Computational Single-Electronics

by Christoph Wasshuber

Overview

From the reviews: "This is a well written book offering a clear and detailed insight into physical processes and numerical procedures essential to the single-electron dynamics in electro-conducting media." Zentralblatt für Mathematik und ihre Grenzgebiete

Product Details

ISBN-13:	9783211835586
Publisher:	Springer Vienna
Publication date:	07/27/2001
Series:	Computational Microelectronics
Edition description:	2001
Pages:	280
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

1 Introduction.- 1.1 Single-Electronics — Made Easy.- 1.2 A Historical Look Back.- 2 Theory.- 2.1 Orthodox Single-Electron Theory.- 2.1.1. Thermodynamic Formulation.- 2.2 Time and Space Correlations.- 2.3 Master Equation of Electron Transport.- 2.4 Extensions to the Orthodox Theory.- 2.4.1 Cotunneling.- 2.4.2 Influence of the Electromagnetic Environment.- Quantum Langevin Theory.- Phase Correlation Theory.- 2.4.3 Different Materials — Different Density of States.- Discrete Energy Levels.- 2.4.4 Superconducting Tunnel Junctions.- Quasiparticle Tunneling.- Parity Effect.- Andreev Reflections.- Coherent Cooper Pair Tunneling.- 2.4.5 Self-Heating.- 2.4.6 Image Charge.- 3 Simulation Methods and Numerical Algorithms.- 3.1 Monte Carlo Method.- 3.1.1 Time-Dependent Tunnel Rates.- 3.1.2 Deterministic Model.- 3.1.3 Random Numbers.- Linear Congruential Generators.- Lagged Fibonacci or Shift Register Generators.- Inverse Congruential Generators.- Resolution Limit for Rare Tunnel Events.- 3.2 Solution of the Master Equation.- 3.2.1 Krylov Subspace Approximate of the Matrix Exponential Operator.- 3.2.2 Schur-Fréchet Algorithm.- 3.3 Coupling with SPICE.- 3.4 Free Energy.- 3.5 Tunnel Transmission Coefficient.- 3.5.1 Analytic Solutions.- 3.5.2 Wentzel-Kramers-Brillouin Approximation.- 3.5.3 Piecewise Potential Approximation.- Three Dimensions.- Transfer Matrix versus Scattering Matrix.- Piecewise-Constant Potential Approximation.- Piecewise-Linear Potential Approximation.- 3.5.4 Finite Differences with Continued Fraction.- 3.5.5 Finite Elements.- 3.5.6 Detour via the Time-Dependent Schrödinger Equation.- Finite Differences.- Spectral Method.- 3.6 Energy Levels.- 3.6.1 Analytic Solutions.- 3.6.2 Bohr-Sommerfeld Quantization Rule.- 3.6.3 Piecewise Potential Approximation.- Transmission Line Analogy.- 3.6.4 Finite Differences with Continued Fraction.- 3.6.5 Time-Dependent Solutions.- 3.7 Evaluation Schemes for Cotunneling.- 3.8 Rate Calculation Including Electromagnetic Environment.- Network Impedance Calculation.- 3.9 Numerical Integration of Tunnel Rates.- 3.10 Time-Dependent Node Voltages and Node Charges.- 3.11 Stability Diagram and Stable States.- 3.12 Capacitance Calculations.- 3.12.1 Analytic Formulas.- 3.12.2 Capacitance of Ellipsoid, Elliptic Disc, and Circular Disc.- 3.12.3 Image Charge Method for Spheres.- Capacitance of Two Equal Spheres.- Capacitance of an Arbitrary Arrangement of Spheres 13.- Capacitance of Two Intersecting Spheres — Capacitance Inversion.- 3.12.4 Source Point Collocation Method.- 3.12.5 Shastic Capacitance Calculation for Rectangular.- Circuits and Applications.- 4.1 Fundamental Circuits.- 4.1.1 Single-Electron Transistor.- 4.1.2 Single-Electron Turnstile.- Asymmetric Turnstile.- 4.1.3 Single-Electron Pump.- 4.1.4 Linear Array of Junctions.- 4.1.5 Two-Dimensional Array of Junctions.- 4.2 Metrology Applications.- 4.2.1 The Quantum Metrology Triangle.- 4.2.2 Electron Pump — Current Standard.- 4.2.3 Supersensitive Electrometer.- 4.2.4 Single-Electron Proximity Probe.- 4.2.5 Coulomb Blockade Thermometer.- 4.3 Memory.- 4.3.1 Single-Electron Flip-Flop.- 4.3.2 Electron Trap Memory.- 4.3.3 Ring Memory.- 4.3.4 Background-Charge-Independent Memory.- 4.3.5 Single-Island Memory.- 4.3.6 Multiple-Island Memory.- 4.3.7 T-Memory Cell.- 4.3.8 Combinatorial Access Memory.- 4.3.9 Switch-Source-Sink Memory.- 4.3.10 Negative Differential Resistance Flip-Flop.- 4.3.11 Multivalued Memory from Asymmetric Tunnel Junctions.- 4.3.12 Nanocrystal Memory.- 4.4 Logic.- 4.4.1 Transistor-like Design — Voltage State Logic.- 4.4.2 Bits by Single Electrons — Charge State Logic.- Binary-Decision Diagram.- Lattice Gas Machines.- Systolic Processors.- 4.4.3 Quantum Cellular Automata.- 4.4.4 Wireless Logic.- 4.4.5 Tunneling Phase Logic.- 4.4.6 Parametron Logic.- 4.5 Interfacing to CMOS.- 4.6 Exotic Circuits.- 4.6.1 Neuronal Networks.- 4.6.2 Boltzmann Machines.- 4.6.3 Mixed Bag.- Negative Differential Resistance.- Digital-to-Analog Converter.- Asymmetric Tunnel Barriers.- 4.7 Evolutionary Circuit Design.- 5 Random Background Charges.- 5.1 The Good Side of High Charge Sensitivity.- 5.2 Solutions on the Material Level.- 5.3 Solutions on the Device Level.- 5.3.1 Refresh for Single-Electron Logic.- 5.3.2 Coulomb Oscillations.- 5.3.3 Resistive Elements.- 5.3.4 One- and Two-Dimensional Island Structures.- 5.4 Solutions on the Circuit and System Level.- 6 Manufacturing Methods and Material Systems.- 6.1 Shadow Evaporation.- 6.2 Step-Edge Cutoff.- 6.3 Nanoimprint.- 6.4 Planar Quantum Dots.- 6.5 Scanning Probe Microscopy.- 6.6 Granular Films.- 6.7 Self-Assembled Structures.- 6.8 Outlook.- Appendixes.- A Fermi’s Golden Rule.- B Capacitance and Resistance Extraction from Measured Data.- C Analytic Solutions of the Cotunneling Rate.- D Algorithms from Number Theory.- E Convex Hull of Point Set.- F Analytic Capacitance Calculation.- References.

Editorial Reviews

"This is a well written book offering a clear and detailed insight into physical processes and numerical procedures essential to the single-electron dynamics in electro-conducting media. The subject of the book is a rapidly developing scientific field which is interesting not only from a purely theoretical point of view but also attracts attention due to a variety of application possibilities in contemporary micro-electronics. The book may be useful both to students as a textbook, and to a more general scientific community dealing with problems involving a single electron dynamics in solids ..." Zentralblatt für Mathematik und ihre Grenzgebiete Vol. 1013/No. 13/2003

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