Mathematical modeling of emission in small-size cathode. (©2020)

• Record Type: Book
• Further Information: Note: Vladimir Danilov, Roman Gaydukov, Vadim Kretov.
• Other Names: Danilov, V. I (Vladimir Ivanovich), 1943-; Gaydukov, Roman; Kretov, Vadim
• Contents: Intro; Preface; Preface to the English Edition; Acknowledgements; Contents; 1 Introduction; 1.1 Brief History of the Electron Emission Discovery; 1.2 Types of Electron Emission; 1.3 Statement of the Problem; 1.4 Mathematical Statement of the Problem. Heat Transfer Model; References; 2 Physical Basis for Field Emission; 2.1 Energy-Band Theory and Fermi Level; 2.2 Conductivity of Semiconductors; 2.2.1 Electron and Hole Concentration; 2.2.2 Effective Mass; 2.2.3 Electron and Hole Mobilities; 2.2.4 Temperature-Dependence of Conductivity in Silicon; 2.3 Thermoelectricity 2.4 Emission Current Density and Nottingham Effect2.4.1 Support Function in Metals; 2.4.2 Electron Tunneling Through the Potential Barrier; 2.4.3 Formula for the Barrier Transparency Factor in the Case of Field Emission Cathode; 2.4.4 Emission Current Density in Metals; 2.4.5 Specific Characteristics of Field Emission from a Semiconductor Cathode; 2.4.6 Approximation of the Formula for the Emission Current Density; 2.4.7 Nottingham Effect; 2.4.8 Optimal Values of Approximation Parameters; 2.4.9 Dependence of the Inversion Temperature on the External Electric Field Strength; References 3 Mathematical Model3.1 Phase Field System and its Use in Heat Transfer Modeling; 3.2 Phase Field System as Regularization of Limiting Problems with Free Boundary; 3.3 Asymptotic Solution of the Phase Field System and Modified Stefan Problem; 3.3.1 Construction of an Asymptotic Solution; 3.3.2 Examples; 3.4 Weak Solution of the Phase Field System and the Melting Zone Model; 3.4.1 Weak Solutions and Rankine-Hugoniot-Type Conditions; 3.4.2 Solutions of ``Wave Train'' Type and the Corresponding Limiting Problem 3.5 Derivation of the Solution of the Limit Stefan-Gibbs-Thomson Problem from a Numerical Solution of the Phase Field System3.6 Generation and Coalescence of Dissipative Waves; References; 4 Numerical Simulation and its Results; 4.1 Nanocathode Model; 4.2 Calculation of the Current Density Inside the Cathode; 4.3 Calculation of the Emission Current Density and Modeling of the Nottingham Effect; 4.4 Difference Scheme; 4.4.1 Difference Scheme for the Equation for the Potential; 4.4.2 Difference Scheme for the Equation for the Order Function; 4.4.3 Difference Scheme for the Heat Equation 4.4.4 Stability of the Difference Scheme4.4.5 One More Version of the Difference Scheme; 4.4.6 Choice of Steps of the Difference Scheme; 4.5 Algorithm for Solving the Difference Equations and Possible Versions of its Parallelization; 4.6 Some Remarks About the Calculation of the Electric Potential; 4.7 Results of Numerical Experiments; 4.7.1 Nonmonotone Behavior of Free Boundaries; 4.7.2 Results of Modeling with Physical Parameters Corresponding to Experimental Data; 4.8 Formation of Melting and Crystallization Nuclei in the Model; 4.9 Conclusion; References
• Publisher Details: Singapore : Springer
• Publication Date: 2020
• Copyright Date: 2020
• Extent: 1 online resource (205 pages)
• Subjects: 539.7/2112; Electrons -- Emission -- Mathematical models; Cathodes -- Mathematical models; Electronic books
• Languages: English
• ISBNs: 9811501955; 9789811501951
• Related ISBNs: 9789811501944
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.