Modelling of limitations of bulk heterojunction architecture in organic solar cells II: 3d model.

Polymer solar cells are considered as very promising candidates for development of photovoltaics of the future. They are cheap and easy to fabricate. However, up to now, they possess fundamental drawback: low effectiveness. In the most popular BHJ (bulk heterojunction) architecture the actual long-standing top efficiency is about 12\% (recent achievements about 15\%). One ask the question how fundamental this limitation is, as certain theoretical considerations suggest that it should be about two times higher. In our paper we analyze the `geometric factor' as one of possible explanation of relatively low efficiency of BHJ architecture. More precisly, we calculate the effective area of the donor-acceptor border in the random mixture of donor and acceptor nanocrystals and further compare it with an ideal 'brush' architecture. In our previous calculation for the two dimensional model, we have found that the maximal value of geometric factor was about 40\%. In the actual three dimensional model, it turned out that both architectures give very close value of the effective area. So the geometric factor seems to be not significant as a factor limiting efficiency. Implications of this fact are discussed: we list two other factors (mentioned but not thoroughly discussed in literature) which can be responsible for limitations of efficiency of BHJ architecture. We estimate their scale, and suggest that these limitations are inevitable, or at least very hard to overcome. We suggest that return to layer architecture could radically improve efficiency limitations -- however, to make breakthrough, materials with large exciton diffusion length have to be invented.