Ferroelectric Perovskites for High-Speed Memory: A Mechanism Revealed by Quantum Bonding Motion

206 Pages·2022·4.503 MB·English

by  Taku Onishi

Ferroelectric Perovskites for High-Speed Memory
Taku Onishi
Ferroelectric Perovskites for
High-Speed Memory
A Mechanism Revealed by Quantum Bonding
Motion
TakuOnishi
DepartmentofChemistry
UniversityofOslo
Oslo,Norway
MieUniversity
Tsu,Japan
ISBN 978-981-19-2668-6 ISBN 978-981-19-2669-3 (eBook)
https://doi.org/10.1007/978-981-19-2669-3
©SpringerNatureSingaporePteLtd.2022
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Preface
Ferroelectricstudywasnotcompletelyestablished.
Bymydiscoveryof“QuantumBondingMotion”inFerroelectricPerovskite,
Isucceededintheclarificationoftheferroelectricmechanism.
Istronglyhope“QuantumBondingMotion”iswidelyregardedasanewscientific
theory.
Thismaybethefirststep.
Definitely,“QuantumBondingMotion”willbeadoorto“NewQuantumWorld”.
Thankyou.
Kobe,Japan TakuOnishi
March2022
v
Acknowledgements
My research work was partially supported by the Research Council of Norway
through its Centres of Excellence scheme, project number 262695. I thank Prof.
Trygve Helgaker for his continuous support and encouragement. Finally, I am
especiallygratefulfortheconstructivediscussionsIhadwithTO.
vii
Overview
Thisbookisfortheoreticalandexperimentalresearcherswhoareinterestedinferro-
electrics and advanced memory. After an explanation of the background of ferro-
electricity, quantum mechanics and quantum computational chemistry are intro-
duced for beginners. Readers are given an understanding of the origin of ferro-
electricity at electron and atomic levels. In perovskite titanium oxides, the ferro-
electricmechanismisexplainedinconcretetermswithmolecularorbitalcalculation
results.Especially,uniquequantumphenomenoninferroelectric,“QuantumBonding
Motion”isexplainedindetail.Finally,thematerialsdesignedforhigh-performance
ferroelectricsareintroduced,andthefutureofhigh-speedmemoryisdiscussed.
Thisbookconsistsofthreeparts:
– PartI:BackgroundofFerroelectricity
– PartII:BackgroundofQuantumSimulation
– PartIII:OriginofFerroelectricityandContinuedFuture
“Quantum Bonding Motion” in ferroelectric perovskite is concretely demon-
strated in Part III. For better understanding, it is recommended to read Part III,
afterPartsIandII.
ix
Contents
PartI BackgroundofFerroelectricity
1 Dielectric ..................................................... 3
1.1 ClassificationofMaterials ................................. 3
1.2 ParallelPlateCapacitor ................................... 4
1.2.1 ElectricFieldAroundPointCharge .................. 5
1.2.2 ElectricFieldAroundChargedPlate ................. 7
1.2.3 ElectricFieldWithinParallelPlateCapacitor ......... 8
1.3 Polarisation ............................................. 11
1.3.1 DipoleMoment ................................... 11
1.3.2 PolarisationinChargeNeutralSystem ............... 11
1.3.3 GeneralFormulaofPolarisation .................... 14
1.4 DielectricInsertedParallelPlateCapacitor ................... 14
References .................................................... 17
2 Perovskites:ApplicationandStructure .......................... 19
2.1 ApplicationofPerovskites ................................. 19
2.1.1 ParallelPlateCapacitor ............................ 20
2.1.2 Battery .......................................... 22
2.1.3 Photocatalyst,PhotoluminescenceandSolarCell
Dye ............................................. 25
2.2 StructureofPerovskites ................................... 26
2.2.1 CompositionFormula ............................. 26
2.2.2 ShannonIonicRadius ............................. 27
2.2.3 GoldschmidtToleranceFactor ...................... 28
2.3 DielectricPerovskites ..................................... 30
2.3.1 BaTiO Perovskite ................................ 30
3
2.3.2 PbTiO Perovskite ................................ 31
3
2.3.3 SrTiO Perovskite ................................ 31
3
2.3.4 CaTiO Perovskite ................................ 32
3
2.3.5 KNbO Perovskite ................................ 32
3
2.3.6 AZrO (A=Ba,Sr,Ca,Pb)Perovskite .............. 32
3
xi
xii Contents
2.3.7 IonSubstitutedPerovskites ......................... 33
References .................................................... 34
3 Memory:WorldofBinaryCode ................................ 37
3.1 Transistor ............................................... 37
3.1.1 BasicsofTransistor ............................... 37
3.1.2 FieldEffectTransistor ............................. 39
3.2 Moore’sLaw ............................................ 39
3.3 Central Processing Unit, Memory and Large Scale
IntegratedCircuit ......................................... 41
3.4 BinaryNumberSystem ................................... 41
3.5 ClassificationofMemories ................................ 42
3.5.1 VolatileMemories ................................ 42
3.5.2 Non-VolatileMemories ............................ 43
3.5.3 HardDiskDrive .................................. 50
3.5.4 SolidStateDrive ................................. 51
References .................................................... 51
4 Ferroelectric .................................................. 53
4.1 Introduction ............................................. 54
4.2 EmpiricalCurie–WeissLaw ............................... 54
4.3 FerroelectricHysteresisLoop .............................. 54
4.4 FerroelectricMechanism .................................. 57
4.5 PolarisationDomain ...................................... 58
4.6 Antiferroelectric ......................................... 60
4.7 Ferroelectric Downsizing Limit: From Grain
toNanoparticle .......................................... 61
References .................................................... 62
5 FerroelectricMaterials:HistoryandPresentStatus .............. 63
5.1 Early-StageResearch ..................................... 63
