Preface xi
Author Biographies xiv
List of Cited Tables and Figures xvi
1 Basic Electromagnetism 1
1.1 Introduction 1
1.2 Magnetic Force, Pole, Field, and Dipole 1
1.3 Magnetic Dipole Moment, Torque, and Energy 3
1.4 Magnetic Flux and Magnetic Induction 5
1.5 Ampere’s Circuital Law, Biot-Savart Law, and Magnetic Field from Magnetic Material 6
1.5.1 Ampere’s Circuital Law 6
1.5.2 Biot-Savart’s Law 8
1.5.3 Magnetic Field from Magnetic Material 10
1.6 Equations, cgs-SI Unit Conversion Tables 11
Homework 13
References 17
2 Magnetism and Magnetic Materials 19
2.1 Introduction 19
2.2 Origin of Magnetization 19
2.2.1 From Ampere to Einstein 19
2.2.2 Precession 21
2.2.3 Electron Spin 22
2.2.4 Spin-Orbit Interaction 24
2.2.5 Hund’s Rules 25
2.3 Classification of Magnetisms 28
2.3.1 Diamagnetism 30
2.3.2 Paramagnetism 30
2.3.3 Ferromagnetism 34
2.3.4 Antiferromagnetism 37
2.3.5 Ferrimagnetism 40
2.4 Exchange Interactions 42
2.4.1 Direct Exchange 43
2.4.2 Indirect Exchange: Superexchange 45
2.4.3 Indirect Exchange: RKKY Interaction 46
2.4.4 Dzyaloshinskii-Moriya Interaction (DMI) 48
2.5 Magnetization in Magnetic Metals and Oxides 49
2.5.1 Slater-Pauling Curve 49
2.5.2 Rigid Band Model 50
2.5.3 Iron Oxides and Iron Garnets 51
2.6 Phenomenology of Magnetic Anisotropy 51
2.6.1 Uniaxial Anisotropy 52
2.6.2 Cubic Anisotropy 53
2.7 Origins of Magnetic Anisotropy 54
2.7.1 Shape Anisotropy 55
2.7.2 Magnetocrystalline Anisotropy (MCA) 56
2.7.3 Perpendicular Magnetic Anisotropy (PMA) 57
2.8 Magnetic Domain and Domain Walls 57
2.8.1 Domain Wall 58
2.8.2 Single Domain and Superparamagnetism 59
Homework 60
References 64
3 Magnetic Thin Films 67
3.1 Introduction 67
3.2 Magnetic Thin Film Growth 67
3.2.1 Sputter Deposition 68
3.2.2 Molecular Beam Epitaxy (MBE) 71
3.3 Magnetic Thin Film Characterization 72
3.3.1 Vibrating-Sample Magnetometer (VSM) 73
3.3.2 Magneto-Optical Kerr Effect (MOKE) 74
References 76
4 Magnetoresistance Effects 77
4.1 Introduction 77
4.2 Anisotropic Magnetoresistance (AMR) 78
4.3 Giant Magnetoresistance (GMR) 79
4.4 Tunneling Magnetoresistance (TMR) 81
4.5 Contemporary MTJ Designs and Characterization 84
4.5.1 Perpendicular MTJ (p-MTJ) 85
4.5.2 Fully Functional p-MTJ 85
4.5.3 CIPT Approach for TMR Characterization 87
Homework 89
References 89
5 Magnetization Switching and Field MRAMs 93
5.1 Introduction 93
5.2 Magnetization Reversible Rotation and Irreversible Switching Under External Field 93
5.2.1 Magnetization Rotation Under an External Field in the Hard Axis Direction 94
5.2.2 Magnetization Rotation and Switching Under an external Field in the Easy Axis Direction 95
5.2.3 Magnetization Rotation and Switching Under Two Orthogonal External Fields 96
5.2.4 Magnetization Behavior of a Synthetic Anti-ferromagnetic Film Stack 97
5.3 Field MRAMs 99
5.3.1 MTJ of Field MRAM 100
5.3.2 Half-Select Bit Disturbance Issue 101
Homework 102
References 103
6 Spin Current and Spin Dynamics 105
6.1 Introduction to Hall Effects 105
6.1.1 Ordinary Hall Effect 105
6.1.2 Anomalous Hall Effect and Spin Hall Effect 106
6.2 Spin Current 109
6.2.1 Electron Spin Polarization in NM/FM/NM Film Stack 109
6.2.2 Spin Current Injection, Diffusion, and Inverse Spin Hall Effect 111
6.2.3 Generalized Carrier and Spin Current Drift-Diffusion Equation 114
6.3 Spin Dynamics 116
6.3.1 Landau-Lifshitz and Landau-Lifshitz-Gilbert Equations of Motion 116
6.3.2 Ferromagnetic Resonance 118
6.3.3 Spin Pumping and Effective Damping in FM/NM Film Stack 120
6.3.4 FM/NM/FM Coupling Through Spin Current 122
6.4 Interaction Between Polarized Conduction Electrons and Local Magnetization 124
6.4.1 Electron Spin Torque Transfer to Local Magnetic Magnetization 124
6.4.2 Macrospin Model 125
6.4.3 Spin-Torque Transfer in a Spin Valve 127
6.4.3.1 Switching Threshold Current Density 128
6.4.3.2 Switching Time 129
6.4.4 Spin-Torque Transfer Switching in Magnetic Tunnel Junction 131
6.4.5 Spin-Torque Ferromagnetic Resonance and Torkance 133
6.5 Spin Current Interaction with Domain Wall 134
6.5.1 Domain Wall Motion under Spin Current 135
6.5.2 Threshold Current Density 137
Homework 138
References 144
7 Spin-Torque-Transfer (STT) MRAM Engineering 151
7.1 Introduction 151
