Introductory nanoelectronics: physical theory and device analysis
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Boca Raton ; London ; New York
CRC Press
2021
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| Ausgabe: | First edition |
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| Beschreibung: | Enthält Literaturangaben |
| Beschreibung: | xxxv, 410 Seiten Illustrationen, Diagramme 28 cm |
| ISBN: | 9780815384267 9780367504038 |
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| 100 | 1 | |a Khanna, Vinod Kumar |d 1952- |e Verfasser |0 (DE-588)129277800 |4 aut | |
| 245 | 1 | 0 | |a Introductory nanoelectronics |b physical theory and device analysis |c Vinod Kumar Khanna |
| 250 | |a First edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2021 | |
| 300 | |a xxxv, 410 Seiten |b Illustrationen, Diagramme |c 28 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Enthält Literaturangaben | ||
| 650 | 4 | |a Nanoelectronics | |
| 650 | 4 | |a Nanoelectronics |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Nanoelektronik |0 (DE-588)4732034-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Nanostruktur |0 (DE-588)4204530-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mesoskopisches System |0 (DE-588)4280799-2 |D s |
| 689 | 0 | 2 | |a Nanostruktur |0 (DE-588)4204530-7 |D s |
| 689 | 0 | 3 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
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Datensatz im Suchindex
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| adam_text | Contents Preface.................................................................................................................................................................................................... xvii Acknowledgements..................................................................................................................................................................................xix Author...................................................................................................................................................................................................... xxi Abbreviations, Acronyms, and Chemical Symbols............................................................................................................................. xxiii Mathematical Notation........................................................................................................................................................................ xxvii About the Book..................................................................................................................................................................................... xxxv 1 Nanoelectronics and Mesoscopic Physics....................................................................................................................................... 1 1.1 Ultra-Small Objects.................................................................................................................................................................. 1 1.1.1 Electron
Radius..........................................................................................................................................................1 1.1.2 Atomic Nucleus Diameter......................................................................................................................................... 1 1.1.3 Atomic and Molecular Sizes..................................................................................................................................... 1 1.2 The Nanoworld.......................................................................................................................................................................... 1 1.3 Mesoscopic Physics....................................................................................................................................................................1 1.3.1 Averaging of Behavior............................................................................................... 2 1.3.2 Surface Area-to-Volume Ratio.................................................................................................................................. 2 1.3.3 Dominance of Electromagnetic Force over Gravitational Force............................................................................. 2 1.3.4 Size Dependence of Properties................................................................................................................................. 3 1.3.5 Classical and Quantum-Mechanical
Laws...............................................................................................................3 1.3.6 Quantization of Conductance.................................................................................................................................... 3 1.3.7 Quantum Confinement.............................................................................................................................................. 5 1.3.8 Quantum-Mechanical TUnneling..............................................................................................................................6 1.3.9 Giant Magnetoresistance Effect................................................................................................................................7 1.3.10 Single-Electron Effects............................................................................................................................................10 1.4 Objectives and Organization of the Book.............................................................................................................................. 10 1.5 Discussion and Conclusions.................................................................................................................................................... 11 Illustrative Exercises.......................................................................................................................................................................... 12
References......................................................................................................................................................................................... 13 Part I Quantum Mechanics for Nanoelectronics 2 Origins of Quantum Theory.......................................................................................................................................................... 17 2.1 Young’s Double-Slit Experiment on Light Diffraction......................................................................................................... 17 2.2 Blackbody Radiation and Planck’s Quantum Hypothesis.................................................................................................... 17 2.3 Photoelectric Effect............................................................................................................................................................... 17 2.4 Emission Spectrum of Atomic Hydrogen and Bohr’s Atomic Model..................................................................................19 2.5 Compton Scattering.................... 21 2.6 de Broglie’s Hypothesis.........................................................................................................................................................21 2.7 Davisson-Germer Experiment on Electron Diffraction...................................................................................................... 22 2.8 Heisenberg’s Uncertainty
Principle...................................................................................................................................... 23 2.9 Discussion and Conclusions.................................................................................................................................................. 24 Illustrative Exercises..........................................................................................................................................................................25 References......................................................................................................................................................................................... 25 3 The Schrodinger Wave Equation.................................................................................................................................................. 27 3.1 Two Forms of Schrodinger Equation.................................................................................................................................... 27 3.1.1 Time-Independent Schrodinger Equation (TISE)................................................................................................. 27 3.1.2 Time-Dependent Schrodinger Equation (TDSE).................................................................................................. 27 3.2 Formulation of Time-Independent Schrodinger Equation (TISE)...................................................................................... 27 3.3 Formulation of Time-Dependent Schrodinger Equation
(TDSE)....................................................................................... 29 3.4 TISE from TDSE: Method of Separation of Variables........................................................................................................ 29 vii
Contents viii 3.5 Deriving the General Equation for Wave Motion................................................................................................................. 30 3.6 Solving the General Equation for Wave Motion bySeparating the Variables...................................................................... 33 3.7 Max Born’s Physical Interpretation of the Wave Function Ψ............................................................................................... 36 3.8 Normalization of the Wave Function.....................................................................................................................................38 3.9 Discussion and Conclusions.................................................................................................................................................... 39 Illustrative Exercises.......................................................................................................................................................................... 40 References.......................................................................................................................................................................................... 42 4 Operator Methods and Postulates of Quantum Mechanics....................................................................................................... 43 4.1 What Are Operators?............................................................................................................................................................. 43 4.2 Main
Operators in Quantum Mechanics.............................................................................................................................. 43 4.2.1 Position Operators..................................................................................................................................................... 43 4.2.2 Linear Momentum Operators..................................................................................................................................43 4.2.3 Kinetic Energy Operators........................................................................................................................................43 4.2.4 Potential Energy Operators......................................................... 44 4.2.5 Total Energy Operators............................................................................................................................................44 4.2.6 Angular Momentum Operator................................................................................................................................ 44 4.3 Linear and Non-Linear Operators........................ 45 4.4 Commutation of Operators and Its Implications.................................................................................................................. 45 4.5 Eigenvalues and Eigenfunctions of an Operator.................................................................................................................. 46 4.6 Schrodinger’s Equation in Operator
Form........................................................................................................................... 46 4.7 Hermitian Operators..............................................................................................................................................................46 4.8 Expectation Value.................................................................................................................................................................. 47 4.9 Postulates of Quantum Mechanics in Analogy to Classical Mechanics..............................................................................47 4.10 Discussion and Conclusions....................................................................................................................................................48 Illustrative Exercises.......................................................................................................................................................................... 48 References......................................................................................................................................................................................... 49 5 Particle-in-a-Box and Related Problems....................................................................................................................... 5.1 Free particle in Quantum Mechanics..................................................................................................................... 5.1.1 Spatial
Dependence................................................................................................................................... 5.1.2 Time Dependence...................................................................................................................................... 5.1.3 Boundary Conditions and Absence of Quantization................................................................................ 5.1.4 Non-Normalization of Wave Function...................................................................................................... 5.1.5 Concept of Wave Packets.......................................................................................................................... 5.2 Particle in a Box or Infinite Potential Well............................................................................................................. 5.2.1 The Solution..................................................................................... ......................................................... 5.2.2 Determination of В................. ................................................................................................................. 5.2.3 Determination of к.................................................................................................................................... 5.2.4 Determination of A................................................................................................................................... 5.2.5 Plotting En, Ψ„, ΙΨ„Ι2 versus x
Graphs....................................................................................................... 5.3 Particle in a Finite Potential Well........................................................................................................................... 5.3.1 Regions I and III........................................................................................................................................ 5.3.2 Region II................................................................................................................................................... 5.3.3 Boundary Conditions................................................................................................................................ 5.3.4 Graphical Solution of Finite Potential Well Equations............................................................................ 5.4 Alternative Method: Determining Solutions for Even (Symmetric) and Odd (Antisymmetric) Wave Functions 5.4.1 Even Solution Boundary Conditions......................................................................................................... 5.4.2 Odd Solution Boundary Conditions.......................................................................................................... 5.4.3 Normalization of Even Wave Functions................................................................................................... 5.4.4 Normalization of Odd Wave Functions.................................................................................................... 5.4.5 Plotting the Wave Functions:
