Relationship between material properties and transparent heater performance for both bulk-like and percolative nanostructured networks.

Transparent heaters are important for many applications and in the future are likely to be fabricated from thin, conducting, nanostructured networks. However, the electrical properties of such networks are almost always controlled by percolative effects. The impact of percolation on heating effects has not been considered, and the material parameter combinations that lead to efficient performance are not known. In fact, figures of merit for transparent heaters have not been elucidated, either in bulk-like or percolative systems. Here, we develop a simple yet comprehensive model describing the operation of transparent heaters. By considering the balance of Joule heating versus power dissipated by both convection and radiation, we derive an expression for the time-dependent heater temperature as a function of both electrical and thermal parameters. This equation can be modified to describe the relationship between temperature, optical transmittance, and electrical/thermal parameters in both bulk-like and percolative systems. By performing experiments on silver nanowire networks, systems known to display both bulk-like and percolative regimes, we show the model to describe real systems extremely well. This work shows the performance of transparent heaters in the percolative regime to be significantly less efficient compared to the bulk-like regime, implying the diameter of the nanowires making up the network to be critical. The model allows the identification of figures of merit for networks in both bulk-like and percolative regimes. We show that metallic nanowire networks are most promising, closely followed by CVD graphene, with networks of solution-processed graphene and carbon nanotubes being much less efficient.