Introducing Molecular Electronics (eBook)

Foreword 6
Preface 8
Contents 10
List of Contributors 16
Introducing Molecular Electronics: A Brief Overview 21
1 A Passage Through Time: Past, Present and Future Challenges 21
2 What You Find in the Book – a Passage Through Its Contents 24
3 What is not Included in the Book – Literature Hints 26
Acknowledgements 28
References 28
Part I Theory 31
Foundations of Molecular Electronics – Charge Transport in Molecular Conduction Junctions 33
1 Prologue 33
2 Theoretical Approaches to Conductance 38
3 The Relationship Between Electron Transfer Rates and Molecular Conduction 41
4 Interaction with Nuclear Degrees of Freedom 42
4.1 Timescale Issues 43
4.2 Transition from Coherent to Incoherent Motion 44
4.3 Heating and Heat Conduction 47
4.4 Inelastic Electron Tunneling Spectroscopy (IETS) 51
5 Remarks and Generalities 53
5.1 Electron Transfer and Conductance: Common Issues 53
5.2 Junction Conductance 54
Acknowledgements 64
References 65
AC-Driven Transport Through Molecular Wires 75
1 Introduction 75
2 Basic Concepts 76
2.1 Model for Driven Molecular Wire Coupled to Leads 76
2.2 Current Through Static Molecular Wire 78
3 Floquet Approach to the Driven Transport Problem 79
3.1 Retarded Green Function 80
3.2 Current Through the Driven Molecular Wire 81
4 Weak-Coupling Approximations 85
4.1 Asymptotic Weak Coupling 85
4.2 Master-Equation Approach 86
5 Photon-Assisted Transport Across a Molecular Bridge 90
6 Conclusions 92
Acknowledgements 93
References 93
Electronic Structure Calculations for Nanomolecular Systems 97
1 Electronic Structure of Nanomolecular Systems 97
2 Selected Applications of Ground-State Electronic Structure Calculations by DFT 99
2.1 Carbon Nanotubes 100
2.2 Model and Realistic DNA-Base Stacks 103
3 Linear Response by TDDFT 108
3.1 Excitation Energies in TDDFT 109
3.2 Comments 112
3.3 Selected Applications of TDDFT 113
4 Wannier Functions for Electronic Structure Calculations 117
4.1 Selected Applications of Wannier Computationin Nanostructures 118
Acknowledgements 126
References 127
Ab-initio Non-Equilibrium Green’s Function Formalism for Calculating Electron Transport in Molecular Devices 137
1 Introduction 137
2 Mean Field Electronic Structure Theory 138
3 Application of DFT to Modeling Molecular Electronics Devices 140
3.1 The Screening Approximation 142
3.2 Calculating the Charge Density Using Green’s Functions 144
3.3 Taking into Account the Electrode Region Through a Self Energy 146
3.4 Calculation of the Electrode Green’s Function 147
3.5 Integrating the Spectral Density with a Complex Contour 148
3.6 Non-Equilibrium Green’s Functions for Finite Bias 148
3.7 Calculating the Effective Potential from the Electron Density 150
3.8 The Complete Self-Consistent Algorithm for the NEGF Calculation 151
3.9 Electron Transport Coe.cients and Currents Obtained from the Green’s Function 153
4 Implementation: McDCAL, TranSIESTA, and Atomistix Virtual NanoLab 154
5 Resistance of Molecular Wires 155
6 Non-Equilibrium Forces 161
7 Conclusion 167
References 167
Tight-Binding DFT for Molecular Electronics (gDFTB) 173
1 Introduction 173
2 The Self-Consistent Density-Functional Tight-Binding 175
3 Setup of the Transport Problem 177
4 The Green’s Function Technique 179
5 The Relationship with the Keldysh Green’s Functions 180
6 The Terminal Currents 183
7 The Poisson Equation 184
8 Atomic Forces 185
9 gDFTB Example Applications 187
10 Incoherent Electron-Phonon Scattering 189
11 Comments on DFT Applied to Transport 199
12 Conclusions 200
References 201
Current-Induced Effects in Nanoscale Conductors 205
1 Current Through a Nanoscale Junction 205
2 Current-Induced Forces 208
3 Shot Noise 210
4 Local Heating 214
5 Inelastic Conductance 220
6 Conclusions 222
Acknowledgements 222
References 222
Single Electron Tunneling in Small Molecules 227
1 Introduction 227
2 Tunneling Transport 228
2.1 Current and Shot-Noise Spectroscopy 228
2.2 Master Equations Current and Shot-Noise 230
3 Electronic Excitations of a Benzene Ring 233
4 Spin Excitations of a [2 × 2] Grid Molecule 235
5 Vibrational Excitations and Multiple Orbitals 239
6 Current Noise (Shot Noise) 242
7 Conclusions 245
Acknowledgments 246
References 246
Transport through Intrinsic Quantum Dots in Interacting Carbon Nanotubes 249
1 Introduction 249
2 Electrical Transport in Individual SWNTs 250
2.1 Field Theory of a Clean SWNT 250
2.2 Double Barrier Problem in a TLL 253
3 Markovian Master Equation Approach 256
3.1 Rate Equations 256
3.2 Conductance Peak Height 258
4 Quantum Monte Carlo Simulations 262
4.1 Dynamical Simulations 262
4.2 Strong Barrier Transmission 262
4.3 Weak Barrier Transmission 264
5 Conclusions 266
Acknowledgments 267
References 267
Part II Experiment 271
