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Index

Symbols2D nucleation, 4212D-3D growth transformation, 1693D island, 4593D nanoislands, 463

AAbrupt changes, 551Abrupt structural transitions, 551Activation energy, 34, 375, 482Activity of sidewall adatoms, 394Adatom, 32, 34Adatom concentration, 26, 162, 164, 334, 337,

429, 484Adatom coverage, 381Adatom diffusion, 354, 375, 382, 388Adatom diffusion length, 40, 342, 346Adatom sink, 421Adatom supersaturation, 71Adatoms, 35, 335, 339, 367, 389Adsorbate, 31Adsorption, 30, 36, 323, 357Adsorption isotherm, 31Adsorption-induced VLS growth, 326AFM images, 246Algorithm, 110AlN buffer layer, 459AlN surface, 459Amino acid monomer, 157, 158Amorphous interlayer, 476Analysis, 97Analytical approximation, 192Analytical description, 86Analytical function, 154

Analytical solution, 88, 91Anisotropic growth, 463Anisotropic nanowire growth, 470Antimony, 245Approximation, 84, 90APT characterization, 442, 446APT measurements, 444Arbitrary size, 138, 141Arrival rate, 365Arsenic, 448As influx, 294Aspect ratio, 169, 205, 262Asymptotic behavior, 163, 343Asymptotic expressions, 103Asymptotic regime, 71, 72Asymptotic representation, 153Asymptotic solution, 116Asymptotic stage, 164Asymptotic terms, 137Asymptotical solutions, 96Atomic concentrations, 432Atomic concentrations of Ga, 556Attractive interactions, 5Au droplets, 278, 281Au islands, 390Au particle, 287Au-assisted GaAs nanowires, 362Au-assisted MBE, 371Au-assisted MBE growth, 370Au-assisted VLS growth, 493Au-catalyzed, 439Au-catalyzed GaAs nanowire, 284, 531Au-catalyzed GaAs wires, 286, 361Au-catalyzed Ge nanowires, 276Au-catalyzed III-V nanowires, 294

V. G. Dubrovskii, Nucleation Theory and Growth of Nanostructures, 591NanoScience and Technology, DOI: 10.1007/978-3-642-39660-1,© Springer-Verlag Berlin Heidelberg 2014

592 Index

Au-catalyzed VLS growth, 498Au-free growth protocols, 448Au-Ga phase diagram, 287, 289Au-In particles, 550Au-seeded MOCVD, 370Au-Si droplets, 290Average occupation, 5Axial nanowire heterostructures, 399

BB atoms, 447Ballistic growth regime, 41Band gap, 506, 508Barrel-like shape, 487Barton solution, 399Base diameter, 254Be doping, 351Beam, 324, 325Benefits, 553BET isotherm, 37Boron, 446Bottom-up approach, 278Boundary, 60, 140Boundary condition, 61, 336, 337, 340, 381,

446Broadening, 94, 103Bulk cohesive energies, 503Bulk energy difference, 528Bulk form, 501Bulk semiconductors, 173

CCalculations, 120, 495Capillary surface forces, 320Capture numbers, 162Catalyst droplet, 382, 383, 444Catalyst metal, 314Catalyst particle, 284Catalytic effect, 290Catalyzed nanowires, 435Cauchy theorem, 155CdTe nanowires, 427, 428Characteristic diffusion radius, 375Characteristic radius, 358Chemical potential, 6, 11, 17, 31, 66, 283, 304,

336, 337, 381, 382, 394, 493, 494,533, 536, 537

Close space sublimation chamber, 427Cluster density, 144Clusters, 45Co diffusion length, 268Co exposure, 267, 268

Co islands, 270, 272Co nanoislands, 265Co nanoparticles, 266Coalescence, 68, 130Coalescence mechanism, 273Coaxial cylinders, 411Cobalt flux, 266Cobalt nanoparticles, 170Coherency domain, 401Coherent island, 169Cohesive energy, 499Collection radius, 346Concentration, 43, 152, 153, 155, 157, 161,

