Designing multijunction solar cells requires optimization of a large number of structural and compositional parameters, such as, band gaps and layer thicknesses of the component materials, but also the interlayer design for the series connection in the case of the industrially more relevant monolithic tandem devices. Numerical device simulation can provide instrumental insight for the identification of the optimum multilayer configuration. In organic tandems, while optical simulation of the thin-film layer stacks is routinely used, full opto-electronic device simulation including the recombination junction formed by the interlayer region is not common. In the case of the perovskite-silicon tandem, the widespread use of silicon hetero-junction technologies featuring combinations of large-scale textures with thin-film contact layers, but also the peculiarities of the perovskite materials in terms of the effects of ion-migration pose challenges to both optical and electrical simulation of such multijunction devices.
We address the above challenges using an integrated optoelectronic device simulation framework designed for the numerical optimization of organic solar cell and light emitting devices. Electrical simulation of all-organic tandems is enabled by a novel hopping transport model for the description of charge transfer across organic-organic interfaces. The (optical) optimization of fully textured perovskite-silicon tandems, on the other hand, is made possible by combining the models for the light scattering at silicon textures and for the wave propagation in thin-film silicon and perovskite layers into a dedicated multi-scale simulation framework.
Fig. 1. (a) Layer stack and (b) energy level alignment of the experimental model system implemented for simulation.
Numerical Simulation Approach
We used Setfos, which for solar cell device simulation combines a 1D drift-diffusion solver for charge carriers and excitons with a multi-scale framework for the optical simulation of quasi-1D architectures. A transfer matrix formalism for the optics of coherent layer stacks and a 3D ray-tracing simulation of scattering at large scale textures are coupled to a net-radiation model for incoherent light propagation. The coupling is performed via extraction of transmission and reflection coefficients from the transfer matrix and ray-tracing models to be used in the net-radiation formalism. The electronic model takes into account the peculiar properties of organic semiconductors in terms of different mobility models reflecting the presence of disorder and localization. For the description of charge transport at hetero-interfaces, which would be suppressed in the drift-diffusion picture, a thermally activated tunneling model is used. Optical and electronic models are coupled via radiative generation and recombination rates. Finally, optimization of photovoltaic device performance can be achieved within SETFOS either by screening the relevant space of configurational parameters (‘sweep’), or by defining targets for local or global optimization algorithms.
A. Optimization of organic tandem solar cells
For the simulation of organic tandem solar cells, we consider the high-efficiency device architecture described in Ref. , consisting of a DR3TSBDT:PC71BM top cell and a DPPEZnP- TBO:PC61BM bottom cell, with a recombination interlayer composed of a combination of ZnO nanoparticles and PEDOT:PSS. Thin layers of CuSCN and PFN are used as anode and cathode buffer layers, respectively. The electrodes are formed by ITO and Al. The layer structure and the energy level alignment of the experimental model system used for the simulation are displayed in Fig. 1. Accordingly, HOMO-LUMO levels are taken as indicated in Ref. , and the electron and hole transport levels of the individual bulk heterojunctions of the subcells are identified as in Fig. 1(b).
Also for the initial layer thicknesses, the values are taken from Ref. 9, with exception of the glass at the top electrode, which was set to 1mm. Accordingly, the glass substrate was treated as an incoherent layer in the optical simulation. In the electrical simulation, ITO and Al were used as the electrodes. The initial layer thicknesses as well as the definition of the simulation domains for optical end electrical simulation are displayed in Fig. 2.
In order to validate the simulation approach and to extract unknown material parameters for the consistent modelling of single junction and tandem cells, the experimental JV-curves in Ref.  are fitted using global multi-parameter optimization routines (dividing rectangles algorithm). Starting values for the optical and electrical parameters were taken from the literature (CuSCN: [10,11], DR3TSBDT: [12,], DPPEZnP-TBO: , PFN: ). In the cases where only absorption data was available, the wavelength-dependent refractive index was obtained from a Kramers-Kronig transformation. The single junction solar cells were implemented following the experimental realization in Ref. , i.e., both absorber materials were sandwiched between PEDOT:PSS as HTL and a PFN/Al contact. For the tandem simulation, the single junction material parameter values were taken as starting values and were kept at the same order of magnitude in the optimization of the new parameters for the CuSCN HTL, the ZnO ETL/interlayer, and the attempt-frequency for LUMO-HOMO transfer at the hopping interface. In this way, a good fit of all the JV-curves could be achieved with a consistent parameter set, as displayed in Fig. 3
After the optimization, we obtain values for all optimization parameters.
Figure 5: Results obtained by fitting the experimental results with Setfos.
We can compare the simulated radiance vs angle with the experimental data. Also, the simulated spectra can be compared to the experimental data to qualify the simulation results.
Figure 6: Comparison between measured data and fitted data for the radiance and the normalized spectrum
Figure 7 shows the comparison between simulation and experiment at five different angles. We can see that there is a good matching between measurement and simulation for both p- and s-polarization at each angle. This is showing the potential of Setfos to understand the main mechanisms regulating light emission from an organic material.
Figure 7: Comparison between measured data and fitted data for spectrum at different angles
In conclusion, the combination of Phelos and Setfos can be used to study light-emitting materials by extracting important parameters, such as the orientation of the dipoles and the width of the emission zone. This allows us to further optimize OLEDs that are using these materials, to reach higher EQEs.