Table Of Content

Nanoscale Energy Transport and Harvesting Pan Stanford Series on Renewable Energy — Volume 2 Nanoscale Energy Transport and Harvesting A COMPUTATIONAL STUDY editors edited by Preben Maegaard Anna Krenz Gang Zhang Wolfgang Palz The Rise of Modern Wind Energy Wind Power for the World CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20150122 International Standard Book Number-13: 978-981-4463-03-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reason- able efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com December15,2014 11:59 PSPBook-9inx6in 00-Gang-Zhang-prelims Contents Preface ix 1 MolecularDynamicsSimulationsforComputingThermal ConductivityofNanomaterials 1 JieChen,GangZhang,andBaowenLi 1.1 IntroductiontoMolecularDynamics 1 1.2 ForceFieldPotential 4 1.2.1 PairPotential 4 1.2.2 Many-BodyPotential 6 1.2.3 MixingRule 8 1.3 IntegrationoftheEquationsofMotion 8 1.4 TemperatureinMolecularDynamics 10 1.4.1 HeatBath 10 1.4.2 QuantumCorrection 11 1.5 Non-equilibriumMolecularDynamics 15 1.5.1 Background 15 1.5.2 EffectsofHeatBath 18 1.5.3 SomeApplications 27 1.6 EquilibriumMolecularDynamics 32 1.6.1 Green–KuboFormula 32 1.6.2 DifferentImplementations 36 1.6.3 DeterminationofCut-OffTime 41 1.6.4 SomeApplications 44 2 Non-equilibriumPhononGreen’sFunctionSimulationand ItsApplicationtoCarbonNanotubes 59 TakahiroYamamoto,KenjiSasaoka,andSatoshiWatanabe 2.1 Introduction:ThermalTransportatNanoscale 59 2.2 TheoryofNanoscalePhononTransport 60 December15,2014 11:59 PSPBook-9inx6in 00-Gang-Zhang-prelims vi Contents 2.2.1 LandauerTheoryofPhononTransport 60 2.2.2 BallisticPhononTransportandQuantizationof ThermalConductance 63 2.2.3 Non-equilibriumGreen’sFunctionMethodfor PhononTransport 65 2.3 ApplicationofLandauer–NEGFMethodtoCarbon Nanotube 70 2.3.1 PhononsinCarbonNanotube 70 2.3.2 ThermalConductanceReductionbyDefect Scattering 72 2.3.3 IsotopeEffectsonThermalTransportin CarbonNanotubes 76 2.3.3.1 Characteristiclengths:meanfreepath andlocalizationlength 76 2.3.3.2 Universalphonon-transmission fluctuation 79 2.3.3.3 Andersonlocalizationofphonons 80 2.4 ConcludingRemarks 81 3 ThermalConductionofGraphene 91 YongXuandWenhuiDuan 3.1 BasicConceptsofQuantumThermalTransport 91 3.1.1 Thermal-TransportCarriers 91 3.1.2 FundamentalLengthScalesofThermal Transport 92 3.1.2.1 Thecharacteristicwavelengthof phononλ 92 3.1.2.2 Thephononmeanfreepathl 92 3.1.3 DifferentTransportRegions 94 3.1.4 TheLandauerFormalism 94 3.1.5 QuantizedThermalConductance 96 3.2 TheNon-equilibriumGreen’sFunctionMethod 98 3.2.1 HamiltonianofThermal-TransportSystems 98 3.2.2 TheNEGFFormalism 100 3.2.2.1 Sixreal-timeGreen’sfunctions 101 3.2.2.2 TheDysonequation 103 3.2.2.3 BasicequationsofNEGF 103 3.2.2.4 WorkflowofNEGF 105 December15,2014 11:59 PSPBook-9inx6in 00-Gang-Zhang-prelims Contents vii 3.2.3 NEGFandThermal-TransportProperties 106 3.2.3.1 PhononDOS 107 3.2.3.2 Thermalcurrent 108 3.2.4 ThermalConductanceandPhonon Transmission 109 3.2.5 TheNEGFMethodandtheLandauer Formalism 110 3.2.6 First-Principles-BasedNEGF 111 3.3 ThermalConductionofGraphene:Experiment 112 3.4 ThermalConductionofGraphene:Theory 115 3.4.1 GrapheneNanoribbons 116 3.4.2 OriginofHighThermalConductivityin Graphene 124 3.4.2.1 Ballisticthermalconductanceof graphene 125 