Quantum-Mechanical Tunneling............................................................. 5.4.6 Unbound States......................................................................................................................................... 5.5 Derivation of Tbnneling Probability Equation...................................................................................................... 5.6 Discussion and Conclusions.................................................................................................................................... Illustrative Exercises........................................................................................................................................................... References........................................................................................................................................................................... 51 51 51 52 54 54 55 57 57 58 58 59 60 62 63 64 64 67 69 70 71 71 73 74 74 74 83 83 84
їх Contents 6 The Hydrogen Atom........................................................................................................................................................................85 6.1 Extension of the Schrodinger Wave Equation for Describing Two-Particle Motion...........................................................85 6.2 Splitting the Schrodinger Equation into Equation for the Hydrogen Atom as a Whole and Equation for Its Internal States........................................................................................................................................................................ 87 6.3 Writing the Schrodinger Equation for Internal Relative Motion of the Electron and Proton.............................................88 6.4 Separation of Variables in the Schrodinger Equation toForm Radial and Angular Equations..........................................89 6.5 Separation of Variables in the Angular Equation toForm Polar and AzimuthalAngle Equations.................................... 90 6.6 Solution of the Radial Equation.............................................................................................................................................91 6.7 Construction and Normalization of the Radial Wave Function...........................................................................................98 6.8 Solution of the Polar Equation.............................................................................................................................................. 99 6.9 Solution of the Azimuthal
Equation.................................................................................................................................... 101 6.10 Combining the Angular Partial Solutions...........................................................................................................................101 6.11 Putting together the Complete Wave Function....................................................................................................................102 6.12 Discussion and Conclusions.................................................................................................................................................102 Illustrative Exercises.........................................................................................................................................................................103 References........................................................................................................................................................................................ 103 Part II Condensed Matter Physics for Nanoelectronics 7 Drude-Lorentz Free Electron Model.........................................................................................................................................107 7.1 Condensed Matter Physics.................................................................................................................................................... 107 7.2 From Kinetic Theory of Gases to the Drude
Model.......................................................................................................... 107 7.3 Electron Densities in Metals................................................................................................................................................108 7.4 Separation between Electrons..............................................................................................................................................109 7.5 Assumptions of the Drude Model........................................................................................................................................109 7.6 Thermal Velocity of Electrons........................................................................................................................................... 110 7.7 DC Electrical Conductivity of Metals................................................................................................................................. 110 7.8 Drude’s Equation of Motion of an Electron in an Electric Field........................................................................................ 112 7.9 AC Electrical Conductivity of Metals................................................................................................................................. 114 7.10 Discussion and Conclusions..................................................................................................................................................115 Illustrative
Exercises.................................................................................... 115 References.............................................................................................................................................................................. 116 8 Sommerfeld Free Electron Fermi Gas Model.......................................................................................................................... 117 8.1 Strengthening Drude Model with Quantum Mechanics......................................................................................................117 8.2 Assumptions of the Sommerfeld Model.............................................................................................................................. 117 8.3 Behavior of a Free Electron Gas in One Dimension...........................................................................................................117 8.3.1 Wave Function with Box Boundary Conditions................................................................................................... 117 8.3.2 Wave Function with Periodic Boundary Conditions............................................................................................ 118 8.3.3 Normalization of the Wave Function.....................................................................................................................118 8.3.4 Quantum Numbers and Filling of Energy States................................................................................................. 118 8.3.5 Fermi
Energy......................................................................................................................................................... 118 8.4 Free Electron Gas in Three Dimensions............................................................................................................................. 119 8.4.1 Potential inside the Box, and the Schrodinger Equation........................................................................................119 8.4.2 Factoring the Wave Function................................................................................................................................. 119 8.4.3 Determination of Constants by Normalization of Wave Function...................................................................... 120 8.4.4 The Complete Wave Function............................................................................................................................... 120 8.4.5 Wave Function with Periodic Boundary Conditions............................................................................................ 121 8.4.6 The Momentum Space...........................................................................................................................................122 8.4.7 Fermi Energy and Related Terms..........................................................................................................................122 8.4.8 Filling of Energy
States.........................................................................................................................................123 8.4.9 Density of States....................................................................................................................................................124 8.5 Fermi Velocity versus Drift Velocity...................................................................................................................................125 8.5.1 Higher Value of Fermi Velocity than Random Thermal Velocity....................................................................... 125 8.5.2 Continuation of the Drift Velocity Concept.................................................................................... 125 8.5.3 Relaxation Time Re-Interpretation........................................................................................................................125
Contents x 8.5.4 Dominant Role of the Small Number of Electrons near the Fermi Surface...................................................... 125 8.5.5 Electron Mean Free Path Determination............................................................................................................... 125 8.6 Reconciliation of the High Fermi Temperature Value........................................................................................................128 8.7 Discussion and Conclusions.................................................................................................................................................. 128 Illustrative Exercises......................................................................................................................................................................... 128 References......................................................................................................................................................................................... 129 9 Kronig-Penney Periodic Potential Model....................................................... 131 9.1 From Particle-in-a-Box to Particle-in-a-Periodic Lattice..................................................................................................... 131 9.2 Simplification of the Problem............................................................................................................................................... 131 9.3 The Periodic
Potential........................................................................................................................................................... 131 9.4 Schrodinger Equations for Regions I and II, and Their Solutions......................................................................................131 9.5 Introducing Bloch Theorem by Symmetry Analysis...........................................................................................................132 9.6 Boundary Conditions........................................................................................................................................................... 134 9.7 Application of Boundary Conditions................................................................................................................................... 134 9.8 Calculation of the Determinant............................................................................................................................................136 9.9 Protrayal of Bandgaps in Tabular and Graphical Formats................................................................................................ 137 9.10 Different Schemes for Drawing Energy-Band Diagrams................................................................................................... 138 9.11 Origin of Bandgaps............................................................................................................................................................... 142 9.12 Concepts of Effective Mass and
Hole....................................................................................................................................143 9.13 Energy-Band Diagrams in Three Dimensions and Related Complexities.......................................................................... 146 9.13.1 Multitude of Bandgaps........................................................................................................................................... 146 9.13.2 Direct- and Indirect-Bandgap Semiconductors.....................................................................................................147 9.13.3 Silicon Band Structure and Two Types of Effective Masses of Carriers.............................................................147 9.14 Discussion and Conclusions................................................................................................................................................... 148 Illustrative Exercises.........................................................................................................................................................................148 References........................................................................................................................................................................................ 157 Part III Electron Behavior in Nanostructures 10 Quantum Confinement and Electronic Structure of Quantum Dots....................................................................................161 10.1 Length Scale for Quantum
Confinement............................................................................................................................. 161 10.2 Recapitulation of the Bohr Radius....................................................................................................................................... 161 10.3 Exciton, Exciton Bohr Radius, and Exciton Binding Energy............................................................................................. 162 10.3.1 Exciton................................................................................................................................................................... 162 10.3.2 Exciton Bohr Radius.............................................................................................................................................. 162 10.3.3 Exciton Binding Energy.........................................................................................................................................164 10.4 Weak, Moderate, and Strong Quantum Confinement..................................................................... 165 10.4.1 Exciton, Electron, and Hole Bohr Radii.............................................................................................................. 165 10.4.2 Explaining the Three Confinement Regimes........................................................................................................165 10.5 Dispersion Relation for
Excitons.........................................................................................................................................165 10.6 Confinement Energies of Electrons and Holes....................................................................................................................166 10.7 Energy Equation of Excitons in Weak Confinement...........................................................................................................171 10.8 Energy Equations of Electrons and Holes in Strong Confinement..................................................................................... 171 10.9 Bottom-Up Approach to the Evolution of the Energy Band Structure of Nanocrystalline Solids.................................... 172 10.10 Discussion and Conclusions................................................................................................................................................. 174 Illustrative Exercises........................................................................................................................................................................ 175 References........................................................................................................................................................................................175 11 Electrons in Quantum Wires and Landauer-Büttiker Formalism........................................................................................177 11.1 Two-Terminal Quantum Wire with Macroscopic
