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Connecting Theory and Practice in Optoelectronics
Whenever you try to answer a research question by using numerical simulation, you start by developing a (or reusing an already developed) mathematical model. Thereafter, you are developing (or reusing already developed) software to perform your numerical simulation. This produces data that you are now analysing and visualising to interpret the discovered results. Finally, you might want to write it all down in an article and publish it on the arXiv and/or in a scientific journal. In this published form the results consist – apart from a couple of figures or tables – mainly of text. In most cases mathematical models, software, data, visualisations and so on are not or not fully shown. This makes it difficult for editors, reviewers and readers alike to fully grasp the research and its results, see e.g. How to get your simulation paper accepted. Moreover, it makes it difficult to validate and in many cases impossible to reproduce the results.
In a time when scholarly publication was limited to printed journals and books it was simply not feasible to provide long rows of numbers not to mention interactive 3D figures or a moving series of pictures. However, with the advent of the digital age and its easy accessible and easy to use infrastructures and tools there is no excuse for not publishing the full research story – and that does not only consist of plain text.
In semiconductor device simulations, one often uses the so-called Boltzmann approximation (an exponential) to link Fermi energy levels to the densities of charge carriers. This corresponds to the classical Einstein relation between diffusion and mobility. However, in organic semiconductors, highly doped regions or at cryogenic temperatures the electron-hole plasma becomes degenerate and Fermi-Dirac statistics can no longer be neglected. The implications are two-fold: First, the distribution function F(η) may no longer be approximated by an exponential (Boltzmann approximation). Second, a generalized Einstein relation now governs the diffusive currents via a nonlinear density-dependent diffusion factor g (the diffusion enhancement). This factor reduces to one in the nondegenerate Boltzmann case and measures the degree of the degeneracy.
The Boltzmann approximation appears in both figures as a straight blue line. For low carrier densities it approximates the Fermi-Dirac integral as well as the Gauss-Fermi integral for organic semiconductors.
The classical Scharfetter-Gummel scheme  in combination with a Voronoï finite volume method provides a numerical solution to the drift-diffusion equations in nondegenerate semiconductors. However, how to approximate the numerical fluxes for degenerate semiconductors (leading to nonlinear diffusion), is still an active area of research. Recently, in  we compared two state-of-the-art numerical flux discretizations:
But which of two is the “best”? Read more of this post
Quantum optics is on the leap from the lab to real world applications. The design of novel devices based on semiconductor quantum dots asks for simulation approaches, which combine classical device physics with quantum mechanics. We connect the well-established fields of classical semiconductor transport theory and theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics .
Topological insulators have attracted a huge amount of attention in the field of condensed matter physics. This new state of matter is characterized by a bulk band gap and conducting surface states. The surface states have linear dispersion resembling relativistic Dirac fermions, in analogy with graphene. In contrast to graphene the 2D fermions on the surface are non-degenerate, whereas electrons in graphene are spin and valley degenerate. The linear dispersion and 2D nature of the electrons in graphene leads to the universal optical absorbance απ≈2.3% given by the fine structure constant , independent on the material parameters and the photon energy. Due to this relatively large absorption for a single atomic layer, graphene is a promising material for optoelectronic applications e.g. photodetectors, which has been demonstrated . Similarly a topological insulator has an absorbance of απ/2≈1.1% for photon energies below the bulk band gap, due to the surface states at the top and bottom surface. It has been shown that the signal-to-noise ratio of photodetector based on a thin slab of the topological insulator Bi2Se3 can be significantly larger than for a graphene based device. For a slab thickness below 6 nm the surface states on opposing sides interact leading to a band gap, which can be tuned by varying the thickness. However, this way of manipulating the optical properties is not very flexible since Bi2Se3 has a layered structure with five atomic layers strongly bound in a quintuple layer, limiting the possible thicknesses to only integer numbers of quintuple layers (QL). If instead strain is used to tune the optical properties, this can be done continuously and dynamically.
Quantum cascade lasers (QCLs) utilize quantized electron states as laser levels, which can be custom-tailored to the specific application by adequately designing the multi-quantum-well active region. With dephasing times between the upper and the lower laser level of about a picosecond, coherent light-matter interaction, along with other effects such as dispersion and spatial hole burning, governs the laser dynamics . Besides leading to multimode instabilities , the ultrafast dynamics in QCLs is increasingly exploited to implement innovative functionalities, such as the generation of frequency combs [2,3] and picosecond optical pulses  in the mid-infrared and terahertz regime.
For a targeted design of such structures and a deeper understanding of the complex QCL dynamics, a detailed theoretical model is required. We have developed a multi-domain simulation approach, which couples a Maxwell-Bloch type description of the light-matter interaction with advanced ensemble Monte Carlo (EMC) carrier transport simulations to eliminate empirical electron lifetimes . In the figure, simulation results for a QCL-based terahertz frequency comb source  are presented. The laser dynamics gives rise to a two-lobed power spectrum consisting of equidistant discrete comb lines [Fig. (a)]. Furthermore, a periodic temporal shifting of the power between the two spectral lobes is observed [Fig. (b)]. The two-lobed comb spectrum and the associated temporal switching dynamics have also been observed in experiment [3,5], validating our simulation model.