3.4.2.2 Longphononmeanfreepathin graphene 129 3.4.3 ThermalTransportinGraphene-BasedDevices 130 3.4.3.1 Contactgeometry 134 3.4.3.2 Ribbonwidth 135 3.4.3.3 Edgeshape 140 3.4.3.4 Connectionangle 141 3.4.3.5 Graphenequantumdots 141 4 BallisticThermalTransportbyPhononsatLowTemperatures inLow-DimensionalQuantumStructures 149 Zhong-XiangXieandKe-QiuChen 4.1 Introduction 150 4.2 Formalism 153 4.2.1 LandauerFormulafortheThermal Conductance 153 4.2.2 ContinuumElasticModel 156 4.2.3 Scattering-MatrixMethod 158 4.3 PropertiesofLow-TemperatureBallisticThermal TransportbyPhononsinLow-DimensionalQuantum Structures 170 4.3.1 PropertiesofBallisticThermalTransportin2D QuantumStructures 170 December15,2014 11:59 PSPBook-9inx6in 00-Gang-Zhang-prelims viii Contents 4.3.2 BallisticThermal-TransportPropertiesin2D Three-TerminalQuantumStructures 176 4.3.3 PropertiesofBallisticThermalTransportin3D QuantumStructures 178 4.3.4 BallisticThermalTransportContributedbythe CoupledP-SVWavesinLow-Dimensional QuantumStructures 180 4.4 Summary 180 5 SurfaceFunctionalization–InducedThermalConductivity AttenuationinSiliconNanowires:AMolecularDynamics Study 189 Hai-PengLiandRui-QinZhang 5.1 Introduction 190 5.2 ModelandMethod 193 5.2.1 StructuralModel 193 5.2.2 Green–KuboMDMethod 194 5.3 SurfaceHydrogenationEffectontheThermal ConductivityofSiNWs 196 5.4 SurfaceNitrogenationEffectontheThermal ConductivityofSiNWs 198 5.5 ConclusionsandRemarks 201 Index 207 December15,2014 11:59 PSPBook-9inx6in 00-Gang-Zhang-prelims Preface Energy shortage is a great bottleneck in the supply of energy resourcestoaneconomy.Theworld’spowerdemandsareexpected to rise 60% by 2030. Actually, people can solve the global energy crisis by enhancing the utilization efficiency of energy. Today, approximately 80% of the world’s power is generated by heat engines that use fossil fuel combustion as a heat source, which is believed to be responsible for a large fraction of carbon dioxide emissions worldwide. The heat engines used in most thermal power station typically operate at 30–40% efficiency. This means that roughly 10 TW of heat energy is lost to the environment. Thermoelectricmodulescanpotentiallyconvertpartofthewasted heat directly into electricity, reduce the usage of fossil fuels, and lower carbon emission. Moreover, microelectronic processors generatehugeamountofheatinverysmallareas.Traditionally,this heat is considered as waste and may lead to the partial or total lossofthefunctionalityoftheprocessors.Powerdissipationissues haverecentlybecomeoneofthegreatestchallengesforintegrated electronic devices, and it is becoming a bottleneck for further development of smaller and faster devices. Currently, for every kilowatt-hourofenergyconsumedbyacomputerinadatacentre, anotherkWhisneededforcooling.Withtheapplicationofadvanced thermal management and energy conversion technologies, world’s householdPCscanbeconvertedtobillionsofminipowerplantsand upto50%electricenergycanbesaved. Inaddition,thermalmanagementisalsosignificantlyimportant for solar energy harvesting. The solar cell technology can harvest and convert part of the solar energy into electricity by using the photovoltaic effect. The efficiency of conventional solar cells is usuallyquitelowandlimitedbecauseabout50%ofthesolarenergy