Geometry of the modeled self-assembled quantum dot. The quantum dot is lens shaped with a base diameter of and a height of . The lines and are the transverse and vertical axes along which the spatial distributions of are plotted in Fig. 2.
Spatial distributions of the hyperfine coupling coefficient for a lens-shaped quantum dot embedded in a buffer (a) along the axis and (b) along the axis of Fig. 1. The coupling coefficient is given by Eq. (5) and is proportional to the electron density. The dashed lines indicate the interface between the dot and the buffer.
Projection of the lowest electron wave function onto the atomic orbitals of different symmetry for lens-shaped quantum dots (QD) with diameter and height . The wave function is calculated with an tight-binding model. Three different alloy materials are considered for quantum dots. For comparison, the wave functions of the lowest conduction band at and in bulk and are also projected onto the atomic orbitals.
Hyperfine-splitting fluctuation , ensemble-spin dephasing time , and effective nuclear magnetic field fluctuation caused by various inhomogeneities for an quantum dot embedded in a buffer. For unpolarized nuclei, each nuclear spin direction is chosen randomly. For dot-size fluctuations, the base diameter is set to and the height to . For alloy disorder, dots are examined and each cation atom is randomly chosen to be an or a atom. For interface disorder, each cation within a thick interface between the dot and the buffer is randomly chosen to be an or a atom, reflecting the experimental observation of mixing near the interface (Ref. 63).
Tight-binding coefficients of the and basis orbitals for the conduction-band-edge wave functions of bulk and , and deduced densities of and orbitals at nuclear sites. The densities and are in units of .
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