Fluctuation Mechanisms in Superconductors (eBook)

Holger Bartolf studied Solid State Physics at the Universities of Karlsruhe and Zürich. In 2011 he relocated at the Swiss Corporate Research Center of a leading company in power and automation technologies where his current interests focus on the applied R&D of the next generation of power semiconductors.

Preface - Vortex-Fluctuation andSingle-Photon Detection with a Nanowire 7
Physical Background 7
Personal Remarks 9
The Scope and Organization of this Book 11
Acknowledgment, Motivation and Funding 13
References 14
Contents 15
Chapter 1 Introduction 20
1.1 Quantum Nature and its Detection 20
1.1.1 Thermal Detectors 21
1.1.2 Ionization Detectors 23
1.2 Cryogenic Quantum Detectors at the Beginning of the 21st Century 24
1.2.1 Transition-Edge Sensors TES 26
1.2.2 Kinetic-Inductance Detectors KID 27
1.2.3 Superconducting Tunnel Junction Detectors STJD 28
1.2.4 Superconducting Nanowire Single-Photon Detectors SNSPD 29
References 33
Part I Nanoscale Manufacturing Process Developments 41
Chapter 2 Considerations for Nanoscale Manufacturing 42
Chapter 3 Superconducting Thin-Film Preparation 44
3.1 DC-Magnetron Sputtering 44
3.1.1 The Physics of a DC Plasma Discharge 44
3.1.2 Magnetron Sputtering of NbN Thin Films 47
3.1.3 Magnetron Sputtering of Additional Superconducting Films 49
3.2 Electron-Beam Evaporation 50
References 51
Chapter 4 Nanoscale-Precise Coordinate System: Scalable, GDSII-Design 54
4.1 Process Layers 55
4.2 Structure References 57
References 59
Chapter 5 Thin-Film Structuring 60
5.1 Easy and Effective Nanoscaled Top-Down Manufacturing 61
5.2 Organic Resists 63
5.2.1 Resist Properties 63
5.2.2 Resist Fabrication: Spin Coating 64
5.3 Microscale Fabrication: Contact Photolithography 65
5.3.1 Principle of Photolithography 65
5.3.2 Physical Limit of Contact Photolithography 67
5.3.3 Perfect Contact Utilizing Newton’s Interference Rings 68
5.3.4 Additive and Subtractive Lithographic Pattern Transfer 70
5.3.5 Alignment Structures 73
5.3.6 Controlling the Undercut during Development 74
5.3.7 Critical Dimensions & Resist Profile
5.4 Nanoscale Fabrication: Electron-Beam Lithography 78
5.4.1 The Electron-Matter Interaction 79
5.4.2 Discrete Beam-Deflection, Exposure Dose and Dynamic Effects 82
5.4.3 Alignment of the Stage Relative to the Beam 84
5.4.4 Clearing-Dose Determination (PMMA950 k) 87
5.4.5 PMMA950 k to Obtain a Lift-Off Profile: Critical Dimension 10nm 89
5.4.6 Proximity Effect Model(s) 91
5.4.7 Simulated Proximity-Effect Correction 94
5.4.8 Manufacturing in the Sub - 100nm RegimeWithout Correctionfor the Proximity Effect 99
5.4.9 ZEP 520A Etch Protection Layer: Critical Dimension 60nm 102
5.5 Symbiotic Optimization of the Nanolithography and RF-Plasma Etching 105
5.6 Reactive Ion Etching 108
5.6.1 Proper Operation of the Radio-Frequency Discharge 108
5.6.2 Etching Rate Determination 111
5.6.3 Etched Photolithographic Critical Dimensions 115
5.7 The 50nm Scale Compared to the Bit-Pattern on a Compact-Disk 117
Appendix 5.1: Phenomenological Electron-Beam Proximity Effect 120
Appendix 5.2: CASINO: Monte Carlo Simulation of the Electron-Matter Interaction 122
References 123
Chapter 6 Device Manufacturing 130
6.1 Fabrication Process Chains 130
6.2 Postfabrication Procedures: Sawing & Wire Bonding
6.3 Manufacturing Twenty Devices in One Run: Small Scale Production 133
References 135
Chapter 7 Proof of Principle of the Above Described Approach 136
7.1 30nm Wide Au-Bridge 136
