potential barriers, 182
potential distribution, 187
thermally induced local polarization, 186
M
Macroscopic theory, 34
holes and electrons, 2
mechanical displacement vector, 3
mobility, 3
piezoelectric constitutive, 2
Magnetic couplings
constants, 11
quasistatic approximation, 11
Magnetoelectric constants, 11
Material constants, 183
MATLAB, 16, 22, 172
Mechanical-to-electrical energy converter, 65
Membrane theory, 140
Metal conductors, 18
Mobile charge redistribution, 167
Modes, 65
Moment equation, 205
Moment-shear force relationship, 157, 205
N
Nonlinearity, 186
Nonlinear waves
amplitude, 75, 76
approximations, 72
classical theory, piezoelectricity, 73
COMSOL, 75
cross-sectional dimension, 75
electric field, 74
electric potential, 74
low doping/low carrier concentration, 73
nonlinear drift current, 74
n-type semiconductor, 72, 73
sinusoidal, 75
trigonometric series, 75
Non-piezoelectric, electromechanical
coupling, 147
Non-piezoelectric semiconductor plate, 144
n-type semiconductor, 95
O
One-dimensional equations
approximation, 34
axial displacement, 31
carrier concentration perturbations, 34, 90
constitutive relations, 91
cross section, 92
deformation and weak fields, 89
displacement, 90
equilibrium, 33
integration constants, 33, 34
lateral stress component relaxation, 31
material constants, 91
mechanical displacement, 35
motion, 92
nonlinear constitutive relations, 32
one-dimensional field equations, 32
piezoelectric semiconductor rod, 31, 32
polarization charge density, 35
rod extensional deformation, 31
rod lateral surface, 31
semiconductor beam, ZnO, 89, 90
shear deformation, 93
strain-displacement/electric field potential,
32
strains and substitute, 91
stress components, 91
three-dimensional material constants, 32
zero-/first-order moments, 92
One-dimensional field equations, 179
One-dimensional material constants, 178
One-dimensional problem, 13
Open-circuit vibration characteristics, 64
Optimal thickness ratio, 167
Ordinary differential equations, 190
P
p-doped nonpiezoelectric semiconductor
plate, 141, 142
Periodic doping, 44, 45
Periodic extension/compression
charges and potentials, 60
distributed body force effect, 59
polarization charges, 60
Phenomenological theory, 1
Piezoelectrically stiffened elastic
constant, 69, 202
Piezoelectric constitutive relations, 5
Piezoelectric coupling, 54, 104, 180
Piezoelectric dielectric layers, 147
Piezoelectric semiconductors, 1, 13, 14
Piezoelectric stiffening effect, 65
Piezomagnetic effects, 11
Plate constitutive equations, 116
Plate thickness-shear strains, 124
PN junction, 14–18, 21, 22
Index
227
potential distribution, 187
thermally induced local polarization, 186
M
Macroscopic theory, 34
holes and electrons, 2
mechanical displacement vector, 3
mobility, 3
piezoelectric constitutive, 2
Magnetic couplings
constants, 11
quasistatic approximation, 11
Magnetoelectric constants, 11
Material constants, 183
MATLAB, 16, 22, 172
Mechanical-to-electrical energy converter, 65
Membrane theory, 140
Metal conductors, 18
Mobile charge redistribution, 167
Modes, 65
Moment equation, 205
Moment-shear force relationship, 157, 205
N
Nonlinearity, 186
Nonlinear waves
amplitude, 75, 76
approximations, 72
classical theory, piezoelectricity, 73
COMSOL, 75
cross-sectional dimension, 75
electric field, 74
electric potential, 74
low doping/low carrier concentration, 73
nonlinear drift current, 74
n-type semiconductor, 72, 73
sinusoidal, 75
trigonometric series, 75
Non-piezoelectric, electromechanical
coupling, 147
Non-piezoelectric semiconductor plate, 144
n-type semiconductor, 95
O
One-dimensional equations
approximation, 34
axial displacement, 31
carrier concentration perturbations, 34, 90
constitutive relations, 91
cross section, 92
deformation and weak fields, 89
displacement, 90
equilibrium, 33
integration constants, 33, 34
lateral stress component relaxation, 31
material constants, 91
mechanical displacement, 35
motion, 92
nonlinear constitutive relations, 32
one-dimensional field equations, 32
piezoelectric semiconductor rod, 31, 32
polarization charge density, 35
rod extensional deformation, 31
rod lateral surface, 31
semiconductor beam, ZnO, 89, 90
shear deformation, 93
strain-displacement/electric field potential,
32
strains and substitute, 91
stress components, 91
three-dimensional material constants, 32
zero-/first-order moments, 92
One-dimensional field equations, 179
One-dimensional material constants, 178
One-dimensional problem, 13
Open-circuit vibration characteristics, 64
Optimal thickness ratio, 167
Ordinary differential equations, 190
P
p-doped nonpiezoelectric semiconductor
plate, 141, 142
Periodic doping, 44, 45
Periodic extension/compression
charges and potentials, 60
distributed body force effect, 59
polarization charges, 60
Phenomenological theory, 1
Piezoelectrically stiffened elastic
constant, 69, 202
Piezoelectric constitutive relations, 5
Piezoelectric coupling, 54, 104, 180
Piezoelectric dielectric layers, 147
Piezoelectric semiconductors, 1, 13, 14
Piezoelectric stiffening effect, 65
Piezomagnetic effects, 11
Plate constitutive equations, 116
Plate thickness-shear strains, 124
PN junction, 14–18, 21, 22
Index
227