Inversion of the exciton built-in dipole moment in In(Ga)As quantum dots via nonlinear piezoelectric effect

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Inversion of the exciton built-in dipole moment in In(Ga)As quantum dots via nonlinear piezoelectric effect

Johannes Aberl, Petr Klenovský, Johannes S. Wildmann, Javier Martín-Sánchez, Thomas Fromherz, Eugenio Zallo, Josef Humlíček, Armando Rastelli, and Rinaldo Trotta

Phys. Rev. B 96, 045414 – Published 13 July 2017

Abstract

We show that anisotropic biaxial stress can be used to tune the built-in dipole moment of excitons confined in In(Ga)As quantum dots up to complete erasure of its magnitude and inversion of its sign. We demonstrate that this phenomenon is due to piezoelectricity. We present a model to calculate the applied stress, taking advantage of the so-called piezotronic effect, which produces significant changes in the current-voltage characteristics of the strained diode-membranes containing the quantum dots. Finally, self-consistent $k \cdot p$ calculations reveal that the experimental findings can be only accounted for by the nonlinear piezoelectric effect, whose importance in quantum dot physics has been theoretically recognized although it has proven difficult to single out experimentally.

Received 28 February 2017
Revised 1 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.045414

Physics Subject Headings (PhySH)

Piezoelectricity

Quantum dots

Photoluminescence k dot p method

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Johannes Aberl^1,*, Petr Klenovský^2,3,†, Johannes S. Wildmann¹, Javier Martín-Sánchez¹, Thomas Fromherz¹, Eugenio Zallo^4,5, Josef Humlíček^2,3, Armando Rastelli¹, and Rinaldo Trotta^1,‡

¹Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstraße 69, A-4040 Linz, Austria
²Department of Condensed Matter Physics, Masaryk University, Kotlářská, CZ-61137 Brno, Czech Republic
³Central European Institute of Technology, Masaryk University, Kamenice 753/5, CZ-62500 Brno, Czech Republic
⁴Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstraße 20, D-01069 Dresden, Germany
⁵Paul-Drude-Institut für Festkörperelektronik, Hausvogteilplatz 5-7, 10117 Berlin, Germany

^*johannes.aberl@jku.at
^†klenovsky@physics.muni.cz
^‡rinaldo.trotta@jku.at

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Vol. 96, Iss. 4 — 15 July 2017

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Images

Figure 1
(a) Sketch of the p-i-n diode bonded onto a PMN-PT piezoelectric substrate. The investigated In(Ga)As QDs were embedded in the central i-GaAs layer (light gray). The emission properties of the QDs can be tuned by using voltages applied to PMN-PT ( $V_{p}$ ) and diode ( $V_{d}$ ). The color-coded $μ$ -PL map in panel (b) shows the transition energies of exciton ( $X$ ), biexciton ( $X X$ ), and negative and positive trions ( $X^{-}$ , $X^{+}$ ) of a single QD as a function of the electric field across the diode $F_{d}$ (for $F_{p} = 0$ ). (c) Shift of the $I − V$ traces ( $I_{d}$ and $V_{d}$ are negative in the displayed range) of the diode in response to applied stress (tensile, T or compressive, C). The built-in voltage $V_{b i}$ was estimated from the intersection of the fitted part of the forward-bias region with the saturation current (red line). The shift of $V_{b i}$ for different steps of $F_{p}$ is ascribed to the piezotronic effect and is provided in the inset.
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Figure 2
(a) Determination of the stress dependence of $E_{0}$ , $p$ , and $β$ for voltages $V_{p}$ in the range from $V_{p} = - 200 V$ up to $V_{p} = 700 V$ . The measured data (green points) are fit with Eq. (1) (black lines) to extract $E_{0}$ , $p$ , and $β$ . In the inset, the linear shift of $E_{0}$ with $F_{p}$ is shown. The change in carrier separation $p / e$ of $X$ is shown in panel (b). The sketches illustrate the strain-induced inversion of the alignment of the electron and hole wave functions. The values obtained for $p$ at $F_{p} = 0$ for all measured excitons are provided in panel (c) along with the corresponding tuning rates $d p / d F_{p}$ .
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Figure 3
(a) Schematic band profile of the studied diode. Hereby $- e ϕ_{n}$ and $- e ϕ_{p}$ denote the quasi-Fermi-levels for electrons and holes, respectively. G and A simply label the different materials GaAs and ${Al}_{0.4} {Ga}_{0.6} As$ . The red curve indicates the strain-induced changes in the band alignment. In panel (b) the induced shear stress $s_{x y}$ in the GaAs layer containing the QDs as well as the resulting electric field $F_{qd}$ are plotted as a function of $θ$ for several (initial) values of the Schottky barrier $ϕ_{S b}$ .
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Figure 4
The dependence of $p / e$ on applied stress is shown for several configurations. The configuration estimated for our structure ( $α = 55^{\circ}$ ) is plotted with (blue) and without (red) taking into account the second-order term of the piezoelectric field. Stress fields with same anisotropy and magnitude but with $S_{1}$ aligned along [110] (green, $α = 45^{\circ}$ ) and [100] (yellow, $α = 0^{\circ}$ ) directions and for the case of purely biaxial stress (brown) are also provided.
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