AMaSiS 2018 Workshop: Abstracts

Poster On van Roosbroeck systems with Gauss-Fermi statistics

Duy Hai Doan, Jürgen Fuhrmann, Annegret Glitzky,

Thomas Koprucki, and Matthias Liero

Weierstrass Institute for Applied Analysis and Stochastics, Berlin

The modeling, numerical treatment, and simulation of novel organic semiconductor devices, such as Vertical Organic Field-Effect Transistors (VOFET) and Organic Permeable Base Transistors (OPBT) [4], set out new challenges due to fundamentally different material properties. In particular, the disorder of energy levels on the organic molecules and the hopping transport of carriers requires to include Gauss-Fermi statistics and complicated nonlinear mobility laws with temperature, density and field dependence.

The poster informs on the discretization of the resulting organic drift-diffusion model. It is based on two ideas: (i) In order to treat the field dependence in the mobility functions within the finite-volume setting, we propose a hybrid finite-volume / finite-element ansatz. (ii) For the Gauss-Fermi statistics a generalized Scharfetter-Gummel scheme for the current flow is discussed, where the methods presented in [2] are adapted to the organic case. We present simulation results that compare calculations for test structures using Boltzmann and Gauss-Fermi statistics. For the second case with mobility laws of the extended Gaussian disorder model, we discuss the influence of the disorder parameter.

Moreover, analytical results for the above system with Gauss-Fermi statistics and field dependent mobility for the stationary problem [1] and the transient model [3] are summarized.

The temperature activated hopping transport in organic semiconductor devices in combination with self-heating and heat conduction leads to hysteretic effects, S-shaped current-voltage relations with regions of negative differential resistance and has considerable influence on the performance of organic semiconductor devices, see [5]. To understand this behavior an electrothermal model is under discussion that couples the generalized van Roosbroeck system to a heat balance. A coarser model type, balancing only the local net current and heat flow, are p⁢(x)-Laplace thermistor models. They were successfully applied in [6] to simulate the electrothermal feedback in large-area organic LEDs, see also the talk of Axel Fischer.

Acknowledgments: This work was supported by the Einstein Center for Mathematics (ECMath) via Matheon project D-SE18.

References

  • 1 D. H. Doan, A. Glitzky, and M. Liero, Drift-diffusion modeling, analysis and simulation of organic semiconductor devices, Submitted. WIAS-Preprint 2493, Berlin, 2018.
  • 2 P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, and T. Koprucki, Drift-Diffusion Models, in: J. Piprek (ed.), Handbook of Optoelectronic Device Modeling and Simulation, chap. 50, CRC Press Taylor & Francis, 2017, 733–771.
  • 3 A. Glitzky and M. Liero, Instationary drift-diffusion problems with Gauss-Fermi statistics and field-dependent mobility for organic semiconductor devices, Submitted. WIAS-Preprint 2523, Berlin, 2018.
  • 4 F. Kaschura, A. Fischer, M. P. Klinger, D. H. Doan, Th. Koprucki, A. Glitzky, D. Kasemann, J. Widmer, and K. Leo, Operation mechanism of high performance organic permeable base transistors with an insulated and perforated base electrode, J. Appl. Phys., 120 (2016), 094501.
  • 5 M. P. Klinger, A. Fischer, H. Kleemann, and K. Leo, Non-linear self-heating in organic transistors reaching high power densities, Scientific Reports, 8, (2018), 9806.
  • 6 M. Liero et al., 3D electrothermal simulations of organic LEDs showing negative differential resistance, Opt. Quantum Electron., 49 (2017), 330/1–330/8.