Theoretical Treatment of Electron Emission and Related Phenomena

Description

This book introduces readers to the physics governing electron emission under high voltages and temperatures, and highlights recent modeling and numerical developments for describing these phenomena.  It begins with a brief introduction, presenting several applications that have driven electron emission research in the last few decades. The authors summarize the most relevant theories including the physics of thermo-field electron emission and the main characteristic parameters. Based on these theories, they subsequently describe numerical multi-physics models and discuss the main findings on the effect of space charges, emitter geometry, pulse duration, etc. Beyond the well-known photoelectric effect, the book reviews recent advanced theories on photon-metal interaction. Distinct phenomena occur when picosecond and femtosecond lasers are used to irradiate a surface. Their consequences on metal electron dynamics and heating are presented and discussed, leading to various emission regimes – in and out of equilibrium. In closing, the book reviews the effects of electron emission on high-voltage operation in vacuum, especially breakdown and conditioning, as the most common examples.  The book offers a uniquely valuable resource for graduate and PhD students whose work involves electron emission, high-voltage holding, laser irradiation of surfaces, vacuum or discharge breakdown, but also for academic researchers and professionals in the field of accelerators and solid state physics with an interest in this highly topical area. Preface Contents Abbreviations Nomenclature Sub-/Super- Script of a Variable A Constants 1 Introduction 1.1 A Bit of History 1.2 Vacuum Electron Devices: Major Examples 1.2.1 Vacuum Electronics 1.2.2 Surface Analysis and Imaging Using Charged Particle Beams (SEM, TEM, FE-SEM, FEM, FIM, STM, …) 1.2.3 Vacuum Devices 1.2.4 Space Systems and Telecom 1.2.5 Fundamental Research 1.2.6 Plasma Related Devices, Photomultiplier and Display 1.2.7 Domestic and Industrial Use of Vacuum Tubes and Beams 1.3 Why this Book? References 2 Fundamental Phenomena of the Thermal-Field Emission at Equilibrium 2.1 Introduction 2.2 Bulk Metal Model 2.2.1 Sommerfeld's Model: Remind on the Calculation of the Density of Available Electron States in a Metal 2.2.2 Occupation of Electron States Within the Metal 2.3 Description of the Metal/Vacuum Interface Without External Electric Field: Work Function 2.3.1 General Information About the Concept of Work Function: Some Values 2.3.2 Modeling of the Metal/Vacuum Interface Without External Electric Field 2.4 Description of the Metal/Vacuum Interface in Presence of an Electric Field: Overview of the Potential Barriers 2.4.1 The Usual Approach 2.4.2 Other Approaches and Particular Cases 2.5 The Transmission Coefficient Through the Potential Barrier in Front of the Metal Surface 2.5.1 Recall on Transmission Coefficient Calculation 2.5.2 Some Examples of Results 2.6 The Emitted Current Density 2.6.1 Expression of the Emitted Current Density 2.6.2 Some Examples of Results 2.6.3 Energy Distribution of the Emitted Electrons 2.6.3.1 Normal Energy Distribution 2.6.3.2 Total Energy Distribution 2.6.3.3 Average Energy and Nottingham (and Henderson) Effect (Cooling or Heating Effect) 2.7 Summary References 3 Thermal-Field Emission Emitted by a Microtip 3.1 Introduction 3.2 Stationary 1D Electron Emission Model 3.2.1 Field Enhancement Coefficient at the Apex of