Contacting Individual Molecules Using Mechanically Controllable Break Junctions 273
1 Introduction 273
2 Experimental Techniques 275
2.1 Fabrication of the Electrodes 275
2.2 Deposition of Molecules 277
2.3 Measurement Techniques 279
3 Simple Molecules 279
4 Molecules Bonded by Thiol Groups to Gold 286
4.1 Low Temperatures 290
5 Conclusions and Prospects 291
Acknowledgements 291
References 291
Intrinsic Electronic Conduction Mechanisms in Self-Assembled Monolayers 295
1 Introduction 295
2 Experiment 297
3 Theoretical Basis 299
3.1 Possible Conduction Mechanisms 299
3.2 Tunneling Models 300
4 Results 302
4.1 Current-Voltage Characteristics 302
4.2 Inelastic Tunneling 308
5 Conclusions 315
Acknowledgements 316
References 316
Making Contacts to Single Molecules: Are We There Yet? 321
1 Introduction 321
2 Contact Resistance in NP Contact Experiments 323
3 Changing the NP Size 327
Acknowledgements 330
References 330
Six Unimolecular Recti.ers and What Lies Ahead 333
1 Introduction 333
2 Metal Contacts 338
3 The Aviram-Ratner Ansatz 338
4 Three Processes for Recti.cation by Organic Monolayers 340
5 Current and Resistance Across a Metal-Molecule-Metal System 341
6 Assembly Techniques: Physisorption Versus Chemisorption 342
7 The “Organic Recti.er Project” 343
8 Electrical Properties of Monolayers and Multilayers 345
9 Rectification of C16H33Q-3CNQ 345
10 Molecular Properties of C16H33Q-3CNQ 346
11 Film Properties of C16H33Q-3CNQ 347
12 Metal – LB Film – Metal Sandwiches of C16H33Q-3CNQ 348
13 Unimolecular Recti.cation by C16H33Q-3CNQ 349
14 Chemisorbed Monolayer Recti.ers 352
15 Three More Recti.ers 355
16 Direction of “Forward Current” in Recti.ers 358
17 Challenges for the Near Future 359
18 Conclusion 363
19 End-Notes 363
Acknowledgments 364
References 364
Quantum Transport in Carbon Nanotubes 371
1 Introduction 371
2 Synthesis 372
3 The Structure of Carbon Nanotubes 374
3.1 Lattice Structure 374
3.2 Structural Investigations of Carbon Nanotubes 374
4 Electronic Structure of Nanotubes 378
4.1 Energy Dispersion and Density of States of Graphene 378
4.2 Band Structure and Density of States of Carbon Nanotubes 379
5 Electron Transport Experiments 381
5.1 Electric Contacts 381
5.2 Ballistic Transport 383
5.3 Diffusive Transport 384
5.4 Effects of the Electron-Electron Interaction 388
6 Conclusions 395
Acknowledgements 395
References 395
Carbon Nanotube Electronics and Optoelectronics 401
1 Introduction 401
2 Schottky Barrier Carbon Nanotube Transistors 402
2.1 Needle-Like Contact Model 404
2.2 In.uence of the Contact Geometry 408
2.3 Effect of Gas Adsorption 410
2.4 Scaling of the SB-CNFET Performance 413
2.5 Scaling of the Drain Voltage 418
2.6 Light-Emission from a SB-CNFET 423
3 Conclusions and Outlook 426
Acknowledgements 427
References 427
Charge Transport in DNA-based Devices 431
1 Introduction 431
2 Direct Electrical Transport Measurements in DNA 435
2.1 Single Molecules 437
2.2 Bundles and Networks 451
2.3 Conclusions from the Experiments about DNA Conductivity 455
3 Conclusions and Perspectives 456
Acknowledgements 458
References 458
Part III Outlook 465
CMOL: Devices, Circuits, and Architectures 467
1 Introduction 467
2 Devices 469
3 Circuits 472
4 CMOL Memories 475
5 CMOL FPGA: Boolean Logic Circuits 480
6 CMOL CrossNets: Neuromorphic Networks 487
7 Conclusions 494
Acknowledgements 494
References 494
Architectures and Simulations for Nanoprocessor Systems Integrated on the Molecular Scale 499
1 Introduction 499
2 Starting at the Bottom: Molecular Scale Devices in Device-Driven Architectures for Nanoprocessors 502
3 Challenges for Nanoelectronics in Developing Nanoprocessors 505
3.1 Overview 505
3.2 Challenges Posed by the Use of Conventional Microprocessor Architectures 506
3.3 Challenges in the Development of Novel Nanoprocessing Architectures 506
4 A Brief Survey of Nanoprocessor System Architectures 510
4.1 Overview 510
4.2 Migration of Conventional Processor Architectures to the Molecular Scale 510
4.3 Overview of Novel Architectures for Nanoelectronics 513
5 Principles of Nanoprocessor Architectures Based on FPGAs and PLAs 516
5.1 Overview 516
5.2 Description of Regular Arrays, FPGAs, and PLAs: Advantages and Challenges 516
5.3 The DeHon-Wilson PLA Architecture 517
6 Sample Simulation of a Circuit Architecture for a Nanowire-Based Programmable Logic Array 519
6.1 Methodology for the Simulation and Analysis of Nanoprocessors 519
6.2 Device Models for System Simulation of the DeHon-Wilson NanoPLA 520
6.3 Simulations and Analyses of the NanoPLA 521
6.4 Further Implications and Issues for System Simulations 524
7 Conclusion 525
References 526
Index 533
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CMOL: Devices, Circuits, and Architectures (p. 447-448)

