Homogeneous rods extension
axial strain and electric field, 178
carrier concentrations, 177
differential equations, 179
electromechanical fields, 177
electron concentration perturbation,
181, 182
four second-order equations, 179
free piezoelectric semiconductor rod,
177, 178
global charge neutrality conditions, 180
one-dimensional material constants, 178
pyroelectric/piezoelectric coupling, 180
static, 179
temperature-induced carrier concentration
perturbation, 181
thermoelastic and piezoelectric effects, 181
thermoelectric couplings, 178
Hyperbolic functions, 47, 153
Hyperbolic wave, 71
I
Index convention, 116, 144
Initial-boundary-value problem, 71
In-plane extensional displacements, 119
Integration, 154
Isotropic piezoelectric materials, 5
J
Junction interface, 171
K
Kirchhoff classical/elementary theory, 124
L
Lamè coefficients, 132
Laplace transform, 71
Linear algebraic equations, 97
Linear analytical analysis, 183
Linear doping, 35
Linear extension, end forces
axial stress, 47
carrier distribution, 45
charge neutrality conditions, 46
concentrated free charges, 46
electromechanical fields, 47
hyperbolic functions, 47
mechanical displacement, 46
mobile charge redistribution, 48
numerical calculation, 47
static extension, 45, 46
symmetric/antisymmetric fields, 47
uniform doping, 46
Linear homogeneous equations, 146
Linearization, 3
Linearized constitutive relations, 6, 183
Linearized theory, 13
Linearly graded PN junction
boundary and continuity conditions, 37
charge neutrality conditions, 37
doping profiles, 36
electric field and potential, 39
global charge neutrality condition, 37
piezoelectric semiconductor, 36
symmetry/antisymmetry, 38
transition zone, 38, 39
Linear theoretical analysis, 75
Lithium niobate (LiNbO 3 ), 217
Lithium tantalate (LiTaO 3 ), 217
Local extension
boundary and continuity conditions, 56
and compression, 58
displacement and potential fields, 57
electromechanical fields, 57
electron distribution, 48, 57
governing equations, 54
local stress, 57
nonlinear numerical analysis, COMSOL, 57
piezoelectric constant, 57
piezoelectric semiconductor rod, 54, 55
polarization charge density, 57, 58
potential barrier and well, 57
static problems, 55
successive substitutions, 55
undetermined constants, 56
ZnO rod, 56
Local temperature change effects
axial electric polarization P, 184
boundary conditions, 186
COMSOL
nonlinear analysis, 186
numerical analysis, 186
critical voltages, 187
four second-order equations, 183
I-V curve, 186
linear analytical analysis, 183
linearized constitutive relations, 183
material constants, 183
nonlinear solution, 186, 188
one-dimensional governing equations, 182
ordinary differential equations, 184
piezoelectric semiconductor rod, 183, 187
226
Index
axial strain and electric field, 178
carrier concentrations, 177
differential equations, 179
electromechanical fields, 177
electron concentration perturbation,
181, 182
four second-order equations, 179
free piezoelectric semiconductor rod,
177, 178
global charge neutrality conditions, 180
one-dimensional material constants, 178
pyroelectric/piezoelectric coupling, 180
static, 179
temperature-induced carrier concentration
perturbation, 181
thermoelastic and piezoelectric effects, 181
thermoelectric couplings, 178
Hyperbolic functions, 47, 153
Hyperbolic wave, 71
I
Index convention, 116, 144
Initial-boundary-value problem, 71
In-plane extensional displacements, 119
Integration, 154
Isotropic piezoelectric materials, 5
J
Junction interface, 171
K
Kirchhoff classical/elementary theory, 124
L
Lamè coefficients, 132
Laplace transform, 71
Linear algebraic equations, 97
Linear analytical analysis, 183
Linear doping, 35
Linear extension, end forces
axial stress, 47
carrier distribution, 45
charge neutrality conditions, 46
concentrated free charges, 46
electromechanical fields, 47
hyperbolic functions, 47
mechanical displacement, 46
mobile charge redistribution, 48
numerical calculation, 47
static extension, 45, 46
symmetric/antisymmetric fields, 47
uniform doping, 46
Linear homogeneous equations, 146
Linearization, 3
Linearized constitutive relations, 6, 183
Linearized theory, 13
Linearly graded PN junction
boundary and continuity conditions, 37
charge neutrality conditions, 37
doping profiles, 36
electric field and potential, 39
global charge neutrality condition, 37
piezoelectric semiconductor, 36
symmetry/antisymmetry, 38
transition zone, 38, 39
Linear theoretical analysis, 75
Lithium niobate (LiNbO 3 ), 217
Lithium tantalate (LiTaO 3 ), 217
Local extension
boundary and continuity conditions, 56
and compression, 58
displacement and potential fields, 57
electromechanical fields, 57
electron distribution, 48, 57
governing equations, 54
local stress, 57
nonlinear numerical analysis, COMSOL, 57
piezoelectric constant, 57
piezoelectric semiconductor rod, 54, 55
polarization charge density, 57, 58
potential barrier and well, 57
static problems, 55
successive substitutions, 55
undetermined constants, 56
ZnO rod, 56
Local temperature change effects
axial electric polarization P, 184
boundary conditions, 186
COMSOL
nonlinear analysis, 186
numerical analysis, 186
critical voltages, 187
four second-order equations, 183
I-V curve, 186
linear analytical analysis, 183
linearized constitutive relations, 183
material constants, 183
nonlinear solution, 186, 188
one-dimensional governing equations, 182
ordinary differential equations, 184
piezoelectric semiconductor rod, 183, 187
226
Index