Graphene-Based Terahertz Electronics and Plasmonics: Detector and Emitter Concepts
Electronic and Plasmonic Properties of Graphene and Graphene StructuresPlasma Waves in Two-Dimensional Electron-Hole System in Gated Graphene HeterostructuresIntroductionEquations of the ModelDispersion Equation for Plasma WavesLimiting CasesLow Temperatures or High Gate VoltagesElevated Temperatures and Low Gate VoltagesGeneral Results and DiscussionAcknowledgmentReferencesDevice Model for Graphene Bilayer Field-Effect TransistorIntroductionGBL-FET Energy Band DiagramsBoltzmann Kinetic Equation and Its SolutionsBallistic Electron TransportCollisional Electron TransportGBL-FET DC TransconductanceGBL-FET AC TransconductanceAnalysis of the Results and DiscussionConclusionsAcknowledgmentsDynamic Response of the Hole System in the Gated SectionReferencesElectrically-Induced n-i-p Junctions in Multiple Graphene Layer StructuresIntroductionEquations of the ModelNumerical ResultsAnalytical ModelThe Reverse CurrentMultiple-GL Structures with Highly Conductive BGLConclusionsAcknowledgmentsReferencesTunneling Recombination in Optically Pumped Graphene with Electron-Hole PuddlesReferencesAnalytical Device Model for Graphene Bilayer Field-Effect Transistors Using Weak Nonlocality ApproximationIntroductionDevice Model and Features of OperationMain Equations of the ModelHigh Top-Gate VoltagesNear Threshold Top-Gate VoltagesLow Top-Gate VoltagesPotential Distributions, Source-Drain Current, and TransconductanceHigh Top-Gate Voltages: Sub-threshold Voltage Range (Δm >> εF)Near Threshold Top-Gate Voltages (Δm ≥ εF)Low Top-Gate Voltages (Δm < εF)DiscussionRole of Geometrical ParametersEffect of Electron ScatteringCharge Inversion in the Gated SectionInterband TunnelingConclusionsAcknowledgmentsVoltage Dependences of the Fermi Energy and the Energy GapReferencesHydrodynamic Model for Electron-Hole Plasma in GrapheneIntroductionDerivation of Hydrodynamic EquationsEffect of Electron-Hole Drag and DC Conductivity of Gated GraphenePlasma and Electron-Hole Sound Waves in GrapheneGeneral Dispersion Relation for Collective ExcitationsAnalytical Solutions for Symmetric Bipolar and Monopolar SystemsVelocities and Damping Rates of the WavesComparison with Other ModelsDiscussion of the ResultsAcknowledgmentDissipative Terms in the Euler EquationsMutual Electron-Hole FrictionFriction Caused by Charged Impurities and PhononsReferencesInterplay of Intra- and Interband Absorption in a Disordered GrapheneIntroductionBasic EquationsDynamic ConductivityPartly Screened Long-Range DisorderRelative AbsorptionSpectral DependenciesComparison with ExperimentConclusionsAcknowledgmentReferencesVoltage-Controlled Surface Plasmon-Polaritons in Double Graphene Layer StructuresIntroductionDevice ModelSPP Dispersion in Double Graphene LayerResults and DiscussionConclusionsAcknowledgementReferencesHydrodynamic Electron Transport and Nonlinear Waves in GrapheneIntroductionDerivation of Hydrodynamic EquationsNonlinear Effects in Plasma-Wave PropagationFormation of Solitons in Gated Graphene'Shallow-Water' Plasma Waves in the Presence of Steady Electron FlowExcitation of Electron Plasma-Waves by Direct CurrentDiscussion of the ResultsConclusionsAcknowledgementCalculation of Average ValuesWeak Nonlocality Approximation for Poisson EquationReferencesEffect of Self-Consistent Electric Field on Characteristics of Graphene p-i-n Tunneling Transit-Time DiodesIntroductionEquations of the ModelSpatial Potential Distributions and Current-Voltage CharacteristicsGTUNNETT AdmittanceDiscussionConclusionsAcknowledgmentsReferencesDamping Mechanism of Terahertz Plasmons in Graphene on Heavily Doped SubstrateIntroductionEquations of the ModelUngated PlasmonsGated PlasmonsConclusionsAcknowledgmentsReferencesActive Guiding of Dirac Plasmons in GrapheneVertical Electron Transport in van der Waals Heterostructures with Graphene LayersIntroductionGeneral Equations of the ModelThe Peltier CoolingElectric Fields versus Current and Current- Voltage CharacteristicsPotential