338, 498Condensation, 24, 42, 143Condensation rate, 56Condensation seeds, 30Contact angle, 17–19, 22, 24, 286, 315, 565Continuing growth, 386, 387Continuum approximation, 55Control parameter, 165, 185Cooperative effects, 398, 482Core, 443Core energy, 400Core radius, 411Core stress, 413Core-shell geometry, 415Core-shell growth mode, 255Core-shell nanowires, 410Corrections, 61Correlation function, 15Counting, 518Critical chemical potential, 531, 571Critical concentration, 289Critical curve, 539Critical diameter, 407Critical diffusion flux, 424Critical dimension, 397, 403, 404, 407, 408Critical exponents, 10Critical flux, 426Critical isotherm, 10Critical length, 344, 371, 385, 386Critical nucleus, 14, 27Critical radius, 401, 403, 468, 469, 525Critical size, 56, 118, 327, 349Critical supersaturation, 66, 90, 107, 124Critical temperature, 6, 9Critical thickness, 181, 214, 215, 218, 221,

224, 243, 258, 399–401, 408, 414,416

Crystal facet, 138, 141Crystal phase, 499, 539Crystal phase engineering, 500, 541

Index 593

Crystal phase heterostructures, 509Crystal structure, 253, 501, 502, 509, 514, 531,

545, 550–552Crystallization, 131Crystallization model, 68Crystallized fraction, 129Crystallographic structure, 462Curvature, 326, 332, 421, 565Curvature effect, 18Cutoff diameter, 306Cylindrical nanowire, 311, 314Cylindrical wire, 323

DDangling bond, 515, 517, 518, 524De Broile wavelength, 176Dense nanowire array, 485, 488Density, 94, 125, 230, 233, 376Density fluctuations, 15Density of islands, 375Density of states, 173, 175, 177Density-functional theory, 506Deposition conditions, 218, 341Deposition flux, 70Deposition rate, 71, 231, 260, 330Desorption, 34, 36Detailed balance, 46, 53Deterministic approximation, 76, 81Deterministic kinetic equation, 82Diameter, 353Diameter independence, 358Differential equation, 146Diffraction streaks, 299Diffusion, 35, 334, 338, 342, 447, 478Diffusion barrier, 338Diffusion equation, 334, 445, 484Diffusion flux, 40, 333, 340, 343, 349, 374,

384, 418, 420, 422, 425, 430Diffusion growth, 276Diffusion growth equation, 276Diffusion growth model, 383Diffusion length, 34, 40, 345, 354, 367, 368,

374, 377, 392, 430, 446, 479, 485Diffusion model, 380Diffusion transport, 350, 356, 358Diffusion-induced growth, 303, 369, 372Diffusion-induced mode, 293, 385Diffusion-induced terms, 392Diffusionlike Gaussian, 96Dimension, 38Dimensional arguments, 403Direct impingement, 472

Discrete levels, 175Discrete theory, 58Dislocation strain field, 400Dislocations, 404, 410Dispersion, 100, 101, 108, 136, 435Dispersion law, 171Displacement fields, 192Displacement strains, 192Distribution, 3, 47, 50, 78, 81, 96, 107, 149Distribution function, 56, 91Distribution normalization, 28Distributions, 3, 105Dopant, 445Dopant distribution, 442Dopant incorporation, 444Doping concentration, 353Doping effects, 354Double exponential distribution, 113Double exponential shape, 87, 148Double exponential solutions, 85Double exponential spectrum, 88Double-exponential distribution, 271Driving force, 463, 466, 469Droplet, 17, 22, 41, 279, 287, 308, 328, 333,

557Droplet collection area, 325Droplet shapes, 567Droplet stability, 310, 313Droplet surface, 566Droplet volume, 286

