In search for a possible remedy, we recently simulated the effect of a *p/n* tunnel junction that replaces most of the *p*-doped layers by highly conductive *n*-doped material. First results look quite promising. [2] As shown by the red lines in the picture, the bias is substantially reduced and the peak lasing power is close to 20W. This simulation assumes a negligible tunnel junction resistance which is not yet accomplished in practical devices. [3] However, the numerical proof of concept hopefully helps stimulate further research efforts into GaN-based tunnel junctions for application in LEDs and lasers.

[1] M. Kawaguchi et al., Proc. SPIE 9748 (2016) 974818

[2] J. Piprek, Compound Semicond. Mag. 23 (2017) no. 5, pp. 34-38

[3] B. P. Yonkee et al., Opt. Express 24 (2016) 256556

I would like to thank all participants and organizers for making this conference a great success and I hope to see many again next year at the 18th NUSOD conference in Hong Kong.

]]>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.

If you think of research as a sequential process consisting of model-software-data-visualisation, as we suggested in the beginning, we will focus in the rump-session (Thursday at NUSOD 2017) primarily on the two ends of the process, namely mathematical models and data visualisations. Thomas will present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge contained in mathematical models, see [1], [2]. Afterwards, Bastian will present how publications maybe enhanced by data visualisations and how this may improve both understandability and visibility of scholarly publications, see [3].

Jointly written with Bastian Drees, Technische Informationsbibliothek (TIB).

- Kohlhase M., Koprucki T., Müller D., Tabelow K.
*Mathematical Models as Research Data via Flexiformal Theory Graphs.*In: Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Artificial Intelligence, vol. 10383, pp. 224-238. Springer (2017). DOI: 10.1007/978-3-319-62075-6_16

- Koprucki, T., Tabelow, K.:
*Mathematical models: a research data category?*In: Mathematical Software – ICMS 2016. Lecture Notes in Computer Science, vol. 9725, pp. 423–428. Springer, (2016). DOI:10.1007/978-3-319-42432-3_53 - B. Drees,
*Make the most of your audio-visual simulation data*. 2nd Leibniz MMS Days, Technische Informationsbibliothek (TIB), (2017). [Video] DOI 10.5446/21907

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”?

Of course one might look at many different criteria. We compared both schemes to the (computationally inefficient but more accurate) generalized Scharfetter-Gummel scheme [2]. The logarithmic absolute error for a range of different (electrostatic) potential differences at neighboring nodes (presuming Blakemore statistics) looks like this:

The picture on the left shows the error for the diffusion averaged flux and the picture on the right the error for the inverse activity based flux. The bold black lines highlight the same contour levels in both plots. The dashed lines show where generalized and modified schemes agree exactly: They agree when there is no diffusion (pure drift current, the horizontal dashed line). The diagonal dashed line is due to the consistency with the thermodynamic equilibrium. So judging from both pictures it seems that the diffusion average flux yields a considerably lower flux error. In both pictures, we fixed the arithmetic average between the electrochemical potentials. What if we raise the diffusion enhancement by increasing the average from 1.5 to 5?

In this case, the superiority of the diffusion-enhanced scheme is even more obvious! So is there possibly a general law behind this? Yes, there is! In [2], we managed to show that the diffusion averaged scheme depends more favorably on the diffusion enhancement than any inverse activity based scheme.

Of course there are other valid criteria which one might examine. In [2], for example, we also studied a full van Roosbroeck simulation of a pin diode. The absolute error in the IV curves also speaks in favor of the diffusion-enhanced scheme.

More details will be presented at the NUSOD 2017 conference (talk ThD2).

- D. Scharfetter, H. Gummel,
*Large-signal analysis of a silicon read diode oscillator*, IEEE Transactions on Electron Devices**16**, 64-77 (1969) DOI: 10.1109/T-ED.1969.16566 - P. Farrell, T. Koprucki, J. Fuhrmann.
*Computational and Analytical Comparison of Flux Discretizations for the Semiconductor Device Equations beyond Boltzmann Statistics*, Journal of Computational Physics,**346**, 497-513 (2017), DOI: 10.1016/j.jcp.2017.06.023 - M. Bessemoulin-Chatard,
*A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme,*Numerische Mathematik**121**, 637-670 (2012) DOI 10.1007/s00211-012-0448-x - T. Koprucki, N. Rotundo, P. Farrell, D. H. Doan, J. Fuhrmann,
*On thermodynamic consistency of a Scharfetter-Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement,*Optical and Quantum Electronics**47**, 1327-1332 (2015) DOI: 10.1007/s11082-014-0050-9 - J. Fuhrmann,
*Comparison and numerical treatment of generalised Nernst-Planck models*, Computer Physics Communications**196**, 166-178 (2015) DOI 10.1016/j.cpc.2015.06.004

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].

We demonstrate our hybrid modeling approach by numerical simulations of an electrically driven single-photon source based on a single quantum dot. We investigate the stationary and the pulsed operation regime and calculate the current flow in combination with the single-photon generation rate and the second order intensity correlation function. More details will be presented at the NUSOD 2017 conference (paper ThD1).

[1] M. Kantner, M. Mittnenzweig and Th. Koprucki: Hybrid quantum-classical modeling of quantum dot devices, WIAS Preprint No. 2412 (2017). DOI: 10.20347/WIAS.PREPRINT.2412

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