Principles of Electron Tunneling Spectroscopy

Second Edition

E. L. Wolf Polytechnic Institute of New York University, USA

OXFORD UNIVERSITY PRESS

Contents

1 Introduction 1.1 Concepts of quantum mechanical tunneling 1.2 Occurrence of tunneling phenomena 1.3 Electron tunneling in solid-state structures 1.4 Superconducting (quasipartide) and Josephson (pair) tunneling 1.5 Tunneling spectroscopies 1.6 The scanning tunneling microscope (STM): spectroscopic images 1.7 Atomic spatial resolution in the scanning tunneling microscope 1.8 Density of electron states (DOS) measurement in STM: STS 1.9 Perspective, scope, and organization

2 Tunneling in normal-state structures: I 2.1 Introduction 2.2 Calculational methods and models

2.2.1 Stationary-state calculations 2.2.2 Transfer Hamiltonian calculations 2.2.3 Ideal barrier transmission

2.3 Basic junction types 2.3.1 Metal-insulator-metal junctions 2.3.2 Metal-insulator-semiconductor junctions 2.3.3 Schottky barrier junctions 2.3.4 pn junction (Esaki diode)—direct case and the Si-Ge diode 2.3.5 Vacuum tunneling 2.3.6 Vacuum tunneling from a spherical STM tip

2.4 Dependence of J(V) and G(V) on band structure and density of states 2.4.1 Fermi surface integrals 2.4.2 Prefactors: wavefunction matching at boundaries

2.5 Nonideal barrier transmission 2.5.1 Approach to ideal behavior 2.5.2 Resonant barrier levels 2.5.3 Two-step tunneling 2.5.4 Barrier interactions

2.6 Assisted tunneling processes 2.7 Comments on the time for tunneling 2.8 Resolution obtained from a scanning tunneling microscope tip

2.8.1 Tersoff and Hamann's model of STM resolution 2.8.2 C. Julian Chen's atomic model of STM resolution

3 Spectroscopy of the superconducting energy gap: quasipartide and pair tunneling 3.1 Basic experiments of Giaever and Josephson tunneling 3.2 Superconductivity 3.3 Electron-phonon coupling and the BCS theory

xi

CONTENTS

3.3.1 The pair ground state 96 3.3.2 Elementary excitations of superconductors 100 3.3.3 Generalizations of BCS theory 101

3.4 Theory of quasiparticle and pair tunneling 103 3.5 Gap spectra of equilibrium BCS superconductors 112 3.6 Gap spectra in more general homogeneous equilibrium superconductor cases 121

3.6.1 Strong-coupling superconductors 121 3.6.2 Gap anisotropy 124 3.6.3 Multiple gaps, two-band superconductivity 128 3.6.4 Excess currents, subharmonic structure 130 3.6.5 Effects of magnetic field 138 3.6.6 Magnetic impurities 145 3.6.7 Pressure effects 147 3.6.8 Interactions with electromagnetic radiation 150 3.6.9 Superconducting fluctuations 158

3.7 Ultrathin-film and small-particle superconductors 160 3.8 Transition from tunnel junction to metallic contact 170

3.8.1 Model of Klapwijk, Blonder, and Tinkham 171

Conventional tunneling spectroscopy of strong-coupling superconductors 173 4.1 Introduction 173 4.2 Eliashberg-Nambu strong-coupling theory of superconductivity 173 4.3 Tunneling density of states 177 4.4 Quantitative inversion for a2F(<w): test of Eliashberg theory 178 4.5 Extension to more general cases 182

4.5.1 Finite temperature 182 4.5.2 Anisotropy 185 4.5.3 Spin fluctuations 187 4.5.4 Electronic density-of-states variation 190

4.6 Limitations of the conventional method 194

Inhomogeneous superconductors: the superconducting proximity effect 197 5.1 Introduction: continuity of the pair wavefunction 197 5.2 Andreev reflection and specular SNS junctions 199 5.3 Survey of phenomena in proximity tunneling structures 206 5.4 Specular theory of tunneling into proximity structures 212 5.5 McMillan's tunneling model of bilayers 223 5.6 The Usadel equations and diffusive SNS junctions 228

5.6.1 Reduction of Gor'kov's equations by Eilenberger and Usadel 228 5.6.2 Application of reduced Gor'kov theory to tunneling problems 229 5.6.3 The experiment of Truscott and Dynes confirming the bound state in clean NS

junctions 230 5.6.4 The experiment of le Sueur et al.: phase dependence of the density of states 231 5.6.5 Proximity effects in a ferromagnetic N layer, in an NS structure 235