ProfilesDiscussionsLimiting CasesRole of the pn - En RelationElectron Heating in the Barrier LayersQuantum CapacitanceContact EffectsConclusionsAcknowledgmentsCapture ParameterReferencesGiant Plasmon Instability in Dual- Grating-Gate Graphene Field-Effect TransistorIntroductionMechanisms of Dyakonov-Shur and Ryzhii-Satou-Shur InstabilitiesSimulation ModelResults and DiscussionConclusionAcknowledgmentsReferencesDetectors Based on Lateral Transport in Graphene and Graphene StructuresPlasma Mechanisms of Resonant Terahertz Detection in a Two-Dimensional Electron Channel with Split GatesIntroductionEquations of the ModelPlasma ResonancesResonant Electron HeatingRectified Current and Detector ResponsivityComparison of Dynamic and Heating MechanismsTemperature Dependences of the Detector Responsivity and DetectivityDiscussionConclusionsAcknowledgmentsReferencesTerahertz and Infrared Photodetection Using p-i-n Multiple-Graphene-Layer StructuresIntroductionResponsivity and DetectivityFeatures of GLPD with Electrically Induced JunctionDynamical ResponseComparison with QWIPs and QDIPsDiscussion and ConclusionsAcknowledgmentsEffect of Vertical Screening in Multiple GL-StructuresReferencesNegative and Positive Terahertz and Infrared Photoconductivity in Uncooled GrapheneIntroductionGL Conductivity Dependence on the Carrier TemperatureGeneration-Recombination and Energy Balance EquationsGL PhotoconductivityClustered Impurities and Decorated GLs: Long-Range ScatteringResponsivity of the GL-Based PhotodetectorsHeavily Doped GLsConclusionsFundingAcknowledgmentsDisclosuresReferencesPopulation Inversion and Negative Conductivity in Graphene and Graphene StructuresNegative Dynamic Conductivity of Graphene with Optical PumpingIntroductionEquations of the ModelWeak PumpingStrong PumpingConclusionsAcknowledgmentReferencesPopulation Inversion of Photoexcited Electrons and Holes in Graphene and Its Negative Terahertz ConductivityIntroductionQualitative PatternFrequency Dependence of the ConductivityHeating of Electrons and HolesDiscussionAcknowledgementsReferencesNegative Terahertz Dynamic Conductivity in Electrically Induced Lateral p-i-n Junction in GrapheneIntroductionDevice Model and Terminal AC ConductanceSelf-Excitation of Plasma OscillationsConclusionsAcknowledgmentsReferencesThreshold of Terahertz Population Inversion and Negative Dynamic Conductivity in Graphene Under Pulse PhotoexcitationIntroductionFormulation of the ModelResults and DiscussionTime Evolution of Quasi-Fermi Level and Carrier TemperatureTime Evolution of Dynamic Conductivity for High-and Low-Quality GrapheneOptical-Phonon Emission versus Other Recombination MechanismsConclusionsAcknowledgmentsReferencesDouble Injection in Graphene p-i-n StructuresIntroductionModelThe Structures Under ConsiderationEquations of the ModelBoundary ConditionsDimensionless Equations and Boundary ConditionsInjection Characteristics (Analytical Approach for a Special Case)Numerical ResultsCurrent-Voltage CharacteristicsDiscussionConclusionsAcknowledgmentsReferencesCarrier-Carrier Scattering and Negative Dynamic Conductivity in Pumped GrapheneIntroductionIntraband Dynamic Conductivity General EquationsAnalysis of Intraband and Net Dynamic ConductivityDiscussion of the ResultsConclusionsEvaluation of Coulomb IntegralsAcknowledgmentsReferencesNegative Terahertz Conductivity in Disordered Graphene Bilayers with Population InversionNegative Terahertz Conductivity in Remotely Doped Graphene Bilayer HeterostructuresIntroductionDevice ModelMain EquationsScattering MechanismsNet THz ConductivityResults and AnalysisDiscussionConclusionsAcknowledgmentsReferencesStimulated Emission and Lasing in Graphene and Graphene StructuresFeasibility of Terahertz Lasing in Optically Pumped Epitaxial Multiple Graphene Layer StructuresIntroductionModelMGL Structure Net Dynamic ConductivityFrequency Characteristics of Dynamic ConductivityRole of the Bottom GLCondition of LasingConclusionsAcknowledgmentsRecombinationReferencesTerahertz Lasers Based on Optically Pumped Multiple Graphene