaristors 444 
12.4  ElectricalPerformances 446 
12.5  ImprovingtheElectricalStability 448 
12.6  MechanismModelofWO3-BasedVaristors 449 
12.7  DopingE?ects 452 
12.7.1  TheAdditionofRareEarthOxides 452 
12.7.2  TheAdditionofCuO 453 
12.7.3  TheAdditionofAl2O3 454 
12.7.4  TheAdditionofTiO2 455 
12.7.5  TheAdditionofOtherAdditives 455 References 456 
Index 461 

Metal oxide varistor (MOV), or ZnO varistor, is a kind of polycrystallinesemiconductor ceramics composed of multiple metal oxides and sinteredby conventional ceramic technology. ZnO varistors have good nonlinearvolt-ampere characteristics and excellent impulse energy-absorbing capacities.These advantages make them widely used in transient overvoltage protectionsfor electrical/electronic systems. Now, varistors have been widely used asguardianstoprotectcircuitsoveraverywiderangeofvoltages,fromafewvoltsin semiconductor circuits to 1000kV AC and ± 1100kV DC in electrical power transmission and distribution networks. Correspondingly, they can also handlean enormous range of energies from a few joules to many megajoules. Remarkably,theyarealsoveryfast,switchinginnanosecondsfromtheirhigh-resistancestate to highly conducting state and then restores to a normal high-impedanceoperatingconditions.
Abulkvaristorisacomplexmultijunctiondevicecomposedoflargenumbersofbothohmicandnonlinearelementsconnectedinarandomnetwork.Thefeatures ofbulkvaristorsarein?uencedbythegeometryandthetopologyofthegranularmicrostructure,aswellasthepropertiesandthedistributionofelectricalcharacteristicsofgrainboundaries.ThisbooktriestobridgetheMacro-Characteristics with the properties in microstructures of ZnO varistors to provide insights into someoftheaspectsinthemicrostructuresofZnOvaristors,whichin?uencethefeatures of the bulk varistors and further the science and the understanding onmicrostructuresofZnOvaristorsandthoseparametersthata?ectthee?ciencyduringthemanufacturingprocess.
The book includes 12 chapters, which mainly focuses on ZnO varistors.Chapter 1 introduces and highlights the fundamental knowledge and applications of ZnO varistors. Chapter 2 introduces the conduction mechanism of theZnO varistor, among the numerous conduction models, the one presented by
G.E. Pike and further developed by G. Blatter and F. Greuter has been widelyrecognized and may meet most of the experimental phenomena. Various additives to improve the electrical characteristics were discovered and the synthesisconditionswereoptimized,whichwillbeintroducedinChapter3.TheelectricalpropertiesofeachindividualgrainboundarywillcontributetotheglobalelectricalcharacteristicsofZnOvaristors,Chapter4characterizesthemicrostructuralelectrical properties of ZnO varistors. The simulation is helpful to reveal theconnection between the microstructure and the macroscopic characteristics of varistor ceramics, the details on how to simulate varistor ceramics will be presented in Chapter 5. The breakdown of ZnO varistors is an originalphenomenonduringtheirapplications,andthefailuremodelsresultindi?erentenergy handling capabilities, which will be introduced in Chapter 6. ZnO varistors can be electrically, chemically, and thermally degraded during use, leadingto the reduction of barrier voltage height and, consequently, to the increaseof leakage current, which could be catastrophic for ZnO varistors, Chapter 7discusses the electrical degradation of ZnO varistors. Chapter 8 introducesother ZnO varistorsystemsinsteadofbismuth, suchaspraseodymium,barium,andvanadium,forovercomingtheshortcomingsofBi2O3-basedZnOvaristors. 
The applications in electronic systems require the miniaturized varistors andlow-voltage varistors. Chemical processing, such as sol–gel, solution, precipitation, microemulsion techniques, etc., facilitates a homogeneous doping at themolecular level to obtain a miniature device with a higher breakdown voltage,which will be introduced in Chapter 9. Interestingly, the ceramic–polymercomposite varistor is a composite one, incorporating varistor particles orsemiconducting particles, and its ?eld-dependent property varies with the ?llerconcentration. The composite varistor, with a lower breakdown voltage, can bea suitable substitute for ZnO-based varistors for the purpose of protection forlow-voltagesystems,whichwillbeintroducedinChapter1.
Besides works on improving the performance of the ZnO varistor material,othernewmaterialshavealsobeensearchedinordertoachieveabetterstabilityand be used for new applications. The titanium-based capacitor–varistor dual-function varistor ceramics, such as TiO2,SrTiO3 CaCu3Ti4O12 (CCTO), and BaTiO3 varistor ceramics, have realized the goal to achieve component miniaturization and provide a superior high-frequency and high-amplitude transientvoltage protection, which will be introduced in Chapter 10. Di?erent fromthe multiphase structure of the ZnO-based varistor, the SnO2-based varistor has a simple microstructure, good stability, and better thermal conductivity,which makes the SnO2-based varistor one of the most promising candidates tocommercially compete with the ZnO-based varistor. The SnO2-based varistors will be introduced in Chapter 11. The WO3-based varistor ceramic is another kind of low-voltage varistor with a low threshold electric ?eld of 5–10Vmm?1 and a high dielectric constant, which enables it to act as a varistor in parallelwithacapacitor,whichwillbeintroducedinChapter12.
Thisbookcoversmainaspectsofmetaloxidevaristors,whichintroducefundamentalandadvancedtheoriesandtechnologiesrelatedtometaloxide varistors, research achievements in the this ?eld, and has re?ected the recent research works of the authors and their students and colleagues in Tsinghua University,especiallythePh.D. dissertationsofDr. ChenQingheng,Dr. HuJun,Dr. LiuJun, Dr. LongWangcheng,Dr. ZhaoHongfeng,Dr.XieJingcheng,Dr.ChengChenlu, andMScthesisofMs. WeiQiaoyuan.Theauthortriedtocoveralltheaspectsofmetaloxidevaristors,butitishardtoavoidtenthousandmayhavebeenleftout. 
ProfessorJinliangHe
TsinghuaUniversityBeijingChina 

