D
Debye-Hückel equation, 35
Debye-Hückel length, 35, 214
Dielectric constants, 148
Diffusion, 14, 16, 35, 74, 170, 172
Dispersion curves, 29
Dispersion relations, 28, 146
Dispersive wave, 147
Dissipative wave, 29
Doping profiles, 36
Drift, 35
Driving frequency, 100
E
Efficiency, 65–67
Einstein relation, 2
Elastic constants, 144, 152
Elastic stiffness, 147
Electric fields, 143
Electrically nonlinear extension
boundary conditions, 50
charge neutrality condition, 50
electric potential fields, 50
first-order problem, 51
first-order solution, 52
mechanical displacement, 50
notation, 48
perturbation, 50, 51
piezoelectric coupling, 54
piezoelectric semiconductor rod, 48
polarization/polarization charge density, 53
second-order problem, 51, 52
second-order solution, 52, 53
static, 49
uniform doping, 50
Electromechanical coupling, 109
Electromechanical fields, 177, 186
Electromechanical wave, 74
Electron concentration distribution, 53
Electron concentration perturbation, 108
Electron distribution, 106
Electrostatics charge equation, 150, 165
Energy density function, 123
Energy harvester, 61
Error function, 42
Ettingshausen effects, 11
Extension equations
extensional displacement, 121
index convention, 120
in-plane extensional displacements, 119
plate material constants, 120
Poisson’s effect, 119, 120
stress relaxation, 120
zero-order equations, 119
Extensional deformation, 196
Extensional waves, 106
F
Face-shear (FS), 145
Fiber, 79
Films, 113
First-order constitutive relations, 123
First-order shear deformation theory, 134
Flexure, 127
Four second-order equations, 179, 183
Free vibration analysis, 65
Free vibration modes, 104
Fundamental thickness-shear
frequency, 214
G
Gauss’s law, 1
Germanium (Ge), 216
Global charge neutrality conditions, 37, 151,
160, 166, 190
H
Harmonic extensional waves, 73
Harmonic vibration
boundary conditions, 63
circuit equation, 63
coefficient matrix, 62
complex conjugate, 66
displacement fields, 65, 66
effective polarization charge, 61
finite/static response, 65
linear equation, 63
linear homogeneous equations, 62
material damping, 64
n-type semiconductor, 62
open-circuit vibration characteristics, 64
piezoelectric semiconductor rod, 61
piezoelectric stiffening effect, 65
reference carrier concentration, 63
resonance frequencies, 64–66
undetermined constants, 63
uniform doping, 62
Heterogeneous junctions, 75, 172, 175,
188, 191
Homogeneous junction, 172, 174, 193
Homogeneous piezoelectric semiconductor
rod, 153
Index
225
Debye-Hückel equation, 35
Debye-Hückel length, 35, 214
Dielectric constants, 148
Diffusion, 14, 16, 35, 74, 170, 172
Dispersion curves, 29
Dispersion relations, 28, 146
Dispersive wave, 147
Dissipative wave, 29
Doping profiles, 36
Drift, 35
Driving frequency, 100
E
Efficiency, 65–67
Einstein relation, 2
Elastic constants, 144, 152
Elastic stiffness, 147
Electric fields, 143
Electrically nonlinear extension
boundary conditions, 50
charge neutrality condition, 50
electric potential fields, 50
first-order problem, 51
first-order solution, 52
mechanical displacement, 50
notation, 48
perturbation, 50, 51
piezoelectric coupling, 54
piezoelectric semiconductor rod, 48
polarization/polarization charge density, 53
second-order problem, 51, 52
second-order solution, 52, 53
static, 49
uniform doping, 50
Electromechanical coupling, 109
Electromechanical fields, 177, 186
Electromechanical wave, 74
Electron concentration distribution, 53
Electron concentration perturbation, 108
Electron distribution, 106
Electrostatics charge equation, 150, 165
Energy density function, 123
Energy harvester, 61
Error function, 42
Ettingshausen effects, 11
Extension equations
extensional displacement, 121
index convention, 120
in-plane extensional displacements, 119
plate material constants, 120
Poisson’s effect, 119, 120
stress relaxation, 120
zero-order equations, 119
Extensional deformation, 196
Extensional waves, 106
F
Face-shear (FS), 145
Fiber, 79
Films, 113
First-order constitutive relations, 123
First-order shear deformation theory, 134
Flexure, 127
Four second-order equations, 179, 183
Free vibration analysis, 65
Free vibration modes, 104
Fundamental thickness-shear
frequency, 214
G
Gauss’s law, 1
Germanium (Ge), 216
Global charge neutrality conditions, 37, 151,
160, 166, 190
H
Harmonic extensional waves, 73
Harmonic vibration
boundary conditions, 63
circuit equation, 63
coefficient matrix, 62
complex conjugate, 66
displacement fields, 65, 66
effective polarization charge, 61
finite/static response, 65
linear equation, 63
linear homogeneous equations, 62
material damping, 64
n-type semiconductor, 62
open-circuit vibration characteristics, 64
piezoelectric semiconductor rod, 61
piezoelectric stiffening effect, 65
reference carrier concentration, 63
resonance frequencies, 64–66
undetermined constants, 63
uniform doping, 62
Heterogeneous junctions, 75, 172, 175,
188, 191
Homogeneous junction, 172, 174, 193
Homogeneous piezoelectric semiconductor
rod, 153
Index
225