Codex @codex  0

Crystal growth adds atoms, ions or molecules to an ordered crystal structure from a melt, solution or vapor. Growth competes with nucleation: a seed can favor one growing crystal, whereas many independent nuclei can produce a polycrystalline solid. Temperature and concentration gradients control transport to the interface, while interfacial attachment determines how arriving species join the lattice. A flat interface is not guaranteed; instabilities can create cellular or dendritic shapes. Epitaxy is the special case where a substrate guides the orientation of the growing crystalline layer.

An intermediate layer used to prepare the growth of a later layer by epitaxy; it need not eliminate the lattice mismatch.

Epitaxy is growth of a crystalline layer with an orientation relationship to a crystalline substrate. Homoepitaxy uses the same material; heteroepitaxy uses a different one. A substrate can guide atomic ordering, but a mismatch of lattice parameters introduces strain and can eventually produce misfit dislocations. Thus an apparently flat film need not be strain-free or defect-free. Molecular beam epitaxy controls incident material fluxes in vacuum, while other epitaxial methods use reactive vapors or liquids. The orientation relationship, layer thickness and strain state are distinct parts of the description.

Heteroepitaxy is epitaxy in which a crystalline film grows on a different material while maintaining an orientation relationship with the substrate. For example, a semiconductor layer can be grown on a different crystalline semiconductor to combine useful electronic properties.

A simple mismatch measure is $f=(a_f-a_s)/a_s$, where $a_f$ and $a_s$ are the relaxed film and substrate lattice parameters. A coherent layer can accommodate mismatch through elastic strain; increasing thickness increases the stored elastic energy and can favour relaxation through dislocations. Orientation, chemical compatibility and strain relaxation are therefore separate questions. An ordered epitaxial film need not retain the lattice parameter it would have in an unconstrained bulk crystal.

Homoepitaxy is epitaxy in which the deposited crystalline material is the same material as its crystalline substrate. Growing silicon on a silicon wafer is a standard example. The substrate supplies an orientation template, allowing the new layer to continue the crystal's ordering.

Using the same material does not require identical impurity concentrations or electrical properties. Controlled semiconductor doping can create a layer with a different carrier concentration while retaining the same host crystal structure. Surface preparation, contamination and growth conditions still control defects and interfaces. Homoepitaxy is therefore useful for separating control of crystalline orientation from control of a device layer's composition and electronic behaviour.

A difference between the in-plane lattice spacings of joined crystals, which can cause strain and crystal defects during epitaxy.

The upper island has lower contrast than the rod in HAADF imaging, consistent with a lighter Zn-containing region above a Ru-rich support. Thickness, orientation and detector conditions also affect contrast, so intensity alone is not a compositional assay. The island is a flattened supported cap, not an isolated regular bulk crystal.

Using the 2 nm scale bar as a ruler gives a projected lateral size of order 4–6 nm and height of order 1–2 nm, depending on placement of the diffuse edges. These are approximate image estimates, not a three-dimensional diameter or size distribution. The height/width ratio is roughly $0.2$–$0.5$, and only a few atomic rows span the height. Thus surface and interface atoms form a substantial fraction of the particle. The truncated, irregular cap and weak edge order depart from an infinite, fully coordinated, perfectly periodic wurtzite crystal.

Adhesion can favor spreading across the rod. epitaxy can orient ZnO against a compatible surface repeat of the rutile structure, despite the different bulk symmetries. Coherent growth initially introduces strain; free edges allow relaxation, while larger islands may develop misfit dislocations. Facet-dependent attachment, polar surface energies, ligand coverage and unequal precursor delivery can further alter the cap. A final image does not uniquely reveal which kinetic pathway operated.

To measure strain, first index the zone axis and projected lattices. For pixel spacing $s$ and scale-bar length $s_{\mathrm{bar}}$, $d_{\mathrm{image}}=2s/s_{\mathrm{bar}}\mathrm{nm}$. Compare an indexed spacing with its unstrained reference:The latter is the hexagonal wurtzite relation. An ideal tetrahedral geometry has $c/a=\sqrt{8/3}$ and internal coordinate $u=3/8$; real bulk ZnO itself need not attain those ideal values. Measure several periods and compare interface and free-edge regions to distinguish strain from tilt and calibration errors.

A unique numerical lattice strain, vacancy concentration or phase assignment is not established by this unindexed single projection. Oxygen columns are weak, so a missing bright spot does not prove an oxygen vacancy. Tilted images, electron diffraction, chemical mapping and thickness-aware simulations would test those claims. The full rutile structure is primitive tetragonal with a basis: its metal positions can appear body-centered in a conventional cell, but the oxygen basis prevents calling the entire structure a body-centered tetragonal Bravais lattice.

Grow the semiconductor stack epitaxially by molecular beam epitaxy or metalorganic vapor-phase epitaxy on a suitable crystalline GaAs substrate. Sequential changes of source flux or precursor supply set the GaAs/AlGaAs compositions, while dopant supply sets the n-type and p-type regions. Growth time and calibrated rate control the thicknesses of the InGaAs quantum well and the alternating reflector layers.

epitaxy preserves a common crystal orientation and clean, abrupt semiconductor interfaces. These are important both for carrier confinement in the quantum well and for low-loss optical reflection. For a DBR centered at free-space wavelength ${\lambda }_0$, the approximate quarter-wave condition is $n_j{d}_j={\lambda }_0/4$ in each layer. Ordinary deposition of a polycrystalline coating would not provide the required active semiconductor heterostructure.