Konstantin K. Likharev and Dmitri B. Strukov
Stony Brook University, Stony Brook, NY 11794, USA

Abstract. This chapter is a brief review of the recent work on various aspects of the prospective hybrid semiconductor/nanowire/molecular ("CMOL") integrated circuits. The basic idea of such circuits is to combine the advantages of the currently dominating CMOS technology (including its flexibility and high fabrication yield) with those of molecular devices with nanometer-scale footprint. Two-terminal molecular devices would be self-assembled on a pre-fabricated nanowire crossbar fabric, enabling very high function density at acceptable fabrication costs. Preliminary estimates show that the density of active devices in CMOL circuits may be as high as 1012 cm-2 and that they may provide an unparalleled information processing performance, up to 1020 operations per cm2 per second, at manageable power consumption. However, CMOL technology imposes substantial requirements (most importantly, that of high defect tolerance) on circuit architectures. In the view of these restrictions, the most straightforward application of CMOL circuits is terabitscale memories, in which powerful bad-bit-exclusion and error-correction techniques may be used to boost the defect tolerance.

The implementation of Boolean logic circuits is more problematic, though our preliminary results for reconfigurable, uniform FPGA-like CMOL circuits look very encouraging. Finally, CMOL technology seems to be uniquely suitable for the implementation of the "CrossNet" family of neuromorphic networks for advanced information processing including, at least, pattern recognition and classification, and quite possibly much more intelligent tasks. We believe that these application prospects justify a large-scale research and development effort focused on the main challenge of the field, the high-yield self-assembly of molecular devices.


1 Introduction

The recent spectacular advances in molecular electronics (for reviews see, e.g., 1–3 and other chapters of this collection), and especially the experimental demonstration of molecular single-electron transistor by several groups [4–8] give hope for the practical introduction, within the next 10 to 20 years, of the first integrated circuits with active single- or few-molecule devices. This long-expected breakthrough could not have arrived more timely. Indeed, the recent results [9,10] indicate that the current VLSI paradigm, based on a combination of lithographic patterning, CMOS circuits, and Boolean logic, can hardly be extended into a-few-nm region. The main reason is that at gate length below 10 nm, the sensitivity of parameters (most importantly, the gate voltage threshold) of silicon field-effect transistors (MOSFETs) to inevitable fabrication spreads grows exponentially. As a result, the gate length should be controlled with a few-angstrom accuracy, far beyond even the longterm projections of the semiconductor industry [11]. Even if such accuracy could be technically implemented using sophisticated patterning technologies, this would send the fabrication facilities costs (growing exponentially even now) skyrocketing, and lead to the end of Moore’s Law some time during the next decade.