Contacts................................................................................................ 177 11.2 Solution of the Schrodinger Equation for the Quantum Wire............................................................................................. 177 11.3 Distribution Function of Electrons in the Quantum Wire under Bias................................................................................. 181 11.4 Transmission Coefficient of Electrons across the Contact/Quantum Wire Interface........................................................ 183 11.5 Current Propagation through the Quantum Wire............................................................................................................... 187 11.6 Determination of Conductance in the Zero Temperature Limit......................................................................................... 191 11.7 Discussion on Landauer’s Formula and the Length Scale of Validity of Ohm’s Law........................................................192
Contents xi 11.8 Alternative Approaches to Landauer’s Formula.................................................................................................................193 11.8.1 Landauer’s Formula for Current Carried by a Single Energy Level in a Single-Mode/Multimode Quantum Wire at Zero Temperature....................................................................................................................193 11.8.2 Landauer Formula for Non-Zero Temperature and Transport through Multiple Energy Channels................. 196 11.8.3 Non-Zero and Zero-Temperature Linear Response Formulae........................................................................... 198 11.9 Multi-Terminal Conductors................................................................................................................................................ 199 11.9.1 Büttiker Formula from Landauer’s Formula Assuming the Current Carried by Single Energy Level and Zero Temperature.................................................................................................................................................. 199 11.9.2 Multi-Terminal Conductor Formula from Landauer’s Formula for the Current Carried by Multiple Energy Levels........................................................................................................................................................ 199 11.9.3 Linearization of Multi-Terminal Conductor Response........................................................................................ 200 11.10 Discussion and
Conclusions................................................................................................................................................200 Illustrative Exercises........................................................................................................................................................................201 References.......................................................................................................................................................................................202 12 Electrons in Quantum Wells....................................................................................................................................................... 203 12.1 Sandwich Quantum Well Structures.................................................................................................................................... 203 12.2 Band Offsets at Abrupt Heterojunctions..............................................................................................................................203 12.3 Analysis of a Single Heterojunction of Dissimilar Bandgap Materials............................................................................205 12.4 Heterojunction Equations...................................................................................................................................... 207 12.4.1 Poisson’s Equation for the Heterojunction........................................................................................................... 207 12.4.2 Schrodinger’s Equation for the
Heterojunction................................................................................................... 209 12.4.3 Electron Concentration Equation.......................................................................................................................... 211 12.4.4 The 2D Density of States and Sheet Density of Electrons.................................................................................. 212 12.4.5 Boundary Conditions............................................................................................................................................ 217 12.4.6 Self-Consistent Solution of Schrodinger’s and Poisson’s Equations................................................................... 217 12.5 Discussion and Conclusions................................................................................................................................................. 217 Illustrative Exercises........................................................................................................................................................................218 References....................................................................................................................................................................................... 219 Part IV Green’s Function Method for Nanoelectronic Device Modeling 13 Dirac Delta and Green’s Function Preliminaries.................................................................................................................... 223 13.1 Dirac Delta
Function........................................................................................................................................................... 223 13.1.1 Describing Variations in Space............................................................................................................................223 13.1.2 Describing Variations in Time.............................................................................................................................224 13.1.3 Noteworthy Observations.....................................................................................................................................226 13.1.4 Physical Interpretation of Delta Function............................................................................................................ 226 13.2 Green’s Function................................................................................................................................................................. 226 13.2.1 Definition.............................................................................................................................................................. 226 13.2.2 How Green’s Function Works?.............................................................................................................................227 13.2.3 Characterization of the Response of a System by Green’s Function.................................................................. 227 13.2.4 Linearity of the Differential
Operator................................................................................................................. 228 13.2.5 Verifying the Solution...........................................................................................................................................228 13.3 Retarded and Advanced Green’s Functions.........................................................................................................................229 13.3.1 Retarded Green’s Function...................................................................................................................................229 13.3.2 Advanced Green’s Function..................................................................................................................................230 13.3.3 Inclusion of Boundary Conditions in Green’s Function Equations.................................................................... 231 13.4 Discussion and Conclusions.................................................................................................................................................233 Illustrative Exercises........................................................................................................................................................................233 References.......................................................................................................................................................................................234 14 Method of Finite Differences and Self-Energy of the
Leads................................................................................................... 235 14.1 Discretization Methods....................................................................................................................................................... 235 14.2 One-Dimensional Matrix Representation of theHamiltonian Operator............................................................................ 235 14.3 Dispersion Relation and Velocity for a DiscreteLattice.................................................................................................... 236 14.4 Two-Dimensional Matrix Representation of theHamiltonian Operator........................................................................... 237
xįį Contents 14.5 14.6 Matrix Truncation................................................................................................................................................................ 237 Self-Energy due to the Leads...............................................................................................................................................240 14.6.1 Wave Function of a Wire Terminating onOne Side..............................................................................................240 14.6.2 Wave Function Expansion..................................................................................................................................... 240 14.6.3 Green’s Function of the Wire.......................................... 241 14.6.4 Contour Integration................................................................................................................................................242 14.7 Discussion and Conclusions.................................................................................................................................................244 Illustrative Exercises........................................................................................................................................................................ 245 References....................................................................................................................................................................................... 246 15 Non-Equilibrium Green’s Function
(NEGF)Formalism.......................................................................................................... 247 15.1 Density Matrix and Correlation Function.......................................................................................................................... 247 15.2 Scattering Functions............................................................................................................................................................248 15.3 Green’s Function and Self-Energy...................................................................................................................................... 248 15.4 NEGF Kinetic Equations......................................................................................................................................................250 15.5 The Evolution of NEGF Equations from Schrodinger’s Equation.....................................................................................251 15.6 Equilibrium Solution............................................................................................................................................................253 15.7 Self-Energy and Scattering Functions due to Interactions within the Conductor............................................................. 253 15.7.1 Electron-Electron Interactions.............................................................................................................................. 254 15.7.2 Electron-Phonon
Interactions............................................................................................................................... 254 15.8 Terminal Current.................................................................................................................................................................255 15.9 Direct Determination of Terminal Currents without Current Density Calculation.......................................................... 259 15.10 Procedure of Solution..........................................................................................................................................................262 15.11 Discussion and Conclusions..................................................................................................................................................264 Illustrative Exercises........................................................................................................................................................................265 References.......................................................................................................................................................................................265 Part V Fabrication and Characterization of Nanostructures 16 Fabrication Tools.......................................................................................................................................................................... 269 16.1 Silicon Single-Crystal
Growth.......................................................................................................................................... 269 16.2 Thermal Oxidation of Silicon............................................................................................................................................ 270 16.3 Mask Making and Lithography..........................................................................................................................................272 16.3.1 Mask Making........................................................................................................................................................ 272 16.3.2 Lithography Principles........................ 272 16.3.3 Optical Resolution.................................................................................................................................................273 16.3.4 The 248 and 193 nm Excimer Laser Lithographies.............................................................................................274 16.3.5 Immersion Lithography........................................................................................................................................274 16.3.6 Extreme UV Lithography.....................................................................................................................................275 16.3.7 Electron-Beam Lithography (E-Beam Lithography)........................................................................................... 276 16.3.8 Ion Beam
Lithography..........................................................................................................................................277 16.3.9 X-Ray Lithography...............................................................................................................................................279 16.3.10 Nanoimprint Lithography (NIL).......................................................................................................................... 279 16.3.11 Dip Pen Nanolithography (DPN)......................................................................................................................... 280 16.3.12 Block Copolymer Lithography............................................................................................................................. 281 16.4 Wet and Dry Etching..........................................................................................................................................................282 16.5 Diffusion of Impurities in Silicon...................................................................................................................................... 282 16.6 Ion Implantation..................................................................................................................................................................284 16.7 Physical Vapor Deposition (PVD)..................................................................................................................................... 284 16.7.1 Vacuum
