Resonant Tunneling

This book studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Compared to its first edition, this book includes four new chapters, redistributes the content between chapters and modifies the estimates of the remainders in the asymptotics of resonant tunneling characteristics. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics.

1. Introduction. - 2. Waveguides. Radiation Principle. Scattering Matrices. - 3. Properties of Scattering Matrices in a Vicinity of Thresholds. - 4. Method for Computing Scattering Matrices. - 5. Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy. - 6. Resonant Tunneling in 2D-Waveguides with Several Resonators. - 7. Resonant Tunneling of High-Energy Electrons in 2D-Waveguides. - 8. Numerical Simulation of High Energy Electron Transport. - 9. The Impact of a Finite Waveguide Work Function on Resonant Tunneling. - 10. Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy. - 11. Resonant Tunneling in 2D Waveguides in Magnetic Field. - 12. Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section. - 13. Asymptotic Analysis of Multichannel Resonant Tunneling. - 14. Electronics Devices Based on Resonant Tunneling.