2.1 Optimization of layer thicknesses

In dependence on the wave length an organic solar cell absorbs the incident light in different ways. While one part of the light energy is absorbed as heat, another part is

invested in the generation of electron-hole pairs, called excitons. This mechanism occures at any point inside the solar cell and the density of created excitons depends on the light absorption density at a given point. Excitons are separated only by utilization of the „built in field" at the pn-junction of the active layers (Fig. 2). Since the diffusion length of the electron-hole pairs is very short, the chance to reach the pn-interface and the separation as a consequence is very slim. It turned out that the average of the diffusion length is only 10nm in each direction from the interface [13]. For that reason most of the generated electron hole pairs recombinate almost instantaneously while only the excitons created near the pn-interface contribute to the generation of photocurrent at the end of the day. As a consequence one has to place a high amount of absorbed energy to this narrow area around the pn-junction interface what requires a proper distribution of the absorption density in the photovoltaic device. As shown in chapter (2) the absorption density ‘a’ does not follow a trivial function and due to the strong dependence on the conductivity ‘o’ of the optical parameters, ‘a’ does not correlate with the distribution of the electric field |E|2 in dependence on the position vector. While the square of the electric field |E|2 is continuous at the interface between two layers, ‘a’ is not. As a consequence the density of absorbed light energy differs

within adjacent layers even near their interface. Taking this into account and considering the diffusion length of the solar cell materials we calculated the absorption in a region of only 10nm from the active interface both in the p-layer and in the n-layer and summed it up to a value called „effective absorption“ Aeff. In order to gain a better understanding of the behavior of the absorption density we figured out the optimal layer thicknesses of the active layers copper-phthalocyanin (CuPC) and BBP-perylene of our solar cell models.

In our simulations we assumed a thickness of 140nm for the ITO layer as it was purchased on 1mm thick glass. We found an effective thickness of arround 140nm for the PEDOT layer of most of our solar cell models as well. For that reason we stayed with dITO=140nm and dPEDOT=140nm through all our simulations unless noted otherwise. Due to its almost constant refractive index throughout the visible sun light spectrum, the covering glass only decreases the amount of light absorption, but does not effect the location of the maximum and minimum of the absorption density inside the photovoltaic device. For that reason we left the glass out of consideration. Furthermore we assumed perpendicular incident light with a wave length of 550nm. In order to gain a tool for a quick determination of proper layer thicknesses we calculated Aeff for a given range of layer thicknesses and for given active materials. The figures 3-4 show the effective absorption Aeff in dependence on the thickness of the active layers dCuPC and dBBP-

perylene. As one can see there is a distinct maximum of Aeff, which corresponds to special thicknesses of the layers. The top-view (Fig. 4) provides the optimized layer thicknesses like a “map”. For this special model we found 55nm for dCuPC and 70nm for dBBP-perylene. In addition to that we found a big difference between the maximum and the minimum of effective absorption. A factor of almost twenty between the worst and the optimal case of efficient light absorption clarifies the importance of the optimal parameter setup for the solar cell layers.

Upon this thickness maps (Fig.4) which show the usability of given layer thicknesses we calculated the spatial distribution of absorption density in the whole solar cell. Figure 5 shows the absorption density in dependence on the position vector ‘z’ for a non — optimized organic solar cell with dCuPC=200nm and dBBP-perylene=150nm. As one can see ‘a(z)’ is almost at a minimum both in the CuPC layer and in the BBP-perylene layer. A solar cell with this configuration will never be a performer. No mater how good the transport properties of the materials are. Since ‘a(z)’ is a measure for the amount of generated excitons, one can see that most of the generated excitons will be lost by

recombination.

In contrast to that the following solar cell (Fig. 6) with the layer thicknesses dcupc= 55nm and dBBP-perylene=70nm is an optimal performer in terms of energy absorption efficiency. The absoption density in the BBP-perylene layer, which is the main absorber in this special case, reaches its maximum near the active interface.

The presented examples show the best and worst case for a given wave length of the incident light. According to given light spectra and taking into account geographical and geological aspects of the place of destination one is able to gain an optimal setup for any situation.