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| Part I Experimental Realization | ||
| 1 | Elements for Designing an X-Ray Diffraction Experiment | 5 |
| 1.1 | X-Ray Sources | 5 |
| 1.2 | Optical Elements | 11 |
| 1.3 | Detectors | 23 |
| 2 | Diffractometers and Reflectometers | 31 |
| 2.1 | X-Ray Reflectometers | 32 |
| 2.2 | High-Resolution Diffractometer | 37 |
| 2.3 | Limits of the Use of Powder Diffractometers | 39 |
| 2.4 | Grazing-Incidence Diffraction | 40 |
| 3 | Scans and Resolution in Angular and Reciprocal Space | 43 |
| 3.1 | Coherence of Radiation and Correlation of Sample Properties | 44 |
| 3.2 | Scans Across the Reciprocal Space | 47 |
| 3.3 | Resolution Elements | 51 |
| Part II Basic Principles | ||
| 4 | Basic Principles | 63 |
| 4.1 | Description of the X-Ray Waveheld in Vacuum | 63 |
| 4.2 | General Description of the Scattering Process | 65 |
| 4.3 | Direction of Scattered Waves | 68 |
| 5 | Kinematical Theory | 75 |
| 5.1 | Scattering From a Perfect Layer | 75 |
| 5.2 | Two-Beam Approximation | 81 |
| 5.3 | Kinematical Scattering From Deformed Crystals | 85 |
| 5.4 | Kinematical Scattering Prom Multilayers | 87 |
| 5.5 | Kinematical Scattering From Randomly Deformed Crystals | 91 |
| 6 | Dynamical Theory | 97 |
| 6.1 | The Wave Equation for a Periodic Medium | 97 |
| 6.2 | Boundary Conditions | 99 |
| 6.3 | X-Ray Reflection | 102 |
| 6.4 | Two-Beam Diffraction | 104 |
| 6.5 | Layered Samples | 112 |
| 6.5.1 | Multilayers: X-Ray Reflection | 116 |
| 6.5.2 | Multilayers: Conventional X-Ray Diffraction | 117 |
| 6.6 | A Comment on the Three-Beam Diffraction | 119 |
| 7 | Semikinematical Theory | 123 |
| 7.1 | Basic Formulas | 123 |
| 7.2 | Examples | 125 |
| 7.2.1 Small-Angle Scattering from Empty Holes in a | ||
| Semi-infinite Matrix | 125 | |
| 7.2.2 Small-Angle Scattering from Pyramidal Islands | ||
| Randomly Placed on a Flat Surface | 128 | |
| 7.2.3 Diffuse Scattering in Diffraction from Empty Holes in | ||
| a Crystal | 129 | |
| 7.2.4 Diffraction from a Thin Layer on a Semi-infinite | ||
| Substrate | 132 | |
| Part III Solution of Experimental Problems | ||
| 8 Determination of Layer Thicknesses of Single Layers and | ||
| Multilayers | 143 | |
| 8.1 | X-Ray Reflection by Single Layers | 144 |
| 8.2 | X-Ray Reflection by Periodical Multilayers | 153 |
| 8.3 | Coplanar X-Ray Diffraction by Single Layers | 161 |
| 8.4 | Coplanar X-Ray Diffraction by Periodical Superlattices | 166 |
| 8.5 | X-Ray Grazing Incidence Diffraction | 171 |
| 8.6 | Buried Layers | 174 |
| 9 Lattice Parameters and Strains in Epitaxial Layers and | ||
| Multilayers | 179 | |
| 9.1 | Conventional Coplanar Diffraction | 179 |
| 9.2 | Reciprocal-Space Mapping | 190 |
| 9.3 | Coplanar Extremely Asymmetric Diffraction | 193 |
| 9.4 | Utilization of Anomalous Scattering Effects | 197 |
| 9.5 | Grazing-Incidence Diffraction | 198 |
Qx scan, 49, 267
Qz scan, 49, 266, 300
Oif scans, 202
cj scan, 260, 299
v scan /20 scan, 33, 38, 49
(j)± set-up, 185
<j>± set-up, 181, 184, 185, 194
Q scan, 49
Umweganregung, 271
Umweganregung, 268, 294, 298
AlAs, 167-169, 176, 178, 190
AlAs/GaAs multilayer, 264
AlAs/GaAs superlattice, 169
AlGaAs, 165, 172, 174-177, 183, 185,
186, 188, 295, 343, 344
A1N, 201
amorphous samples, 80
amplitude contrast, 174
amplitude equations, 98, 102, 104, 108,
119, 120
analyzer, 12, 41, 53
analyzer streak, 54, 299
angle-dispersive reflectometer, 33
