Applied Electromagnetism and Materials[原版非扫描]:Contents
Chapter 1. Dielectrics under varying regimes:
phenomenological study of dielectric relaxation.................... 1
1.1. Definitions for dielectric permittivities and dielectric
conductivity and classification of dielectric phenomena ................... .. .1
1.1.1. Absolute permittivity.......................................................................... 1
1.1.2. Relative permittivity........................................................................... 2
1.1.3. Complex relative permittivity............................................................. 2
1.1.4. Limited permittivity............................................................................ 3
1.1.5. Dielectric conductivity....................................................................... 3
1.1.6. Classification of diverse dielectric phenomena.................................4
1.2. Classic study of the Debye dipolar absorption (DDA).............................6
1.2.1. The form of the polarization under a continuous
(stationary) regime............................................................................ 6
1.2.2. Dipolar polarization as a function of time........................................7
1.2.3. Debye equations and the Argand diagram........................................8
1.2.4. Practical representations.................................................................10
1.3. The double-well potential model: physical representations.................12
1.3.1. Introduction......................................................................................12
1.3.2. Polarization associated with the displacement of electrons
between two positions separated by a potential barrier................ 12
1.3.3. Dipole rotation due to an electric field............................................17
1.3.4. Practical determination of the depth of potential wells..................19
1.4. Problems.....................................................................................................21
1.4.1. Problem 1. The double- well potential at a state of equilibrium....21
1.4.2. Problem 2. The Cole􀀐Cole diagram................................................25
1.4.3. Problem 3. The Cole􀀐Davidson diagram........................................30
1.4.4. Problem 4. Linear relationships based on the Debye equations:
the Cole􀀐Brot equations..................................................................33
Chapter 2. Characterization of dielectrics............................................ 39
2.1. Introduction: representation of a dielectric with an equivalent
circuit........................................................................................................ 39
2.2. Circuits exhibiting relaxation phenomena as possible
equivalents to real dielectrics: plots of 􀁈’ = f(􀁚) and 􀁈’’ = g(􀁚)....... 40
2.2.1. Parallel circuit .............................................................................. 40
2.2.2. Circuit in series............................................................................... 41
2.2.3. Association of serial and parallel circuits and relaxation plots... 42
2.3. Resonating circuit.................................................................................... 44
2.4. Representation of a heterogeneous dielectric (powders) using
a model of layers: two parallel circuits in series and the
Maxwell􀀐Wagner􀀐Sillars effect............................................................. 45
2.5. Impedance spectroscopy.......................................................................... 48
2.5.1. Example using a parallel circuit..................................................... 48
2.5.2. Summary......................................................................................... 49
2.6. Dielectric measurements: summary of the analytical apparatus
used with respect to frequency domain................................................. 51
2.6.1. Opening remark: expressions for the quality factor and
tangential loss for the different circuits equivalent to
capacitors or bobbins...................................................................... 51
2.6.2. Very low frequencies (0 to 10 Hz).................................................. 53
2.6.3. From low frequencies to radio frequencies (10 to 107 Hz)............ 55
2.6.4. Radio frequencies and shortwave (103 to 108 Hz).......................... 57
2.6.5. High frequencies............................................................................. 59
2.7. Applied determination of dielectric parameters for frequencies
below 108Hz (classic range for dielectric studies)................................. 60
2.7.1. Condenser form................................................................................60
2.7.2. Connections and the effect of connecting wire capacities..............60
2.7.3. Preparing equations to calculate 􀁈’ and 􀁈’’....................................61
2.8. Problems.................................................................................................... 64
2.8.1. Problem 1. R-C in series..................................................................64
2.8.2. Problem 2. R-C in series and in parallel with a
capacitor (Cp)........................ ..........................................................65
2.8.3. Problem 3. R-C in parallel and in series with
a resistor (Rs)................................................................................ 66
2.8.4. Problem 4. R-C in parallel and in series with
a capacitor (Cs).............................................................................. 67
2.8.5. Problem 5. R-C in parallel and in series with
a parallel R-C................................................................................. 68
Chapter 3. Spectroscopy of dielectrics and the Krönig-Kramers
relations.............................................................................. 71
3.1. Introduction: dielectric response and direct current.......................... 72
3.1.1. A résumé of the components that make up the dielectric
response......................................................................................... 71