Evaporation............................................................................................................................................ 284 16.7.2 Molecular Beam Epitaxy (MBE)......................................................................................................................... 285 16.7.3 Sputtering............................................................................................................................................................. 285 16.7.4 Laser Ablation Deposition (LAD) or Photoablation Deposition........................................................................ 286 16.8 Chemical Vapor Deposition (C VD)................................................................................................................................... 287 16.8.1 Generic CVD Process.......................................................................................................................................... 287 16.8.2 Metal-Organic Chemical Vapor Deposition(MOCVD)......................................................................................288 16.8.3 Atomic Layer Deposition (ALD).........................................................................................................................290
Contents xiii 16.9 Synthesis of Carbon Nanotubes................. ........................................................................................................................292 16.9.1 CNTs by a DC Arc-Discharge Method...............................................................................................................292 16.9.2 CNTs by Laser Ablation..................................................................................................................................... 292 16.9.3 CVD Growth of CNTs.......................................................................................................................................... 293 16.10 Discussion and Conclusions.............................................................................................................................................. 294 Illustrative Exercises......................................................................................................................................................................294 References..................................................................................................................................................................................... 296 17 Characterization Facilities.........................................................................................................................................................299 17.1 Four-Point Probe for Sheet Resistance Measurements......................................................................................................299
17.1.1 Bulk Sample.......................................................................................................................................................... 299 17.1.2 Thin Sheet..............................................................................................................................................................301 17.2 X-Ray Diffraction (XRD) Crystallography...................................................................................................................... 301 17.3 Scanning Electron Microscope (SEM)............................................................................................................................. 302 17.3.1 Secondary and Backscattered Electrons.............................................................................................................. 302 17.3.2 SEM Micrography................................................................................................................................................. 302 17.3.3 Energy Dispersive X-Ray (EDX) Analysis...........................................................................................................303 17.3.4 SEM Components................................................................................................................................................. 303 17.4 Transmission Electron Microscope (ТЕМ)........................................................................................................................304 17.5 Scanning TUnneling Microscope
(STM).......................................................................................................................... 305 17.5.1 Dependence of the TUnneling Current onSample-to-Tip Spacing....................................................................... 305 17.5.2 STM Components.................................................................................................................................................306 17.5.3 Imaging Procedure................................................................................................................................................ 306 17.5.4 Imaging Modes..................................................................................................................................................... 306 17.6 Atomic Force Microscope (AFM).................................................................................................................................... 307 17.6.1 Competition with Other Microscopes..................................................................................................................307 17.6.2 Imaging Principle.................................................................................................................................................. 307 17.6.3 Measurement of Deflection of the Cantilever..................................................................................................... 309 17.6.4 Usage and Operational
Modes.............................................................................................................................309 17.7 Discussion and Conclusions............................................................................................................................................... 309 Illustrative Exercises.......................................................................................................................................................................310 References...................................................................................................................................................................................... 311 Part VI Exemplar Nanoelectronic Devices 18 Resonant TUnneling Diodes.........................................................................................................................................................315 18.1 The Constituent Layers....................................................................................................................................................... 315 18.1.1 Structure and Juxtapositioning of Layers.............................................................................................................315 18.1.2 Stuffing a 2D System between Two 3D Systems...................................................................................................315 18.2 Operational
Modes...............................................................................................................................................................315 18.2.1 Without External Bias: Equilibrium Condition....................................................................................................315 18.2.2 Low External Bias: In-Resonance Condition.......................................................................................................316 18.2.3 High External Bias: Off-Resonance Condition.....................................................................................................317 18.2.4 Higher External Bias: Second Resonance Condition...........................................................................................318 18.3 Understanding Resonant TUnnel Diode Operation from OpticalAnalogy........................................................................ 318 18.4. Parameters of the Resonant TUnneling Diode.....................................................................................................................319 18.4.1 Peak-to-Valley Ratio.............................................................................................................................................. 319 18.4.2 Operational Speed................................................................................................................................................ 319 18.5 Two Types of Double Barrier Resonant
TUnneling.............................................................................................................319 18.5.1 Coherent TUnneling............................................................................................................................................... 319 18.5.2 Sequential TUnneling.............................................................................................................................................324 18.6 Competition of the Resonant TUnneling Diode with Other Devices................................................................................. 325 18.7 Discussion and Conclusions................................................................................................................................................ 325 Illustrative Exercises........................................................................................................................................................................326 References....................................................................................................................................................................................... 328
XIV Contents 19 Nanoscale MOSFETs and Similar Devices................................................................................................................................ 329 19.1 Short-Channel Effects in a Conventional Planar Bulk MOSFET..................................................................................... 329 19.1.1 Drain-Induced Barrier Lowering (DIBL) and ThresholdVoltage Roll-Off......................................................... 329 19.1.2 Carrier Velocity Saturation...................................................................................................................................335 19.1.3 Hot Carrier Effects................................................................................................................................ 342 19.1.4 Carrier Mobility Degradation by Surface Scattering...........................................................................................342 19.1.5 Regenerative Feedback between Avalanche Breakdownand Parasitic Bipolar Transistor................................ 343 19.2 From Bulk Silicon-MOSFET to SOI-MOSFET Technology............................................................................................ 343 19.2.1 PD-SOI-MOSFET..................................................................................................................................................344 19.2.2 FD-SOI-MOSFET..................................................................................................................................................344 19.3 From 2D MOSFET to 3D
MOSFET: The FinFET.............................................................................................................344 19.4 Semiconductor Nanowire Transistors.................................................................................................................................348 19.4.1 Reasons for Interest in Semiconductor Nanowire Transistors............................................................................ 348 19.4.2 Back-Gated Silicon Nanowire FETs..................................................................................................................... 348 19.4.2.1 Preparation and Deposition of Silicon Nanowires..............................................................................348 19.4.2.2 Source/Drain Metallization.................................................................................................................. 348 19.4.2.3 Rapid Thermal Annealing (RTA)........................................................................................................348 19.4.2.4 Nanowire Surface Modification...........................................................................................................348 19.4.2.5 Nanowire FET Characteristics............................................................................................................. 349 19.4.3 Junctionless Multigate Nanowire FETs............................................................................................................... 349 19.4.3.1 Electron-Beam Lithography for Nanowire
Delineation......................................................................350 19.4.3.2 Gate Dielectric Formation.................................................................................................................... 350 19.4.3.3 Nanowire Doping................................................................................................................................. 350 19.4.3.4 a-Si Deposition on the Gate Oxide and Its Doping.............................................................................350 19.4.3.5 Crystallization of a-Si to Make P+·Polysilicon Gate Electrodes........................................................ 350 19.4.3.6 Patterning and Etching of Gate Electrodes.........................................................................................350 19.4.3.7 Source/Drain Electrode Formation......................................................................................................350 19.4.3.8 Nanowire FET Characteristics.............................................................................................................350 19.5 CNT-FETs........................ 350 19.5.1 SB-CNT-FETs....................................................................................................................................................... 350 19.5.2 MOSFET-Like CNT FETs....................................................................................................................................350 19.5.2.1 Patterned CNT
Growth........................................................................................................................351 19.5.2.2 Zirconium Oxide Top-Gate Formation by Atomic Layer Deposition.................................................351 19.5.2.3 Top-Gate Electrode Deposition............................................................................................................351 19.5.2.4 MOS-Like CNT-FET Characteristics..................................................................................................351 19.6 Discussion and Conclusions................................................................................................................................................ 351 Illustrative Exercises........................................................................................................................................................................353 References.......................................................................................................................................................................................354 20 High-Electron-Mobility Transistors.......................................................................................................................................... 355 20.1 MOSFET, MESFET, and HEMT.......................................................................................... 355 20.2 HEMT Operation................................................................................................................................................................
