Physics of Crystal Growth [Kõva köide]

Preface		xiii	(2)
List of symbols		xv
1 Morphology of a crystal surface		1	(22)
1.1 A high-symmetry surface observed with a microscope		2	(5)
1.2 In situ microscopy and diffraction		7	(1)
1.3 Step free energy and thermal roughness of a surface		7	(3)
1.4 The roughening transition		10	(2)
1.5 Smooth and rough surfaces		12	(3)
1.6 The SOS model and other models		15	(1)
1.7 Roughening transition of a vicinal crystal surface		16	(1)
1.8 The roughening transition: a very weak transition		17	(4)
1.9 Conclusion		21	(2)
2 Surface free energy, step free energy, and chemical potential		23	(20)
2.1 Surface tension		23	(3)
2.2 Small surface fluctuations and surface rigidity		26	(1)
2.3 Singularities of the surface tension		27	(1)
2.4 Chemical potential		28	(5)
2.5 Step line tension and step chemical potential		33	(2)
2.6 Step line tension close to a high-symmetry direction at low T		35	(2)
2.7 Thermal fluctuations at the midpoint of a line of tension Gamma		37	(1)
2.8 The case of a compressible solid body		38	(1)
2.9 Step-step interactions		39	(4)
3 The equilibrium crystal shape		43	(17)
3.1 Equilibrium shape: general principles		43	(3)
3.2 The Wulff construction		46	(1)
3.3 The Legendre transformation		47	(1)
3.4 Legendre transform and crystal shape		48	(2)
3.5 Surface shape near a facet		50	(1)
3.6 The double tangent construction		51	(2)
3.7 The shape of a two-dimensional crystal		53	(2)
3.8 Adsorption of impurities and the equilibrium shape		55	(1)
3.9 Pedal, taupins and Legendre transform		56	(1)
3.10 Conclusion		57	(3)
4 Growth and dissolution crystal shapes: Frank's model		60	(10)
4.1 Frank's model		61	(1)
4.2 Kinematic Wulff's construction		62	(2)
4.3 Stability of self-similar shapes		64	(2)
4.4 Frank's theorem		66	(1)
4.5 Examples		66	(3)
4.6 Experiments		69	(1)
4.7 Roughening and faceting		69	(1)
4.8 Conclusion		69	(1)
5 Crystal growth: the abc		70	(18)
5.1 The different types of heterogrowth		70	(3)
5.2 Wetting		73	(1)
5.3 Commensurate and incommensurate growth		73	(2)
5.4 Effects of the elasticity of the solid		75	(1)
5.5 Nucleation, steps, dislocations, Frank-Read sources		75	(3)
5.6 Supersaturation		78	(1)
5.7 Kinetic roughening during growth at small supersaturation		79	(2)
5.8 Evaporation rate, saturating vapour pressure, cohesive energy, and sticking coefficient		81	(2)
5.9 Growth from the vapour		83	(1)
5.10 Segregation, interdiffusion, buffer layers		84	(4)
6 Growth and evaporation of a stepped surface		88	(23)
6.1 General equations		89	(1)
6.2 The quasi-static approximation		90	(2)
6.3 The case without evaporation: validity of the BCF model		92	(2)
6.4 The Schwoebel effect		94	(3)
6.5 Advacancies and evaporation		97	(1)
6.6 Validity of the BCF model in the case of evaporation		98	(2)
6.7 Step bunching and macrosteps		100	(11)
7 Diffusion		111	(19)
7.1 Mass diffusion and tracer diffusion		112	(2)
7.2 Conservation law and current density		114	(1)
7.3 Vacancies and interstitial defects in a bulk solid		114	(2)
7.4 Surface diffusion		116	(1)
7.5 Diffusion under the effect of a chemical potential gradient		117	(2)
7.6 Diffusion of radioactive tracers		119	(1)
7.7 Activation energy		119	(4)
7.8 Surface melting		123	(1)
7.9 Calculation of the diffusion constant		124	(1)
7.10 Diffusion of big adsorbed clusters		124	(6)
8 Thermal smoothing of a surface		130	(14)
8.1 General features		131	(1)
8.2 The three ways to transport matter		132	(1)
8.3 Smoothing of a surface above its roughening transition		133	(3)
8.4 Thermal smoothing due to diffusion in the bulk solid		136	(1)
8.5 Smoothing below the roughening transition		137	(3)
