 | Freund L.B. Thin film materials: stress, defect formation, and surface evolution / L.B.Freund, S.Suresh. - Cambridge; New York: Cambridge University Press, 2003 (2006). - xviii, 750 p.: ill. - Ref.: p.713-737. - Auth. ind.: p.739-744. - Sub. ind.: p.745-750.
- ISBN 978-0-521-82281-7
Шифр: (И/З.84-F90) 02
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Preface ....................................................... xvi
1 Introduction and Overview .................................. 1
1.1 A classification of thin film configurations ............... 2
1.2 Film deposition methods .................................... 6
1.2.1 Physical vapor deposition ........................... 6
1.2.2 Chemical vapor deposition ........................... 9
1.2.3 Thermal spray deposition ........................... 10
1.2.4 Example: Thermal barrier coatings .................. 13
1.3 Modes of film growth by vapor deposition .................. 15
1.3.1 From vapor to adatoms .............................. 15
1.3.2 From adatoms to film growth ........................ 17
1.3.3 Energy density of a free surface or an interface ... 20
1.3.4 Surface stress ..................................... 25
1.3.5 Growth modes based on surface energies ............. 27
1.4 Film microstructures ...................................... 30
1.4.1 Epitaxial films .................................... 31
1.4.2 Example: Vertical-cavity surface-emitting lasers ... 39
1.4.3 Polycrystalline films .............................. 40
1.4.4 Example: Films for magnetic storage media .......... 45
1.5 Processing of microelectronic structures .................. 47
1.5.1 Lithography ........................................ 48
1.5.2 The damascene process for copper interconnects ..... 50
1.6 Processing of MEMS structures ............................. 52
1.6.1 Bulk micromachining ................................ 52
1.6.2 Surface micromachining ............................. 53
1.6.3 Molding processes .................................. 55
1.6.4 NEMS structures .................................... 55
1.6.5 Example: Vibrating beam bacterium detector ......... 59
1.7 Origins of film stress .................................... 60
1.7.1 Classification of film stress ...................... 60
1.7.2 Stress in epitaxial films .......................... 62
1.8 Growth stress in polycrystalline films .................... 63
1.8.1 Compressive stress prior to island coalescence ..... 65
1.8.2 Example: Influence of areal coverage ............... 68
1.8.3 Tensile stress due to island contiguity ............ 69
1.8.4 Compressive stress during continued growth ......... 70
1.8.5 Correlations between final stress and grain
structure .......................................... 72
1.8.6 Other mechanisms of stress evolution ............... 73
1.9 Consequences of stress in films ........................... 83
1.10 Exercises ................................................. 83
2 Film stress and substrate curvature ....................... 86
2.1 The Stoney formula ........................................ 87
2.1.1 Example: Curvature due to epitaxial strain ......... 92
2.1.2 Example: Curvature due to thermal strain ........... 93
2.2 Influence of film thickness on bilayer curvature .......... 93
2.2.1 Substrate curvature for arbitrary film thickness ... 95
2.2.2 Example: Maximum thermal stress in a bilayer ...... 101
2.2.3 Historical note on thermostatic bimetals .......... 102
2.3 Methods for curvature measurement ........................ 104
2.3.1 Scanning laser method ............................. 106
2.3.2 Multi-beam optical stress sensor .................. 107
2.3.3 Grid reflection method ............................ 109
2.3.4 Coherent gradient sensor method ................... 111
2.4 Layered and compositionally graded films ................. 114
2.4.1 Nonuniform mismatch strain and elastic
properties ........................................ 116
2.4.2 Constant gradient in mismatch strain .............. 120
2.4.3 Example: Stress in compositionally graded films ... 121
2.4.4 Periodic multilayer film .......................... 123
2.4.5 Example: Overall thermoelastic response of
a multilayer ...................................... 124
2.4.6 Multilayer film with small total thickness ........ 125
2.4.7 Example: Stress in a thin multilayer film ......... 126
2.5 Geometrically nonlinear deformation range ................ 127
2.5.1 Limit to the linear range ......................... 128
2.5.2 Axially symmetric deformation in the nonlinear
