Two-dimensional drift-diffusion study of mid-gap states and subsequent vacuum level shifts at interfaces in bulk-heterojunction solar cells

In recent years, there have been numerous observations of large vacuum level shifts, often attributed to the presence of mid-gap states, at many different metal/organic and organic/organic interfaces. Many of the same interfaces are found in bulk-heterojunction (BHJ) solar cells, where the large vacuum level shifts may alter the energy level alignment compared to common assumption. In this work, we have used a two-dimensional drift-diffusion simulation to calculate the vacuum level landscape for BHJ solar cells. We see that the large concentrations of mid-gap states required for experimentally observed vacuum level shifts to occur completely change the energetics of the device. When such mid-gap states are present, at thermal equilibrium, we find that the vacuum level landscape is dominated by abrupt changes in the vacuum level at interfaces and a constant value for the vacuum level within the donor and acceptor phases. Under illumination, for mid-gap-state depths larger than a certain threshold, the population of mid-gap states becomes dominated by the capture of free charge carriers. This behavior sets an upper limit for the electric field within the donor and acceptor phases which is much smaller than typical values for the electric field in the device under operational conditions. Our results show that, in general, simply adding experimental values for vacuum level shifts obtained for the individual interface will not produce the real vacuum level landscape in the device. The magnitude of the vacuum level shift at any one interface depends not only on the surface density and energy of the mid-gap states at that interface but also on the alignment at other interfaces throughout the device.