Lecture 6 Nucleation and growth of thin films and nanostructures

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$Low Energy Electron Diffraction and Microscopy$

Physics 9826b Homogeneous Nucleation Kinetics - At steady state, when no new nuclei are created Rate Rate flux n A F A t 2D L attach n2DD A 2 L Solve for n 2D : - Assume two atoms for a dimer when they sit on adjacent sites separated by a D 2 Ratedimer A n2D khop pocc A n2D 4n2Da 2 a 2 Rate 4ADn Rate 4Dn dimer dimer 2D 4ADn 1 10 Rate D 4 L 2 t (10L ) L 2D 2 2D attach n2D A t D 40F L - Saturation should be assured when enough nuclei have formed to have average separation L, so that saturation density is (b) Dendritic Growth in 1 st layer: - aside C. Ratsch PRL 72 (1994) 3194 27 6.6 Epitaxy Epitaxy (“arrangement on”) refers loosely to control of the orientation of the growing phase by the crystal structure of the substrate homoepitaxy: host and growing phase are the same material heteroepitaxy: host and growing phase are different Orientation and Strain There exist orientational relations between dissimilar crystal lattices in contact (e.g., fcc (111)/bcc (110); fcc (100) /rocksalt (100) Nishiyama- Wasserman Kurdjimov -Sachs Zangwill, Ch.16 28 January 30 – February 4, 2013 14
Physics 9826b Epitaxial energy NW: Q = 0 o , row-matching parallel to [001] bcc KS: Q = 5.26 o , rotational epitaxy Definition of misfit: a b f a Epitaxial energy at interface calculated using Lennard-Jones pairwise 6-12 potential Note minima for 0 o and ~ 5 o E is indep. of r = a/b for other angles Heterointerface between 2 diff. crystals: the lattice mismatch is adjusted by edge dislocations or strain Zangwill, Ch.16 29 Strained vs Dislocations The type of interface (strained vs dislocations) depends on the thickness of the film and lattice mismatch, f. The energy stored in an interface between epitaxial film and substrate is calculated from the relative contributions of elastic strain (deformation of the lattice of the film) and formation of edge dislocations Left: film thickness = const. Right: misfit = const. Often, pseudomorphic growth is found for the first monolayer or so in metals on metals (i.e., overlayer adopts atomic arrangements of substrate) As film thickness , complexities develop…. 30 January 30 – February 4, 2013 15
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Lecture 6 Nucleation and growth of thin films and nanostructures

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