range ............................................. 130
2.6 Bifurcation in equilibrium shape ......................... 132
2.6.1 Bifurcation analysis with uniform curvature ....... 134
2.6.2 Visualization of states of uniform curvature ...... 142
2.6.3 Bifurcation for general curvature variation ....... 145
2.6.4 A substrate curvature deformation map ............. 149
2.6.5 Example: A curvature map for a Cu/Si system ....... 150
2.7 Exercises ............................................... 151
3 Stress in anisotropic and patterned films ................ 154
3.1 Elastic anisotropy ....................................... 155
3.2 Elastic constants of cubic crystals ...................... 157
3.2.1 Directional variation of effective modulus ........ 158
3.2.2 Isotropy as a special case ........................ 161
3.3 Elastic constants of non-cubic crystals .................. 161
3.4 Elastic strain in layered epitaxial materials ............ 163
3.5 Film stress for a general mismatch strain ................ 166
3.5.1 Arbitrary orientation of the film material ........ 166
3.5.2 Example: Cubic thin film with a (111)
orientation ....................................... 169
3.6 Film stress from x-ray diffraction measurement ........... 171
3.6.1 Relationship between stress and ^/-spacing ........ 172
3.6.2 Example: Stress implied by measured ^/-spacing .... 174
3.6.3 Stress-free ^-spacing from asymmetric
diffraction ....................................... 174
3.6.4 Example: Determination of reference lattice
spacing ........................................... 179
3.7 Substrate curvature due to anisotropic films ............. 180
3.7.1 Anisotropic thin film on an isotropic substrate ... 180
3.7.2 Aligned orthotropic materials ..................... 182
3.8 Piezoelectric thin film .................................. 185
3.8.1 Mismatch strain due to an electric field .......... 186
3.8.2 Example: Substrate curvature due to an electric
field ............................................. 187
3.9 Periodic array of parallel film cracks ................... 188
3.9.1 Plane strain curvature change due to film
cracks ............................................ 190
3.9.2 Biaxial curvature due to film cracks .............. 197
3.10 Periodic array of parallel lines or stripes .............. 201
3.10.1 Biaxial curvature due to lines .................... 201
3.10.2 Volume averaged stress in terms of curvature ...... 206
3.10.3 Volume averaged stress in a damascene structure ... 209
3.11 Measurement of stress in patterned thin films ............ 212
3.11.1 The substrate curvature method .................... 212
3.11.2 The x-ray diffraction method ...................... 213
3.11.3 Micro-Raman spectroscopy .......................... 214
3.12 Exercises ................................................ 216
4 Delamination and fracture ................................ 220
4.1 Stress concentration near a film edge .................... 221
4.1.1 A membrane film ................................... 223
4.1.2 Example: An equation governing interfacial shear
stress ............................................ 226
4.1.3 More general descriptions of edge stress .......... 227
4.2 Fracture mechanics concepts .............................. 232
4.2.1 Energy release rate and the Griffith criterion .... 233
4.2.2 Example: Interface toughness of a laminated
composite ......................................... 237
4.2.3 Crack edge stress fields .......................... 239
4.2.4 Phase angle of the local stress state ............. 243
4.2.5 Driving force for interface delamination .......... 243
4.3 Work of fracture ......................................... 246
4.3.1 Characterization of interface separation
behavior .......................................... 246
4.3.2 Effects of processing and interface chemistry ..... 250
4.3.3 Effect of local phase angle on fracture energy .... 253
4.3.4 Example: Fracture resistance of nacre ............. 256
4.4 Film delamination due to residual stress ................. 258
4.4.1 A straight delamination front ..................... 262
4.4.2 Example: Delamination due to thermal strain ....... 263
4.4.3 An expanding circular delamination front .......... 264
4.4.4 Phase angle of the stress concentration field ..... 268
4.4.5 Delamination approaching a film edge .............. 270
4.5 Methods for interface toughness measurement .............. 272
4.5.1 Double cantilever test configuration .............. 273
4.5.2 Four-point flexure beam test configuration ........ 274
