**Organic Solar - Organic Solar Cell Simulation and Tuning with Optimizer**

In recent times there has been considerable interest in the use of organic materials in display technologies. Recognition of the benefits of inexpensive materials and processing as well as large area conformal construction have also placed high interest in organic solutions for solar energy applications. Silvaco has long been a leading supplier of organic simulation tools for organic light emitting devices, OLEDs, and organic thin film transistors, OTFTs, as well as crystalline solar cell simulation in general. Recently, Silvaco has released a product addressing the simulation needs of the organic solar cell technologists. This product, aptly named Organic Solar, is described in this article.

Organic Solar models bulk heterojunction (BHJ) organic solar cells using the approach of Korster et al. (1) This model can be described as follows. BHJ solar cells consist of an interpenetrating mixture of donor and acceptor materials. Absorbed light generates excess excitons which are charge neutral and diffuse to the acceptor-donor interface where they dissociate into free electron-hole pairs. The electron-hole pairs are then separated by the internal field and are swept up at the contacts as in crystalline photodetectors.

The model includes the standard drift-diffusion equations (Poisson’s equation and the electron and hole continuity equations) augmented by the singlet exciton continuity equation:

where S is the singlet concentration, *G _{ph}* is the photogeneration rate, KNRS.EXCITON is the non-radiative singlet decay rate,

*R*is the exciton dissociation rate and

_{D}np*R*is the Langevin recombination rate.

_{L}npThe equation governing the exciton dissociation is given by:

Here *r _{L}* is the Langevin recombination rate constant. A.SINGLET and S.BINDING are user specified parameters representing the electron hole pair distance and the singlet exciton binding energy, J1 is the first order Bessel function, S is the singlet concentration and the b parameter is given by:

where E is the local electric field, εr is the relative permativity and T the temperature.

We also added a parameter, QE.EXCITON that describes the fraction of absorbed photons that generate singlets (as opposed to electron hole pairs). Generally this parameter should be assigned to one. We should note that all of the optical absorption models available in our Luminous simulator are also available in Organic Solar. These include geometric ray tracing, transfer matrix, beam propagation and finite difference time domain methods.

To calibrate this model we attempted to reproduce the experimental results presented in the Korster paper. These measurements were performed on a 120 nm thick OC_{1}C_{10}-PPV/PCBM (20:80 wt %) BHJ solar cell. The authors suggested the parameter values shown in Table 1.

Table 1: Suggested Parameter Values

The singlet binding energy, S.BINDING, was not specified but a value less than 0.4 eV was implied. We chose as a baseline to use 0.35 eV.

As for photogeneration, the authors suggested a constant photogeneration rate throughout the device of 2.7x10^{21} cm-3s^{-1}. Our own calculations indicate that for complete light collection of AM1.5 solar spectrum a value of 3.6x10^{22} cm^{-3}s^{-1} would be appropriate. The latter value ignores front reflections or light passing through the device.

Based on the suggested parameter values we ran the simulation. Figure 1 shows the comparison of our simulation with the presented experimental results. Although the short circuit current is a good match, the remainder of the curve varies quite a bit from the experiment. Due to our lack of knowledge of various parameters and models such as the Langevin recombination model in the Korster paper, we decided to use the DeckBuild Optimizer to tune the result.

Figure 1. |

The DeckBuild Optimizer is a multi-target, multi-parameter optimization tool that uses the modified Levenberg-Marquart algorithm to build a response surface of results versus input parameters as the iterations progress. The interface is conveniently embedded inside of DeckBuild and presents the user with easy to use worksheet based GUI. We felt that this application was well suited to such an approach since the simulations were one-dimensional and thus fast and there were few input parameters.

The input parameter worksheet is shown in Figure 2.

Figure 2. |

Here we can see that we chose the decay rate (KNRS.EXCITON), the pair distance (A.SINGLET), the binding energy (S.BINDING) and a scale factor on the photogeneration rate (B1) as the variable parameters. The target was chosen as the digitized experimental data as shown in Figure 1.

Then with a single mouse click the optimizer performs a series of iterations of running the simulation automatically adjusting the input parameters each simulation until convergence to the target is met. The results of each iteration are shown on the Optimizer Results worksheet shown in Figure 3.

Figure 3. |

Here we see that convergence was obtained in only 14 iterations. A comparison of the experimental results with the optimized and unoptimized results is shown in Figure 4.

Figure 4. |

We see that a good match has been obtained, not just in the short circuit current, but also the open circuit voltage and the entire curve.

If we return to the results worksheet in Figure 3, we can examine how the input parameters were changed to match the experimental results. In comparison with the original parameters we can see that the decay rate and electron-hole spacing are reasonably close to the original values.

The binding energy has changed somewhat but we can take comfort in the fact that value used by Korster et al was not given. Finally we see that the photogeneration rate was reduced to roughly 58% of the suggested value. With respect to experiment this seems reasonable since the assumed constant generation rate was probably not measured. In all we are quite satisfied with the tuning experiment and feel confident that such an approach can be applied to other devices/materials.

Before concluding we would like to remark that we used the Optimizer simply as a tuning device.

For more complicated situations such as larger simulations with many unknowns we acknowledge that the Optimizer may not be the best approach. We also point out that the number of inputs can usually be reduced. For example referring back to equation 2 we note that A.SINGLET and S.BINDING could have been replaced by a single parameter in the optimization.

In conclusion, we have demonstrated the newest TCAD device simulation tool at Silvaco. We feel confident that Organic Solar can be of use in the accurate prediction of performance of organic solar cells. We have also demonstrated in a practical example the use of the DeckBuild Optimizer.

**References**

- Korster, L.J.A, Smits, E.C.P., Mihailetchi, V.D., and Blom, P.W.M. “Device model for the operation of polymer/fullerene bulk heterojunction solar cell”, Physical Review B, Vol. 72, (2005) pp. 085205-1, 085205-9.