Hall Effect Devices, Second Edition

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ISBN: 9780750308557 | 0750308559
Cover: Hardcover
Copyright: 12/1/2003

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This is the second edition of a very popular 1991 book describing the physics and technology of semiconductor electronic devices exploiting the Hall effect. These are magnetic field sensitive devices such as Hall elements, magnetoresistors, and magnetotransistors. Hall effect devices are commonly used as magnetic field sensors and as means for characterizing semiconductors. The book provides a clear analysis of the relationship between the basic physical phenomena in solids, the appropriate materials characteristics, and the characteristics of Hall effect devices. Particular emphasis is placed on important developments inspired and made possible by recent advances in microelectronics. A special feature of the book is its broad scope. The book provides physical basics of Hall effect devices, clear guidelines for the design of practical Hall elements, detailed descriptions of the best interface electronic circuits, examples of the most successful industrial products in the field, and interesting examples of their applications.

Preface

xiii

Acknowledgments

xiv

1 Introduction

(10)

1.1 The basic physical effects

(4)

1.1.1 The Hall effect

(2)

1.1.2 The magnetoresistance effect

(1)

1.2 Hall effect devices and their applications

(4)

1.2.1 Hall plates

(1)

1.2.2 Other Hall effect devices

(1)

1.2.3 Applications of Hall effect devices

(1)

References

(2)

2 Semiconductor physics: a summary

(52)

2.1 Energy bands

(8)

2.1.1 Conductor, semiconductor, insulator

(1)

2.1.2 Permitted and forbidden energy bands

(2)

2.1.3 Electrons in solids

(1)

2.1.4 Electrons in the conduction band

(2)

2.1.5 Holes in the valence band

(2)

2.2 Distribution and concentration of carriers

(14)

2.2.1 Density of states

(2)

2.2.2 Distribution function

(2)

2.2.3 Carrier concentration

(1)

2.2.4 Intrinsic semiconductors

(1)

2.2.5 Extrinsic semiconductors

(7)

2.2.6 Heavy doping effects

(1)

2.3 Scattering of carriers

(5)

2.3.1 Free transit time

(3)

2.3.2 Relaxation time

(1)

2.4 Charge transport

(16)

2.4.1 Drift in a weak electric field

(9)

2.4.2 High electric fields

(2)

2.4.3 Diffusion current

(3)

2.4.4 Non-stationary transport

(1)

2.5 Other relevant phenomena

(7)

2.5.1 Recombination and generation

(1)

2.5.2 PN junction

(1)

2.5.3 Noise

(2)

2.5.4 Piezoresistance

(2)

References

(2)

3 Galvanomagnetic effects

(108)

3.1 Approximate analysis

(24)

3.1.1 The (original) Hall effect

(6)

3.1.2 The current deflection effect

(3)

3.1.3 The magnetoresistance effect

(2)

3.1.4 Galvanomagnetic current components

(5)

3.1.5 Charge carrier transport in very high magnetic fields

(3)

3.1.6 The role of collisions

(2)

3.1.7 Summary and further questions

(2)

3.2 Kinetic equation approach

(18)

3.2.1 Kinetic equation

(2)

3.2.2 Relaxation time

(1)

3.2.3 Solution for the steady state

(3)

3.2.4 Non-equilibrium distribution function

(2)

3.2.5 Galvanomagnetic transport of carriers. Current density

(4)

3.2.6 Kinetic coefficients

101

(3)

3.2.7 Magnetic field dependence of the kinetic coefficients

104

(2)

3.3 An accurate analysis

106

(32)

3.3.1 Basic equations

106

(2)

3.3.2 Drift current density at B = 0

108

(1)

3.3.3 Current density in a plate under perpendicular magnetic field

109

(2)

3.3.4 Boundary conditions for B E

111

(3)

3.3.5 Infinitely short plate with B E. Corbino conductivity and Hall mobility

114

(3)

3.3.6 Infinitely long plate with B E. Physical magnetoresistance and Hall effect

117

(5)

3.3.7 The galvanomagnetic effects in a mixed conductor

122

(3)