4.5.3 Compression test specimen configurations .......... 277
4.5.4 The superlayer test configuration ................. 280
4.6 Film cracking due to residual stress ..................... 282
4.6.1 A surface crack in a film ......................... 283
4.6.2 A tunnel crack in a buried layer .................. 290
4.6.3 An array of cracks ................................ 292
4.6.4 Example: Cracking of an epitaxial film ............ 297
4.7 Crack deflection at an interface ......................... 297
4.7.1 Crack deflection out of an interface .............. 299
4.7.2 Crack deflection into an interface ................ 302
4.8 Exercises ................................................ 309
5 Film buckling, bulging and peeling ....................... 312
5.1 Buckling of a strip of uniform width ..................... 313
5.1.1 Post-buckling response ............................ 314
5.1.2 Driving force for growth of delamination .......... 319
5.1.3 Phase angle of local stress state at interface .... 321
5.1.4 Limitations for elastic-plastic materials ......... 325
5.2 Buckling of a circular patch ............................. 327
5.2.1 Post-buckling response ............................ 328
5.2.2 Example: Temperature change for buckling of
a debond .......................................... 332
5.2.3 Driving force for delamination .................... 333
5.2.4 Example: Buckling of an oxide film ................ 337
5.3 Secondary buckling ....................................... 338
5.4 Experimental observations ................................ 341
5.4.1 Edge delamination ................................. 341
5.4.2 Initially circular delamination ................... 341
5.4.3 Effects of imperfections on buckling
delamination ...................................... 345
5.4.4 Example: Buckling instability of carbon films ..... 348
5.5 Film buckling without delamination ....................... 350
5.5.1 Soft elastic substrate ............................ 350
5.5.2 Viscous substrate ................................. 353
5.5.3 Example: Buckling wavelength for a glass
substrate ......................................... 354
5.6 Pressurized bulge of uniform width ....................... 355
5.6.1 Small deflection bending response ................. 355
5.6.2 Large deflection response ......................... 357
5.6.3 Membrane response ................................. 360
5.6.4 Mechanics of delamination ......................... 363
5.7 Circular pressurized bulge ............................... 366
5.7.1 Small deflection bending response ................. 367
5.7.2 Membrane response ................................. 367
5.7.3 Large deflection response ......................... 371
5.7.4 The influence of residual stress .................. 372
5.7.5 Delamination mechanics ............................ 374
5.7.6 Bulge test configurations ......................... 377
5.8 Example: MEMS capacitive transducer ...................... 378
5.9 Film peeling ............................................. 382
5.9.1 The driving force for delamination ................ 382
5.9.2 Mechanics of delamination ......................... 383
5.10 Exercises ................................................ 385
6 Dislocation formation in epitaxial systems ............... 387
6.1 Dislocation mechanics concepts ........................... 388
6.1.1 Dislocation equilibrium and stability ............. 388
6.1.2 Elastic field of a dislocation near a free
surface ........................................... 391
6.2 Critical thickness of a strained epitaxial film .......... 396
6.2.1 The critical thickness criterion .................. 397
6.2.2 Dependence of critical thickness on mismatch
strain ............................................ 400
6.2.3 Example: Critical thickness of a SiGe film on
Si(001) ........................................... 402
6.2.4 Experimental results for critical thickness ....... 403
6.2.5 Example: Influence of crystallographic
orientation on hcr ................................ 404
6.3 The isolated threading dislocation ....................... 406
6.3.1 Condition for advance of a threading dislocation .. 406
6.3.2 Limitations of the critical thickness condition ... 411
6.3.3 Threading dislocation under nonequilibrium
conditions ........................................ 413
6.4 Layered and graded films ................................. 416
6.4.1 Uniform strained layer capped by an unstrained
layer ............................................. 418
6.4.2 Strained layer superlattice ....................... 422
