X-ray atomic mapping of quantum dots

Arka B. Dey, Milan K. Sanyal, Denis T. Keane, Gavin P. Campbell, Bo-Hong Liu, Ian Farrer, David A. Ritchie, and Michael J. Bedzyk

Phys. Rev. Materials 4, 056002 – Published 6 May 2020

Abstract

We report a model-independent atomic-mapping technique for quantum dots (QDs) by combining Bragg reflection x-ray standing wave (XSW) and grazing incidence diffraction (GID) measurements. In this study, we choose GaAs capped InGaAs QDs/GaAs(001) as a model system to show the locations and arrangements of indium atoms within the QDs along various $[h k l]$ directions. This technique directly reveals the actual amount of positional anisotropy and ordering fraction of indium atoms within the QDs by probing the ( $\bar{1} 11$ ), (111), (311), ( $\bar{1} 31$ ), (113), and ( $\bar{1} 13$ ) crystallographic planes. We find that indium atoms are outwardly shifted along the [001] direction by small fractions of the lattice constant, $0.04 a_{GaAs}$ and $0.06 a_{GaAs}$ from Ga sites for 50- and 150-Å GaAs capped InGaAs QDs, respectively. We observe that an improved coherency factor of the indium atoms within the QDs by 45–60% along the [001] and [011] directions reduces the photoluminescence linewidth by 22%, thus making the QDs efficient for QD-laser and optoelectronic device applications. We also find that the position and ordering of In atoms along the (113) and ( $\bar{1} 13$ ) planes are most sensitive to the thickness of the GaAs cap layer. Our XSW-based results are supported by numerical calculations using a QD-macroscopic structural model based on our GID study. We thus show that this atomic-mapping technique will be useful for studying various quantum structures and tuning their properties.

Received 18 December 2019
Revised 17 March 2020
Accepted 16 April 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.056002

Physics Subject Headings (PhySH)

Optoelectronics

Quantum dots

Molecular beam epitaxy X-ray scattering X-ray standing waves

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Arka B. Dey ^1,*, Milan K. Sanyal ¹, Denis T. Keane², Gavin P. Campbell², Bo-Hong Liu², Ian Farrer ³, David A. Ritchie⁴, and Michael J. Bedzyk^2,5

¹Surface Physics and Material Science Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
²Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
³Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom
⁴Department of Physics, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
⁵Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

^*Present address: Deutsches Elecktronen-Synchrotron, Notkestraße 85, 22607, Hamburg, Germany; arka.bikash.dey@desy.de

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Vol. 4, Iss. 5 — May 2020

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Images

Figure 1
Reflectivity $R (θ)$ and normalized indium $L α$ fluorescence yield $Y (θ)$ as a function of x-ray incident angle. Left: 50-Å GaAs cap InGaAs-QDs/GaAs (001); right: 150-Å GaAs cap InGaAs-QDs/GaAs(001) for measured Bragg reflections as indicated above for each subfigure. The solid blue and red lines are best fits to the experimental data (symbols) of the reflectivity and fluorescence yield, respectively.
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Figure 2
(a), (d) XSW-measured model-independent 3D indium atomic map for (a) 50-Å-capped and (d) 150-Å-capped InGaAs-QDs/GaAs(001). The outlined black cube is larger than the GaAs unit cell to demonstrate the indium atom positions. The $x, y,$ and $z$ axes are in units of fractional GaAs unit-cell lattice vectors $a, b$ , and $c$ with the origin placed at the Ga site. (b), (e) Atomic density of indium on the (100) plane located at $x = 0$ of the GaAs unit cell for (b) 50-Å-capped and (e) 150-Å-capped QDs sample. Five red spots denote indium atom positions at expected fcc sites. Due to strain the indium atoms are outwardly shifted from the Ga atom positions of the GaAs weighted unit cell. (c), (f) In 3D density plotted along the $c$ axis to produce a 1D In atomic density as a function of the fractional $c$ -axis coordinate $z$ for the GaAs unit cell for (c) sample A and (f) sample B. Red, blue, green lines are along ( $0, 0, z$ ), ( $0, 0.5, z$ ), and ( $0.25, 0.25, z$ ), respectively.
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Figure 3
(a) Schematic sketch of an average GaAs cap InGaAs-QDs/GaAs(001). (b) Unstrained GaAs atomic arrangement showing atoms Ga (red circle) and As (green circle) along with (004) and (111) bulk planes as blue and red lines, respectively. (c) Illustration showing how the XSW measured values for $P_{004}$ and $P_{111}$ are used to triangulate the average In atomic (blue dot) position relative to the unstrained substrate GaAs atomic arrangement. (d) The 50-Å GaAs capped QD is segmented into 13 In/Ga atomic sublayers (blue ellipsoidal platelets). Sublayers 7 and 13 are shown for reference. Here, $a_{7}$ and $h_{7}$ denotes the major axis dimension and height of the seventh sublayer of the GaAs substrate. (e), (f) Ordered fractions ( $s_{j}$ ) and out-of-plane ordered positions ( $p_{j}$ ) of the 13 indium atomic sublayers for (e) sample A and the 12 indium atomic sublayers for (f) sample B with reference to unstrained GaAs unit cell. The numbers indicate the sublayer numbers. (g) Reduction of FWHM of ground, first and second excited-state PL transition lines indicated by the blue arrow. PL spectra for sample B is shown in the inset for reference.
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