Deterministic modelling of carbon nanotube near-infrared solar cells

Abstract

Photovoltaics (PVs) using single-walled carbon nanotubes (SWNTs) as near-infrared photo-absorbers have progressed rapidly, offering promise for long-wavelength light harvesting devices. Despite this interest the fundamental design questions remain, such as optimal device thickness, nanotube orientation, density, and the impact of impurities. To address this challenge, we develop a deterministic model of SWNT PVs derived directly from SWNT photophysics using photon, exciton, and charge carrier population balances. The model accounts for arbitrary distributions of nanotube chiralities, lengths, orientations, defect types and concentrations, bundle fraction and size, and density. We show that feasible devices can achieve external quantum efficiencies above 60%. We reveal a sharply optimal device thickness that is a function of nanotube density, orientation, and quenching site concentration. This thickness stems from a tradeoff between exciton generation and diffusion to the electrodes, and is at a minimum at the limit of close-packed nanotube density. We show that this minimum characterizes a given device design and scales with mean nanotube length to exponent 0.4. The normalized difference between optimal thickness and this close-packed limit scales inversely with density to the 0.24 power. Practically, in-plane aligned nanotube configurations yield optimal thicknesses less than 10 nm, increasing to a range of 50 to 200 nm for vertical alignment. Due to weak inter-SWNT exciton transport relative to exceptional intra-SWNT diffusion, vertically-aligned films are unambiguously favored at densities above 3% of the close-packed limit; at lower densities however an optimum emerges at an intermediate angle to compensate for weaker light absorption of vertical nanotubes. Comparison to published experimental devices displays the model's utility for device design.