EEdge, 414Edge energy, 184Edge facet, 320Effective diffusion length, 377Effective supersaturations, 386Effective surface energy, 312, 528, 530Elastic constants, 191Elastic energy, 193, 194, 200, 201, 207, 209,

401, 408, 413, 414Elastic model, 411Elastic relaxation, 168, 190, 196, 197, 202,

203, 295, 410Elastic strain energy, 460Elastic stress, 193Elastic stress relaxation, 416Elastic substrate, 196Elasticity theory, 191Electron beam lithography, 301Elementary processes, 32Elongation rate, 338, 341, 376, 381

594 Index

Elongation rate of GaAs nanowires, 371Emission spectra, 259Empirical pseudopotentials, 506Energetic parameters, 181Energy difference, 504Energy levels, 172Energy spectrum, 172Epitaxial nanostructures, 168Epitaxial nanowire, 404Equation of state, 5Equilibrium chemical potential, 6Equilibrium critical radius, 523Equilibrium densities, 7, 9Equilibrium phases, 11Equilibrium thickness, 209Exact solution, 47, 48, 50, 54, 147, 153Excessive Ga influx, 452Experimental histogram, 272Experimental observations, 509Explanation, 560Exponents, 11Exposition time, 234Extended area, 141Extended volume, 130External fluxes, 44Extremely high vapor supersaturation, 556

FFacet, 139, 364, 515Filling factor, 68, 131Film surface, 134Film thickness, 37, 136Finite element calculations, 197Fit, 360Fitting curve, 362Fitting parameters, 359, 392, 430Fluctuation, 80, 96, 112, 121Fluctuational term, 79, 99Fluorite surface steps, 270Flux, 123Fokker-Plank type kinetic equation, 77Formation, 156Formation cycle, 309Formation energy, 24, 28, 47, 79, 185, 199,

207, 208, 210, 311Free energy, 12, 316, 320Free energy functional, 14Free lateral surfaces, 179Freestanding nanowires, 397

GGa adatoms, 453, 477

Ga atoms, 456Ga concentration, 289, 557Ga droplet, 448, 450Ga droplet flux, 453Ga flux, 292, 472Ga influx, 294Ga nanodroplet, 450Ga rich conditions, 454Ga-As-Au alloy, 495Ga-catalyzed GaAs nanowires, 448, 559, 561,

567Ga-catalyzed growth, 450Ga-rich conditions, 449GaAs, 548GaAs nanoneedle, 169, 250, 251, 253, 260, 261GaAs nanowire, 284, 309, 378, 388, 416, 439,

448, 449, 509, 513, 534, 558, 560,564

GaAs wires, 281GaAs/sapphire system, 252Gallium, 472Gallium adatoms, 478, 481Gallium atoms, 471Gallium rate, 481GaN, 482GaN island, 457, 460GaN nanowire, 284, 301, 398, 457, 462, 473GaN nuclei, 459GaP, 549GaP nanowires, 426Gaussian, 48, 49, 98, 100, 105Ge clusters, 245Ge islands, 244Ge nanowire, 306, 390, 394Ge/Si system, 221, 243, 245Generating function, 51, 52, 146, 152Geometrical distribution, 50Gibbs-Thomson, 17Gibbs-Thomson effect, 304–306, 329, 332Gibbs-Thomson radii, 331Givargizov-Chernov curve, 306Givargizov-Chernov expression, 305Gold migration, 290Green function, 48, 76, 96, 99, 101Group III metals, 293Group V element, 433, 435Group V fluxes, 383Growth, 188, 219, 263, 306, 343, 456Growth chronology, 379Growth conditions, 232, 301, 323, 341Growth cycles, 439Growth diagram, 114Growth equation, 342, 374

