NUSOD Blog

Connecting Theory and Practice in Optoelectronics

On a Database of Simulated TEM Images for In(Ga)As/GaAs Quantum Dots with Various Shapes

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Quantum dot geometry and FEM mesh (top) and simulated TEM image (bottom)

The fabrication of semiconductor quantum dots (QDs) with desired electronic properties would highly benefit from the assessment of QD geometry, distribution, and strain profile in a feedback loop between epitaxial growth and analysis of their properties. In [1, 2] we introduced a novel concept for 3D model-based geometry reconstruction (MBGR) of QDs from TEM imaging (see NUSOD 2018 blog). The approach is based on (a) an appropriate model for the QD configuration in real space including a categorization of QD shapes (e.g., pyramidal or lens-shaped) and continuous parameters (e.g., size, height), (b) a database of simulated TEM images covering a large number of possible QD configurations and image acquisition parameters (e.g. bright field/dark field, sample tilt), as well as (c) a statistical procedure for the estimation of QD properties and classification of QD types based on acquired TEM image data.
Here we present a database of simulated transmission electron microscopy (TEM) images for In(Ga)As quantum dots (QDs) embedded in bulk-like GaAs samples. The database contains series of TEM images for QDs with various shapes, e.g. pyramidal and lens-shaped, depending on the size and indium concentration as well as on the excitation conditions of the electron beam.
For the generation of TEM images for the database we use a parametric geometry description of the QD shape, e.g. using base length and height of the QD. In the database the geometrical model, the computed strain profile, the multi-beam solution as obtained by the solution of the Darwin-Howie-Whelan equations and the resulting TEM images are stored together with necessary meta data. Our aim is a comprehensive database covering all the different types and shapes of QDs as introduced in [3].

More details will be presented at the NUSOD 2019 conference in Ottawa (paper MB2).

References

  1. T. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow and J. Polzehl, Towards Model-Based Geometry Reconstruction of Quantum Dots from TEM, 2018 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), pp. 115-116, 2018. DOI: 10.1109/NUSOD.2018.8570246
  2. A. Maltsi, T. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, Proc. Appl. Math. Mech., vol. 18, e201800398, 2018. DOI: 10.1002/pamm.201800398
  3. A. Schliwa, M. Winkelnkemper, D. Bimberg, Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots,
    Phys. Rev. B, vol. 76, 205324, 2007. DOI: 10.1103/PhysRevB.76.205324
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Atomistic Analysis of transport properties of InGaN/GaN multi-quantum wells

InGaN/GaN based devices are of interest for realizing light emitting diodes (LEDs) that emit in the visible spectral range. However, even though InGaN based LEDs have some widespread applications, several underlying physical phenomena are still not fully understood, for instance, the “droop” effect [1]. Therefore, the full potential of these LEDs for energy efficient lighting applications has yet to be exploited.

Often, when investigating transport through such systems, the device is described by average parameters and the underlying microscopic structure is neglected. Both experimental and theoretical studies have shown that alloy fluctuations have a significant influence on the electronic and optical properties of these systems [2]. Standard approaches do not capture these phenomena. Therefore, we aim to investigate the impact of the underlying alloy microstructure on transport properties of nitride-based devices in a combined atomistic and quantum mechanical picture.

Figure 1. (a) Side view of model system. (b) Dimensions of the supercell used.

The electronic structure calculations are performed using an sp3 TB model [3]. This allows us to capture fluctuations due to a (random) Indium atom distribution in the QW regions in a 3-dimensional frame. The resulting Hamiltonian is used as input to the Non-Equilibrium Green’s function solver OMEN [4] in order to compute transport properties in a quantum mechanical framework. Figure 1 shows a model system used containing two InGaN/GaN QWs with 15% Indium content.

We focus our attention on transmission probabilities and how this changes with alloy composition. More specifically, we compare results from virtual crystal approximation (VCA) calculations with then outcome of atomistic calculations in which the “level of randomness” changes. We turn our attention initially to electrons and later to hole transport properties.

Our calculations show that random alloy fluctuations can significantly affect transmission probabilities, leading for instance to a broadening and a reduction of these probabilities when compared to VCA calculations.

More details will be presented at the NUSOD 2019 conference in Ottawa (paper MB4).