3.1.2. Influence of “pseudofree” charges on electric behavior.............. 72
3.1.3. Separation of dielectric response from DC conductivity.............. 73
3.2. Complex conductivity............................................................................. 73
3.2.1. General equations for real and imaginary components of
conductivity................................................................................... 73
3.2.2. Dielectric conductivity due to residual free or bound charges..... 76
3.3. Theoretical study of the dielectric function: the relaxation function,
the Krönig􀀐Kramers equations and their use....................................... 82
3.3.1. Preliminary remarks...................................................................... 82
3.3.2. The impulsive response and the relaxation function.................... 82
3.3.3. Introducing the general expression for the response
to a signal...................................................................................... 84
3.3.4. Relation between dielectric permittivities and the relaxation
function........................................................................................... 85
3.3.5. The Krönig􀀐Kramers relations....................................................... 86
3.3.6. Application to Debye relaxations.................................................... 88
3.3.7. Generalization of the Krönig􀀐Kramers relations...........................90
3.3.8. Application of the Krönig􀀐Kramers relations.................................92
3.4. Complete polarization of dielectrics, characteristics of spectra
from dielectrics, and an introduction to spectroscopy......................... 93
3.4.1. Electronic polarization and the relation between the angular
frequency of an electronic resonance and the gap in an
insulator.......................................................................................... 93
3.4.2. Ionic polarization.............................................................................97
3.4.3. Resultant polarization in an insulator............................................ 97
3.4.4. The resultant dielectric spectrum ...................................................98
3.4.5. Coefficient for the optical and peak absorptions............................99
3.5. Problems...................................................................................................101
3.5.1. Problem 1. Alternative conductivity...............................................101
3.5.2. Problem 2. Optical properties of gaseous electrons......................105
3.5.3. Problem 3. Relation between the function of
relaxation (macroscopic magnitude) and the
autocorrelation function (microscopic magnitude) .....................107
Chapter 4. Interactions of electromagnetic waves and solid semiconductors..............................................................................
111
4.1. Wave equations in solids: from Maxwell's to Schrödinger's
equations via the de Broglie relation.....................................................112
4.2. Bonds within solids: weak and strong bond approximations........... 113
4.2.1. Weak bonds.................................................................................. 113
4.2.2. Strong bonds................................................................................. 115
4.2.3. Choosing approximations for either strong or weak bonds.... ....116
4.3. Evidence for the band structure in weak bonds................................ 117
4.3.1. Preliminary result for the zero- order approximation................. 117
4.3.2. Physical origin of the forbidden bands....................................... 118
4.3.3. Simple estimation of the size of the forbidden band.................. 121
4.4. Insulator, semiconductors, and metals: charge carrier
generation in the bands......................................................................... 121
4.4.1. Distinctions between an insulator, a semiconductor, and a
metal................................................................................................. 121
4.4.2. Populating permitted bands......................................................... 122
4.5. Optical properties of semiconductors: reflectivity, gap size, and
the dielectric permittivity..................................................................... 128
4.5.1. The dielectric function and reflectivity......................................... 128
4.5.2. The relation between static permittivity and the size of
the gap............................................................................................. 130
4.5.3. Absorption..................................................................................... 132
4.6. Optoelectronic properties: electron-photon interactions and
radiative transitions.............................................................................. 132
4.6.1. The various absorption and emission mechanisms.................... 132
4.6.2. Band-to-band transitions and the conditions for radiative
transitions................................................................................... 135
4.7. Level of absorption and emission....................................................... 139
4.7.1. Optical function of the state density........................................... 139
4.7.2. Probabilities of occupation.......................................................... 141
4.7.3. Probabilities for radiative transitions........................................... 141
4.7.4. Overall level of emission or absorption transitions..................... 142
4.7.5. Absorption coefficient .................................................................. 142
4.8. Problem....................................................................................................145
Chapter 5. Electrical and magnetic properties of
semiconductors ................................................................... 147
5.1. Introduction ........................................................................................... 147
5.2. Properties of a semiconductor under an electric field....................... 148
5.2.1. Ohm’s law for a semiconductor................................................... 148
