# NUSOD Blog

Connecting Theory and Practice in Optoelectronics

## Tag Archives: device simulation

## NUSOD 2017 Preview Rump Session: Words cannot express…! Research results are more than just plain text.

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.

## NUSOD 2017 Preview: Comparison of Consistent Flux Discretizations for Drift Diffusion beyond Boltzmann Statistics

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 [1] 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 [2] we compared two state-of-the-art numerical flux discretizations:

But which of two is the “best”? Read more of this post

## NUSOD 2017 Preview: Simulation of quantum dot devices by coupling of quantum master equations and semi-classical transport theory

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 [1].