5.1.1 FerroelectricHysteresisLoopofRochelleSalt ........ 63
5.1.2 PotassiumDihydrogenPhosphate ................... 65
5.2 DiscoveryofFerroelectricityinBaTiO Perovskite ............ 66
3
5.3 FerroelectricPbZr Ti O Perovskites ...................... 67
x 1-x 3
5.4 Pb-FreeFerroelectricPerovskites ........................... 68
5.4.1 KNbO Perovskite ................................ 68
3
5.4.2 Bi Na TiO Perovskite .......................... 68
1/2 1/2 3
5.4.3 AurivilliusTypePerovskite:SrBi Ta O ............. 68
2 2 9
5.5 FerroelectricTungstenBronzePerovskite .................... 68
5.6 FerroelectricHafniumDioxide ............................. 69
5.7 Summary ............................................... 69
References .................................................... 69
Contents xiii
PartII BackgroundofQuantumSimulation
6 QuantumMechanics .......................................... 73
6.1 Introduction ............................................. 73
6.2 Wave-ParticleDuality ..................................... 74
6.2.1 WaveinClassicalTheory .......................... 74
6.2.2 IncorporationofWaveCharacterintoParticle ......... 75
6.3 SchrödingerEquation ..................................... 76
6.3.1 Derivation ....................................... 76
6.3.2 IncorporationofPotential .......................... 78
6.3.3 Time-IndependentPotential ........................ 78
6.3.4 Time-IndependentSchrödingerEquation ............. 79
6.4 InterpretationofQuantumWaveFunction .................... 81
6.5 QuantumTigerLaw ...................................... 82
Reference ..................................................... 83
7 SchrödingerEquationinOne-ElectronSystem:Hydrogenic
Atom ......................................................... 85
7.1 Introduction ............................................. 85
7.2 SchrödingerEquationforHydrogenicAtom .................. 86
7.3 SeparationofVariables .................................... 86
7.4 QuantumWaveFunctionforHydrogenicAtom ............... 88
7.4.1 ThreeQuantumNumbers .......................... 88
7.4.2 DifferentialEquation .............................. 90
7.4.3 1sAtomicOrbital ................................. 91
7.4.4 2pAtomicOrbital ................................ 91
7.4.5 3dAtomicOrbital ................................ 92
7.5 TotalEnergyforHydrogenicAtom ......................... 93
7.6 PictorialRepresentationofAtomicOrbital ................... 94
References .................................................... 95
8 SchrödingerEquationinMany-ElectronSystem:Helium,
Cluster ....................................................... 97
8.1 QuantumInteractioninHeliumAtom ....................... 97
8.2 Many-ElectronSystem .................................... 99
8.2.1 HamiltonianforMany-ElectronSystem .............. 99
8.2.2 Born–OppenheimerApproximation ................. 99
8.3 ElectronSpin ............................................ 100
8.4 SpinOrbital ............................................. 101
8.5 TotalQuantumWaveFunction ............................. 102
8.5.1 HartreeProduct ................................... 102
8.5.2 SlaterDeterminant ................................ 102
FurtherReading ................................................ 103
xiv Contents
9 Hartree–FockEquation ........................................ 105
9.1 TotalEnergyinBorn–OppenheimerApproximation ........... 105
9.1.1 n-electronAtom .................................. 106
9.1.2 n-electronCluster ................................. 108
9.2 Hartree–FockEquation .................................... 109
9.2.1 DerivationofOne-ElectronEquation ................ 109
9.2.2 ClosedShellSystem .............................. 111
9.2.3 OpenShellSystem ................................ 116
FurtherReading ................................................ 123
10 MolecularOrbitalCalculation .................................. 125
10.1 BasisFunction(1) ........................................ 126
10.2 Hartree–FockMatrixEquationforClosedShellSystem ........ 126
10.3 Hartree–FockEquationsforOpenShellSystem ............... 128
10.3.1 EquationforαSpatialOrbital ...................... 128
10.3.2 EquationforβSpatialOrbital ....................... 130
10.4 Hartree–FockMatrixEquationsforOpenShellSystem ........ 131
10.5 BasisFunction(2) ........................................ 133
10.5.1 BasisSet ........................................ 133
10.5.2 InitialAtomicOrbital ............................. 134
10.5.3 Slater-TypeBasisFunctionVersusGaussian-Type
BasisFunction ................................... 134
10.5.4 Contraction ...................................... 135
10.5.5 Split-Valence ..................................... 136
10.6 ElectronCorrelation ...................................... 137
10.7 DensityFunctionalTheory ................................ 137
10.8 SelectionofBasisSetandCalculationMethod ............... 139
10.9 OrbitalAnalysis .......................................... 139
10.9.1 VirtualOrbital .................................... 139
10.9.2 ChemicalBondingRule ........................... 140
10.9.3 MullikenPopulationAnalysis ...................... 140
FurtherReadings ............................................... 141
PartIII OriginofFerroelectricityandContinuedFuture
11 QuantumBondingMotioninFerroelectricBaTiO Perovskite ..... 145
3
11.1 PointCharge-BasedMotion ................................ 145
11.2 ChemicalBonding-BasedMotion ........................... 147
11.3 PeriodicQuantumBondingMotion ......................... 150
11.4 AperiodicQuantumBondingMotion ........................ 150
11.5 Ion-ConductionofBariumCationNearTetragonalCentre ...... 152
11.6 CubicStructure .......................................... 154
11.7 DirectionofFerroelectricQuantumBondingMotion .......... 157
11.8 FerroelectricNanoparticle ................................. 159
References .................................................... 160