LEADER 06971nam 22007815 450 001 9910299841803321 005 20230810184244.0 010 $a3-319-15105-3 024 7 $a10.1007/978-3-319-15105-2 035 $a(CKB)3710000000412158 035 $a(EBL)2120603 035 $a(OCoLC)908762901 035 $a(SSID)ssj0001501267 035 $a(PQKBManifestationID)11918668 035 $a(PQKBTitleCode)TC0001501267 035 $a(PQKBWorkID)11536281 035 $a(PQKB)11412478 035 $a(DE-He213)978-3-319-15105-2 035 $a(MiAaPQ)EBC2120603 035 $a(PPN)186031432 035 $a(EXLCZ)993710000000412158 100 $a20150507d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aResonant Tunneling $eQuantum Waveguides of Variable Cross-Section, Asymptotics, Numerics, and Applications /$fby Lev Baskin, Pekka Neittaanmäki, Boris Plamenevskii, Oleg Sarafanov 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (281 p.) 225 1 $aLecture Notes on Numerical Methods in Engineering and Sciences,$x1877-735X 300 $aDescription based upon print version of record. 311 $a3-319-15104-5 320 $aIncludes bibliographical references. 327 $aPreface -- 1 Introduction -- 2 Waveguides. Radiation Principle. Scattering Matrices -- 2.1 Boundary Value Problem in a Cylinder -- 2.2 Problem in a Domain G with Cylindrical Ends -- 2.3 Waves and Scattering Matrices -- 3 Properties of Scattering Matrices in a Vicinity of Thresholds -- 3.1 Augmented Space of Waves -- 3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices -- 3.3 Other Properties of the Scattering Matrices -- 4 Method for Computing Scattering Matrices -- 4.1 A Method for Computing Scattering Matrices outside Thresholds -- 4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds -- 5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy -- 5.1 Statement of the Problem -- 5.2 Limit Problems -- 5.3 Special Solutions to the First Kind Homogeneous Problems -- 5.4 Asymptotic Formulas -- 5.5 Justification of the Asymptotics -- 5.6 Comparison of Asymptotic and Numerical Results -- 5.7 The Impact of a Finite Waveguide Work Function on Resonant Tunneling -- 6 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy -- 6.1 Statement of the Problem and Outline of the Results -- 6.2 Limit Problems -- 6.3 Tunneling in a Waveguide with One Narrow -- 6.4 Tunneling in a Waveguide with Two Narrows -- 7 Resonant Tunneling in 2D Waveguides in Magnetic Field -- 7.1 Statement of the Problem -- 7.2 The Limit Problems -- 7.3 Special Solutions to Homogeneous First Kind Limit Problems -- 7.4 Asymptotic Formulas -- 7.5 Justification of the Asymptotics -- 7.6 Comparison of Asymptotic and Numerical Approaches -- 8 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section -- 8.1 Introduction -- 8.2 Statement of the Problem -- 8.3 Limit Problems -- 8.4 Special Solutions of Limit Problems -- 8.5 Asymptotic Formulas -- 8.6 Justification of the Asymptotics -- 9 Numerical Simulation of High Energy Electron Transport -- 9.1 Numerical Simulation of Multichannel Resonant Tunneling -- 9.2 Fano Resonances -- 10 Asymptotic Analysis of Multichannel Resonant Tunneling -- 10.1 Statement of the Problem and Limit problems -- 10.2 Tunneling in a Waveguide with One Narrow -- 10.3 Tunneling in a Waveguide with Two Narrows -- 11 Electronics Devices Based on Resonant Tunneling -- 11.1 Magnetic Field Sensors Based on Quantum Waveguides -- 11.2 Transistors Based on Quantum Waveguides -- 11.3 Electron Flow Switch for Quantum Nets -- Bibliography. 330 $aThis volume studies electron resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-sections in the time-independent approach. Mathematical models are suggested for the resonant tunneling and develop asymptotic and numerical approaches for investigating the models. Also, schemes are presented for several electronics devices based on the phenomenon of resonant tunneling. Devices based on the phenomenon of electron resonant tunneling are widely used in electronics. Efforts are directed towards refining properties of resonance structures. There are prospects for building new nanosize electronics elements based on quantum dot systems. However, the role of resonance structure can also be given to a quantum wire of variable cross-section. Instead of an "electrode - quantum dot - electrode" system, one can use a quantum wire with two narrows. A waveguide narrow is an effective potential barrier for longitudinal electron motion along a waveguide. The part of the waveguide between two narrows becomes a "resonator" , where electron resonant tunneling can occur. This phenomenon consists in the fact that, for an electron with energy E, the probability T(E) to pass from one part of the waveguide to the other part through the resonator has a sharp peak at E = Eres, where Eres denotes a "resonant" energy. Such quantum resonators can find applications as elements of nanoelectronics devices and provide some advantages in regard to operation properties and production technology. The book is addressed to mathematicians, physicists, and engineers interested in waveguide theory and its applications in electronics. 410 0$aLecture Notes on Numerical Methods in Engineering and Sciences,$x1877-735X 606 $aMicrotechnology 606 $aMicroelectromechanical systems 606 $aMathematical physics 606 $aMathematics$xData processing 606 $aElectronic circuits 606 $aMicrosystems and MEMS 606 $aTheoretical, Mathematical and Computational Physics 606 $aComputational Science and Engineering 606 $aElectronic Circuits and Systems 615 0$aMicrotechnology. 615 0$aMicroelectromechanical systems. 615 0$aMathematical physics. 615 0$aMathematics$xData processing. 615 0$aElectronic circuits. 615 14$aMicrosystems and MEMS. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aComputational Science and Engineering. 615 24$aElectronic Circuits and Systems. 676 $a530.416 700 $aBaskin$b Lev$4aut$4http://id.loc.gov/vocabulary/relators/aut$0851988 702 $aNeittaanmäki$b Pekka$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPlamenevskii$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSarafanov$b Oleg$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299841803321 996 $aResonant tunneling$91902347 997 $aUNINA