6.4.3 Compositionally graded film ....................... 423
6.5 Model system based on the screw dislocation .............. 424
6.5.1 Critical thickness condition for the model
system ............................................ 424
6.5.2 The influence of film-substrate modulus
difference ........................................ 426
6.5.3 Example: Modulus difference and dislocation
formation ......................................... 429
6.6 Non-planar epitaxial systems ............................. 430
6.6.1 A buried strained quantum wire .................... 432
6.6.2 Effect of a free surface on quantum wire
stability ......................................... 437
6.7 The influence of substrate compliance .................... 441
6.7.1 A critical thickness estimate ..................... 442
6.7.2 Example: Critical thickness for a compliant
substrate ......................................... 444
6.7.3 Misfit strain relaxation due to a viscous
underlayer ........................................ 445
6.7.4 Force on a dislocation in a layer ................. 448
6.8 Dislocation nucleation ................................... 451
6.8.1 Spontaneous formation of a surface dislocation
loop .............................................. 453
6.8.2 Dislocation nucleation in a perfect crystal ....... 455
6.8.3 Effect of a stress concentrator on nucleation ..... 458
6.9 Exercises ................................................ 461
7 Dislocation interactions and strain relaxation ........... 464
7.1 Interaction of parallel misfit dislocations .............. 465
7.1.1 Spacing based on mean strain ...................... 466
7.1.2 Spacing for simultaneous formation of
dislocations ...................................... 467
7.1.3 Spacing based on insertion of the last
dislocation ....................................... 469
7.2 Interaction of intersecting misfit dislocations .......... 470
7.2.1 Blocking of a threading dislocation ............... 472
7.2.2 Intersecting arrays of misfit dislocations ........ 477
7.3 Strain relaxation due to dislocation formation ........... 480
7.3.1 Construction of a relaxation model ................ 480
7.3.2 Example: Dislocation control in semiconductor
films ............................................. 484
7.4 Continuum analysis of ideally plastic films .............. 488
7.4.1 Plastic deformation of a bilayer .................. 488
7.4.2 Thin film subjected to temperature cycling ........ 494
7.4.1 7.5 Strain-hardening response of thin films ...... 496
7.5.1 Isotropic hardening ............................... 499
7.5.2 Example: Temperature cycling with isotropic
hardening ......................................... 501
7.5.3 Kinematic hardening ............................... 502
7.5.4 Proportional stress history ....................... 505
7.6 Models based on plastic rate equations ................... 508
7.6.1 Thermally activated dislocation glide past
obstacles ......................................... 510
7.6.2 Influence of grain boundary diffusion ............. 512
7.7 Structure evolution during thermal excursion ............. 515
7.7.1 Experimental observation of grain structure
evolution ......................................... 515
7.7.2 Experimental observation of threading
dislocations ...................................... 517
7.7.3 Strain relaxation mechanisms during temperature
cycling ........................................... 520
7.8 Size-dependence of plastic yielding in thin films ........ 527
7.8.1 Observation of plastic response ................... 527
7.8.2 Models for size-dependent plastic flow ............ 531
7.8.3 Influence of a weak film-substrate interface ...... 534
7.9 Methods to determine plastic response of films ........... 535
7.9.1 Tensile testing of thin films ..................... 535
7.9.2 Microbeam deflection method ....................... 537
7.9.3 Example: Thin film undergoing plane strain
extension ......................................... 539
7.9.4 Substrate curvature method ........................ 542
7.9.5 Instrumented nanoindentation ...................... 543
7.10 Exercises ................................................ 547
8 Equilibrium and stability of surfaces .................... 550
8.1 A thermodynamic framework ................................ 551
8.2 Chemical potential of a material surface ................. 553
8.2.1 An evolving free surface .......................... 553
8.2.2 Mass transport along a bimaterial interface ....... 558
8.2.3 Migration of a material interface ................. 560