Acknowledgments 
My research works on metal oxide varistors in Tsinghua University weresupported by the National Natural Science Foundations of China under Grants59907001, 50425721, 50677029, and 50737001, and was supported in part bythe 11th Five-Year Science and Technology Support Plan of China, and by theNational Basic Research Program of China under grant 2014CB239504.
Enormous references hadbeencited inourbook,all hadbeenlistedineverychapter, but it is hard to avoid careless omission, in this case, I beg your pardon.I am so sorry,some formulas areunable to ?ndthe originalreferences wheretheycame from. 
I have had a long-term cooperation in the research of metal oxide varistorswith Prof. Nan Cewen of Tsinghua University, who is an Academician of ChineseAcademy of Sciences, and Prof. Lin Yuanhua, who is the Dean of the School ofMaterialsScience andTechnology in TsinghuaUniversity,I havelearnta lotfromthem, and many cooperation results have been collected in the book. I would like to extend my sincere thanks to them.
Special thanks go to Dr. Han-Goo Cho and Dr. Se-Won Han, from KoreaElectrotechnology Research Institute (KERI), for providing me the chance to doresearch works in the ?eld of metal oxide varistors during 1997–1998. KERI iswhereIstartedmyresearchinthis?eld.
Special thanks also go to my students, including Dr. Long Wangcheng, Dr. LuoFengchao, Dr. Xie Jingcheng, Ms. Wei Qiaoyuan, and Mr. Meng Pengfei, for theirassistance on preparing the draft of the book and to my colleagues for their generous help in many ways so as to allow me to allocate time working on the book.GreatgratitudeisgiventoProf.HuJunforpreparingthemanuscriptofChapter5,Dr.ChengChenluforpreparingpartmanuscriptsofChapters2and7,andDr.LiuJun for preparing the part manuscript of Chapter 7.
Gratitude is extended to Mr. Lesley Jebaraj, Project Editor at Wiley, for hiseditorial and technical reviews on this book. His professionalism and experiencehave greatly enhanced the quality and value of this book.
Lastly, but not least, my most special gratitude goes to my supporting andunderstanding family, my mother, Yang Ruiru, who taught me working hard andenjoying the wonderful life; my wife, Prof. Tu Youping, who had done and hasbeen still doing a great job on supporting the family. Most of all, I am indebted tomy son, Ziyu, I have not spent much time to enjoying his grow-up process, but itis gratifying that he is working hard to become a scientist in the ?eld of statisticsand machine learning. 
Jinliang He 

Introduction of Varistor Ceramics 
Zinc oxide (ZnO) varistor, which is a kind of polycrystalline semiconductorceramic composed of multiple metal oxides and sintered using conventionalceramic technology, is a voltage-dependent switching device, which exhibitshighly nonohmic current–voltage characteristics above the breakdown voltage.Basic information on ZnO varistors, including the fabrication, microstructure,and typical electrical parameters, is introduced. The history and applications ofZnOvaristorsarealsopresented.Thepanoramaofalternativevaristorceramicsfor Bi2O3-based ZnO varistors is mapped out. Especially, the ceramic–polymercomposite varistors with lower breakdown voltage, incorporating varistorparticlessuchassemiconductingparticles,acombinationofmetalandsemiconducting particles, and ZnO microvaristors, in a polymeric matrix are reported.Now, varistors are available that can protect circuits over a very wide range ofvoltages, from a few volts for low voltage varistors in semiconductor circuits to1000kVACand ±1100kVDCinelectricalpowertransmissionanddistribution networks. Correspondingly,theyalsocanhandleanenormousrangeofenergiesfromafewjoulestomanymegajoules. 
1.1 ZnO Varistors 
A varistor is an electronic component with a “diode-like” nonlinear current– voltage characteristic, which is a portmanteau of variable resistor [1]. Function-ally,varistorsareequivalenttoaback-to-backZenerdiodeandaretypicallyusedin parallel with circuits to protect them against excessive transient voltages insuch a way that, when tri