3.3.8 The Hall effect in a many-valley semiconductor

125

(7)

3.3.9 The planar Hall effect

132

(2)

3.3.10 Alternative forms of the basic equations

134

(2)

3.3.11 Relation between the magnetoresistance effect and the planar Hall effect. Magnetoresistivity for an arbitrary direction of B

136

(2)

3.4 Galvanomagnetic coefficients

138

(18)

3.4.1 Scattering factors. Hall factor

138

(6)

3.4.2 Corbino conductivity

144

(1)

3.4.3 Hall mobility

145

(3)

3.4.4 Planar Hall-current coefficient

148

(1)

3.4.5 Magnetoresistivity

148

(1)

3.4.6 Hall coefficient

149

(6)

3.4.7 Planar Hall coefficient

155

(1)

3.5 Related effects

156

(12)

3.5.1 Diffusion current. Complete galvanomagnetic equation

156

(3)

3.5.2 Magnetoconcentration effect

159

(2)

3.5.3 Galvanothermomagnetic effects

161

(2)

3.5.4 The Hall effect at a high electric field

163

(3)

3.5.5 The piezo-Hall effect

166

(2)

References

168

(3)

4 Hall plates and magnetoresistors. Basic properties

171

(65)

4.1 Galvanomagnetic effects: integral quantities

171

(4)

4.1.1 From the basic equation to integral quantities

172

(2)

4.1.2 Hall plate as a two-port device

174

(1)

4.2 Influence of the plate geometry

175

(29)

4.2.1 Plates neither long nor short. Geometrical factors

176

(1)

4.2.2 Conformal mapping: method and results

177

(6)

4.2.3 Conformal mapping: examples

183

(5)

4.2.4 Numerical analysis using circuit simulation method

188

(5)

4.2.5 Common shapes of Hall plates and magnetoresistors

193

(4)

4.2.6 Geometrical factor of Hall voltage

197

(5)

4.2.7 Geometrical factor of magnetoresistance

202

(2)

4.3 The Hall voltage mode of operation

204

(14)

4.3.1 Input and output resistances

205

(3)

4.3.2 Output voltage

208

(1)

4.3.3 Hall voltage

209

(3)

4.3.4 Offset voltage

212

(2)

4.3.5 Noise voltage

214

(1)

4.3.6 Signal-to-noise ratio

215

(2)

4.3.7 Self magnetic fields

217

(1)

4.4 The Hall current mode of operation

218

(18)

4.4.1 Large-contact Hall devices

218

(1)

4.4.2 Dual Hall devices. Hall current

219

(3)

4.5 The magnetoresistance mode of operation

222

(2)

4.5.1 Magnetoresistance ratio

223

(1)

4.6 High-frequency effects

224

(9)

4.6.1 Local high-frequency effects

224

(2)

4.6.2 Global capacitive effects

226

(4)

4.6.3 Inductive effects

230

(3)

References

233

(3)

5 Hall magnetic sensors

236

(88)

5.1 Basic characteristics

237

(12)

5.1.1 Sensitivity

237

(2)

5.1.2 Offset-equivalent magnetic field

239

(1)

5.1.3 Noise-equivalent magnetic field

240

(1)

5.1.4 Cross-sensitivity

241

(1)

5.1.5 Non-linearity

242

(4)

5.1.6 Frequency response

246

(1)

5.1.7 Stability

247

(2)

5.2 Material and technology

249

(3)

5.2.1 Choice of material

250

(2)

5.2.2 Technology

252

(1)

5.3 Examples of Hall plates

252

(7)

5.3.1 High mobility thin-film Hall plates

253

(1)

5.3.2 Silicon and GaAs Hall plates

254

(3)

5.3.3 2DEG Hall plates

257

(2)

5.4 Non-plate-like Hall magnetic sensors

259

(7)

5.4.1 Generalizing the criteria for a good Hall device

259

(2)

5.4.2 Vertical Hall devices

261

(3)

5.4.3 Cylindrical Hall device

264

(2)

5.4.4 Three-axis Hall magnetic sensor

266

(1)

5.5 Very small Hall devices

266

(9)