8.6 Smoothing of a macroscopic profile below T(R)		140	(2)
8.7 Grooves parallel to a high-symmetry orientation		142	(2)
9 Silicon and other semiconducting materials		144	(12)
9.1 The crystal structure		144	(2)
9.2 The (001) face of semiconductors		146	(1)
9.3 Surface reconstruction		147	(1)
9.4 Anisotropy of surface diffusion and sticking at steps		148	(1)
9.5 Crystalline growth vs. amorphous growth		148	(1)
9.6 The binary compounds AB		149	(1)
9.7 Step and kink structure		150	(1)
9.8 The (111) face of semiconductors		150	(1)
9.9 Order of magnitude		151	(5)
10 Growth instabilities of a planar front		156	(25)
10.1 Diffusion limited aggregation: shape instabilities		156	(2)
10.2 Linear stability analysis: the Bales-Zangwill instability		158	(4)
10.3 Stabilizing effects: line or surface tension		162	(2)
10.4 Stability of a regular array of straight steps: the general case		164	(3)
10.5 The case of MBE growth without evaporation		167	(1)
10.6 Beyond the linear stability analysis: cellular instabilities		168	(2)
10.7 The Mullins-Sekerka instability		170	(4)
10.8 Growth instabilities in metallurgy		174	(2)
10.9 Dendrites		176	(1)
10.10 Conclusion		177	(4)
11 Nucleation and the adatom diffusion length		181	(20)
11.1 The definition of the diffusion length		182	(1)
11.2 The nucleation process		183	(2)
11.3 Adatom lifetime and adatom density		185	(1)
11.4 Adatom-adatom and adatom-island collisions		185	(1)
11.5 The case i* = 1		186	(1)
11.6 Numerical simulations and controversies		187	(1)
11.7 Experiments		188	(2)
11.8 The case i* = 2		190	(4)
11.9 Generalization		194	(1)
11.10 Diffraction oscillations in MBE		195	(1)
11.11 Critical nucleus size and numerical simulations		196	(1)
11.12 Surfactants		197	(4)
12 Growth roughness at long lengthscales in the linear approximation		201	(10)
12.1 What is a rough surface?		201	(1)
12.2 Random fluctuations and healing mechanisms		202	(2)
12.3 A subject of fundamental, rather than technological, interest		204	(1)
12.4 The linear approximation (Edwards & Wilkinson 1982)		205	(1)
12.5 Lower and upper critical dimensions		206	(1)
12.6 Correlation length		207	(1)
12.7 Scaling behaviour and exponents		208	(3)
13 The Kardar-Parisi-Zhang equation		211	(10)
13.1 The most general growth equation		211	(2)
13.2 Relevant and irrelevant terms in (13.1): the KPZ equation		213	(2)
13.3 Upper critical dimension and exponents		215	(2)
13.4 Behaviour of Lambda near solid-fluid equilibrium		217	(1)
13.5 A relation between the exponents of the KPZ model		218	(1)
13.6 Numerical values of the coefficients Lambda and Nu		219	(1)
13.7 The KPZ model without fluctuations ((Delta)f = 0)		219	(2)
14 Growth without evaporation		221	(9)
14.1 Where Lambda is shown to vanish in the KPZ equation		221	(1)
14.2 Diffusion bias and the Eaglesham-Gilmer instability		222	(2)
14.3 A theorist's problem: the case Lambda = Nu = 0		224	(1)
14.4 Calculation of the roughness exponents		225	(2)
14.5 Numerical simulations		227	(1)
14.6 The Montreal model		227	(1)
14.7 Conclusion		228	(2)
15 Elastic interactions between defects on a crystal surface		230	(19)
15.1 Introduction		231	(1)
15.2 Elastic interaction between two adatoms at a distance r		232	(2)
15.3 Interaction between two parallel rows of adatoms		234	(2)
15.4 Interaction between two semi-infinite adsorbed layers		236	(2)
15.5 Steps on a clean surface		238	(3)
15.6 More general formulae for elastic interactions		241	(2)
15.7 Instability of a constrained adsorbate		243	(6)
16 General equations of an elastic solid		249	(28)
16.1 Memento of elasticity in a bulk solid		249	(3)
16.2 Elasticity with an interface		252	(3)
16.3 The isotropic solid		255	(1)