357 20.2.1 The 2DEG Channel Formation.............................................................................................................................357 20.2.2 Modulation of the Channel: Enhancement and Depletion Mode HEMTs..........................................................359 20.3 Recessed-Gate and Self-Aligned Gate HEMTs.................................................................................................................359 20.3.1 Non-Self-Aligned Recessed-Gate HEMT Fabrication........................................................................................ 359 20.3.2 Self-Aligned Т-Gate HEMT Fabrication............................................................................................................. 359 20.3.3 Pseudomorphic and Metamorphic HEMTs...................................................................... 359 20.4 The Sheet Density of Electrons......................................................................................................................................... 360 20.4.1 Energy Levels of Electrons in a Triangular Well with Infinitely High Potential Wall ΔEc............................. 360 20.4.2 Carrier Concentration Ns in 2DEG for One Occupied Confined Energy Level................................................ 363 20.5 Linear Charge-Control Model of HEMTs......................................................................................................................... 366 20.6 Discussion and
Conclusions............................................................................................................................................... 370 Illustrative Exercises...................................................................................................................................................................... 372 References...................................................................................................................................................................................... 372
Contents XV 21 Single-Electron Transistors.........................................................................................................................................................373 21.1 Energy Used in Charging a Conductive Island................................................................................................................... 373 21.2 Other Energy Components, Work Done by Voltage Sources, and the Helmholtz Free Energy.......................................373 21.3 Capacitance of a Spherical Conductive Island................................................................................................................... 374 21.4 Dependence of Charging Energy on the Island Size andCoulomb Blockade Effect........................................................ 374 21.5 Orthodox Theory of Single-Electron Thnneling................................................................................................................ 375 21.5.1 Thnnel Junction......................................................................................................................................................375 21.5.2 Minimum TUnnel Resistance................................................................................................................................ 376 21.5.3 Conductive Island with Two Thnnel Junctions....................................................................................................377 21.5.4 Coupling a Gate Electrode to the Double Thnnel
Junction.................................................................................384 21.6 Single-Electron Transistor Fabrication by Nanowire-Based Process................................................................................ 390 21.7 Discussion and Conclusions................................................................................................................................................ 390 Illustrative Exercises........................................................................................................................................................................ 393 References....................................................................................................................................................................................... 394 22 Heterostructure Optoelectronic Devices.................................................................................................................................... 395 22.1 Heterojunction Laser Diode................................................................................................................................................. 395 22.1.1 Double Heterostructure Laser............................................................................................................................... 395 22.1.2 Quantum Well Laser............................................................................................................................................. 396 22.2 Quantum Well and Barrier Layer Structures in
LEDs...................................................................................................... 399 22.2.1 Effect of Thickness of the Quantum Barrier Layer in Multiple Quantum Well GaN LEDs.............................399 22.2.2 Suppression of the QCSE by Silicon Doping of Quantum Barriers................................................................... 399 22.2.3 Effect of the Number of Quantum Wells on LED Performance.........................................................................401 22.2.4 Overcoming Auger Recombination-Engendered Efficiency Reduction in MQW LEDs by Linearly Graded InN Composition Profile..........................................................................................................................401 22.3 Quantum Well Solar Cell.................................................................................................................................................... 402 22.4 Discussion and Conclusions................................................................................................................................................402 Illustrative Exercises....................................................................................................................................................................... 405 References.......................................................................................................................................................................................406 Index ,407
This introductory text develops the reader s fundamental understanding of core principles and experimental aspects underlying the operation ot nanoelectronic devices. The author makes a thorough and systematic presentation of electron transport in quantumconfined systems such as quantum dots, quantum wires, and quantum wells together with Landauer-Biittiker formalism and nonequilibrium Green s function approach. The coverage encompasses nanofabrication techniques and characterization tools followed by a comprehensive exposition of nanoelectronic devices including resonant tunneling diodes, nanoscale MOSFETs, carbon nanotube FETs. high-electron-mobility transistors, single-electron transistors, and heterostructure optoelectronic devices. The writing throughout is simple and straightforward, with clearly drawn illustrations and extensive self-study exercises for each chapter. • Introduces the basic concepts underlying the operation of nanoelectronic devices. • Offers a broad overview of the field, including state-of-the-art developments. • Covers the relevant quantum and solid-state physics and nanoelectronic device principles. • Written in lucid language with accessible mathematical treatment. • Includes extensive end-ot-chapter exercises and many insightful diagrams. Physics in informa business CRC Press Taylor Francis Croup an Informa business ISBN 978-0-8153-8426-7 9780815384267
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Contents Preface. xvii Acknowledgements.xix Author. xxi Abbreviations, Acronyms, and Chemical Symbols. xxiii Mathematical Notation. xxvii About the Book. xxxv 1 Nanoelectronics and Mesoscopic Physics. 1 1.1 Ultra-Small Objects. 1 1.1.1 Electron
Radius.1 1.1.2 Atomic Nucleus Diameter. 1 1.1.3 Atomic and Molecular Sizes. 1 1.2 The Nanoworld. 1 1.3 Mesoscopic Physics.1 1.3.1 Averaging of Behavior. 2 1.3.2 Surface Area-to-Volume Ratio. 2 1.3.3 Dominance of Electromagnetic Force over Gravitational Force. 2 1.3.4 Size Dependence of Properties. 3 1.3.5 Classical and Quantum-Mechanical