References

[1] J. Piprek, “How to decide between competing efficiency droop models for GaN-based light- emitting diodes” Appl. Phys. Lett. 107, 031101 (2015)

[2] P. Dawson, et al., “The nature of carrier localisation in polar and nonpolar InGaN/GaN quantum wells”, J. Appl. Phys. 119, 181505 (2016)

[3] S. Schulz, et al., “Atomistic analysis of the impact of alloy and well-width fluctuations on the electronic and optical properties of InGaN/GaN quantum wells”, Phys. Rev. B. 91 035439 (2015)

[4] M. Luisier, et al., “Atomistic simulation of nanowires in the sp3d5s* tight-binding formalism: From boundary conditions to strain calculation”, Phys. Rev. B. 74, 205323, (2006)

Quantum Plasmonic Metasurface Analyzed by Time-Dependent Density Functional Theory

A plasmonic metasurface in which metallic nano-objects are periodically placed on a plane has been attracting substantial attention in terms of its exotic optical characteristics [1]. Although investigations have been devoted mostly to metasurfaces with wavelength or sub-wavelength gap distances between constituent nano-objects, experimental studies have been reported recently for periodic structures with much smaller gap distances, reaching to sub-nanometer [2]. In isolated systems with a sub-nanometer gap such as a metallic nanodimer, it has been revealed that optical properties show substantial differences between theoretical descriptions using classical and quantum theories [3]. The difference becomes remarkable for gap distances less than 0.4 nm [4] where the quantum tunneling across the gap becomes sizable. For metasurfaces, however to the best of our knowledge, there have not been any theoretical reports discussing quantum effects, although measurements have been carried out for metasurfaces with the gap distance as small as 0.45nm [2].

Fig. 1. (a-b) Schematic illustration of the studied metasurface consisting of jellium nanospheres. (a) Top view. (b) Side view. (c-d) Spectral distributions of the transmission rates of the metasurfaces calculated by the TDDFT (c) and the classical electromagnetic analysis (d), respectively.

We theoretically and numerically investigate optical properties of a quantum plasmonic metasurface composed of metallic nanoparticles that are arranged in a two-dimensional matrix form with sub-nanometer gaps as shown in Figs. 1 (a) and (b), where a, d, and l denote the diameter of the spheres, the gap distance, and the length of the period, respectively. To take into account quantum mechanical effects in the analysis, we employ time-dependent density functional theory (TDDFT) treating the constituent nano-particles by a jellium model. Figs. 1 (c) and (d) show calculated transmission rate of the metasurfaces, T, for various gap distances, d = -0.1 – 0.4 nm. We show results using TDDFT in (c), and results of classical electromagnetic analysis using FDTD calculation in (d). Both TDDFT and FDTD calculations have been performed using open-source software SALMON (Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience, https://salmon-tddft.jp/ ) that is developed in our group [5]. In the classical calculation shown in Fig. 1(d), we find typical plasmonic peaks and their red-shifts for 0 < d ≦ 0.4 nm while sudden blue-shifts are observed for the two plasmon peaks for d ≦ 0.0 nm. In contrast, the TDDFT calculation shown in Fig. 1 (c) presents qualitatively different features: the plasmonic peaks become smaller and much broader as d decreases and no blue-shifts are observed from stem to stern. These differences are caused by the tunneling currents that flow in the gap region between nanospheres [3, 4]. More details will be presented at the NUSOD 2019 conference in Ottawa (paper ThC2).

REFERENCES
[1] N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces”, Nat. Photonics, vol. 8, pp. 889–898, Dec. 2014.
[2] D. Doyle, N. Charipar, C. Argyropoulos, S. A. Trammell, R. Nita, J. Naciri, A. Piqué, J. B. Herzog, and J. Fontana, “Tunable Subnanometer Gap Plasmonic Metasurfaces”, ACS Photonics, vol. 5, pp. 1012–1018, Dec. 2017.
[3] W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec1, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps”, Nat. Commun., vol. 7, pp. 11495–11508, Jun. 2016.
[4] K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics”, Nature, vol. 491, pp. 574–577, Nov. 2012.
[5] M. Noda, S. A. Sato, Y. Hirokawa, M. Uemoto, T. Takeuchi, S. Yamada, A. Yamada, Y. Shinohara, M. Yamaguchi, K. Iida, I. Floss, T. Otobe, K.-M. Lee, K. Ishimura, T. Boku, G. F. Bertsch, K. Nobusada, K. Yabana, “SALMON: Scalable Ab-initio Light–Matter simulator for Optics and Nanoscience”, Comput. Phys. Comm, vol. 235, pp. 356–365, Feb. 2019.