anomalous scattering, 197, 384
anticathode, 6
area detector, 28, 29
asymmetric coplanar diffraction, 72,
187, 334
asymmetry angle, 13, 70, 72, 181
asymmetry factor, 13, 50, 71
atomic scattering factor, 12, 78, 82
atomistic calculation of the deforma- tion, 370
Au, 224
averaged lattice, 206
band pass, 14
beam compressor, 18, 33
bent monochromator, 39
Bloch theorem, 68, 98
BN, 145
boundary conditions, 99, 102, 107, 108,
114, 121
Bragg angle, 12, 14, 16, 70, 180
Bragg case, 70, 108, 110
Bragg-like peak, 263
Bragg-like resonant scattering, 263
bremsstrahlung, 5
brightness, 8
brilliance, 8
Brillouin zone, 98
Brownian motion, 240
buried grating, 334, 336, 338, 340
buried layer, 174, 175, 185, 189
carbon, 163
CaSrF2, 195
CdCaTe, 195, 196
CdTe, 196, 231
channel-cut monochromator, 17, 37
characteristic function, 237
characteristic radiation, 5
classical electron radius, 13, 75
coherent reflectivity, 243-245
coherent scattering, 64, 91
coherent superposition of amplitudes, 162
coherent wave, 93, 235
collimator, 12, 15
commensurate lateral grating, 285
composition gradient, 165, 173, 192,
196, 236, 299
composition modulation, 344
compositional grading, 174
compositional grating, 328
conventional diffraction, 101, 108, 115,
117, 129, 132, 169, 179
coplanar geometry, 43, 48, 50, 70, 100, 106, 107, 115, 205, 221, 279, 294, 334, 371, 380
core scattering, 209, 211
correlated roughness, 244
correlation function, 92, 207, 225, 229,
238, 239, 258, 357
correlation function, in-plane, 239
correlation function, inter-plane, 240
correlation function, vertical, 241
correlation length, 43, 64, 125
correlation length, lateral, 240, 243,
247, 262
correlation length, vertical, 241
correlation of the island position, 356
covariance, 93, 207, 256, 257, 260, 369
coverage, 238
Cr/TbFe/W, 249
critical angle of total external reflection, 33, 102, 104, 111, 127, 144, 147, 155, 160, 194, 222
critical thickness, 182
cross pattern, 323, 327
crystal truncation rod, 41, 50, 54, 56, 69, 79, 80, 94, 108, 212, 224, 242, 286, 359, 364, 371
dead time, 24
defect cluster, 212
defect core, 207
defect density, 206
defect strength, 209, 216
deformation depth, 325
deformed crystal, 85
degree of relaxation, 182, 185, 190, 193,
199, 228
depth resolution, 173
detector, 12, 23
differential cross section, 67, 123,
125-128, 223, 252
diffracted wave, 70
diffraction condition, 70, 80
diffraction vector, 70, 104, 113
diffractivity, 109, 111, 116, 118, 162, 169, 193
diffuse scattering, 94, 205, 208, 235, 252, 259
dislocation, 225
dislocation density, 225, 228
dispersion condition, 68, 99, 102, 105,
106, 108, 119
dispersion surface, 99, 101, 102, 105,
109, 113
dispersive arrangement, 15
displacement probability density, 237
disturbance, 123, 126, 130, 223, 291
double-crystal arrangement, 14
DuMond diagram, 16
duMond diagram, 16, 38
DWBA, 124, 132, 205, 208, 222, 223,
252, 279, 291, 293, 294, 297, 381
dynamical fringes, 260
dynamical scattering, 97
dynamical scattering effects, 260
dynamical strain grating, 351
dynamical x-ray scattering, 97, 131, 153, 287
Ehrlich-Schwoebel barrier, 354
elastic constants, 180, 216, 217, 319
elastic displacement, 85, 206, 213, 283,
284, 320, 325
elastic equilibrium, 216
elastic Green function, 218
elastic isotropy, 209
elastic scattering, 63
electron density, 75, 76, 81, 98, 102,
146-148, 160, 161, 172
electron density gradient, 164
electron lifetime, 10
electron optics, 7
energy-dispersive arrangement, 34, 35,