Laws.3 1.3.6 Quantization of Conductance. 3 1.3.7 Quantum Confinement. 5 1.3.8 Quantum-Mechanical TUnneling.6 1.3.9 Giant Magnetoresistance Effect.7 1.3.10 Single-Electron Effects.10 1.4 Objectives and Organization of the Book. 10 1.5 Discussion and Conclusions. 11 Illustrative Exercises. 12
References. 13 Part I Quantum Mechanics for Nanoelectronics 2 Origins of Quantum Theory. 17 2.1 Young’s Double-Slit Experiment on Light Diffraction. 17 2.2 Blackbody Radiation and Planck’s Quantum Hypothesis. 17 2.3 Photoelectric Effect. 17 2.4 Emission Spectrum of Atomic Hydrogen and Bohr’s Atomic Model.19 2.5 Compton Scattering. 21 2.6 de Broglie’s Hypothesis.21 2.7 Davisson-Germer Experiment on Electron Diffraction. 22 2.8 Heisenberg’s Uncertainty
Principle. 23 2.9 Discussion and Conclusions. 24 Illustrative Exercises.25 References. 25 3 The Schrodinger Wave Equation. 27 3.1 Two Forms of Schrodinger Equation. 27 3.1.1 Time-Independent Schrodinger Equation (TISE). 27 3.1.2 Time-Dependent Schrodinger Equation (TDSE). 27 3.2 Formulation of Time-Independent Schrodinger Equation (TISE). 27 3.3 Formulation of Time-Dependent Schrodinger Equation
(TDSE). 29 3.4 TISE from TDSE: Method of Separation of Variables. 29 vii
Contents viii 3.5 Deriving the General Equation for Wave Motion. 30 3.6 Solving the General Equation for Wave Motion bySeparating the Variables. 33 3.7 Max Born’s Physical Interpretation of the Wave Function Ψ. 36 3.8 Normalization of the Wave Function.38 3.9 Discussion and Conclusions. 39 Illustrative Exercises. 40 References. 42 4 Operator Methods and Postulates of Quantum Mechanics. 43 4.1 What Are Operators?. 43 4.2 Main
Operators in Quantum Mechanics. 43 4.2.1 Position Operators. 43 4.2.2 Linear Momentum Operators.43 4.2.3 Kinetic Energy Operators.43 4.2.4 Potential Energy Operators. 44 4.2.5 Total Energy Operators.44 4.2.6 Angular Momentum Operator. 44 4.3 Linear and Non-Linear Operators. 45 4.4 Commutation of Operators and Its Implications. 45 4.5 Eigenvalues and Eigenfunctions of an Operator. 46 4.6 Schrodinger’s Equation in Operator
Form. 46 4.7 Hermitian Operators.46 4.8 Expectation Value. 47 4.9 Postulates of Quantum Mechanics in Analogy to Classical Mechanics.47 4.10 Discussion and Conclusions.48 Illustrative Exercises. 48 References. 49 5 Particle-in-a-Box and Related Problems. 5.1 Free particle in Quantum Mechanics. 5.1.1 Spatial
Dependence. 5.1.2 Time Dependence. 5.1.3 Boundary Conditions and Absence of Quantization. 5.1.4 Non-Normalization of Wave Function. 5.1.5 Concept of Wave Packets. 5.2 Particle in a Box or Infinite Potential Well. 5.2.1 The Solution. . 5.2.2 Determination of В. . 5.2.3 Determination of к. 5.2.4 Determination of A. 5.2.5 Plotting En, Ψ„, ΙΨ„Ι2 versus x
Graphs. 5.3 Particle in a Finite Potential Well. 5.3.1 Regions I and III. 5.3.2 Region II. 5.3.3 Boundary Conditions. 5.3.4 Graphical Solution of Finite Potential Well Equations. 5.4 Alternative Method: Determining Solutions for Even (Symmetric) and Odd (Antisymmetric) Wave Functions 5.4.1 Even Solution Boundary Conditions. 5.4.2 Odd Solution Boundary Conditions. 5.4.3 Normalization of Even Wave Functions. 5.4.4 Normalization of Odd Wave Functions. 5.4.5 Plotting the Wave Functions:
Quantum-Mechanical Tunneling. 5.4.6 Unbound States. 5.5 Derivation of Tbnneling Probability Equation. 5.6 Discussion and Conclusions. Illustrative Exercises. References. 51 51 51 52 54 54 55 57 57 58 58 59 60 62 63 64 64 67 69 70 71 71 73 74 74 74 83 83 84
їх Contents 6 The Hydrogen Atom.85 6.1 Extension of the Schrodinger Wave Equation for Describing Two-Particle Motion.85 6.2 Splitting the Schrodinger Equation into Equation for the Hydrogen Atom as a Whole and Equation for Its Internal States. 87 6.3 Writing the Schrodinger Equation for Internal Relative Motion of the Electron and Proton.88 6.4 Separation of Variables in the Schrodinger Equation toForm Radial and Angular Equations.89 6.5 Separation of Variables in the Angular Equation toForm Polar and AzimuthalAngle Equations. 90 6.6 Solution of the Radial Equation.91 6.7 Construction and Normalization of the Radial Wave Function.98 6.8 Solution of the Polar Equation. 99 6.9 Solution of the Azimuthal
Equation. 101 6.10 Combining the Angular Partial Solutions.101 6.11 Putting together the Complete Wave Function.102 6.12 Discussion and Conclusions.102 Illustrative Exercises.103 References. 103 Part II Condensed Matter Physics for Nanoelectronics 7 Drude-Lorentz Free Electron Model.107 7.1 Condensed Matter Physics. 107 7.2 From Kinetic Theory of Gases to the Drude
Model. 107 7.3 Electron Densities in Metals.108 7.4 Separation between Electrons.109 7.5 Assumptions of the Drude Model.109 7.6 Thermal Velocity of Electrons. 110 7.7 DC Electrical Conductivity of Metals. 110 7.8 Drude’s Equation of Motion of an Electron in an Electric Field. 112 7.9 AC Electrical Conductivity of Metals. 114 7.10 Discussion and Conclusions.115 Illustrative
Exercises. 115 References. 116 8 Sommerfeld Free Electron Fermi Gas Model. 117 8.1 Strengthening Drude Model with Quantum Mechanics.117 8.2 Assumptions of the Sommerfeld Model. 117 8.3 Behavior of a Free Electron Gas in One Dimension.117 8.3.1 Wave Function with Box Boundary Conditions. 117 8.3.2 Wave Function with Periodic Boundary Conditions. 118 8.3.3 Normalization of the Wave Function.118 8.3.4 Quantum Numbers and Filling of Energy States. 118 8.3.5 Fermi
Energy. 118 8.4 Free Electron Gas in Three Dimensions. 119 8.4.1 Potential inside the Box, and the Schrodinger Equation.119 8.4.2 Factoring the Wave Function. 119 8.4.3 Determination of Constants by Normalization of Wave Function. 120 8.4.4 The Complete Wave Function. 120 8.4.5 Wave Function with Periodic Boundary Conditions. 121 8.4.6 The Momentum Space.122 8.4.7 Fermi Energy and Related Terms.122 8.4.8 Filling of Energy
States.123 8.4.9 Density of States.124 8.5 Fermi Velocity versus Drift Velocity.125 8.5.1 Higher Value of Fermi Velocity than Random Thermal Velocity. 125 8.5.2 Continuation of the Drift Velocity Concept. 125 8.5.3 Relaxation Time Re-Interpretation.125
Contents x 8.5.4 Dominant Role of the Small Number of Electrons near the Fermi Surface. 125 8.5.5 Electron Mean Free Path Determination. 125 8.6 Reconciliation of the High Fermi Temperature Value.128 8.7 Discussion and Conclusions. 128 Illustrative Exercises. 128 References. 129 9 Kronig-Penney Periodic Potential Model. 131 9.1 From Particle-in-a-Box to Particle-in-a-Periodic Lattice. 131 9.2 Simplification of the Problem. 131 9.3 The Periodic
Potential. 131 9.4 Schrodinger Equations for Regions I and II, and Their Solutions.131 9.5 Introducing Bloch Theorem by Symmetry Analysis.132 9.6 Boundary Conditions. 134 9.7 Application of Boundary Conditions. 134 9.8 Calculation of the Determinant.136 9.9 Protrayal of Bandgaps in Tabular and Graphical Formats. 137 9.10 Different Schemes for Drawing Energy-Band Diagrams. 138 9.11 Origin of Bandgaps. 142 9.12 Concepts of Effective Mass and
Hole.143 9.13 Energy-Band Diagrams in Three Dimensions and Related Complexities. 146 9.13.1 Multitude of Bandgaps. 146 9.13.2 Direct- and Indirect-Bandgap Semiconductors.147 9.13.3 Silicon Band Structure and Two Types of Effective Masses of Carriers.147 9.14 Discussion and Conclusions. 148 Illustrative Exercises.148 References. 157 Part III Electron Behavior in Nanostructures 10 Quantum Confinement and Electronic Structure of Quantum Dots.161 10.1 Length Scale for Quantum
Confinement. 161 10.2 Recapitulation of the Bohr Radius. 161 10.3 Exciton, Exciton Bohr Radius, and Exciton Binding Energy. 162 10.3.1 Exciton. 162 10.3.2 Exciton Bohr Radius. 162 10.3.3 Exciton Binding Energy.164 10.4 Weak, Moderate, and Strong Quantum Confinement. 165 10.4.1 Exciton, Electron, and Hole Bohr Radii. 165 10.4.2 Explaining the Three Confinement Regimes.165 10.5 Dispersion Relation for
Excitons.165 10.6 Confinement Energies of Electrons and Holes.166 10.7 Energy Equation of Excitons in Weak Confinement.171 10.8 Energy Equations of Electrons and Holes in Strong Confinement. 171 10.9 Bottom-Up Approach to the Evolution of the Energy Band Structure of Nanocrystalline Solids. 172 10.10 Discussion and Conclusions. 174 Illustrative Exercises. 175 References.175 11 Electrons in Quantum Wires and Landauer-Büttiker Formalism.177 11.1 Two-Terminal Quantum Wire with Macroscopic
Contacts. 177 11.2 Solution of the Schrodinger Equation for the Quantum Wire. 177 11.3 Distribution Function of Electrons in the Quantum Wire under Bias. 181 11.4 Transmission Coefficient of Electrons across the Contact/Quantum Wire Interface. 183 11.5 Current Propagation through the Quantum Wire. 187 11.6 Determination of Conductance in the Zero Temperature Limit. 191 11.7 Discussion on Landauer’s Formula and the Length Scale of Validity of Ohm’s Law.192
