NUSOD Blog

Connecting Theory and Practice in Optoelectronics

NUSOD 2018 Preview: Towards Model-Based Geometry Reconstruction of Quantum Dots from TEM

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TEM images of InAs QDs (Courtesy of TU Berlin [1])

The growth 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. However, the reconstruction of geometric properties of semiconductor quantum dots (QDs) from imaging of bulk-like samples (thickness 100-300 nm) by transmission electron microscopy (TEM) is a difficult problem. A direct reconstruction by solving the tomography problem is not feasible due to the limited image resolution (0.5-1 nm), the highly nonlinear behavior of the dynamic electron scattering, nonlocal effects due to strain and strong stochastic influences due to uncertainties in the experiment. Here, we outline a novel concept for 3D model-based geometry reconstruction (MBGR) of QDs from TEM images. This will include (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. To this end we need an accurate mathematical model for the numerical simulation of the TEM images.

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NUSOD 2018 Preview: Ultrashort solitons and their control in the regime of event horizons in nonlinear dispersive optical media

We introduce several settings for the description of pulse propagation in dispersive nonlinear optical media.

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A short and intense optical soliton that propagates along a fiber with Kerr nonlinearity, creates a localized nonlinear perturbation of the refractive index. A low-intensity pump wave of similar group velocity can be reflected at the solitonic barrier, thereby undergoing a pronounced frequency change [1,2]. During the reflection process the pump wave and the soliton exchange energy, and the soliton is compressed or dispersed, and propagates with changed peak power and shifted frequency. The soliton can be compressed up to a few-cycle regime. As a result, a soliton can be manipulated by a much weaker control wave. For instance, it can be switched on and off [1], or be used to model event horizons [3] by trapping the pump wave [4]. We present an analytic theory [5] of interactions like the one shown in Fig. 1, quantify optimal pulse parameters [6], and demonstrate how a pump wave can be suitably chosen so as to compensate the Raman effect robustly [7]. Read more of this post

NUSOD 2018 Preview: Highly Accurate Discretizations for non-Boltzmann Charge Transport in Semiconductors

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Suppose one wants to predict charge carrier transport in semiconductors with very high precision, in particular for non-Boltzmann (e.g. Fermi-Dirac and Gauss-Fermi) statistics.
How could one go about this? The van Roosbroeck system models the charge carrier flow in the presence of a self-consistent electrical field. When discretizing the van Roosbroeck system using the Voronoï finite volume method [1-3], the crucial part is the approximation of the carrier fluxes between neighboring control volumes. The Scharfetter-Gummel (SG) scheme provides a thermodynamically consistent discrete carrier flux approximation for non-degenerate semiconductors. Degeneracy effects requiring non-Boltzmann statistics become relevant e.g. at cryogenic temperatures, for high doping concentrations or in organic materials. Read more of this post

NUSOD 2018 Preview: Data-driven Electronic Structure Calculations for Nanostructures

bsMultiband k·p models, in particular the six- and eight-band approaches, represent the back bone of electronic structure simulations of semiconductor nanostructures for about two decades and have allowed deep insights into the electronic properties of quantum wells, -wires, and -dots. However, apart from the fundamental limitation that all k·p models in combination with envelope functions lack the description of the underlying atomic lattice, the well-established eight-band model contains other shortcomings that renders it unsuitable for certain applications.
This model includes the top three valence bands as well as the bottom conduction band with their respective spin-up and spin-down components as basis functions. It is therefore a priori clear that any material in which other relevant bands occur, as e.g. wurtzite GaAs where a second energetically close conduction band exists at the Brillouin zone centre, cannot be described with this formalism.
Moreover, typical eight-band models are constructed such that they provide an accurate description of the band structure around the Brillouin zone centre, making the description of indirect band gap materials such as Si impossible.
Finally, so-called spurious solutions can occur if large k-values become relevant for the electronic properties of a particular nanostructure, of which one possible origin is the erroneous description of the band structure in the remote regions of the Brillouin zone. Read more of this post

NUSOD 2018 Preview: Light-Matter Interaction in NEGF Simulations of Intersubband-Emitting Devices

For optoelectronic devices, the light-matter interaction is essential. In nonequilibrium Green’s function (NEGF) formalism [1], it can be included either through appropriate selfenergy [2–4] or time-dependent (ac) potential incorporated into device Hamiltonian [5]. For unipolar devices, utilizing intersubband transitions, only the “ac” approach was used [5–7]. This approach requires solving the full set of NEGF equations for several higher harmonic of fundamental frequency what generates huge numerical load. On the contrary, the selfenergy approach generates only little additional load as the light-matter selfenergy (like other selfenergies) is included into NEGF equations for the steady state. In this contribution, the selfenergy approach is used to perform simulations of quantum cascade laser.

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Figure 1. (left) Gain spectra for the increasing photon flux (up-to-down) set at ℎ𝜈 = 𝐸𝛾 = 126 meV. (right) Gain at ℎ𝜈 = 𝐸𝛾 and current density as a function of photon flux set at ℎ𝜈 = 𝐸𝛾 = 126 meV calculated with the NEGF method (symbols).

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Figure 2 (left) Current-voltage and light-current characteristics calculated with or without electron-photon selfenergies included into NEGF formalism; (right) gain peak for these two cases. Lines show experimental data [12].

Some results are presented in Figs. 1 and 2. In Fig. 1, the calculated gain-flux and current-flux  dependencies  are compared with the relations predicted by the 2-state rate equations model [6, 7] (lines).  These calculations have been done for a fixed bias voltage. The current-voltage-light characteristics are shown in Fig. 2. They were calculated for electron-photon interaction turn off or on. For the latter case, the mono-chromatic field with energy 𝐸𝛾 = 0.126 eV was used, and photon flux was increased until the gain was clamped to its threshold value described by the total losses.  As can be seen, the agreement with the experimental data of [12] (lines) is not bad, especially if we take into account that the only adjustable parameter of the model is the roughness of the interfaces which was assumed as one third of the monolayer spacing. The observed differences are probably due to the overestimated losses assumed in the model as well as the doping of the core in the real samples that might have been higher than the nominal value used in the simulations. Read more of this post