AMaSiS 2018 Workshop: Abstracts

Poster Refined drift-diffusion model for the simulation of charge transport across layer interfaces in organic semiconductor devices

Stéphane Altazin${}^{\mathbf{\text{(1)}}}$, Christoph Kirsch${}^{\mathbf{\text{(2)}}}$, Evelyne Knapp${}^{\mathbf{\text{(2)}}}$, Alexandre Stous${}^{\mathbf{\text{(1)}}}$,

and Beat Ruhstaller${}^{\mathbf{\text{(1,2)}}}$

(1) Fluxim AG, Winterthur

(2) Zurich University of Applied Sciences, Institute of Computational Physics

We present a new mathematical model for the transport of charge carriers across material interfaces in organic semiconductor devices. This new interface model is combined with a drift-diffusion model for the charge transport in the bulk; it has been implemented in the simulation software Setfos by Fluxim AG, allowing for fast device simulations [1].

Based on hopping theory, the new interface model takes into account both recombination and generation mechanisms across the material interface, enabling the modeling of charge-generation/recombination interfaces for the numerical simulation of tandem organic light-emitting diodes as well as multi-layer organic photovoltaic devices. Using this approach it is also possible to simulate devices which employ hexaazatriphenylenehexacarbonitrile (HAT-CN) in a hole-injection layer, for example. This particular material has a very deep HOMO (highest occupied molecular orbital) level in the range of $-7.4\mathrm{eV}$ to $-9.6\mathrm{eV}$, which would seemingly prevent such a material to be used in a hole-injection layer in the framework of interface models based on quasi-Fermi level continuity.

If we consider two adjacent material layers, in each of which the charge transport is described by a drift-diffusion model consisting of partial differential equations for the electron and hole number densities $n,p$ $[{\mathrm{m}}^{-3}]$ and for the electron and hole fluxes $J_n,J_p$ $[{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}]$, the question is how to couple these equations across the material interface to obtain a complete device model. We propose to couple the left-sided and right-sided interface limit values of the fluxes $J_n^{\pm },J_p^{\pm }$ with the left-sided and right-sided interface limit values of the charge carrier number densities $n^{\pm },p^{\pm }$ via effective interfacial diffusivities $[{\mathrm{m}}^2{\mathrm{s}}^{-1}]$, which describe the charge transfers between the HOMO and LUMO (lowest unoccupied molecular orbital) levels across the interface. The values of these interfacial diffusivities may be computed from Miller-Abrahams hopping rates [2], for example.

In the bulk-interface coupling the LUMO$\leftrightarrow$LUMO and HOMO$\leftrightarrow$HOMO transfers are coupled with the drift and diffusion fluxes on either side of the interface, whereas the LUMO$\to$HOMO and HOMO$\to$LUMO transfers correspond to recombination and generation terms, respectively, at the material interface in the continuum model.

While approaches similar to ours for the sole description of material interfaces have been presented previously, very few of these publications cover the numerical simulation of complete organic electronic semiconductor devices, as in [3], for example.

Acknowledgement This research was funded by the Swiss National Science Foundation within the CARDYN project (project no. 151563).