Contents xi 11.8 Alternative Approaches to Landauer’s Formula.193 11.8.1 Landauer’s Formula for Current Carried by a Single Energy Level in a Single-Mode/Multimode Quantum Wire at Zero Temperature.193 11.8.2 Landauer Formula for Non-Zero Temperature and Transport through Multiple Energy Channels. 196 11.8.3 Non-Zero and Zero-Temperature Linear Response Formulae. 198 11.9 Multi-Terminal Conductors. 199 11.9.1 Büttiker Formula from Landauer’s Formula Assuming the Current Carried by Single Energy Level and Zero Temperature. 199 11.9.2 Multi-Terminal Conductor Formula from Landauer’s Formula for the Current Carried by Multiple Energy Levels. 199 11.9.3 Linearization of Multi-Terminal Conductor Response. 200 11.10 Discussion and
Conclusions.200 Illustrative Exercises.201 References.202 12 Electrons in Quantum Wells. 203 12.1 Sandwich Quantum Well Structures. 203 12.2 Band Offsets at Abrupt Heterojunctions.203 12.3 Analysis of a Single Heterojunction of Dissimilar Bandgap Materials.205 12.4 Heterojunction Equations. 207 12.4.1 Poisson’s Equation for the Heterojunction. 207 12.4.2 Schrodinger’s Equation for the
Heterojunction. 209 12.4.3 Electron Concentration Equation. 211 12.4.4 The 2D Density of States and Sheet Density of Electrons. 212 12.4.5 Boundary Conditions. 217 12.4.6 Self-Consistent Solution of Schrodinger’s and Poisson’s Equations. 217 12.5 Discussion and Conclusions. 217 Illustrative Exercises.218 References. 219 Part IV Green’s Function Method for Nanoelectronic Device Modeling 13 Dirac Delta and Green’s Function Preliminaries. 223 13.1 Dirac Delta
Function. 223 13.1.1 Describing Variations in Space.223 13.1.2 Describing Variations in Time.224 13.1.3 Noteworthy Observations.226 13.1.4 Physical Interpretation of Delta Function. 226 13.2 Green’s Function. 226 13.2.1 Definition. 226 13.2.2 How Green’s Function Works?.227 13.2.3 Characterization of the Response of a System by Green’s Function. 227 13.2.4 Linearity of the Differential
Operator. 228 13.2.5 Verifying the Solution.228 13.3 Retarded and Advanced Green’s Functions.229 13.3.1 Retarded Green’s Function.229 13.3.2 Advanced Green’s Function.230 13.3.3 Inclusion of Boundary Conditions in Green’s Function Equations. 231 13.4 Discussion and Conclusions.233 Illustrative Exercises.233 References.234 14 Method of Finite Differences and Self-Energy of the
Leads. 235 14.1 Discretization Methods. 235 14.2 One-Dimensional Matrix Representation of theHamiltonian Operator. 235 14.3 Dispersion Relation and Velocity for a DiscreteLattice. 236 14.4 Two-Dimensional Matrix Representation of theHamiltonian Operator. 237
xįį Contents 14.5 14.6 Matrix Truncation. 237 Self-Energy due to the Leads.240 14.6.1 Wave Function of a Wire Terminating onOne Side.240 14.6.2 Wave Function Expansion. 240 14.6.3 Green’s Function of the Wire. 241 14.6.4 Contour Integration.242 14.7 Discussion and Conclusions.244 Illustrative Exercises. 245 References. 246 15 Non-Equilibrium Green’s Function
(NEGF)Formalism. 247 15.1 Density Matrix and Correlation Function. 247 15.2 Scattering Functions.248 15.3 Green’s Function and Self-Energy. 248 15.4 NEGF Kinetic Equations.250 15.5 The Evolution of NEGF Equations from Schrodinger’s Equation.251 15.6 Equilibrium Solution.253 15.7 Self-Energy and Scattering Functions due to Interactions within the Conductor. 253 15.7.1 Electron-Electron Interactions. 254 15.7.2 Electron-Phonon
Interactions. 254 15.8 Terminal Current.255 15.9 Direct Determination of Terminal Currents without Current Density Calculation. 259 15.10 Procedure of Solution.262 15.11 Discussion and Conclusions.264 Illustrative Exercises.265 References.265 Part V Fabrication and Characterization of Nanostructures 16 Fabrication Tools. 269 16.1 Silicon Single-Crystal
Growth. 269 16.2 Thermal Oxidation of Silicon. 270 16.3 Mask Making and Lithography.272 16.3.1 Mask Making. 272 16.3.2 Lithography Principles. 272 16.3.3 Optical Resolution.273 16.3.4 The 248 and 193 nm Excimer Laser Lithographies.274 16.3.5 Immersion Lithography.274 16.3.6 Extreme UV Lithography.275 16.3.7 Electron-Beam Lithography (E-Beam Lithography). 276 16.3.8 Ion Beam
Lithography.277 16.3.9 X-Ray Lithography.279 16.3.10 Nanoimprint Lithography (NIL). 279 16.3.11 Dip Pen Nanolithography (DPN). 280 16.3.12 Block Copolymer Lithography. 281 16.4 Wet and Dry Etching.282 16.5 Diffusion of Impurities in Silicon. 282 16.6 Ion Implantation.284 16.7 Physical Vapor Deposition (PVD). 284 16.7.1 Vacuum
Evaporation. 284 16.7.2 Molecular Beam Epitaxy (MBE). 285 16.7.3 Sputtering. 285 16.7.4 Laser Ablation Deposition (LAD) or Photoablation Deposition. 286 16.8 Chemical Vapor Deposition (C VD). 287 16.8.1 Generic CVD Process. 287 16.8.2 Metal-Organic Chemical Vapor Deposition(MOCVD).288 16.8.3 Atomic Layer Deposition (ALD).290
Contents xiii 16.9 Synthesis of Carbon Nanotubes. .292 16.9.1 CNTs by a DC Arc-Discharge Method.292 16.9.2 CNTs by Laser Ablation. 292 16.9.3 CVD Growth of CNTs. 293 16.10 Discussion and Conclusions. 294 Illustrative Exercises.294 References. 296 17 Characterization Facilities.299 17.1 Four-Point Probe for Sheet Resistance Measurements.299
17.1.1 Bulk Sample. 299 17.1.2 Thin Sheet.301 17.2 X-Ray Diffraction (XRD) Crystallography. 301 17.3 Scanning Electron Microscope (SEM). 302 17.3.1 Secondary and Backscattered Electrons. 302 17.3.2 SEM Micrography. 302 17.3.3 Energy Dispersive X-Ray (EDX) Analysis.303 17.3.4 SEM Components. 303 17.4 Transmission Electron Microscope (ТЕМ).304 17.5 Scanning TUnneling Microscope
(STM). 305 17.5.1 Dependence of the TUnneling Current onSample-to-Tip Spacing. 305 17.5.2 STM Components.306 17.5.3 Imaging Procedure. 306 17.5.4 Imaging Modes. 306 17.6 Atomic Force Microscope (AFM). 307 17.6.1 Competition with Other Microscopes.307 17.6.2 Imaging Principle. 307 17.6.3 Measurement of Deflection of the Cantilever. 309 17.6.4 Usage and Operational
Modes.309 17.7 Discussion and Conclusions. 309 Illustrative Exercises.310 References. 311 Part VI Exemplar Nanoelectronic Devices 18 Resonant TUnneling Diodes.315 18.1 The Constituent Layers. 315 18.1.1 Structure and Juxtapositioning of Layers.315 18.1.2 Stuffing a 2D System between Two 3D Systems.315 18.2 Operational
Modes.315 18.2.1 Without External Bias: Equilibrium Condition.315 18.2.2 Low External Bias: In-Resonance Condition.316 18.2.3 High External Bias: Off-Resonance Condition.317 18.2.4 Higher External Bias: Second Resonance Condition.318 18.3 Understanding Resonant TUnnel Diode Operation from OpticalAnalogy. 318 18.4. Parameters of the Resonant TUnneling Diode.319 18.4.1 Peak-to-Valley Ratio. 319 18.4.2 Operational Speed. 319 18.5 Two Types of Double Barrier Resonant
TUnneling.319 18.5.1 Coherent TUnneling. 319 18.5.2 Sequential TUnneling.324 18.6 Competition of the Resonant TUnneling Diode with Other Devices. 325 18.7 Discussion and Conclusions. 325 Illustrative Exercises.326 References. 328
XIV Contents 19 Nanoscale MOSFETs and Similar Devices. 329 19.1 Short-Channel Effects in a Conventional Planar Bulk MOSFET. 329 19.1.1 Drain-Induced Barrier Lowering (DIBL) and ThresholdVoltage Roll-Off. 329 19.1.2 Carrier Velocity Saturation.335 19.1.3 Hot Carrier Effects. 342 19.1.4 Carrier Mobility Degradation by Surface Scattering.342 19.1.5 Regenerative Feedback between Avalanche Breakdownand Parasitic Bipolar Transistor. 343 19.2 From Bulk Silicon-MOSFET to SOI-MOSFET Technology. 343 19.2.1 PD-SOI-MOSFET.344 19.2.2 FD-SOI-MOSFET.344 19.3 From 2D MOSFET to 3D
MOSFET: The FinFET.344 19.4 Semiconductor Nanowire Transistors.348 19.4.1 Reasons for Interest in Semiconductor Nanowire Transistors. 348 19.4.2 Back-Gated Silicon Nanowire FETs. 348 19.4.2.1 Preparation and Deposition of Silicon Nanowires.348 19.4.2.2 Source/Drain Metallization. 348 19.4.2.3 Rapid Thermal Annealing (RTA).348 19.4.2.4 Nanowire Surface Modification.348 19.4.2.5 Nanowire FET Characteristics. 349 19.4.3 Junctionless Multigate Nanowire FETs. 349 19.4.3.1 Electron-Beam Lithography for Nanowire
Delineation.350 19.4.3.2 Gate Dielectric Formation. 350 19.4.3.3 Nanowire Doping. 350 19.4.3.4 a-Si Deposition on the Gate Oxide and Its Doping.350 19.4.3.5 Crystallization of a-Si to Make P+·Polysilicon Gate Electrodes. 350 19.4.3.6 Patterning and Etching of Gate Electrodes.350 19.4.3.7 Source/Drain Electrode Formation.350 19.4.3.8 Nanowire FET Characteristics.350 19.5 CNT-FETs. 350 19.5.1 SB-CNT-FETs. 350 19.5.2 MOSFET-Like CNT FETs.350 19.5.2.1 Patterned CNT
Growth.351 19.5.2.2 Zirconium Oxide Top-Gate Formation by Atomic Layer Deposition.351 19.5.2.3 Top-Gate Electrode Deposition.351 19.5.2.4 MOS-Like CNT-FET Characteristics.351 19.6 Discussion and Conclusions. 351 Illustrative Exercises.353 References.354 20 High-Electron-Mobility Transistors. 355 20.1 MOSFET, MESFET, and HEMT. 355 20.2 HEMT Operation.
