coefficient matrix, 146
compact matrix notation, 144
constitutive relations, 144, 145
decaying behavior, 142
dispersion relations, 146
dispersive and dissipative, 147
elastic and dielectric constants, 145
elastic half space, 147
electric fields, 143
electric potential, 145
FS, 145
plate thickness, 144
possible solutions, 142
propagation, 141
semiconductor plate, 143
SH, 146
two-dimensional Laplacian, 142
zero-order equations, 143
Symmetric/antisymmetric fields, 47
T
Temperature effects, composite beams
carrier concentration perturbations, 204
constitutive relations, 204, 205
differential element, 208, 211
electric potential and field, 204
electrostatics charge equation, 206
free and isolated beams, 207
global charge neutrality conditions, 207
hole/electron concentration perturbation,
209, 210
integrations, 205
moment equation, 205
moment-shear force relationship, 206
nonpiezoelectric semiconductor layer,
203, 204
one-dimensional conservation, 206
piezoelectric dielectric layer, 203, 204
second-order equation, 207
static deformation, 207
temperature-induced redistributions, 208
undetermined constants, 208
Temperature sensitivity, 196
Thermal couplings
electrostatics, 9
holes and electrons, 10
Thermal effects, composite rods extension
axial strain and electric field, 197
carrier concentration, 201, 202
carrier distribution, 201
cross-sectional areas, 199
differential element, 199, 202
electric displacement, 199
electron concentration perturbation, 202
extensional deformation, 196
global charge neutrality conditions, 200
material constants, 197
mechanical displacement, 200
nonpiezoelectric semiconductor layer,
196, 197
one-dimensional continuity equations, 199
piezoelectric dielectric layers, 196, 197
polarization charge density/vector, 200
pyroelectric coupling, 198
Thermally induced local polarization, 186
Thermal/temperature effects, PN junctions
boundary and continuity conditions, 189
built-in fields, 190, 192, 193
global charge neutrality conditions, 190
heterogeneous, 188, 191, 195
heterogeneous vs. homogeneous junction,
193, 194
homogeneous, 193
linear equations, 191
material parameters, 190
numerical analysis, COMSOL, 195
one-dimensional material parameters, 195
polarization charge density, 191, 193, 195
symmetric/antisymmetric curves, 193
temperature sensitivity, 196
undetermined constants, 190, 191
ZnO rod, 188, 189
Thermoelastic constants, 10
Thermoelectric constants, 10
Thermoelectric couplings, 178
Thickness-shear approximation, 162
differential relationship, 130
electromechanical coupling factor, 130
long-wave approximation, 130
propagating waves, 129
small flexural deformation, 129
waves, 130
Thickness-shear correction, 126
Thickness-shear vibrations
correction factor, 129
first-order plate equations, 128
nodal planes, 128
three-dimensional equations, 129
time-harmonic motions, 129
unelectroded plate, 128
Thickness-shear waves propagation
dispersion relations, 131
dispersive and dissipative, 132
frequency, 132
homogeneous equation, 131
piezoelectric dielectric plate, 132
straight-crested waves, 131
Index
229
compact matrix notation, 144
constitutive relations, 144, 145
decaying behavior, 142
dispersion relations, 146
dispersive and dissipative, 147
elastic and dielectric constants, 145
elastic half space, 147
electric fields, 143
electric potential, 145
FS, 145
plate thickness, 144
possible solutions, 142
propagation, 141
semiconductor plate, 143
SH, 146
two-dimensional Laplacian, 142
zero-order equations, 143
Symmetric/antisymmetric fields, 47
T
Temperature effects, composite beams
carrier concentration perturbations, 204
constitutive relations, 204, 205
differential element, 208, 211
electric potential and field, 204
electrostatics charge equation, 206
free and isolated beams, 207
global charge neutrality conditions, 207
hole/electron concentration perturbation,
209, 210
integrations, 205
moment equation, 205
moment-shear force relationship, 206
nonpiezoelectric semiconductor layer,
203, 204
one-dimensional conservation, 206
piezoelectric dielectric layer, 203, 204
second-order equation, 207
static deformation, 207
temperature-induced redistributions, 208
undetermined constants, 208
Temperature sensitivity, 196
Thermal couplings
electrostatics, 9
holes and electrons, 10
Thermal effects, composite rods extension
axial strain and electric field, 197
carrier concentration, 201, 202
carrier distribution, 201
cross-sectional areas, 199
differential element, 199, 202
electric displacement, 199
electron concentration perturbation, 202
extensional deformation, 196
global charge neutrality conditions, 200
material constants, 197
mechanical displacement, 200
nonpiezoelectric semiconductor layer,
196, 197
one-dimensional continuity equations, 199
piezoelectric dielectric layers, 196, 197
polarization charge density/vector, 200
pyroelectric coupling, 198
Thermally induced local polarization, 186
Thermal/temperature effects, PN junctions
boundary and continuity conditions, 189
built-in fields, 190, 192, 193
global charge neutrality conditions, 190
heterogeneous, 188, 191, 195
heterogeneous vs. homogeneous junction,
193, 194
homogeneous, 193
linear equations, 191
material parameters, 190
numerical analysis, COMSOL, 195
one-dimensional material parameters, 195
polarization charge density, 191, 193, 195
symmetric/antisymmetric curves, 193
temperature sensitivity, 196
undetermined constants, 190, 191
ZnO rod, 188, 189
Thermoelastic constants, 10
Thermoelectric constants, 10
Thermoelectric couplings, 178
Thickness-shear approximation, 162
differential relationship, 130
electromechanical coupling factor, 130
long-wave approximation, 130
propagating waves, 129
small flexural deformation, 129
waves, 130
Thickness-shear correction, 126
Thickness-shear vibrations
correction factor, 129
first-order plate equations, 128
nodal planes, 128
three-dimensional equations, 129
time-harmonic motions, 129
unelectroded plate, 128
Thickness-shear waves propagation
dispersion relations, 131
dispersive and dissipative, 132
frequency, 132
homogeneous equation, 131
piezoelectric dielectric plate, 132
straight-crested waves, 131
Index
229