Structures with Slot-Line and Dielectric WaveguidesIntroductionDevice ModelResults and DiscussionConclusionsAcknowledgmentsReferencesObservation of Amplified Stimulated Terahertz Emission from Optically Pumped Heteroepitaxial Graphene-on-Silicon MaterialsIntroductionTheoretical ModelGraphene on Silicon Sample for the ExperimentExperimentalResults and DiscussionConclusionAcknowledgmentsReferencesToward the Creation of Terahertz Graphene Injection LaserIntroductionDevice ModelEquations of the ModelEffective Temperatures and Current-Voltage Characteristics (Analytical Analysis)Low VoltagesSpecial CasesLong Optical Phonon Decay TimeEffective Temperatures and Current-Voltage Characteristics (Numerical Results)Dynamic ConductivityLimitations of the Model and DiscussionConclusionsAcknowledgmentsReferencesUltrafast Carrier Dynamics and Terahertz Emission in Optically Pumped Graphene at Room TemperatureIntroductionTheory and BackgroundSample and CharacterizationExperimentsResults and DiscussionConclusionAcknowledgmentsReferencesSpectroscopic Study on Ultrafast Carrier Dynamics and Terahertz Amplified Stimulated Emission in Optically Pumped GrapheneIntroductionCarrier Relaxation and Recombination Dynamics in Optically Pumped GrapheneExperimentsExperimental SetupSamples and CharacterizationsExfoliated graphene on SiО2/SiHeteroepitaxial graphene on 3C-SiC/SiResults and DiscussionsExfoliated graphene on SiО2/SiHeteroepitaxial graphene on 3C-SiC/SiConclusionAcknowledgementsReferencesGain Enhancement in Graphene Terahertz Amplifiers with Resonant StructuresIntroductionFDTD ModelResults and DiscussionConclusionsAcknowledgmentsReferencesPlasmonic Terahertz Lasing in an Array of Graphene NanocavitiesThe Gain Enhancement Effect of Surface Plasmon Polaritons on Terahertz Stimulated Emission in Optically Pumped Monolayer GrapheneIntroductionStimulated Terahertz (THz) Photon and Plasmon Emission in Optically Pumped GrapheneExperimental Observation of THz Stimulated Plasmon Emission in Optically Pumped GrapheneExperimental Setup and Sample PreparationTemporal Profile and Fourier Spectrum of the Population-Inverted Graphene to the THz Pulse IrradiationSpatial Field Distribution of the THz Probe Pulse IntensitiesConclusionAcknowledgmentsReferencesGraphene Surface Emitting Terahertz Laser: Diffusion Pumping ConceptEnhanced Terahertz Emission from Monolayer Graphene with Metal Mesh StructureIntroductionPrincipleExperimentalBasic Structure of THz AmplifierMeasurement MethodEM Simulation ModelResults and DiscussionGaAs + GrapheneGaAs + MetalGaAs + Metal + GrapheneConclusionReferencesTerahertz Light-Emitting Graphene-Channel Transistor Toward Single-Mode LasingIntroductionDevice Design and FabricationDesign and Fabrication DetailsPrinciples of OperationResults and DiscussionsBroadband THz Light EmissionTowards Single-Mode LasingConclusionsAcknowledgmentsReferencesSupplementary MaterialExperimental MethodsDFB Cavity Design ParametersDetectors and Emitters Based on Photon/Plasmon Assisted Tunneling between Graphene LayersInjection Terahertz Laser Using the Resonant Inter-Layer Radiative Transitions in Double-Graphene-Layer StructureDouble-Graphene-Layer Terahertz Laser: Concept, Characteristics, and ComparisonIntroductionDevice Structures and Principles of OperationInter-GL and Intra-GL Dynamic ConductivitiesTerahertz Gain and Gain-Overlap FactorsFrequency and Voltage Dependences of the THz GainDiscussionConclusionAcknowledgmentsReferencesSurface-Plasmons Lasing in Double-Graphene-Layer StructuresIntroductionDynamic Conductivity TensorElectric Field Distributions, Gain-Overlap Factor, and Modal GainConclusionsAcknowledgmentsReferencesDouble Injection, Resonant-Tunneling Recombination, and Current-Voltage Characteristics in Double-Graphene-Layer StructuresIntroductionModel and the Pertinent EquationsSpatial and Voltage Dependences of Fermi Energy, Energy Gap, and PotentialRole of Scattering on DisorderCurrent-Voltage CharacteristicsConclusionsAcknowledgmentsFunctions l(μ) and σ(μ)ReferencesVoltage-Tunable Terahertz