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Concept# Miller index

Summary

Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices.
In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and ℓ, the Miller indices. They are written (hkℓ), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to \mathbf{g}_{hk\ell} = h\mathbf{b}_1 + k\mathbf{b}_2 + \ell\mathbf{b}_3 , where \mathbf{b}_i are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice. (Note that the plane is not always orthogonal to the linear combination of direct or original lattice vectors h\mathbf{a}_1 + k\mathbf{a}_2 + \ell\mathbf{a}_3 because the direct lattice vectors need not be mutually orthogonal.) This is based on the fact that a reciprocal lattice vector \mathbf{g} (the vector indicating a reciprocal lattice point from the reciprocal latti

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We report on the epitaxial growth of high-quality core-shell nonpolar m-plane GaN/InAlN multiple quantum wells (MQWs) on the sidewall facets of c-oriented hexagonal GaN wires. Pseudomorphic growth without generation of threading dislocations has been established for planar GaN/InAlN (In = 15%) MQWs grown on m-GaN substrates, although m-plane InAlN epilayers cannot be grown perfectly lattice-matched to GaN along the two in-plane directions. Calculations based on elasticity theory indicate that the significant amount of strain oriented along the c-axis is the likely factor favoring the formation of cracks along this direction. For the core-shell wire geometry, such cracks are not observed, leading to high structural quality MQWs. A significant UV emission centered around 3.7 eV at room temperature with a strong polarization perpendicular to the wire axis is observed for those core-shell wires, which is consistent with k.p method calculations, proving the absence of quantum confined Stark effect on nonpolar m-plane surfaces. These excellent optical features reported in the UV spectral range are attributed to the defect-free nature of the GaN/InAlN MQWs, thereby opening promising opportunities for the realization of UV light emitters.

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