Are There Fundamental Limitations on the Sheet Resistance and Transmittance of Thin Graphene Films?

Abstract

From published transmittance and sheet resistance data, we have calculated a figure of merit for transparent, conducting graphene films; the DC to optical conductivity ratio, σ_DC/σ_Op. For most reported results, this conductivity ratio clusters around the values σ_DC/σ_Op = 0.7, 4.5, and 11. We show that these represent fundamental limiting values for networks of graphene flakes, undoped graphene stacks, and graphite films, respectively. The limiting value for graphene flake networks is much too low for transparent-electrode applications. For graphite, a conductivity ratio of 11 gives R_s = 377Ω/◻ for T = 90%, far short of the 10 Ω/◻ minimum requirement for transparent conductors in current driven applications. However, we suggest that substrate-induced doping can potentially increase the 2-dimensional DC conductivity enough to make graphene a viable transparent conductor. We show that four randomly stacked graphene layers can display T ≈ 90% and 10 Ω/◻ if the product of carrier density and mobility reaches nμ = 1.3 × 10¹⁷ V⁻¹ s⁻¹. Given achieved doping values and attainable mobilities, this is just possible, resulting in potential values of σ_DC/σ_Op of up to 330. This is high enough for any transparent conductor application.