16.4 Homogeneous solid under uniform hydrostatic pressure		256	(1)
16.5 Free energy		257	(2)
16.6 The equilibrium free energy as a surface integral		259	(2)
16.7 Solid adsorbate in epitaxy with a semi-infinite crystal		261	(3)
16.8 The Grinfeld instability		264	(4)
16.9 Dynamics of the Grinfeld instability		268	(1)
16.10 Surface stress and surface tension: Shuttleworth relation		268	(2)
16.11 Force dipoles, adatoms and steps		270	(7)
17 Technology, crystal growth and surface science		277	(12)
17.1 Introduction		277	(1)
17.2 The first half of the twentieth century: the age of the radio		278	(1)
17.3 The third quarter of the twentieth century: the age of transistors		278	(3)
17.4 The last quarter of the twentieth century: the age of chips		281	(1)
17.5 MOSFETS and memories		282	(2)
17.6 From electronics to optics		284	(1)
17.7 Semiconductor lasers		285	(2)
17.8 Quantum wells		287	(2)
Appendix A -- From the discrete Gaussian model to the two-dimensional Coulomb gas		289	(4)
Appendix B -- The renormalization group applied to the two-dimensional Coulomb gas		293	(3)
Appendix C -- Entropic interaction between steps or other linear defects		296	(4)
Appendix D -- Wulff's theorem finally proved		300	(4)
Appendix E -- Proof of Frank's theorem		304	(5)
Appendix F -- Step flow with a Schwoebel effect		309	(3)
Appendix G -- Dispersion relations for the fluctuations of a train of steps		312	(4)
Appendix H -- Adatom diffusion length l(s) and nucleation		316	(3)
Appendix I -- The Edwards-Wilkinson model		319	(3)
Appendix J -- Calculation of the coefficients of (13.1) for a stepped surface		322	(2)
Appendix K -- Molecular beam epitaxy, the KPZ model, the Edwards-Wilkinson model, and similar models		324	(2)
Appendix L -- Renormalization of the KPZ model		326	(6)
Appendix M -- Elasticity in a discrete lattice		332	(3)
Appendix N -- Linear response of a semi-infinite elastic, homogeneous medium		335	(7)
Appendix O -- Elastic dipoles in the z direction		342	(3)
Appendix P -- Elastic constants of a cubic crystal		345	(2)
References		347	(27)
Index		374

Alberto Pimpinelli is Executive Director of the Smalley-Curl Institute and Faculty Fellow in the Materials Science and Nanoengineering Department at Rice University, Houston, full Professor in the Physics Department at the Université Blaise Pascal, Clermont-Ferrand, France, and Visiting Professor at the University of Maryland, College Park. From 2008 to 2012, he was one of the Attaches for Science and Technology of the French Embassy in the US. Trained as a theoretical physicist, Pimpinelli obtained his PhD from the University of Parma, Italy, with a thesis dealing with statistical physics models of magnetism in insulating systems. His interests shifted towards crystal surfaces and crystal growth when, after receiving fellowships from the Accademia dei Lincei and the European Union, he left Italy for the Centre d'Etudes Nucleaires and the Laue Langevin Institute in Grenoble (19917). In 1997, he was appointed Professor at the Université Blaise Pascal in Clermont-Ferrand, where he taught statistical and solid state physics, as well as introductory courses in nanosciences. In 2004, he was invited to the Materials Research Science and Engineering Center at the University of Maryland, where he was appointed Visiting Professor the following year. He has acted as a reviewer for many institutions and scientific agencies, such as the MNEST, the ANR, the NSF, the EU, the EC, and the Romanian Government. He has authored or co-authored more than 150 scientific papers and book chapters, and has been invited to talk at many international conferences.