Index 595

Growth experiment, 218Growth index, 42, 43Growth kinetics, 129, 134, 186, 363, 379, 514Growth mode, 137, 241Growth model, 158, 392Growth modeling, 75, 275, 427, 428, 476Growth parameters, 550Growth procedure, 281Growth process, 67, 152, 190, 217, 335Growth rate, 38, 39, 94, 112, 130, 131, 138,

141, 212, 229, 237, 239, 271, 345,347–349, 353, 355–358, 365, 485,556

Growth regimes, 42Growth scenarios, 197, 204Growth stage, 43, 73, 76, 112, 223, 274Growth steps, 476Growth temperature, 239, 244, 263, 331, 361,

424, 545, 550Growth thermodynamics, 298

HHeight-radius dependence, 467Hemispherical droplet, 324Heteroepitaxial system, 183Heteroepitaxy, 20, 135Heterogeneous integration, 168Heterogeneous nucleation, 45, 227Heterointerface, 401Heterostructure, 295Hexagonal polytypes, 504Hexagonal shape, 284Hexagonality, 504Hexahedral nanowire, 465, 515High growth rate, 553Homoepitaxy, 20Hooke’s law, 192Hut-to-dome shape transformation, 187

IIdeal supersaturation, 44, 70, 83, 89, 125III–V materials, 501III–V nanoneedles, 249, 568III-V compounds, 505III-V nanowires, 404, 493, 500, 514, 525, 531,

536, 538, 541–543, 551In adatoms, 485InAs, 549InAs islands, 180InAs nanowires, 370, 371, 484, 487, 511, 545,

552InAs quantum dots, 240

InAs wetting layer, 190InAs/GaAs quantum dots, 190, 238, 239InAs/GaAs system, 235InAs/GaAs(100) system, 237InAs/InP heterostructure, 353Incorporation, 429Incorporation probability, 473Incorporation process, 445Inequality, 23Infinite growth, 386Initial length, 387, 389InP, 549InP nanowires, 354, 360, 511, 512, 545InSb, 548InSb growth rate, 368InSb length, 489, 492InSb morphology, 364InSb-InAs nanowires, 366, 488InSb/InAs, 542Instability, 23Instantaneous growth rate, 380Integral equation, 84Intensity profile, 380Interaction energies, 517Interface, 16, 40, 509Interface energy, 20Interpolation, 142Interpolation formula, 139Invariant character, 81Invariant nanowire length, 394Invariant size, 43, 68, 77–79, 108, 118Irreversible growth, 55, 77, 143, 145Irreversible system, 155Island, 25, 26, 36, 39, 64, 71, 103, 187, 213,

241, 268, 270, 457, 465Island density, 72, 93, 126, 163, 217, 236, 269Island formation, 184, 225, 244Island formation process, 245Island geometr, 195Island growth rate, 211Island morphology, 244, 267Island nucleation, 169, 182, 239, 438Island perimeter, 376Island shape, 463Island size, 125Island size distribution, 224Island-substrate interface, 192Isolated system, 144Isotherms, 6, 8Isotropic growth, 463Iterations, 84

596 Index

KKinetic control, 76Kinetic control parameter, 123, 215, 216, 247Kinetic equation, 49, 51, 54, 56, 75, 87, 99,

109, 112, 118, 144, 434, 446, 473Kinetic fluctuations, 97, 110Kinetic growth theory, 266Kinetic mechanisms, 189Kinetic model, 135Kinetic modeling, 298Kinetic radii, 538, 541Kinetic theory, 12, 526Kinetically controlled engineering, 231Kolmogorov approach, 77Kolmogorov exponent, 132, 141Kolmogorov indices, 133Kolmogorov scheme, 140Kolmogorov-Johnson-Mehl-Avrami model,

131, 132

LLandau theory, 15Laplace method, 58Laplacian pressure, 16, 18Large parameter, 83, 214Lateral dimension, 401Lateral size, 184, 224, 230, 233, 238, 244Lattice, 256Lattice constant, 194, 502Lattice gas, 31Lattice mismatch, 178, 180, 183, 185, 194,