and Infrared Photodetectors Based on Double-Graphene-Layer StructuresPlasmons in Tunnel-Coupled Graphene Layers: Backward Waves with Quantum Cascade GainIntroductionDispersion Relation for Plasmons in Tunnel-Coupled LayersHigh-Frequency Nonlocal Tunnel CurrentPlasmons in the Presence of TunnelingEffects of Interlayer TwistDiscussion and ConclusionsAcknowledgmentsPlasmon Modes Supported by the Double LayerEstimate of the Tight-Binding ParametersAnalytical Results for the Conductivity: In-Plane ConductivityTunnel ConductivityReferencesTerahertz Wave Generation and Detection in Double-Graphene Layered van der Waals HeterostructuresIntroductionDevice Description and Principles of OperationExperimental MethodsResults and DiscussionsConclusionAcknowledgmentsFundingReferencesSupplementary InformationGraphene Layers' Rotation Angle Sensitive Current- Voltage CharacteristicsReferenceUltra-Compact Injection Terahertz Laser Using the Resonant Inter-Layer Radiative Transitions in Multi-Graphene-Layer StructureIntroductionDevice ModelResults and DiscussionConclusionCalculation of the Tunnel Resonance BroadeningFundingReferencesGraphene Based van der Waals Heterostructures for THz Detectors and EmittersGraphene Vertical Hot-Electron Terahertz DetectorsIntroductionDevice Structures and Principle of OperationVertical Electron Dark Current and PhotocurrentElectron Heating by Incoming THz RadiationResponsivityDark Current Limited DetectivityRole of the Electron CaptureEffect of Plasmonic ResonancesLimitations of the ModelDiscussionConclusionsAcknowledgmentsReferencesElectron Capture in van der Waals Graphene-Based Heterostructures with WS2 Barrier LayersIntroductionModel and Electron Wave FunctionsElectron Capture Probability at Different Scattering MechanismsCapture due to the Emission of Barrier Optical PhononsCapture due to the Emission of GL Optical PhononsCapture Associated with the Electron-Electron InteractionResults of Numerical CalculationsCapture Parameter and Capture VelocityConclusionAcknowledgmentsReferencesResonant Plasmonic Terahertz Detection in Vertical Graphene-Base Hot-Electron TransistorsIntroductionDevice Model and Related EquationsPlasma Oscillations and Rectified CurrentGB-HET Detector ResponsivityCurrent ResponsivityVoltage ResponsivityDiscussionConclusionsAcknowledgmentsReferencesNonlinear Response of Infrared Photodetectors Based on van der Waals Heterostructures with Graphene LayersIntroductionDevice Structure and ModelMain EquationsDark CharacteristicsPhotoresponse at Low IR Radiation IntensitiesNonlinear Response: High IR Radiation IntensitiesCommentsConclusionsThermionic Electron EmissionSaturation of AbsorptionFundingAcknowledgmentsReferencesEffect of Doping on the Characteristics of Infrared Photodetectors Based on van der Waals Heterostructures with Multiple Graphene LayersIntroductionStructure of GLIPs and Their Operation PrincipleEquations of the ModelGLIP ResponsivityGUP DetectivityDiscussionConclusionsAcknowledgmentsReferencesReal-Space-Transfer Mechanism of Negative Differential Conductivity in Gated Graphene-Phosphorene Hybrid Structures: Phenomenological Heating ModelIntroductionModelMain Equations of the ModelConductivity of the G-P ChannelCarrier Interband BalanceGeneration-Recombination and Energy Balance EquationsGeneral Set of the EquationsNumerical ResultsDiscussionScreening in the G-P ChannelMutual Scattering of Electrons and HolesOptical Phonon HeatingRelaxation of Substrate Optical PhononsPossible Applications of the G-P DevicesConclusionsAcknowledgmentsReferencesNegative Photoconductivity and Hot-Carrier Bolometric Detection of Terahertz Radiation in Graphene- Phosphorene Hybrid StructuresIntroductionModelConductivity of the G-P-ChannelNegative Photoconductivity in the G-P ChannelsResponsivity of the GP-PhotodetectorsBandwidth and Gain-Bandwidth ProductDetectivity of the GP-BolometersDiscussionGeneral CommentsAssumptionsConclusionsShort-Range versus Long-Range ScatteringFrequency Dependence of the GP- and G-Channel ConductivityAcknowledgmentsReferences