51, 55, 151, 161
energy-dispersive detector, 24
ensemble averaging, 64, 91, 243, 244
EuSe, 197, 198
Ewald construction, 69, 78, 101, 102,
107, 170
Ewald sphere, 69, 94, 102, 265, 272, 349
extinction length, 135
Fewster-Curling effect, 187
finite-element method, 325, 370
flux, 109
footprint correction, 147
four-bounce monochromator, 17
four-reflection monochromator, 17, 33,
38, 39, 46, 53, 54
fractal dimension, 240
fractal exponent, 240
Fraunhofer approximation, 66
Fraunhofer diffraction, 44, 47
free-electron laser, 10
Fresnel coefficients, 81, 103, 116, 126, 127, 144, 154, 209, 222, 223, 244-246, 289, 294
Fresnel zone, 67
Gôbel mirror, 19, 33, 37
GaAs, 149, 150, 163, 167 169, 171-173, 178, 184, 190, 192, 194, 197, 199, 201, 247, 248, 298, 377
GaAs overgrown by AlGaAs, 344
GaAs/AlAs, 261
GaAs/AlAs multilayer, 250, 263, 271
GaAs/AlAs quantum dot, 333
GaAs/AlAs superlattice, 260
GaAs/AlGaAs multilayer, 172
GaAsP, 188, 377
GalnAs/InP multilayer grating, 312
GalnAsP superlattice grating, 341
GaN, 201, 202
Ge, 357, 380
Ge/Si, 259
general dynamical diffraction, 110, 115, 132, 169
geometrical factor of periodic multi- layer, 90
geometrical factor of the crystal, 77, 78, 80, 86
geometrical factor of the defect
positions, 224
geometrical factor of the interface
disturbance, 255
geometrical factor of the island
positions, 359, 362, 364, 369
geometrical factor of the layer, 88, 134, 208
GISAX, 58, 314
GISAXS, 128, 223, 224, 357, 361, 365, 368
graded interface profile, 235
graded layer, 165, 192, 236
grating, 279, 298, 309, 325
grating depth, 299, 307
grating form factor, 282, 283, 293, 306, 320
grating period, 279, 281
grating reflectivity, 287
grating rod, 279, 282, 320, 328, 333, 347
grating rod pattern, 311
grating shape, 279
grating shape function, 282
grating structure factor, 281, 325
grating-induced displacement, 284
grating-induced strain, 283, 328
grazing-incidence diffraction, 40, 43, 55, 72, 100, 107, 111, 172-174, 198-203, 205, 214, 216, 222, 235, 267, 279, 291, 300, 301, 309, 327, 328, 333, 335, 337, 341, 342, 344, 349, 357, 378
Green function, 65, 77
height-height correlation function, 240
high-resolution diffraction, 179
high-resolution diffractometer, 17, 37,
39, 43, 299
homogeneous wavefield, 65, 67, 86, 93
Huang scattering, 209-211, 218-221
InAs, 356, 382
inclination angle, 181, 183
incoherent wave, 94, 208, 235
infinite crystal, 98
InGaAs, 163, 164, 172, 173, 176, 178, 184-186, 188-190, 197, 199, 200, 344, 377
InGaAs/InP grating, 300, 324, 327, 328, 330
InGaAs/InP multilayer grating, 310
InGaAs/InP trapezoidal grating, 322, 323
InGaAsP, 183, 187
InGaAsP multilayer, 341
InGaAsP/InP buried grating, 339
InGaAsP/InP grating, 337, 341
InGaAsP/InP multilayer grating, 330
InP, 178, 187
integrated intensity, 84
intensity distribution in reciprocal space, 45, 65, 79, 81, 82, 93, 94, 208, 321, 371
intensity envelope, 321
inter-rod scattering, 289
interdiffusion, 165, 197, 203, 236, 353, 377
interface roughness, 236
intra-rod scattering, 290
intrinsic roughness, 239, 251
ion implantation, 223, 342
iso-strain method, 380
Kiessig fringes, 32, 36, 144, 156, 157,
159, 162, 169, 177, 178, 248, 308
kinematic approximation, 66, 75, 80, 97, 98, 121, 124, 128, 153, 166, 205, 242, 245, 279, 284, 286, 357
kinetic roughening, 240, 241, 266
knife-edge, 33
Langmuir-Blodgett film, 148, 152, 153,
158-160
laser structure, 187, 188, 190
lateral diffraction condition, 68, 70, 72,
77, 78, 80, 108