199, 203, 205, 226, 251, 252, 295,404, 409

Lattice mismatched material systems, 167Lattice mismatched substrates, 190Length, 353Length distribution, 390, 395Length-diameter curve, 361Length-diameter dependences, 360Length-radius correlation, 306, 345, 347, 350,

361, 369Length-radius dependence, 305, 349, 362, 369Length-radius dependences, 355Length-time dependences, 261Lifetime, 33Lifshitz–Slezov distributions, 119Lifshitz–Slezov shape, 120Lifshitz–Slezov theory, 119Limitation on the maximum length, 395Linear model, 55Liquid, 25Liquid catalyst, 433

Liquid chemical potentials, 495Liquid Ga, 453Liquid particle, 289Liquid supersaturation, 309, 317, 337, 538, 555Liquid–solid interface, 279Local fluctuations, 9Loop dislocations, 414Low density, 228Low temperature growth, 389

MMüller-Kern model, 182, 226Magnetization, 8Mass conservation, 116, 268Mass transport, 41, 298Material balance, 44, 82, 83, 89, 213, 220, 365Material influx, 90, 93, 94, 102, 107, 222Material parameters, 331Material refill, 65Maximum growth rate, 482Maxwell’s rule, 7MBE, 361, 416, 448, 456, 475MBE conditions, 240MBE deposition, 281MBE growth, 215, 291, 301, 350, 426, 512,

536MBE growth conditions, 231, 536MBE growth experiments, 389Mean diffusion length, 372Mean field approximation, 5Mean field equation, 8Mean size, 51, 53, 71, 72, 100, 106, 112,

148–150, 221, 236Mean thickness, 134, 137Melting point, 299Metal-semiconductor alloy, 279Metallic nanoparticles, 288Metallic particle, 290Microfacets, 285Minimum nanowire radius, 332Minimum radius, 329Minimum surface energy, 19, 22, 563, 566, 567Misfit defects, 257Mismatch, 249Mismatched growth, 258Mismatched substrates, 403Misorientation angle, 226Model system, 144Modeling, 223, 275, 500Molecular beam epitaxy, 180Monolayer, 311, 318Monolithic integration, 249

Index 597

Monomer concentration, 145, 151Monomer sink, 148Monomer source, 115Monomers, 13, 44, 150Mononuclear growth, 309, 432Mononuclear mode, 309Morphological properties, 188Morphology, 129, 236, 351, 366Multilayer adsorbate, 37Multilayer film, 137

NNanocrystals, 300Nanoislands, 301Nanoneedle, 196, 203, 249, 263, 265Nanoneedle sidewall, 252Nanopillar, 256, 257, 410, 415Nanopillar lasers, 260Nanostructure morphology, 127Nanostructure t, 193Nanostructures, 190Nanowire, 66, 198, 203, 278, 285, 288, 294,

295, 297, 299, 301, 303, 310, 313,315, 319, 322, 329, 336, 340, 342,344, 346, 351, 353–355, 357, 358,360, 361, 363, 364, 368, 370, 374,382, 386, 388, 389, 392, 403, 407,454, 458, 466–469, 471, 476, 478,481, 499, 516, 521, 523, 529, 533,546

Nanowire composition, 379Nanowire diameter, 351Nanowire elongation, 384Nanowire elongation rate, 281, 305, 479Nanowire growth, 275, 293, 345, 350, 383,

398, 482Nanowire growth chronology, 380Nanowire growth modes, 392Nanowire growth rate, 325, 329, 359Nanowire heterostructures, 397, 410, 416, 542Nanowire length, 333, 343, 365, 380, 387, 391,

476, 479Nanowire morphology, 450Nanowire radius, 286Nanowire samples, 359Nanowire shape, 429Nanowire sidewall energy, 306Nanowire sidewalls, 284, 515Nanowire tilt angle, 392Nanowire-catalyst interfaces, 319Narrowing, 390Narrowing effect, 394