Drift-diffusion simulations of thermally activated delayed fluorescence OLEDs

The design of blue emitters for organic light emitting diode (OLED) displays represents one of the most significant issue in organic optoelectronics. This is due to the limited lifetime of materials having wide bandgap [1]. As demonstrated by Uoyama et al. [2] in 2012, the use of thermally activated delayed fluorescence (TADF) materials allows to overcome these limitations by harvesting both the singlets and triplets exciton decay via the reverse inter-system crossing (RISC) mechanism, therefore avoiding the performance degradation typically due to the triplet-to-triplet annihilation (TTA) mechanism.
The proper optical engineering of the guest material within the emitter layer, i.e. by guaranteeing an energy difference between singlets and triplets less than 100 meV, ideally allows achieving an internal quantum efficiency IQE of 100%. Indeed, as result of the triplets recovery via RISC, the radiative emission which would be normally based on the prompt fluorescence will be increased by the delayed fluorescence contribution.
Given the complexity of mechanisms that determine the optical operation of the TADF OLEDs, we exploit the versatility of a multiparticle drift-diffusion model (mp-DD) [3], which is developed with the aim to calculate the carrier transport within the device by explicitly accounting for both charged carriers and excitons. This tool allows to define different species of sub-populations in the same region, and couple them with each other using generation-recombination models.
We simulated the operation of the typical blue TADF OLED depicted in Fig.1, for which we report the energy level diagram and indicate layer by layer the sub-populations included in the system.

Fig. 1. Schematic LUMO-HOMO level diagram of carrier sub-populations, and energy levels of excitons included in the system.

We investigated the internal quantum efficiency (IQE) roll-off effect, which in these devices typically takes place at high current density [4]. To do this, we include in the model charge transfer between HOMO and LUMO of the EML, and the inter-system crossing process aided by thermal activation (see Fig. 2), which can contribute by more than 60% on the total internal radiative emission.


Fig. 2. Summary of exciton states and recombination rate
constants accounted for within the host–guest system of the emitter.

According to experimental observations, we model both the triplet-to-triplet annihilation [4] and triplet-to-polaron quenching [5], that represent the most important processes which affect the luminescent efficiency in TADF OLEDs.

Fig. 2. Quantum efficiency contributions from non-radiative recombination, TPQ, TTA and internal radiative emission at different current densities.

In Fig. 3 we report the contributions of the different loss mechanisms to the quantum efficiency. In agreement with the experimental results, the TTA is strongly dependent on the current density. In particular, at high current densities a roll off of the IQE is observed, which is apparently due to a nonlinear increase in TTA. The latter can be explained by the fact, that TTA is of second order in the triplet density, while radiative decay is of first order. This is similar to the situation in III-nitride LEDs, where IQE drops at high current densities due to Auger recombination.

More details will be presented at the 2019 NUSOD conference in Ottawa (paper FA1)

REFERENCES
[1] X. Yang, X. Xu, and G. Zhou, J. Mater. Chem. C, vol. 3, no. 5, pp. 913–944, 2015.
[2] H. Uoyama, K. Goushi, K. Shizu, H. Nomura, and C. Adachi, Nature, vol. 492, no. 7428, p. 234, 2012.
[3] D. Rossi, F. Santoni, M. Auf der Maur, and A. Di Carlo, IEEE Trans. Electron Devices, vol. 66, no. 6, 2019.
[4] K. Masui, H. Nakanotani, and C. Adachi, Org. Electron., vol. 14, no. 11, pp. 2721–2726, 2013.
[5] R. Coehoorn, L. Zhang, P. Bobbert, and H. Van Eersel, Physical Review B, vol. 95, no. 13, p. 134202, 2017.

Design of Monolithically Integrated Photodetector and Improvement using Plasmonics

Waveguide-coupled photodetectors with high quantum efficiency and cutoff frequency are key components in photonic integrated circuits. While the state-of-art coupling approach is achieved vertically, we propose three horizontal coupling geometries, shown in Fig. 1, with device performance optimized using 3D optoelectrical simulations. It is also shown that using plasmonics can further improve the performance.

Fig. 1: Structures with (a) side coupling, (b) butt coupling
without offshoot, (c) butt coupling with n-offshoots.

Two structure parameters are crucial for design optimization in our study. One is the waveguide height. The other is the photodetector i-region length along the propagation direction. These parameters are optimized based on mode formation within waveguide and 3dB optical and electrical cutoff frequency. We show side coupling structure is the best strategy, with max. IQE of 91% and optical (electrical) cutoff frequency of 800GHz (30THz).

The optical cutoff frequency of the butt coupling structure with n-offshoots can be improved from 70 GHz to 300 GHz, by introducing two Ag rods are added on top of the i-region, as sketched in Fig. 2. This improvement comes from the fact that plasmonics significantly enhances the electric field in the unbiased i-region.

Fig. 2: (a) 60 nm-spaced double 40×40 nm Ag rods on top of
i-region in butt coupling structure with n-offshoots, (b) optical
generation rate profile along n-i-n direction cut; E-field in i-
region of structure (c) without Ag and (d) with Ag.

More details will be presented at the NUSOD 2019 conference in Ottawa (paper FA2).