Microcrack-induced strain relief in $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ quantum dots grown on Si(111)

Microcrack-induced strain relief in $Ga N ∕ Al N$ quantum dots grown on Si(111)

G. Sarusi, O. Moshe, S. Khatsevich, D. H. Rich, and B. Damilano

Phys. Rev. B 75, 075306 – Published 6 February 2007

Abstract

The optical properties of vertically stacked self-assembled $Ga N ∕ Al N$ quantum dots (QD’s) grown on Si substrates were studied by means of temporally and spatially resolved cathodoluminescence (CL). An analysis of the CL spectra, thermal activation energies, and measured decay times of the QD luminescence was performed near stress-induced microcracks, revealing changes in the optical properties that can be attributed to stress-dependent variations in the band edges, the polarization field, and the oscillator strength between electrons and holes. Three-dimensional $6 \times 6$ $k ∙ p$ calculations of the QD electron and hole wave functions and eigenstates were performed to examine the influence of biaxial and uniaxial stresses on the optical properties in varying proximity to the microcracks.

Received 24 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.075306

Authors & Affiliations

G. Sarusi, O. Moshe, S. Khatsevich, and D. H. Rich

Department of Physics, The Ilse Katz Center for Nano and Meso Scale Science and Technology, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel

B. Damilano

Centre de recherché sur l’Hetero-Epitaxie et ses Applications, Centre National de la Recherche, Rue B. Gregory, Sophia Antipolis, 06560 Valbonne, France

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Vol. 75, Iss. 7 — 15 February 2007

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Figure 1
Spatially integrated CL spectra of the S-40 and S-85 QD samples at $T = 300 K$ . The beam current $I_{b}$ and electron-beam energy $E_{b}$ were $150 pA$ and $15 keV$ , respectively. The resulting calculated values of $E_{x}$ are shown by the four vertical dotted lines for each sample which indicate distances of 0, 1, 2, and $3 μ m$ from the microcrack of each sample.Reuse & Permissions
Figure 2
Monochromatic CL image (a) and CL decay time image (b) of sample S-85. The beam current $I_{b}$ and electron-beam energy $E_{b}$ were $150 pA$ and $15 keV$ , respectively, for the CL imaging. The gray scale bar represents the mapping of the decay time $τ$ in (b).Reuse & Permissions
Figure 3
The decay time $τ$ as a function of distance from a microcrack for samples S-40 (a) and S-85 (b). Time decay curves in a semilogarithmic plot (upper panel) are shown for $e$ -beam positions both near and far from the crack (distances of $\sim 0$ and $\sim 3 μ m$ , respectively, for the top and bottom curves). The calculated radiative decay time $τ_{R}$ is also plotted in (a) and (b) to illustrate an agreement between theory and experiment with regards to relative changes in lifetime for various distances from the microcrack. The values for $τ_{R}$ (theory) are reduced by factors of 12 and 2 in (a) and (b), respectively, to enable a comparison between theory and experiment.Reuse & Permissions
Figure 4
The change in the activation energy, $Δ E_{A}$ , vs distance from a microcrack for samples S-40 and S-85. The average change in band edge relative to the QD $e − h$ levels, $Δ E_{B}$ , from the calculations is also shown as a function of distance to illustrate the strong correlation with $Δ E_{A}$ , which is referenced to the biaxially stressed regions far from the microcracks. The logarithm of the integrated QD emission intensity vs $1 ∕ k_{B} T$ for samples S-40 and S-85, from which $E_{A}$ is determined, is shown in the inset for $e$ -beam positions both near and far from the microcrack (distances $Δ x$ of $\sim 0$ and $\sim 3 μ m$ , respectively).Reuse & Permissions
Figure 5
The band-edge profile along the $z$ direction (growth direction) for the model truncated pyramidal QD’s of the S-40 and S-85 samples at $T = 300 K$ . The geometric parameters of height and areas for the top and bottom faces for each pyramid are indicated. The probability densities for the electron and hole wave functions integrated over the $x − y$ plane, ${∣ ψ_{e, h} (z) ∣}^{2}$ , are shown to illustrate the expected small wave function overlap. A 3D representation of the QD truncated pyramid and isosurfaces of the $e − h$ wave functions for ${∣ ψ_{e} (r) ∣}^{2} = 0.5$ and ${∣ ψ_{h} (r) ∣}^{2} = 0.15$ are illustrated in the insets.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Microcrack-induced strain relief in $Ga N ∕ Al N$ quantum dots grown on Si(111)

G. Sarusi, O. Moshe, S. Khatsevich, D. H. Rich, and B. Damilano

Phys. Rev. B 75, 075306 – Published 6 February 2007

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Physical Review B

covering condensed matter and materials physics

Microcrack-induced strain relief in GaN∕AlN quantum dots grown on Si(111)

G. Sarusi, O. Moshe, S. Khatsevich, D. H. Rich, and B. Damilano

Phys. Rev. B 75, 075306 – Published 6 February 2007

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Microcrack-induced strain relief in $Ga N ∕ Al N$ quantum dots grown on Si(111)