Near-critical region, 59Nearest neighbors, 517Negative growth, 386Negative nanowire growth, 388Neighboring nanowire, 489Net flux, 323Non-linear effects, 384Non-monotonic behavior, 365Non-monotonous diameter dependence, 368Non-planar growth interfaces, 318Non-wetting, 22Non-wetting configuration, 312Normalization, 28Nucleation, 2, 26, 29, 62, 65, 66, 70, 86, 98,

131, 201, 217, 229, 248, 265, 297,318, 322, 328, 349, 355, 356, 358,436, 454, 529, 532

Nucleation barrier, 13, 27, 30, 123, 197, 200,205, 209, 210, 227, 318, 327, 482,528, 530, 539

Nucleation events, 432, 434Nucleation mode, 90, 128Nucleation model, 206Nucleation position, 350Nucleation probabilities, 2, 432, 435, 437–440Nucleation process, 216Nucleation pulses, 397Nucleation rate, 14, 58, 61, 62, 67, 89, 91, 93,

109, 229, 269, 273, 308, 327, 416,420, 483, 485

Nucleation rate a, 3Nucleation stage, 68, 81, 83, 86, 88, 94, 100,

101, 105, 186, 213, 223, 224, 439Nucleation statistics, 142, 397, 430, 433Nucleation theory, 1, 4, 11, 24, 30, 54, 56, 167,

214, 420Nucleation time, 94, 437Nucleation-condensation process, 75Nuclei, 43, 57, 60, 68, 107, 116Nucleus, 38, 107, 316

OOccupation number, 5Off-cut GaAs(100) substrates, 240Onduloid, 565Onduloid shape, 566Open irreversible systems, 161Optical method, 241Optical properties, 259Order parameter, 2, 7, 9, 14Oscillation, 380Ostwald ripening, 76, 114, 115, 117–119Oxide layer, 292

598 Index

PParabolic droplet, 564Peak position, 235, 238Peptide, 156, 161Peptide chains, 156Periodic step nucleation, 320Phase diagram, 219, 290Phase transition, 1, 4, 11, 12, 14, 15, 312Photoluminescence (PL) properties, 235Plastic deformation, 399Plastic relaxation, 401, 403, 408Poisson distribution, 48Poisson spectrum, 48Poissonian form, 154Poissonian nucleation process, 129Polya distribution, 52Polymer chains, 160Polymer length, 157Polymerization rate constant, 160Polynucleation, 309Polytype, 504, 523–525Polytypism, 278, 285, 509Position, 328Potential barrier, 422Power index, 474Preferred aspect ratio, 197, 201, 203, 205, 206Preferred crystal structure, 543Probabilities, 33, 49, 52, 65, 134, 135, 374, 434Probability density, 436Pulsed nucleation, 435Pure ZB phase, 553Purely ZB part, 559Pyrolysis efficiencies, 368

QQuantum confinement, 177Quantum dot, 169, 172, 175, 176, 180, 181,

183, 187, 199, 202, 215, 231, 238Quantum well, 171, 175, 176Quantum wire, 172, 175, 176Quasi-equilibrium distribution, 28Quasi-equilibrium state, 46Quasi-equilibrium temperature, 216

RRadial growth, 416, 420, 422, 429, 450, 474Radial growth rate, 488Radius-dependent curves, 547Radius-time relationship, 453Rate constant, 50, 54, 55, 144, 151, 153, 159Rate equations, 47Ratsch-Zangwill formula, 227

Re-emission, 488Re-emission probability, 489Re-emitted species, 489Reaction, 156Reaction scheme, 45, 143, 158Readsorption probability, 492Reciprocal space, 173Refill, 436Refill time, 437, 438Regrowth, 450, 454Regrowth process, 450Regular growth, 453Regular growth rate, 80Regular shape of nanowires, 389Regular solution model, 494Regular surface morphology, 266Relaxation, 196, 208Relaxation mechanisms, 254Relaxation time, 102Relaxed size, 102Representative size, 98RHEED intensities, 459RHEED pattern, 292, 457Rigid substrate, 196Roughness, 136