7.2 Thermal Stability Energy and Switching Energy 152
7.3 STT Switching Properties 154
7.3.1 Switching Probability and Write Error Rate (WER) 156
7.3.2 Switching Current in Precessional Regime 160
7.3.3 Switching Delay of an STT-MRAM Cell 161
7.3.4 Read Disturb Rate 161
7.3.5 Switching Under a Magnetic Field – Phase Diagram 162
7.3.6 MTJ Switching Abnormality 164
7.3.6.1 Magnetic Back-Hopping 164
7.3.6.2 Bifurcation Switching (Ballooning in WER) 165
7.3.6.3 Domain Mediated Magnetization Reversal 166
7.4 The Integrity of MTJ Tunnel Barrier 166
7.4.1 MgO Degradation Model 167
7.5 Data Retention 169
7.5.1 Retention Determination Based on Bit Switching Probability 169
7.5.2 Energy Barrier Determination Based on Aiding Field 170
7.5.3 Energy Barrier Extraction with Retention Bake at Chip Level 171
7.5.4 Data Retention Fail at the Chip Level 173
7.6 The Cell Design Considerations and Scaling 173
7.6.1 STT-MRAM Bit Cell and Array 174
7.6.2 CMOS Options 174
7.6.3 Cell Switching Efficiency 176
7.6.4 Cell Design Considerations 177
7.6.4.1 WRITE Current and Cell Size 178
7.6.4.2 READ Access Performance and RA Product of MTJ 178
7.6.4.3 READ and WRITE Voltage Margins 178
7.6.4.4 Stray Field Control for Perpendicular MTJ 179
7.6.4.5 Suppress Stochastic Switching Time Variation Ideas 181
7.6.5 The Scaling of MTJ for Memory 182
7.6.5.1 In-Plane MTJ 183
7.6.5.2 Out-of-Plane (Perpendicular) MTJ 184
7.7 MTJ SPICE Models 188
7.7.1 Basic MTJ Equivalent Circuit Model for Circuit Design Simulation 188
7.7.2 MTJ SPICE Circuit Model with Embedded Macrospin Calculator 189
7.8 Test Chip, Test, and Chip-Level Weak Bit Screening 191
7.8.1 Read Marginal Bits 192
7.8.2 Write Marginal Bits 193
7.8.3 Short Retention Bits 193
7.8.4 Low Endurance Bits 194
Homework 195
References 197
8 Advanced Switching MRAM Modes 205
8.1 Introduction 205
8.2 Current-Induced-Domain-Wall Motion (CIDM) Memory 206
8.2.1 Single-Bit Cell 207
8.2.2 Multibit Cell: Racetrack 209
8.3 Spin-Orbit Torque (SOT) Memory 211
8.3.1 Spin Orbit Torque (SOT) MRAM Cells 211
8.3.1.1 In-Plane SOT Cell 212
8.3.1.2 Perpendicular SOT Cell 218
8.3.2 Materials Choice for SOT-MRAM Cell 219
8.3.2.1 Transition Metals and their Alloys 219
8.3.2.2 Emergent Materials Systems 221
8.3.2.3 Benchmarking of SOT Switching Efficiency 222
8.4 Magneto-Electric Effect and Voltage-Control Magnetic Anisotropy (VCMA) MRAM 224
8.4.1 Magneto-Electric Effects 224
8.4.2 VCMA-Assisted MRAMs 227
8.4.2.1 VCMA-Assisted Field-MRAM 227
8.4.2.2 VCMA-Assisted Multi-bit-Word SOT-MRAM 229
8.4.2.3 VCMA-Assisted Precession-Toggle MRAM 229
8.5 Relative Merit of Advanced Switching Mode MRAMs 231
Homework 233
References 233
9 MRAM Applications and Production 241
9.1 Introduction 241
9.2 Intrinsic Characteristics and Product Attributes of Emerging Nonvolatile Memories 242
9.2.1 Intrinsic Properties 243
9.2.2 Product Attributes 244
9.3 Memory Landscape and MRAM Opportunity 247
9.3.1 MRAM as Embedded Memory in Logic Chips 248
9.3.1.1 Integration Issues of Embedded MRAM 248
9.3.1.2 MRAM as Embedded Flash in Microcontroller 249
9.3.1.3 Embedded MRAM Cell Size 250
9.3.1.4 MRAM as Cache Memory in Processor 250
9.3.1.5 Improvement of Access Latency 251
9.3.2 High-Density Discrete MRAM 254
9.3.2.1 Technology Status 254
9.3.2.2 Ideal CMOS Technology for High-Density MRAM 256
9.3.2.3 Improvement to Endurance and Write Error Rate with Error Buffer in Chip Architecture 258
9.3.3 Applications and Market Opportunity of MRAM 258
9.3.3.1 Battery-Backed DRAM Applications 260
9.3.3.2 Internet of Things (IoT) and Cybersecurity Applications 261
9.3.3.3 Applications to In-Memory Computing, and Artificial Intelligence (AI) 264
9.3.3.4 MRAM-Based Memory-Driven Computer 265
9.4 MRAM Production 266
9.4.1 MRAM Production Ecosystem 266
9.4.2 MRAM Product History 267
9.4.2.1 First-Generation MRAM – Field MRAM (Also Called Toggle MRAM) 268
9.4.2.2 The Second-Generation MRAM – STT-MRAM 269
9.4.2.3 The Potential Third-Generation MRAM – SOT MRAM 270
Homework 271
References 271
Appendix A Retention Bake (Including Two-Way Flip) 277
Appendix B Memory Functionality-Based Scaling 279
Appendix C High-Bandwidth Design Considerations for STT-MRAM 299
Index 323