5.2.2. Effect of a concentration gradient and the diffusion current..... 150
5.2.3. Inhomogeneous semiconductor, the internal field, and
Einstein’s relation........................................................................ 152
5.2.4. Measuring the conductivity of a semiconductor and resistance
squared.......................................................................................... 154
5.2.5. Resistance per square or more simply put resistance squared
and denoted R􀀀.............................................................................. 158
5.3. Magnetoelectric characterization of semiconductors ......................... 160
5.3.1. The Hall effect................................................................................160
5.3.2. Magnetoresistance and magnetoconductance............................. 162
5.4. The Gunn effect and microwave emissions.......................................... 167
5.4.1. Expressions for 􀁖, j, and <v> for carriers in a semiconductor
with a conduction band of two minima.................... 167
5.4.2. Emission of an electromagnetic wave in the microwave
region.......................................................................................... 171
5.5. Problems ............................................................................................... 173
5.5.1. Problem 1. Hall constant............................................................ 173
5.5.2. Problem 2. Seebeck effect........................................................... 175
Chapter 6. Introduction to nonlinear effects.................................... 181
6.1. Context................................................................................................ 181
6.2. Mechanical generation of the second harmonic
(in one dimension) ........................... ................................................... 182
6.2.1. Effect of an intense optical field E􀁚 ........................................ 182
6.2.2. Putting the problem into equations............................................ 183
6.2.3. Solution to the problem of displacement terms........................ 185
6.2.4. Solution to the problem in terms of polarization..................... 187
6.2.5. Comments.................................................................................... 189
6.3. Electrooptical effects and the basic equations.................................... 190
6.3.1. Excitation from two pulsations and an introduction to the
Pockels effect.............................................................................. 190
6.3.2. Basic equations for nonlinear optics.......................................... 192
6.4. Principle of electrooptical modulators................................................ 194
6.4.1. Phase modulator.......................................................................... 194
6.4.2. Amplitude modulator................................................................... 197
6.4.3. The merit factor........................................................................... 198
6.5. Problems............................................................................................... 199
6.5.1. Problem 1. Second-order susceptibility and molecular
centrosymmetry........................................................................ 199
6.5.2. Problem 2. Phenomenological study of the Pockels effect...... 200
Chapter 7. Electromagnetic cavities.................................................... 207
7.1. Definition.............................................................................................. 207
7.2. Resonance conditions for a cavity and proper resonance modes.... 207
7.3. Fabry􀀐Perot- type optical cavities..................................................... 209
7.3.1. Generalities and the Fabry􀀐Perot resonator............................. 209
7.3.2. Form of stationary wave system: resonance modes.................. 210
7.3.3. An alternative point of view and the Fabry􀀐 Perot
interferometer.............................................................................. 211
7.4. The Airy laser formula.......................................................................... 212
7.5. Modification of spontaneous emission in a planar cavity
and the angular diagram..................................................................... 214
7.6. Microcavities and photonic forbidden band (PFB) structures......... 216
7.6.1. Exampled scale effects ............................................................... 216
7.6.2. PFB structures............................................................................. 217
7.7. Microcavities using whispering gallery modes..................................... 219
7.7.1 Generalities.................................................................................... 219
7.7.2 Principle......................................................................................... 220
7.7.3 Basic equations for whispering gallery modes..............................221
7.7.4. Photon lifetimes and extraction of the radiation....................... 223
7.8. Problem................................................................................................... 223
Chapter 8. Particles in electromagnetic fields:
ionic and electronic optics.................................................. .. 227
8.1. Mechanics of particles in an electromagnetic field.............................. 227
8.1.1. Introduction to mechanics: an aide-mémoire............................ 227
8.1.2. Movement of a charged particle in an electric or
magnetic field................................................................................ 229
8.2. Ionic or electronic optics: the electrostatic lens .................................. 236
8.2.1. The analogue to the refractive index: trajectorial
refraction of a charged particle placed in a succession of
equipotential zones....................................................................... 236
8.2.2. Practical determination of equipotential surfaces
(and thus field lines).................................................................... 238
8.2.3. Focusing trajectories with an electrostatic lens of axial