lattice misfit, 168, 180, 184, 192, 317, 319, 320
lattice mismatch, 144, 176, 179, 180,
182, 209
lattice parameter, 182, 199
Laue case, 70, 72, 109
Laue point, 105
layer, 187
layer thickness, 143, 144, 146, 157, 161,
162, 164, 237
LiNb03, 352
linear polarization factor, 12, 75, 78
long-range-order model, 362
longitudinal scan, 302, 337
many-beam scattering, 83, 87, 99, 119
mass density, 148
matrix formalism, 114
mesoscopic superstructure, 279, 304
mica, 157, 158, 178
mirror, 12
misfit dislocations, 182, 225, 227, 356
Mo, 177, 178
modified diffraction condition, 155, 157, 262
Moire pattern, 347
monochromator, 12, 14-18, 22
monochromator streak, 54, 271, 299, 307
monolayer steps, 354
mosaic structure, 229, 230
multilayer, 87, 112, 116, 118, 132, 156, 158, 160, 170, 172, 177, 178, 184, 192, 196, 197, 199, 237, 241
multilayer grating, 282, 283, 310, 317
multilayer mirror, 20, 21
multiple diffraction effects, 295
multiple scattering effects, 290
mutual coherence function, 44, 64, 78, 85, 92
Nb/Si multilayer, 263
nearly forbidden reflection, 298
non-commensurate lateral grating, 286
non-coplanar geometry, 50, 70, 72, 265,
302, 327
non-dispersive arrangement, 15
non-disturbed system, 123, 125, 128,
129, 132, 205, 223, 253, 257, 288, 291
non-disturbed wavefield, 124, 127, 128,
132, 253, 254, 257, 269, 288, 291
non-disturbed wavefields, 130
non-specular x-ray reflectivity, 252
non-uniform strain relaxation, 324
occupation number, 205
offset scan, 49, 50
one-beam approximation, 97, 98, 102
optical element, 11, 43, 45, 46
pair correlation function, 361
parasitic rods, 313
PbEuTe, 356
PbSe, 197, 198, 356, 371
PbSe/PbEuTe quantum dots, 372
penetration depth, 41, 199
periodic multilayer, 88, 153, 166, 249
phase contrast, 174
plastic relaxation, 228, 356
Poisson ratio, 210, 217
polarizability, 12, 65, 75, 81, 92, 98, 113, 126, 144, 236, 254, 280, 281, 335, 357
polycapillary optics, 7
polymer grating, 315
position-sensitive detector, 26
powder diffractometer, 39, 43, 145
precipitate, 215
proportional counter, 23
pseudomorph structure, 87, 112, 162, 166, 184, 185, 268, 304, 317
quantum dots, 282, 332, 346, 354, 357,
371, 380, 382
quantum well, 172, 175, 185, 190, 343
quantum wires, 279, 354, 374, 377
quaternary system, 182
radial scan, 49
random deformation, 91
reciproca-space map, 341
reciprocal grating vector, 281
reciprocal-space map, 37, 43, 50, 80, 95, 127, 131, 190-192, 212, 215, 226, 227, 230, 258, 261, 263, 264, 298, 300, 321, 322, 324, 327, 336, 372
recurrence formula, 115, 117, 119, 162
reduced scattering vector, 77, 94, 135,
206, 208, 284
reflectivity, 116, 117, 146, 154
refractive index, 102, 144, 155, 168
relaxation line, 191
replication function, 239
replication model, 239, 250
resolution area, 51, 55, 57
resolution element, 43, 44, 54, 307
resonant diffuse scattering, 260, 262, 271
root mean square roughness, 238, 246
rough interfaces, 238, 241, 294
rough multilayer, 235
rough surface, 236, 245, 257
roughness, 165, 235
roughness of wire, 315
S and P polarizations, 75, 99, 103, 109
sapphire, 158, 201-203
SASE, 10
satellite branches, 311
Sb, 149, 150
scattered wave, 63, 66, 75
scattering contrast, 144, 173
scattering operator, 66, 75, 91, 286
scattering plane, 43, 75
scattering potential, 65, 75, 123, 236, 253, 280, 282, 284, 296, 319
scattering potential, effective, 242
scattering processes, 256, 260
scattering vector, 43, 48, 67, 128, 254, 297
scintillation counter, 24