8.2.4 Growth or healing of crack surfaces ............... 564
8.3 Elliptic hole in a biaxially stressed material ........... 567
8.3.1 Chemical potential ................................ 568
8.3.2 Shape stability ................................... 570
8.4 Periodic perturbation of a flat surface .................. 573
8.4.1 Small amplitude sinusoidal fluctuation ............ 573
8.4.2 Example: Stability of a strained epitaxial film ... 578
8.4.3 Influence of substrate stiffness on surface
stability ......................................... 578
8.4.4 Second order surface perturbation ................. 582
8.4.5 Example: Validity of the small slope
approximation ..................................... 586
8.5 General perturbation of a flat surface ................... 588
8.5.1 Two-dimensional configurations ................... 588
8.5.2 Three-dimensional configurations .................. 589
8.5.3 Example: Doubly periodic surface perturbation ..... 590
8.6 Contact of material surfaces with cohesion ............... 592
8.6.1 Force-deflection relationship for spherical
surfaces .......................................... 592
8.6.2 Example: Stress generated when islands impinge .... 597
8.7 Consequences of misfit dislocation strain fields ......... 598
8.7.1 Surface waviness due to misfit dislocations ....... 599
8.7.2 Growth patterning due to misfit dislocations ...... 602
8.8 Surface energy anisotropy in strained materials .......... 604
8.8.1 Implications of mechanical equilibrium ............ 605
8.8.2 Surface chemical potential ........................ 608
8.8.3 Energy of a strained vicinal surface .............. 610
8.8.4 Example: Stepped surface near (001) for strained
Si ................................................ 615
8.9 Strained epitaxial islands ............................... 615
8.9.1 An isolated island ................................ 618
8.9.2 Influence of an intervening strained layer ........ 624
8.9.3 Influence of surface energy anisotropy ............ 626
8.9.4 Nucleation barrier for islands on stable
surfaces .......................................... 628
8.9.5 Shape transition for preferred side wall
orientations ...................................... 630
8.9.6 Observations of island formation .................. 632
8.10 Exercises ................................................ 638
9 The role of stress in mass transport ..................... 641
9.1 Mechanisms of surface evolution .......................... 643
9.1.1 Surface diffusion ................................. 643
9.1.2 Condensation-evaporation .......................... 647
9.2 Evolution of small surface perturbations ................. 648
9.2.1 One-dimensional sinusoidal surface ................ 649
9.2.2 Example: The characteristic time .................. 650
9.2.3 General surface perturbations ..................... 651
9.2.4 An isolated surface mound ......................... 654
9.3 A variational approach to surface evolution .............. 657
9.3.1 A variational principle for surface flux .......... 658
9.3.2 Application to second order surface perturbation .. 662
9.4 Growth of islands with stepped surfaces .................. 665
9.4.1 Free energy change ................................ 666
9.4.2 Formation and interaction of islands .............. 668
9.5 Diffusion along interfaces ............................... 673
9.5.1 Stress relaxation by grain boundary diffusion ..... 674
9.5.2 Diffusion along shear bands during deformation .... 678
9.6 Compositional variations in solid solutions .............. 681
9.6.1 Free energy of a homogeneous solution ............. 682
9.6.2 Stability of a uniform composition ................ 685
9.6.3 Example: Elastic stabilization of a composition ... 689
9.6.4 Evolution of compositional variations ............. 690
9.6.5 Coupled deformation-composition evolution ......... 692
9.7 Stress-assisted diffusion: electromigration .............. 697
9.7.1 Atom transport during electromigration ............ 698
9.7.2 The drift test .................................... 704
9.7.3 Effects of microstructure on electromigration
damage ............................................ 706
9.7.4 Assessment of interconnect reliability ............ 709
9.8 Exercises ................................................ 711
References .................................................... 713
Author index .................................................. 738
Subject index ................................................. 745
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