An Analytical Solution for Exciton Generation, Reaction, and Diffusion in Nanotube and Nanowire-Based Solar Cells

Excitonic solar cells based on aligned or unaligned networks of nanotubes or nanowires offer advantages with respect of optical absorption, and control of excition and electrical carrier transport; however, there is a lack of predictive models of the optimal orientation and packing density of such devices to maximize efficiency. Here-in, we develop a concise analytical framework that describes the orientation and density trade-off on exciton collection computed from a deterministic model of a carbon nanotube (CNT) photovoltaic device under steady-state operation that incorporates single- and aggregate-nanotube photophysics published earlier (Energy Environ Sci, 2014, 7, 3769). We show that the maximal film efficiency is determined by a parameter grouping, α, representing the product of the network density and the effective exciton diffusion length, reflecting a cooperativity between the rate of exciton generation and the rate of exciton transport. This allows for a simple, master plot of EQE versus film thickness, parametric in α allowing for optimal design. This analysis extends to any excitonic solar cell with anisotropic transport elements, including polymer, nanowire, quantum dot, and nanocarbon photovoltaics.