symmetry (generating a radial field) .......................................... 240
8.2.4. Electrostatic lens with a rotational symmetry (generating
an electrical field consisting of radial and longitudinal
components).................................................................................. 243
8.2.5. Equation for the trajectory in the electrostatic lens ................... 247
8.2.6. Focal length of a three-electrode lens ......................................... 249
8.3. Problems................................................................................................. 251
8.3.1. Problem 1. Mathematical study of a cycloid ............................... 251
8.3.2. Problem 2. The effect of a crossed field E􀁵B
􀁇 􀁇
on a charged
particle q ...................................................................................... 252
8.3.3. Problem 3. Movement of a particle in a uniform B field........... 257
Chapter 9. Electromagnetic processes applied to a large-scale
apparatus: the ion accelerator........................................... 265
9.1. Introduction: general principles and overall design of a
machine for implanting ions................................................................ 265
9.2. Setup of an ion beam............................................................................ 266
9.2.1. Overall description........................................................................ 266
9.2.2. Use and distribution of high tensions within the apparatus...... 267
9.2.3. The Wien filter............................................................................... 269
9.2.4. The neutrals’ trap.......................................................................... 272
9.2.5. Sweeping........................................................................................ 273
9.2.6. Determination of the number of implanted ions and the
Faraday cage................................................................................. 274
9.2.7. General remarks on the mechanism used to produce ions......... 275
9.2.8. Nature of the electric discharge.................................................... 277
9.3. ECR-type source of ions (“cyclotronic resonance”) ........................... 279
9.3.1. Principals of an ECR source ........................................................ 279
9.3.2. Magnetic field effects on the pathway and confinement of
electrons: increasing the ionisation yield.................................... 281
9.4. Problem....................................................................................................285
Chapter 10. Electromagnetic ion–material interactions...................... 295
10.1. High-energy collisions between atoms and ions: the
nature of the interaction potentials..................................................... 295
10.1.1. General form of interaction potentials.......................................295
10.1.2. The Thomas􀀐Fermi model......................................................... 298
10.1.3. The universal interatomic potential............................................ 300
10.2. Hypotheses for the dynamics of inelastic and elastic collisions
between two bodies and various energy losses and electron
and nuclear stopping powers............................................................... 301
10.2.1. Introduction ................................................................................ 301
10.2.2. Various hypotheses and assumptions concerning classic
(Rutherford) diffusion theory...................................................... 302
10.2.3. Elastic and inelastic collisions.................................................... 302
10.2.4. Origin of electronic and nuclear energy losses ......................... 302
10.2.5. Electronic stopping power........................................................... 303
10.2.6. Nuclear stopping power............................................................... 306
10.3. The principal stages in calculating stopping powers.........................306
10.3.1. Rutherford-type diffusion for a particle of charge + Z1 e
and mass M1, by a particle of charge + Z2e and mass M2.......... 306
10.3.2. Low-velocity incident particle (inferior to the velocity of
electrons in the K layer): expression for the electronic
stopping power Se.......................................................................... 314
10.3.3. Nuclear stopping power.............................................................. 316
10.3.4. Total energy loss......................................................................... 317
10.4. The various phenomena of ion􀀐material interactions and their
applications..........................................................................................319
10.4.1. The various phenomena.............................................................. 319
10.4.2. Ionic implantation........................................................................320
10.4.3. Target amorphism and “mixing” in the volume of initially
surface-deposited atoms (“Ion beam mixing”)............................ 321
10.4.4. Mechanism of physical pulverization..........................................322
10.4.5. Ion-beam􀀐 assisted deposition.....................................................324
10.5. Additional information on various ion sources and their
functioning...........................................................................................327
10.5.1. The electron cyclotron resonance (ECR) source...................... 327
10.5.2. Basic element in an ion source; the Penning source................ 327
10.5.3. The hollow cathode source......................................................... 328
10.5.4. Grid sources and broad beams.................................................... 329
10.6. Problem..................................................................................................332
References...................................................................................................341
Index...........................................................................................................343
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