5.7 Proximity electron tunneling spectroscopy (PETS) 236 5.8 Effects of elastic scattering in the N layer 245 5.9 Proximity corrections to conventional results 250 5.10 Further applications of proximity effect models 251

CONTENTS xiii

6 Superconducting phonon spectra and a2F(co) 256 6.1 Introduction 256 6.2 s-p band elements 256 6.3 Crystalline s-p band alloys and compounds 263

6.3.1 Crystalline s-p band alloy superconductors 263 6.3.2 s-p band compounds 270

6.4 Amorphous metals 273 6.5 Transition metals, alloys, and compounds 281 6.6 Extreme weak-coupling metals 291 6.7 Local-mode and resonance-mode superconductors 295 6.8 Systematics of superconductivity 298 6.9 Effects of external conditions and parameters on strong-coupling features 302 6.10 Eliashberg inversion of bismuthate and cuprate superconductor

tunneling data 306

7 High-7^ electron-coupled superconductivity: cuprate and iron-based superconductors 310 7.1 The discovery of cuprate superconductivity by Bednorz and Müller 312 7.2 The Mott antiferromagnetic CuÜ2 insulator and its doping to a metal 313

7.2.1 Paired holes in copper oxide planes 313 7.2.2 Hubbard and t-J models in two dimensions 316

7.3 Hole-doped cuprates Bi2212 and YBCO 317 7.3.1 Phase diagram for superconductivity in hole-doped cuprate 317 7.3.2 Crystal structures of common cuprates: I 318 7.3.3 Early tunneling measurements on hole-doped superconductors 319

7.4 Crystal structures of common cuprates: II 325 7.4.1 Range of Tc vs. number of copper oxide planes 325 7.4.2 Disorder sites and doping of cuprate superconductors 325 7.4.3 Comments on disorder and inhomogeneity in STS images 327

7.5 Andreev-St. James tunneling spectroscopy 328 7.6 Experimental signatures of nodal superconductivity 328

7.6.1 Specific heat at transition 330 7.7 Josephson junctions in d-wave cases 332 7.8 Further examples of non-BCS superconductors 335

8 Tunneling in normal-state structures: II 336 8.1 Introduction 336 8.2 Final-state effects: I 336

8.2.1 Two-dimensional final states 336 8.2.2 Quantum size effects in metal films 338 8.2.3 Accumulation layers at semiconductor surfaces 339 8.2.4 Spin-polarized tunneling as a probe of ferromagnets 343 8.2.5 Julliere's model of ferromagnetic tunnel junctions 350 8.2.6 Other bulk band structure effects 352

8.3 Assisted tunneling: threshold spectroscopies 357 8.3.1 Phonons 358 8.3.2 Inelastic electron tunneling spectroscopy of molecular

vibrations 366 8.3.3 Inelastic excitations of spin waves (magnons) 367 8.3.4 Inelastic excitation of surface and bulk plasmons 368 8.3.5 Light emission by inelastic tunneling 369 8.3.6 Spin-flip and Kondo scattering 372 8.3.7 Excitation of electronic transitions 378

CONTENTS

8.4 Final-state effects: II 384 8.4.1 More general many-body theories of tunneling 384 8.4.2 Tunneling studies of electron correlation and localization in metallic systems 389 8.4.3 Phonon self-energy effects in degenerate semiconductors 394 8.4.4 Electron scattering in the Kondo ground state 401

8.5 Zero-bias anomalies 407 8.5.1 Giant resistance peak 407 8.5.2 Semiconductor conductance minima 409 8.5.3 Assorted maxima and minima in metals 411 8.5.4 The Giaever-Zeller resistance peak model 414

9 Scanning tunneling spectroscopy (STS) of single atoms and molecules 419 9.1 Theory of observation of single atoms in STS and experiment 419 9.2 Friedel oscillations in 2-D surface state 422

9.2.1 Effect of surface state: inference of wavevector 425 9.2.2 Fourier-transform STM/STS 425

9.3 Quantum corrals 426 9.3.1 Elliptical corrals and focusing effects: quantum mirage 427

9.4 Pair-breaking single adatoms on superconductors 429 9.4.1 Mn and Cr on Pb 430 9.4.2 Zn impurity atoms imaged in cuprate planes 431

9.5 Spectroscopy of Kondo and spin-flip scattering 432 9.5.1 Introduction 432 9.5.2 Kondo spectroscopy of a single trapped electron 433 9.5.3 Spectroscopy of localized moments in Si: As Schottky junctions 435 9.5.4 Comparison of the two Kondo spectroscopy experiments 436