SSalt concentration, 158, 160Samples, 246Sapphire substrates, 250Sb flux, 247Scaling, 475Scaling behavior, 163Scaling dependence, 464Scaling growth kinetics, 471Scaling growth laws, 474Scenarios of nanowire growth, 385Schrödinger equation, 170Secondary nanowire, 455Seeding layer, 272Selective area GaAs nanowire growth, 302Self-catalyzed growth, 449Self-catalyzed III-V nanowires, 290Self-consistent approach, 330Self-consistent curve, 331Self-consistent growth equation, 360Self-consistent growth models, 347Self-induced anisotropic growth, 467Self-induced GaN nanowires, 456, 475Self-induced growth, 462Self-induced islands, 167Self-induced nanoneedles, 571

Index 599

SEM image, 364, 365Semiconductor nanostructures, 170Semiconductor nanowires, 275, 278Shadow effect, 398, 473, 483Shadowed height, 488Shadowing, 484Shape modification, 416Shape transformation, 463, 469, 470, 564Shape transition, 458, 460Shchukin’s model, 183Shell radius, 411Shell thickness, 414Si nanowires, 290, 442, 447Si substrates, 250, 456Si(111) substrates, 290Side facets, 546Sidewall, 257, 260, 297, 334, 337, 339, 344,

367, 377, 383, 394, 422, 425, 430,472, 500, 515, 521

Sidewall adatoms, 368, 416, 419Sidewall facets, 251, 528Silicon, 301Single InPAs nanowire, 379Size distribution, 61, 68, 76, 85, 86, 90, 93, 94,

104, 122, 146, 147, 182, 223, 246,265

Size quantization, 170Size quantization effect, 175Size relaxation stage, 220Size spectra, 159–161Size spectru, 87Size spectrum, 80, 101, 154, 222Solid diffusion, 299Solid metallic particles, 300Solid surface, 32Solid-liquid surface energy, 555Solutions, 53Space dimension, 10Spatial distribution, 270Spectrum, 96, 103, 104, 107, 110, 118, 120,

128Spectrum maximum, 149Spectrum shape, 77, 150Spectrum width, 112, 114Spherical cap islands, 465Spherical caps, 458Spherical droplet, 311Spinodal, 9Spreading, 97Stability, 21, 23Stacking sequenc, 503State of metallic particle, 286Stationary distribution, 58, 60, 80, 212

Stationary droplet configuration, 565Stationary growth model, 386Stationary size distribution, 62Stationary state, 3, 59, 61Statistical analysis, 391Statistical sum, 4Steps, 35Strain, 254, 414Strain energy, 179, 195Strain relaxation, 179, 400Strain-free state, 191Stranski-Krastanow growth, 168, 178, 188,

217, 222, 224Stranski-Krastanow islands, 207, 212, 215,

219, 232Stranski-Krastanow quantum dots, 223Stress relaxation, 181, 184, 255, 413Stress-driven diffusion, 211Stress-driven islanding, 185Stringfellow’s scheme, 495Structural phase transitions, 532Structural transition, 538Sub-Poissonian character, 433Subcritical islands, 228, 229Subcritical nucleation mode, 92Subcritical quantum dots, 228, 230, 231Subcritical sample, 244Substrate, 26, 168, 195, 197, 339Substrate adatoms, 339Substrate surfaces, 344Supercritical nuclei, 110Supersaturated environment, 13Supersaturatio, 86, 322Supersaturation, 1, 2, 27, 30, 32, 39, 57, 61,