357 20.2.1 The 2DEG Channel Formation.357 20.2.2 Modulation of the Channel: Enhancement and Depletion Mode HEMTs.359 20.3 Recessed-Gate and Self-Aligned Gate HEMTs.359 20.3.1 Non-Self-Aligned Recessed-Gate HEMT Fabrication. 359 20.3.2 Self-Aligned Т-Gate HEMT Fabrication. 359 20.3.3 Pseudomorphic and Metamorphic HEMTs. 359 20.4 The Sheet Density of Electrons. 360 20.4.1 Energy Levels of Electrons in a Triangular Well with Infinitely High Potential Wall ΔEc. 360 20.4.2 Carrier Concentration Ns in 2DEG for One Occupied Confined Energy Level. 363 20.5 Linear Charge-Control Model of HEMTs. 366 20.6 Discussion and
Conclusions. 370 Illustrative Exercises. 372 References. 372
Contents XV 21 Single-Electron Transistors.373 21.1 Energy Used in Charging a Conductive Island. 373 21.2 Other Energy Components, Work Done by Voltage Sources, and the Helmholtz Free Energy.373 21.3 Capacitance of a Spherical Conductive Island. 374 21.4 Dependence of Charging Energy on the Island Size andCoulomb Blockade Effect. 374 21.5 Orthodox Theory of Single-Electron Thnneling. 375 21.5.1 Thnnel Junction.375 21.5.2 Minimum TUnnel Resistance. 376 21.5.3 Conductive Island with Two Thnnel Junctions.377 21.5.4 Coupling a Gate Electrode to the Double Thnnel
Junction.384 21.6 Single-Electron Transistor Fabrication by Nanowire-Based Process. 390 21.7 Discussion and Conclusions. 390 Illustrative Exercises. 393 References. 394 22 Heterostructure Optoelectronic Devices. 395 22.1 Heterojunction Laser Diode. 395 22.1.1 Double Heterostructure Laser. 395 22.1.2 Quantum Well Laser. 396 22.2 Quantum Well and Barrier Layer Structures in
LEDs. 399 22.2.1 Effect of Thickness of the Quantum Barrier Layer in Multiple Quantum Well GaN LEDs.399 22.2.2 Suppression of the QCSE by Silicon Doping of Quantum Barriers. 399 22.2.3 Effect of the Number of Quantum Wells on LED Performance.401 22.2.4 Overcoming Auger Recombination-Engendered Efficiency Reduction in MQW LEDs by Linearly Graded InN Composition Profile.401 22.3 Quantum Well Solar Cell. 402 22.4 Discussion and Conclusions.402 Illustrative Exercises. 405 References.406 Index ,407
This introductory text develops the reader's fundamental understanding of core principles and experimental aspects underlying the operation ot nanoelectronic devices. The author makes a thorough and systematic presentation of electron transport in quantumconfined systems such as quantum dots, quantum wires, and quantum wells together with Landauer-Biittiker formalism and nonequilibrium Green's function approach. The coverage encompasses nanofabrication techniques and characterization tools followed by a comprehensive exposition of nanoelectronic devices including resonant tunneling diodes, nanoscale MOSFETs, carbon nanotube FETs. high-electron-mobility transistors, single-electron transistors, and heterostructure optoelectronic devices. The writing throughout is simple and straightforward, with clearly drawn illustrations and extensive self-study exercises for each chapter. • Introduces the basic concepts underlying the operation of nanoelectronic devices. • Offers a broad overview of the field, including state-of-the-art developments. • Covers the relevant quantum and solid-state physics and nanoelectronic device principles. • Written in lucid language with accessible mathematical treatment. • Includes extensive end-ot-chapter exercises and many insightful diagrams. Physics in informa business CRC Press Taylor Francis Croup an Informa business ISBN 978-0-8153-8426-7 9780815384267 |
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| dewey-full | 621.381 |
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| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | First edition |
| format | Book |
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| index_date | 2024-07-03T15:56:23Z |
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| isbn | 9780815384267 9780367504038 |
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| spelling | Khanna, Vinod Kumar 1952- Verfasser (DE-588)129277800 aut Introductory nanoelectronics physical theory and device analysis Vinod Kumar Khanna First edition Boca Raton ; London ; New York CRC Press 2021 xxxv, 410 Seiten Illustrationen, Diagramme 28 cm txt rdacontent n rdamedia nc rdacarrier Enthält Literaturangaben Nanoelectronics Nanoelectronics Problems, exercises, etc Nanoelektronik (DE-588)4732034-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Mesoskopisches System (DE-588)4280799-2 gnd rswk-swf Nanostruktur (DE-588)4204530-7 gnd rswk-swf Nanoelektronik (DE-588)4732034-5 s Mesoskopisches System (DE-588)4280799-2 s Nanostruktur (DE-588)4204530-7 s Quantenmechanik (DE-588)4047989-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-351-20467-5 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032407220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032407220&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Khanna, Vinod Kumar 1952- Introductory nanoelectronics physical theory and device analysis Nanoelectronics Nanoelectronics Problems, exercises, etc Nanoelektronik (DE-588)4732034-5 gnd Quantenmechanik (DE-588)4047989-4 gnd Mesoskopisches System (DE-588)4280799-2 gnd Nanostruktur (DE-588)4204530-7 gnd |
| subject_GND | (DE-588)4732034-5 (DE-588)4047989-4 (DE-588)4280799-2 (DE-588)4204530-7 |
| title | Introductory nanoelectronics physical theory and device analysis |
| title_auth | Introductory nanoelectronics physical theory and device analysis |
| title_exact_search | Introductory nanoelectronics physical theory and device analysis |
| title_exact_search_txtP | Introductory nanoelectronics physical theory and device analysis |
| title_full | Introductory nanoelectronics physical theory and device analysis Vinod Kumar Khanna |
| title_fullStr | Introductory nanoelectronics physical theory and device analysis Vinod Kumar Khanna |
| title_full_unstemmed | Introductory nanoelectronics physical theory and device analysis Vinod Kumar Khanna |
| title_short | Introductory nanoelectronics |
| title_sort | introductory nanoelectronics physical theory and device analysis |
| title_sub | physical theory and device analysis |
| topic | Nanoelectronics Nanoelectronics Problems, exercises, etc Nanoelektronik (DE-588)4732034-5 gnd Quantenmechanik (DE-588)4047989-4 gnd Mesoskopisches System (DE-588)4280799-2 gnd Nanostruktur (DE-588)4204530-7 gnd |
| topic_facet | Nanoelectronics Nanoelectronics Problems, exercises, etc Nanoelektronik Quantenmechanik Mesoskopisches System Nanostruktur |
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