9.6 STM spectroscopy of magnetic adatoms 436 9.7 Molecules and their vibrational spectra 443

10 Scanning tunneling spectroscopy of superconducting cuprates and magnetic manganites 447 10.1 Gap imaging of optimally doped cuprates 447

10.1.1 Site dependence of apparent gap 447 10.1.2 Overdoped case 449 10.1.3 Anticorrelation of gap and zero-bias density of states 449 10.1.4 Internal proximity effect 449

10.2 Localized state at Zn impurity 452 10.3 Model for spectral distortions of noncuprate layers 456 10.4 Superlattice modulation in Bi2212 45 8 10.5 Fourier-transform STS (FT-STS) and application 460 10.6 Observations of charge ordering in cuprate superconductors 460 10.7 Relation of STS to angle-resolved photoemission spectroscopy (ARPES) 464 10.8 Evidence for electron-spin wave coupling 467 10.9 Colossal magnetoresistance: Mott transition in doped manganites 470

10.9.1 Introduction: mechanism of colossal magnetoresistance (CMR) 470 10.9.2 Pseudogap in manganite LSMO observed by ARPES 472

10.10 Relation of cuprates to ferromagnetic CMR manganites 473

11 Applications of barrier tunneling phenomena 475 11.1 Introduction 475 11.2 Josephson junction interferometers 477

CONTENTS

11.3 SQUID detectors: the scanning SQUID microscope 11.3.1 Establishing d-wave nature of cuprate pairing

11.4 Josephson junction logic: rapid single-flux quantum devices 11.4.1 The single-flux quantum voltage pulse 11.4.2 Analog to digital conversion (ADC) using RSFQ logic

11.5 Detection of radiation 11.5.1 SIS detectors 11.5.2 Josephson effect detectors 11.5.3 Optical point-contact antennas (high-speed MIM junctions)

11.6 Tunnel-junction magnetoresistance sensors

Appendix A Experimental methods of junction fabrication and characterization

A. 1 Thin-film electrodes A. 1.1 Evaporated films A. 1.2 Film thickness measurement A. 1.3 Substrate temperature A. 1.4 Sputtered films A. 1.5 Chemical vapor-deposited films A. 1.6 Epitaxial single-crystal films A. 1.7 Atomic layer deposition

A.2 Foil and single-crystal electrodes A.3 Characterization of tunneling electrodes A.4 Preparation of oxide tunneling barriers

A.4.1 Thermal oxide barriers A.4.2 Plasma oxidation processes

A.5 Artificial barriers A.5.1 Totally oxidized metal overlayers A.5.2 Directly deposited artificial barriers A.5.3 Polymerized organic films

A.6 Point-contact barrier tunneling methods A.6.1 Anodized metal probes A.6.2 Schottky barrier probes A.6.3 Deformable metal vacuum tunneling probes A.6.4 Analysis of point-contact data

A.7 Characterization of tunnel junctions A.7.1 Initial characterization of junctions A.7.2 Derivative measurement circuitry

Appendix B Methods of scanning tunneling spectroscopy and competing approaches

B.l STM basics, tip production, and characterization; single atom tips B.2 Noise-free x, y, z translation; vibration isolation

B.2.1 The cryogenic STM of Wilson Ho B.2.2 The 240-mK STM design of Pan, Hudson, and J. C. Davis

B.3 Atomic force microscope; combination STM/AFM B.4 Scanning tunneling potentiometry and point-contact measurements B.5 Ballistic electron emission microscopy (BEEM) B.6 Scanning charge microscopy and spectroscopy

B.6.1 Scanning single-electron-transistor electrometry B.6.2 Scanning subsurface charge accumulation microscopy: STM/SCAM B.6.3 Single electron capacitance spectroscopy

B.7 Scanning Hall probe microscopy

xvi CONTENTS

Appendix C Tabulated results 542 Table C. 1 s, p elements 543 Table C.2 Alloys and unusual phases: s, p elements 544 Table C.3 d-band elements 545 Table C.4 d-band alloys, oxides, and compounds 546 Table C.5 f-band elements 548 Table C.6 Metal overlayers for barrier formation 548 Table C.7 Studies of Tomasch oscillations in thick superconducting films

and of McMillan-Rowell oscillations in thick normal films 548 Table C.8 Tunneling studies of superconductor phonons under hydrostatic

pressure 548 Tables C.9 Cuprate superconductors 549

Table C.9a Gap values for Bi2Sr2CaCu208+(s (Bi2212) 549 Table C.9b Gap values for YBa2Cu307+,5 550 Table C.9c Gap values for HgBa2Ca„_iCun02n+2+,5 551

References 553

Index 583