62, 64, 65, 68, 73, 83, 85, 105, 113,201, 203, 205, 296, 320, 326, 329,330, 347, 348, 356, 420, 438, 534

Supersaturation kinetics, 439Supersaturation oscillations, 441Supersaturation-dependent polytypism, 543Superstress, 186, 209, 210, 215Surface, 35, 36, 344Surface adatoms, 378Surface curvature, 17Surface density, 164, 273, 374, 377Surface diffusion, 33, 161, 281, 463Surface effects, 278Surface energetics, 186Surface energy, 16, 19, 22, 26, 63, 66, 201,

207, 208, 310, 312, 314, 348, 463,466, 468, 469, 500, 515, 517, 521,530, 564, 567

Surface islands, 20, 94

600 Index

Surface layer, 134Surface morphology, 247Surface roughness, 137Surface step, 225, 228Surface stress tensor, 184Surface temperature, 218Surfactant properties, 245Synthesis process, 306

TTailoring, 122Taper angle, 263TEM image, 254, 442TEM studies, 509Temperature, 126, 231, 267Temperature and flux dependence, 124, 376Temperature behavior, 125, 387, 424Temperature conditions, 370Temperature dependence, 123, 125, 240, 370,

372, 377, 551Theoretical analysis, 411Theoretical curves, 378Theoretical fits, 361Theoretical model, 479Theoretical values, 521Theory, 83Thermodynamic fluctuations, 13Thermodynamic values, 125Thermodynamics, 4, 12, 129Thin films, 30, 133Threshold, 248Threshold behavior, 247Time evolution, 71, 101, 106, 234, 392Time-invariant shape, 148Timescale hierarchy, 86, 107, 220, 221, 438Top facet, 311Transformation, 77Transformed area, 140Triple phase line, 21, 528–530Triple phase line nucleation, 315, 530Truncated edge, 318Truncation, 319, 320Two-parametric equation, 422Two-step growth procedure, 266

VVan der Waals loops, 6Vapor, 25Vapor supersaturation, 307, 331, 553Vapor–liquid–solid growth, 280Vapor–liquid–solid growth mechanism, 277Vapour flux, 161

Vertical growth rate, 139, 372, 418Vertical plane, 324Very high supersaturation, 553Vicinal substrate, 225, 227Vicinal surface, 226VLS configuration, 315, 563, 567VLS growth, 278, 283, 296, 305, 318, 355,

357, 563VLS growth temperature, 279VLS mechanism, 442VLS nanowire growth, 281VLS nanowire synthesis, 281VLS nanowires, 283, 294, 509VLS process, 281Volmer-Weber growth, 269Volmer-Weber islands, 273Volmer-Weber mode, 459Volmer-Weber nanoislands, 469

WWagner-Ellis expression, 304Wagner-Ellis formula, 326, 331Water solutions, 156Wavelength, 176Wavelength shift, 236Wetting, 20Wetting force, 208Wetting layer, 179, 180, 183, 188, 189,

210–213, 229Wetting mode, 563Wetting VLS configuration, 313Wire, 22Wire growth, 300Wire shape, 421, 423, 424, 426Wurtzite, 252, 499Wurtzite phase formation, 526Wurtzite structure, 568WZ layers, 504WZ nanoneedle, 570WZ percentage, 533, 534, 536, 546WZ phase, 542WZ phase formation, 534, 537, 557WZ phase suppression, 553WZ segments, 511WZ structure, 508, 512, 532

YYoung’s equation, 19

ZZB and WZ nanowires, 539

Index 601

ZB crystal structure, 568ZB to WZ phase transition, 524ZB to WZ transition, 560ZB-WZ polytypism, 525ZB-WZ structural transitions, 541Zeldovich equation, 64Zeldovich expression, 212

Zeldovich factor, 59

Zeldovich formula, 59

Zeldovich nucleation rate, 57, 230

Zincblende, 252

Zincblende structure, 559

Zincblende-wurtzite transition, 523