Vacuum Nanoelectronic Devices

Anatoliy Evtukh, National Academy of Sciences of Ukraine, Kyiv
 
Hans Hartnagel, Technische Universität Darmstadt, Germany
 
Oktay Yilmazoglu, Technische Universität Darmstadt, Germany
 
Hidenori Mimura, Shizuoka University, Hamamatsu, Japan
 
Dimitris Pavlidis, Boston University, USA

Introducing up-to-date coverage of research in electron field emission from nanostructures, Vacuum Nanoelectronic Devices outlines the physics of quantum nanostructures, basic principles of electron field emission, and vacuum nanoelectronic devices operation, and offers as insight state-of-the-art and future researches and developments.
 
This book also evaluates the results of research and development of novel quantum electron sources that will determine the future development of vacuum nanoelectronics. Further to this, the influence of quantum mechanical effects on high frequency vacuum nanoelectronic devices is also assessed.
 
Key features:
 
* In-depth description and analysis of the fundamentals of Quantum Electron effects in novel electron sources.
 
* Comprehensive and up-to-date summary of the physics and technologies for THz sources for students of physical and engineering specialties and electronics engineers.
 
* Unique coverage of quantum physical results for electron-field emission and novel electron sources with quantum effects, relevant for many applications such as electron microscopy, electron lithography, imaging and communication systems and signal processing.
 
* New approaches for realization of electron sources with required and optimal parameters in electronic devices such as vacuum micro and nanoelectronics.
 
This is an essential reference for researchers working in terahertz technology wanting to expand their knowledge of electron beam generation in vacuum and electron source quantum concepts. It is also valuable to advanced students in electronics engineering and physics who want to deepen their understanding of this topic. Ultimately, the progress of the quantum nanostructure theory and technology will promote the progress and development of electron sources as main part of vacuum macro-, micro- and nanoelectronics.

Introducing up-to-date coverage of research in electron field emission from nanostructures, Vacuum Nanoelectronic Devices outlines the physics of quantum nanostructures, basic principles of electron field emission, and vacuum nanoelectronic devices operation, and offers as insight state-of-the-art and future researches and developments.

Preface xi
 
Part I THEORETICAL BACKGROUNDS OF QUANTUM ELECTRON SOURCES
 
1 Transport through the Energy Barriers: Transition Probability 3
 
1.1 Transfer Matrix Technique 3
 
1.2 Tunneling through the Barriers and Wells 7
 
1.2.1 The Particle Moves on the Potential Step 7
 
1.2.2 The Particle Moves above the Potential Barrier 13
 
1.2.3 The Particle Moves above the Well 16
 
1.2.4 The Particle Moves through the Potential Barrier 18
 
1.3 Tunneling through Triangular Barrier at Electron Field Emission 22
 
1.4 Effect of Trapped Charge in the Barrier 24
 
1.5 Transmission Probability in Resonant Tunneling Structures: Coherent Tunneling 28
 
1.6 Lorentzian Approximation 32
 
1.7 Time Parameters of Resonant Tunneling 34
 
1.8 Transmission Probability at Electric Fields 38
 
1.9 Temperature Effects 42
 
1.9.1 One Barrier 42
 
1.9.2 Double-Barrier Resonance Tunneling Structure 45
 
References 46
 
2 Supply Function 48
 
2.1 Effective Mass Approximation 48
 
2.2 Electron in Potential Box 49
 
2.3 Density of States 52
 
2.3.1 Three-Dimension (3D) Case 52
 
2.3.2 Two-Dimension (2D) Case 58
 
2.3.3 One-Dimension (1D) Case 62
 
2.3.4 Zero Dimension (0D) Case 64
 
2.4 Fermi Distribution Function and Electron Concentration 66
 
2.4.1 Electron Concentration for 3D Structures 67
 
2.4.2 Electron Concentration for 2D Structures 71
 
2.5 Supply Function at Electron Field Emission 71
 
2.6 Electron in Potential Well 73
 
2.6.1 Quantum Well with Parabolic Shape of the Potential 76
 
2.7 Two-Dimensional Electron Gas in Heterojunction GaN-AlGaN 79
 
2.8 Electron Properties of Quantum-Size Semiconductor Films 82
 
References 86
 
3 Band Bending and Work Function 87
 
3.1 Surface Space-Charge Region 87
 
3.2 Quantization of the Energy Spectrum of Electrons in Surface Semiconductor Layer 91
 
3.3 Image Charge Potential 96
 
3.4 Work Function 99
 
3.4.1 Energy of Ionic Cores ( ion) 102
 
3.4.2 Exchange-Correlation Potential (Uxc) 103
 
3.4.3 Dipole Term (Delta ) 104
 
3.4.4 Work Function of Semiconductor 106
 
3.4.5 Work Function of Cathode with Coating 107
 
3.5 Field and Temperature Dependences of Barrier Height 109
 
3.6 Influence of Surface Adatoms on Work Function 110
 
References 117
 
4 Current through the Barrier Structures 119
 
4.1 Current through One Barrier Structure 119
 
4.1.1 Case 1: High Bias 122
 
4.1.2 Case 2: High Bias and Low Temperature 122
 
4.1.3 Case 3: Small Bias: Linear Response 122
 
4.1.4 Case 4: Small Bias and Low Temperature 123
 
4.2 Field Emission Current 123
 
4.3 Electron Field Emission from Semiconductors 127
 
4.4 Current through Double Barrier Structures 134
 
4.4.1 Coherent Resonant Tunneling 134
 
4.4.2 Sequential Tunneling 139
 
4.5 Electron Field Emission from Multilayer Nanostructures and Nanoparticles 142
 
4.5.1 Resonant Tunneling at Electron Field Emission from Nanostructures 142
 
4.5.2 Two-Step Electron Tunneling through Electronic States in a Nanoparticle 150
 
4.5.3 Single-Electron Field Emission 159
 
References 167
 
5 Electron Energy Distribution 172
 
5.1 Theory of Electron Energy Distribution 172
 
5.2 Experimental Set Up 175
 
5.3 Peculiarities of Electron Energy Distribution Spectra at Emission from Semiconductors 177
 
5.3.1 Electron Energy Distrib