ddfermi is an open-source software prototype which simulates drift diffusion processes in classical and organic semiconductors.

Key features

  • finite volume discretization of the semiconductor equations (van Roosbroeck system)
  • thermodynamically consistent Scharfetter-Gummel flux discretizations
  • general statistics: Fermi-Dirac, Gauss-Fermi, Blakemore and Boltzmann
  • multidimensional devices
  • based on pdelib and interfaced via Python or Lua


DOI for Citations and BibTex (also accessible via

author = "Doan, D. H. and Farrell, P. and Fuhrmann, J. and Kantner, M. and Koprucki, T. and Rotundo, N.",
year = 2016,
title = "ddfermi -- a drift-diffusion simulation tool",
doi = {10.20347/WIAS.SOFTWARE.DDFERMI},
type = "Version 0.1.0",
institution = "Weierstrass Institute (WIAS)"
url = {} }

Related Publications

  1. M. Bessemoulin-Chatard. A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme, Numerische Mathematik 121 (2012), pp. 637-670, doi
  2. P. Farrell, J. Fuhrmann, T. Koprucki. Computational and Analytical Comparison of Flux Discretizations for the Semiconductor Device Equations beyond Boltzmann Statistics, Journal of Computational Physics 346 (2017), pp. 497-513, preprint, doi
  3. P. Farrell, N. Rotundo, H. Doan, M. Kantner, J. Fuhrmann, T. Koprucki. Drift-Diffusion Models, book chapter, accepted in: Handbook of Optoelectronic Device Modeling and Simulation, J. Piprek (ed), Taylor & Francis,(2017), preprint, link
  4. J. Fuhrmann. Comparison and numerical treatment of generalised Nernst-Planck models, Computer Physics Communications 196 (2015), pp. 166-178, preprint, doi
  5. K. Gärtner. Existence of bounded discrete steady state solutions of the van Roosbroeck system with monotone Fermi-Dirac statistic functions, Journal of Computational Electronics 3 (2015), pp. 773-787, preprint, doi
  6. T. Koprucki, K. Gärtner. Discretization scheme for drift-diffusion equations with strong diffusion enhancement, Optical and Quantum Electronics 45 (2013), pp. 791-796, preprint, doi
  7. T. Koprucki, N. Rotundo, P. Farrell, 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, 47-6 (2015), pp. 1327-1332, preprint, doi
  8. M. Patriarca, P. Farrell, J. Fuhrmann, T. Koprucki. Highly Accurate Quadrature-based Scharfetter-Gummel Schemes for Charge Transport in Degenerate Semiconductors, Computer Physics Communications 235 (2018), pp. 40-49, preprint, doi
  9. F. Sawatzki, D. Doan, H. Kleemann, M. Liero, A. Glitzky, T. Koprucki, K. Leo. Balance of Horizontal and Vertical Charge Transport in Organic Field-Effect Transistors, Physical Review Applied 10 (2018), pp. 034069, doi
  10. D. Scharfetter, H. Gummel. Large-signal analysis of a silicon Read diode oscillator, IEEE Transactions on Electron Devices 16 (1969), pp. 64-77