a Cylindrical Tip 3.2.2 Heat Transfer Inside a Cylindrical Tip 3.2.3 Extrapolation to 1D1/2 Model of Electron Emission 3.3 2D Temporal Electron Emission Model 3.3.1 Electric Field Calculation 3.3.2 Thermal Model 3.3.3 Current Conservation 3.3.4 Time Dependant Coupled Simulation 3.3.4.1 Self-Consistent Thermal-Field Simulation 3.3.4.2 Spatial Resolution 3.3.4.3 Temporal Resolution 3.3.5 Evolution Towards a Permanent Regime 3.3.6 Joule Effect Versus Nottingham Effect 3.3.7 Surface Emission 3.3.8 Model of Electron Emission and Its Impact on the Heating of the MT 3.4 Space Charge Effect on Electron Emission 3.4.1 Barbour Model 3.4.2 Particle-In-Cell Model 3.4.3 Poisson-Trajectory Model 3.4.3.1 DC High Voltage Emission with Space Charge 3.4.3.2 Fast Pulsed High Voltage Emission with Space Charge 3.5 Interaction Between Tips 3.5.1 3D Modeling 3.5.2 Electrostatic Interactions 3.5.3 Thermal Interactions 3.5.4 Variations of the Predominate Tip with the Electric Field 3.5.5 Application of the 3D Model to Study the Optimal Spacing of a Carbon Nanocone Array 3.6 Summary Conclusions References 4 Vacuum Breakdown 4.1 Introduction 4.2 Electron Emission, Sources of Vacuum Breakdown for Small Inter-Electrode Gap 4.2.1 Experimental Evidences 4.2.2 Surface Migration and Buildup of the Microtip 4.2.3 Pulse Duration on Prebreakdown 4.2.4 Effect of the Metal on Vacuum Insulation of a Microtip 4.2.5 Effect of the Microtip Geometry on Vacuum Insulation 4.2.6 Space Charge Effect on Prebreakdown 4.3 Microparticles, Sources of Breakdown for Large Inter-Electrode Gaps 4.3.1 Origin of Microparticles 4.3.2 First Models 4.3.3 Multi-Transit Impact Model Proposed by Latham 4.3.4 Microtip Heating Caused by the Approach of a MP 4.3.5 Model of Interaction Between an Electron Beam and a Microparticle: MP Dynamics in the Inter-Electrode Space 4.3.5.1 Electric Field Distribution in the Inter-Electrode Space 4.3.5.2 Electron Current Distribution in the Inter-Electrode Space 4.3.5.3 Initial Charge of a MP 4.3.5.4 MP-Electron Interaction Cross Section 4.3.5.5 Electron Stopping Power and Heating of the MP 4.3.5.6 Secondary Electron Emission 4.3.5.7 Thermal-Field Emission of the MP 4.3.5.8 Example of MP Trajectory for Different Currents 4.3.5.9 Scenarios of the MP Dynamics 4.4 Summary Conclusions References 5 Photoemission 5.1 Short Overview of Photoelectron Related Phenomena 5.2 `Surface' Versus `Volume' Photoelectric Effect 5.3 Electron Photoemission Under External Electric Field 5.3.1 Quantum Efficiency of Photoelectron Emission 5.3.1.1 Photon Absorption and Electron Excitation 5.3.1.2 Transport of Photoexcited Electrons Through the Metal 5.3.1.3 Probability of the Excited Electron to Leave the Metal 5.3.1.4 Quantum Efficiency of Electron Photoemission per Absorbed Photon 5.3.2 Model of Electron Photoemission Under High Electric Field 5.3.2.1 Limits of the Photoemission Model Assisted by Electric Field 5.3.2.2 Field Dependency of Quantum Efficiency 5.3.2.3 Nottingham Effect for Photo-Excited Electrons 5.3.3 Photo-Field Emission and Heating of the Emitter Under Picosecond Laser Pulses 5.3.3.1 Two-Temperature Model of Photoemission 5.3.3.2 Specific Effects of Photoemission at Equilibrium 5.3.3.3 Photoemission Current Under Stationary Electric Field 5.4 Photoelectric Effect at High Laser Intensities 5.4.1 Multi-Photon Absorption 5.4.2 Electron Distribution Out of Equilibrium 5.4.3 Electron Emission Current with Femtosecond Laser in the Strongly Non-linear Regime 5.5 Summary and Perspectives References