5.5.1 Scaling down a Hall plate

267

(7)

5.5.2 Examples of micrometre and submicrometre Hall devices

274

(1)

5.6 Incorporating a Hall device into a circuit

275

(17)

5.6.1 Circuit model of a Hall device

275

(5)

5.6.2 Biasing a Hall device. Temperature cross-sensitivity and non-linearity

280

(2)

5.6.3 Reducing offset and 1/f noise

282

(4)

5.6.4 Amplifying the output signal

286

(3)

5.6.5 Integrated Hall magnetic sensors

289

(3)

5.7 Hall sensors with magnetic concentrators

292

(13)

5.7.1 Basic characteristics of magnetic concentrators

293

(3)

5.7.2 Discrete and hybrid magnetic concentrators

296

(1)

5.7.3 Integrated magnetic concentrators

297

(8)

5.8 Packaging Hall magnetic sensors

305

(3)

5.8.1 Packaging stress

305

(2)

5.8.2 Reducing packaging stress

307

(1)

5.9 Applications of Hall magnetic sensors

308

(10)

5.9.1 Measuring magnetic fields

308

(1)

5.9.2 Mechanical displacement transducers

309

(5)

5.9.3 Measuring electric current, power and energy

314

(4)

References

318

(6)

6 Hall devices as means for characterizing semiconductors

324

(28)

6.1 Extraction of material characteristics

324

(8)

6.1.1 Homogeneous plates and layers

324

(3)

6.1.2 Inhomogenous layers

327

(4)

6.1.3 Measurement of profiles

331

(1)

6.2 Measurement methods for characterizing material

332

(14)

6.2.1 Measurements on a long slab

332

(2)

6.2.2 Van der Pauw method

334

(4)

6.2.3 Four-point probe methods

338

(4)

6.2.4 Measurements on a large-contact sample

342

(2)

6.2.5 The Hall mobility of minority carriers

344

(2)

6.3 Measuring packaging stress

346

(4)

6.3.1 Measurement method

347

(1)

6.3.2 Examples of the measurement results

348

(2)

References

350

(2)

7 Magnetic-sensitive field-effect and bipolar devices

352

(45)

7.1 MOS Hall effect devices

353

(9)

7.1.1 MOS Hall plates

353

(3)

7.1.2 Split-drain MOS devices

356

(6)

7.2 Magnetodiodes

362

(3)

7.2.1 The magnetodiode effect

362

(2)

7.2.2 Structures and technology

364

(1)

7.3 Magnetotransistors

365

(21)

7.3.1 The current deflection mechanism

366

(5)

7.3.2 Injection modulation

371

(6)

7.3.3 The magnetodiode effect in magnetotransistors

377

(1)

7.3.4 Magnetotransistor figures of merit

378

(5)

7.3.5 Magnetotransistor circuits

383

(3)

7.4 Carrier-domain magnetic-sensitive devices

386

(8)

7.4.1 Three-layer carrier-domain devices

387

(3)

7.4.2 Four-layer carrier-domain devices

390

(4)

References

394

(3)

8 Comparing Hall sensors with other galvanomagnetic sensors

397

(10)

8.1 Hall elements versus other Hall effect devices

397

(3)

8.1.1 Hall elements: Hall voltage mode versus Hall current mode and magnetoresistance mode of operation

398

(1)

8.1.2 Hall Elements versus magnetodiodes, MagFETs, MagBJTs,

399

(1)

8.2 Hall sensors versus ferromagnetic magnetoresistors

400

(6)

8.2.1 Performance of integrated Hall magnetic sensors

400

(1)

8.2.2 Performance of ferromagnetic magnetoresistors

400

(3)

8.2.3 Integrated Hall sensors versus AMRs and GMRs

403

(2)

8.2.4 Looking into a crystal ball

405

(1)

References

406

(1)

Appendices

A International system of units

407

(1)

B Physical constants

408

(1)

C Properties of some semiconductors

409

(1)

D Magnetic quantities, units, relations and values

410

(1)

E Mathematical relations

411

(2)

Index

413

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Hall Effect Devices, Second Edition

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Table of Contents

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