PN junction extension
boundary and continuity conditions, 77
carrier concentration perturbations, 78
COMSOL
nonlinear solution, 79
numerical analysis, 85
numerical solution, 82
current-voltage relation/I-V curve, 83
global charge neutrality conditions, 77
heterogeneous, 75, 78, 79, 82–85
jump dicontinuity, 80
linear analytical vs. nonlinear numerical
solutions, 82, 83
linear theoretical analysis, 75
one-dimensional governing equations, 77
piezoelectric semiconductor rod, 75, 76
polarization charge density, 77, 79, 81
polarization fields, 79, 80
second-order ordinary differential
equations, 77
symmetric/antisymmetric curves, 80
undetermined constants, 79
PN junctions bending
axial electric polarization P 3 , 169
carrier concentration distributions, 173
charge neutrality conditions, 171
electromechanical fields, 170
field equations, 168
heterogeneous, 172
homogeneous, 168, 174
junction interface, 171
MATLAB, 172
one-dimensional constitutive relations, 169
p and n distributions, 172
piezoelectric semiconductor beams, 168
piezotronic devices, 172
undetermined constants, 170
Poisson-Boltzmann equation, 35
Poisson’s effect, 119, 120, 122
Poisson’s equation, 35
Polarization charges, 43, 54, 60, 191,
193, 195, 200
Polarization vector, 151
Polarized ceramics (PZT), 147
Potential barriers, 60, 186, 187
Potential wells, 60, 186, 187
Power series, 113, 134
Pyroelectric constants, 10
Pyroelectric coupling, 180, 198
R
Relaxed material constants, 122
Resonance frequencies, 64
Resonances, 100
Rotatory inertia, 124, 165
S
Second-order equation, 207
Semiconductors, 18
Semi-infinite crack, 24
Shear correction factors, 122, 123
Shear deformation
beam shear strain, 94
constitutive relations, 94, 95
extension, 93
field equations, 94
inertia, 95
Shear electromechanical coupling factor, 130
Shear force Q, 164, 205
Shear-horizontal (SH) waves, 27–29, 146
Shell structures
bending
shear deformations, 139
and twisting moments, 139
carrier concentration perturbations, 134, 136
curvilinear coordinate systems, 132
dependence, 134
differential shell element, 132, 133
electric displacement/surface charge, 138
mechanical resultants/surface loads, 137
membrane theory, 140
scalar field gradient, 133
shear correction factors, 138
strain-displacement relations, 132
stress relaxations, 139
three-dimensional constitutive relations,
138
transverse shear forces, 136
two-dimensional charge equations, 136
two-dimensional continuity equations, 137
two-dimensional equations, 132, 136
vector field divergence, 134
Silicon (Si), 147, 219
Sinusoidal wave motion, 74
Smoothly graded PN junction
boundary conditions, 40
convergence domain, 42
doping profiles, 40, 42
error function, 41
local charge distribution, 40
mobile/polarization charge effect, 42, 43
recurrence relation, 41
Static bending analysis, 100
Static extension, 179
Stress relaxation, 143, 163
Surface waves
anti-plane motions, 141
boundary/continuity conditions, 143
228
Index
boundary and continuity conditions, 77
carrier concentration perturbations, 78
COMSOL
nonlinear solution, 79
numerical analysis, 85
numerical solution, 82
current-voltage relation/I-V curve, 83
global charge neutrality conditions, 77
heterogeneous, 75, 78, 79, 82–85
jump dicontinuity, 80
linear analytical vs. nonlinear numerical
solutions, 82, 83
linear theoretical analysis, 75
one-dimensional governing equations, 77
piezoelectric semiconductor rod, 75, 76
polarization charge density, 77, 79, 81
polarization fields, 79, 80
second-order ordinary differential
equations, 77
symmetric/antisymmetric curves, 80
undetermined constants, 79
PN junctions bending
axial electric polarization P 3 , 169
carrier concentration distributions, 173
charge neutrality conditions, 171
electromechanical fields, 170
field equations, 168
heterogeneous, 172
homogeneous, 168, 174
junction interface, 171
MATLAB, 172
one-dimensional constitutive relations, 169
p and n distributions, 172
piezoelectric semiconductor beams, 168
piezotronic devices, 172
undetermined constants, 170
Poisson-Boltzmann equation, 35
Poisson’s effect, 119, 120, 122
Poisson’s equation, 35
Polarization charges, 43, 54, 60, 191,
193, 195, 200
Polarization vector, 151
Polarized ceramics (PZT), 147
Potential barriers, 60, 186, 187
Potential wells, 60, 186, 187
Power series, 113, 134
Pyroelectric constants, 10
Pyroelectric coupling, 180, 198
R
Relaxed material constants, 122
Resonance frequencies, 64
Resonances, 100
Rotatory inertia, 124, 165
S
Second-order equation, 207
Semiconductors, 18
Semi-infinite crack, 24
Shear correction factors, 122, 123
Shear deformation
beam shear strain, 94
constitutive relations, 94, 95
extension, 93
field equations, 94
inertia, 95
Shear electromechanical coupling factor, 130
Shear force Q, 164, 205
Shear-horizontal (SH) waves, 27–29, 146
Shell structures
bending
shear deformations, 139
and twisting moments, 139
carrier concentration perturbations, 134, 136
curvilinear coordinate systems, 132
dependence, 134
differential shell element, 132, 133
electric displacement/surface charge, 138
mechanical resultants/surface loads, 137
membrane theory, 140
scalar field gradient, 133
shear correction factors, 138
strain-displacement relations, 132
stress relaxations, 139
three-dimensional constitutive relations,
138
transverse shear forces, 136
two-dimensional charge equations, 136
two-dimensional continuity equations, 137
two-dimensional equations, 132, 136
vector field divergence, 134
Silicon (Si), 147, 219
Sinusoidal wave motion, 74
Smoothly graded PN junction
boundary conditions, 40
convergence domain, 42
doping profiles, 40, 42
error function, 41
local charge distribution, 40
mobile/polarization charge effect, 42, 43
recurrence relation, 41
Static bending analysis, 100
Static extension, 179
Stress relaxation, 143, 163
Surface waves
anti-plane motions, 141
boundary/continuity conditions, 143
228
Index