secondary resonant diffuse scattering, 272
self-organization, 343, 346, 353
semi-infinite crystal, 103, 108-110, 125, 162, 218, 226
semikinematical approximation, 123, 124, 132, 135, 162, 166, 168, 170, 222, 223, 242, 279, 284, 296, 314, 325, 331, 357, 368
shape function of the crystal, 76, 77
shape function of the defect, 207, 216, 224
shape function of the island, 358, 369
shape function of the mosaic block, 229
short-range-order model, 359, 373
Si, 146, 149, 150, 156, 170, 202, 203,
212-216, 223, 245, 246, 349
Si/C/Ge quantum dots, 365
Si/Nb multilayer, 251
SiC, 215
SiGe, 156, 170, 184, 185, 192, 196, 356,
358, 374, 378
SiGe quantum dots, 303, 333, 361, 368
single-reflection approximation, 153
Si02, 146, 150
slits, 11, 32
slope of the grating side walls, 307
solid-state detector, 25, 26, 161
Soller slit, 12
specular scan, 49, 51
specular x-ray reflectivity, 243, 250
spherical inclusion, 209, 219
ssuperlattice maximum, 155
stacking fault, 213, 214
static Debye-Waller factor, 93, 135,
205, 206, 225, 229, 363
static Debye-Waller-like factor, 314
statistical ensemble, 64, 91
statistically homogeneous sample, 92
step-bunching, 304, 354
step-flow growth, 353
strain energy, 179
strain grating, 284, 323, 325, 328, 346
strain grating by focussed ion-
implantation, 342
strain profile, 327
strain tensor, 85, 323, 339
Stranski-Krastanow growth, 353, 354
strong defects, 205, 206, 225
strongly asymmetric diffraction, 107,
110, 193, 268
structure amplitude, 82
structure factor, 169
structure factor of the multilayer
period, 89, 91
structure factor of the unit cell, 77, 78,
80, 81, 87
subsidiary maxima, 80, 144
super-mirror, 21, 152
superlattice maximum, 90, 155, 167,
178, 251, 311
surface acoustic wave, 351
surface energy density, 355
surface gratings, 275
surface reconstruction, 355
surface sensitive scattering, 235
surface stress relaxation, 205, 209, 215,
317, 319-321
symmetric coplanar diffraction, 72, 170, 327, 330
synchrotron radiation, 7, 39, 44, 146
synchrotron radiation spectrum, 7
Takagi approximation, 85, 87, 92, 93, 207
ternary system, 343
terrace, 354
thickness fringes, 90
three-beam approximation, 119
tie point, 101, 106-108, 113-115, 120
tilt-induced maximum, 348
tilt-interfacial dislocations, 348
total external reflection, 102, 104
total thickness, 156, 157, 169
translational symmetry, 68
transversal scan, 302, 337
transverse scan, 299
trapezoidal grating, 307, 310
truncation rod, 202
twist-interfacial dislocations, 346
two-beam approximation, 81, 97, 99, 104, 281
two-dimensional characteristic function, 238
Umweganregung, 264
undulator, 8, 9
V, 157, 178
Vegard's law, 182, 193
vertical diffraction condition, 80
volume defects, 205
W/sapphire, 247, 258
W/Si multilayer, 266, 267
W/Si multilayer grating, 312, 313
wafer bonding, 346, 347, 349
wave equation, 65, 97, 123
wavelength streak, 54
weak defects, 205, 206, 215
wetting layer, 355
wiggler, 8, 9
wire shape function, 282, 320
x-ray coherence, 8, 11, 80
x-ray coherence length, 11, 43
x-ray coherence length, effective, 46
x-ray coherence length, lateral, 45
x-ray coherence length, longitudinal, 44
x-ray microfocus tube, 7
x-ray reflection, 32, 70, 72, 81, 97, 102,
115, 116, 177, 178, 184, 261, 292
x-ray refraction, 80
x-ray rotating anode, 7
x-ray sealed tube, 6
x-ray sources, 5
x-ray target, 6
x-ray tube, 5, 32
Yoneda wing, 271
Yoneda wings, 111, 127, 209, 222, 260,
263, 359, 376
Yoneda-like wings, 308
ZnSe, 191, 192