7.2 Superconducting Nb and NbN Meander 137
References 139
Part II Nanoscaled Superconductivity and its Application in Single-Photon Detectors 143
Chapter 8 Motivation for Part II 144
References 146
Chapter 9 Metallic and Superconducting States 147
9.1 Quantum Nature of the Solid State 147
9.2 Low-Temperature Superconductivity 150
9.2.1 Phenomenological London Theory 150
9.2.2 The Role of the Phonons:Weakly- and Strongly-Coupled Superconductors 152
9.2.3 Microscopic Bardeen-Cooper-Schrieffer (BCS) Theory 152
9.2.4 Depairing Critical Current 155
9.2.5 Phenomenological Ginzburg-Landau Theory 157
9.2.6 About Type-II Superconductivity 157
9.2.7 Ginzburg-Landau and BCS Theory (Clean- and Dirty Limit) 160
9.3 NbN Thin Films: Extremely Dirty Type-II Superconductors 162
9.3.1 Coherence Length, Diffusivity & Resistivity
9.3.2 Energy Gap for Strongly-Coupled NbN 164
9.3.3 Magnetic Penetration Depth 164
9.3.4 Depairing-Critical Current in NanoscaledWires 165
9.3.5 Current-Dependence of the Energy Gap 169
Appendix 9.1: BCS Energy-Gap Formulæ 170
Appendix 9.2: Clean & Dirty Limit Expressions for theCharacteristic Length Scales of a BCS-Superconductor
Appendix 9.3: Quasiparticle Diffusivity in the Dirty Limit 181
Appendix 9.4: Thermodynamic Critical Field 182
Appendix 9.5: Depairing Critical Current Density 186
References 190
Chapter 10 Fluctuation Mechanisms in Superconductors 195
References 197
Chapter 11 Static Electronic Transport Measurements 199
11.1 Low Current Resistivity Measurements 199
11.2 Weak-Localization and Fluctuation Paraconductivity 200
11.3 Resistivity Measurements in a Magnetic Field 204
11.4 Vortex-Dissipation: BKT vs. Edge-Barrier Model 204
11.5 Critical-Current Measurements 211
11.6 Tables of Measured Sample and Material Parameters 212
Appendix 11.1: BKT Resistance for Finite Size Systems 217
References 219
Chapter 12 Theoretical Models of Current-Induced Fluctuations 223
12.1 Berezinskii-Kosterlitz-Thouless (BKT) Transition:Current-Assisted Thermal Unbinding of Vortex-Antivortex Pairs 223
12.2 Edge Barrier for Thermal and Quantum-Mechanical Vortex-Entry 225
12.2.1 Thermally-Induced Vortex Hopping 226
12.2.2 Quantum-Mechanical Vortex Tunneling 228
12.2.3 Cross-Over Temperature Tco 229
12.3 Thermal and Quantum Phase-Slip Mechanisms 229
12.4 Energy Scales for Fluctuations 231
12.5 Table of Calculated Model Parameters 233
12.6 Prediction of Fluctuation-Rates 234
Appendix 12.1: Minimum Energy of VAP under Bias 234
Appendix 12.2: Vortex-Entry Barrier Formalism 238
Appendix 12.3: Phase-Slip Formalism (LAMH Theory) 241
References 250
Chapter 13Time-Resolved Photon- andFluctuation Detection 253
13.1 Detailed Model of the Detection Mechanism 253
13.2 Experimental Setup 257
13.2.1 Electronics 257
13.2.2 Single-Pulses Induced by Thermal Fluctuations 258
13.3 Dark Counts: Harbingers of the Current-Induced Transition into the Metallic State 261
13.4 Detection of Single-Photons in the400nm- 3 ?m Spectral Region 264
13.4.1 Photon Source 264
13.4.2 Analysis 265
13.4.3 Spectral Sensitivity 266
13.4.4 Count Rate at ? = 400nm 267
13.4.5 Conclusion from Photon Detection 269
Appendix 13.1: Single-Photon Detection by a SNSPD 269
References 271
Concluding Remarks and Recent Nanowire Developments 274
References 286
Fundamental Constants, Units*, Prefixes 292
List of Symbols 294
References 306
List of Abbreviations 307
List of Figures 310
List of Tables 313
Appendix Manufacturing Process Recipe 314
About the Author 327
Index 329