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Core size dependence of the confinement energies, barrier heights, and hole lifetimes in Ge-core/Si-shell nanocrystals
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color online) Ge/Si core-shell NC (4 nm Ge core and 5 nm Si shell around Ge core). The total number of atoms is 63976 (63448 Si atoms and 528 Ge atoms). The lighter gray dots are Si atoms and darker (red) dots are Ge atoms.

Image of FIG. 2.
FIG. 2.

(Color online) Energy diagram and wavefunction distribution in the Ge/Si core-shell NC. The offsets shown in the band edges correspond to the bulk Si and Ge parameters used in the calculations. Dashed lines show the two different hole escape mechanisms resulting in the two lifetimes, and .

Image of FIG. 3.
FIG. 3.

(Color online) Quantum confinement energy ( ( )) and barrier height ( ( )) as a function of Ge core size. The number associated with each point on the curve is the orbital number ( ) associated with the barrier height. is the calculated quantum confinement energy using Eq. (1) from Ref. 15 .

Image of FIG. 4.
FIG. 4.

(Color online) Magnitude of the wavefunctions squared plotted for (a) the highest localized state and (b) the highest delocalized state in the Si(5 nm)-Ge(4 nm)-Si(5 nm) NC. The values are taken from a two-dimensional slice through the center of the NC. In this case, .

Image of FIG. 5.
FIG. 5.

Localized hole effective mass in the Ge core region as a function of Ge core size.

Image of FIG. 6.
FIG. 6.

(Color online) Minimum energy gap ( ), the valence band maximum and the conduction band minimum as a function of the Ge core size (nm) with a fixed 5 nm Si shell.

Image of FIG. 7.
FIG. 7.

(Color online) (a) The magnitude squared of the HLO ( ) plotted vs radial position in the Si shell and the superimposed exponential fit for the NC with a 4 nm Ge core. (b) Ground state hole tunneling wave vector in the Si shell ( ) vs Ge core diameter. (c) Parabolic tunneling effective mass of the ground state hole in the Si shell as a function of Ge core size.

Image of FIG. 8.
FIG. 8.

(Color online) Direct tunneling lifetime (dashed line) and thermionic lifetime (solid line) vs Ge core diameter with a 5 nm Si shell.

Image of FIG. 9.
FIG. 9.

Si shell size vs Ge core size such that the quantum tunneling lifetime is equal to the thermionic emission lifetime.

Image of FIG. 10.
FIG. 10.

(Color online) Band diagram of the bulk Ge/Si/ system. The dashed line illustrates the imaginary dispersion in the bandgap, and the horizontal line shows the energy at which is calculated from Eq. (7) . The short-dashed red line illustrates the thermionic escape rate ( ) that provides the attempt rate for quantum tunneling through the .

Image of FIG. 11.
FIG. 11.

(Color online) Total hole lifetime in the Ge/Si/ system at thicknesses of 1, 2, and 3 nm.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Core size dependence of the confinement energies, barrier heights, and hole lifetimes in Ge-core/Si-shell nanocrystals