Stochastic approaches to electron transport in micro- and nanostructures /
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| Author / Creator: | Nedjalkov, Mihail, author. |
|---|---|
| Imprint: | Cham : Birkhäuser, [2021] |
| Description: | 1 online resource. |
| Language: | English |
| Series: | Modeling and simulation in science, engineering and technology Modeling and simulation in science, engineering & technology. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12611857 |
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| 100 | 1 | |a Nedjalkov, Mihail, |e author. |0 http://id.loc.gov/authorities/names/no2019003063 | |
| 245 | 1 | 0 | |a Stochastic approaches to electron transport in micro- and nanostructures / |c Mihail Nedjalkov, Ivan Dimov, Siegfried Selberherr. |
| 264 | 1 | |a Cham : |b Birkhäuser, |c [2021] | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Modeling and simulation in science, engineering and technology | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a The book serves as a synergistic link between the development of mathematical models and the emergence of stochastic (Monte Carlo) methods applied for the simulation of current transport in electronic devices. Regarding the models, the historical evolution path, beginning from the classical charge carrier transport models for microelectronics to current quantum-based nanoelectronics, is explicatively followed. Accordingly, the solution methods are elucidated from the early phenomenological single particle algorithms applicable for stationary homogeneous physical conditions up to the complex algorithms required for quantum transport, based on particle generation and annihilation. The book fills the gap between monographs focusing on the development of the theory and the physical aspects of models, their application, and their solution methods and monographs dealing with the purely theoretical approaches for finding stochastic solutions of Fredholm integral equations. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed April 14, 2021). | |
| 505 | 0 | |a Intro -- Preface -- Introduction to the Parts -- Contents -- Part I Aspects of Electron Transport Modeling -- 1 Concepts of Device Modeling -- 1.1 About Microelectronics -- 1.2 The Role of Modeling -- 1.3 Modeling of Semiconductor Devices -- 1.3.1 Basic Modules -- 1.3.2 Transport Models -- 1.3.3 Device Modeling: Aspects -- 2 The Semiconductor Model: Fundamentals -- 2.1 Crystal Lattice Electrons -- 2.1.1 Band Structure -- 2.1.2 Carrier Dynamics -- 2.1.3 Charge Transport -- 2.2 Lattice Imperfections -- 2.2.1 Phonons -- 2.2.2 Phonon Scattering -- 3 Transport Theories in Phase Space | |
| 505 | 8 | |a 3.1 Classical Transport: Boltzmann Equation -- 3.1.1 Phenomenological Derivation -- 3.1.2 Parametrization -- 3.1.3 Classical Distribution Function -- 3.2 Quantum Transport: Wigner Equation -- 3.2.1 Operator Mechanics -- 3.2.2 Quantum Mechanics in Phase Space -- 3.2.3 Derivation of the Wigner Equation -- 3.2.4 Properties of the Wigner Equation -- 3.2.5 Classical Limit of the Wigner Equation -- 4 Monte Carlo Computing -- 4.1 The Monte Carlo Method for Solving Integrals -- 4.2 The Monte Carlo Method for Solving Integral Equations -- 4.3 Monte Carlo Integration and Variance Analysis | |
| 505 | 8 | |a Part II Stochastic Algorithms for Boltzmann Transport -- 5 Homogeneous Transport: Empirical Approach -- 5.1 Single-Particle Algorithm -- 5.1.1 Single-Particle Trajectory -- 5.1.2 Mean Values -- 5.1.3 Concept of Self-Scattering -- 5.1.4 Boundary Conditions -- 5.2 Ensemble Algorithm -- 5.3 Algorithms for Statistical Enhancement -- 6 Homogeneous Transport: Stochastic Approach -- 6.1 Trajectory Integral Algorithm -- 6.2 Backward Algorithm -- 6.3 Iteration Approach -- 6.3.1 Derivation of the Backward Algorithm -- 6.3.2 Derivation of Empirical Algorithms -- 6.3.3 Featured Applications | |
| 505 | 8 | |a 7 Small Signal Analysis -- 7.1 Empirical Approach -- 7.1.1 Stationary Algorithms -- 7.1.2 Time Dependent Algorithms -- 7.2 Iteration Approach: Stochastic Model -- 7.3 Iteration Approach: Generalizing the Empirical Algorithms -- 7.3.1 Derivation of Finite Difference Algorithms -- 7.3.2 Derivation of Collinear Perturbation Algorithms -- 8 Inhomogeneous Stationary Transport -- 8.1 Stationary Conditions -- 8.2 Iteration Approach: Forward Stochastic Model -- 8.2.1 Adjoint Equation -- 8.2.2 Boundary Conditions -- 8.3 Iteration Approach: Single-Particle Algorithm and Ergodicity | |
| 505 | 8 | |a 8.3.1 Averaging on Before-Scattering States -- 8.3.2 Averaging in Time: Ergodicity -- 8.3.3 The Choice of Boundary -- 8.4 Iteration Approach: Trajectory Splitting Algorithm -- 8.5 Iteration Approach: Modified Backward Algorithm -- 8.6 A Comparison of Forward and Backward Approaches -- 9 General Transport: Self-Consistent Mixed Problem -- 9.1 Formulation of the Problem -- 9.2 The Adjoint Equation -- 9.3 Initial and Boundary Conditions -- 9.3.1 Initial Condition -- 9.3.2 Boundary Conditions -- 9.3.3 Carrier Number Fluctuations -- 9.4 Stochastic Device Modeling: Features -- 10 Event Biasing | |
| 650 | 0 | |a Electron transport |x Mathematical models. | |
| 650 | 0 | |a Charge carrier processes. |0 http://id.loc.gov/authorities/subjects/sh2020006681 | |
| 650 | 0 | |a Microelectronics |x Mathematical models. | |
| 650 | 0 | |a Nanoelectronics |x Mathematical models. | |
| 650 | 0 | |a Monte Carlo method. |0 http://id.loc.gov/authorities/subjects/sh85087032 | |
| 650 | 7 | |a Charge carrier processes. |2 fast |0 (OCoLC)fst02021220 | |
| 650 | 7 | |a Electron transport |x Mathematical models. |2 fast |0 (OCoLC)fst00906717 | |
| 650 | 7 | |a Microelectronics |x Mathematical models. |2 fast |0 (OCoLC)fst01019775 | |
| 650 | 7 | |a Monte Carlo method. |2 fast |0 (OCoLC)fst01025819 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Dimov, Ivan, |d 1963- |e author. |0 http://id.loc.gov/authorities/names/n90715987 | |
| 700 | 1 | |a Selberherr, Siegfried, |d 1955- |e author. |0 http://id.loc.gov/authorities/names/n84016939 | |
| 776 | 0 | 8 | |c Original |z 3030679160 |z 9783030679163 |w (OCoLC)1227382714 |
| 830 | 0 | |a Modeling and simulation in science, engineering & technology. |0 http://id.loc.gov/authorities/names/n96087523 | |
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| 928 | |t Library of Congress classification |a QC175.25.S8 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-030-67917-0 |z Springer Nature |g ebooks |i 12627465 | ||