Random networks of carbon nanotubes optimized for transistor mass-production: multi-variable problem

Random networks of single-walled carbon nanotubes (CNTs) usually contain both metallic (m-CNTs) and semiconducting (s-CNTs) nanotubes with an approximate ratio of 1:2, which leads to a trade-off between on-conductance and on/off ratio. We demonstrate how the design problem can be solved with a realistic numerical approach. We determine CNT density, length, and channel dimensions for which CNT thin-film transistors (TFTs) simultaneously attain on-conductance higher than $1\mu \mathrm{S}$ and on/off ratio higher than ${10}^4$. Fact that asymmetric systems have more pronounced finite-size scaling behavior than symmetric, enables us additional design freedom. A realisation probability of desired characteristics higher than 99% is obtained only with channel aspect length to width ratios $L_{\mathrm{C}\mathrm{H}}\mathrm{/}{W}_{\mathrm{C}\mathrm{H}}<1.2$ and normalized channel size $L_{\mathrm{C}\mathrm{H}}{W}_{\mathrm{C}\mathrm{H}}\mathrm{/}{l}_{\mathrm{C}\mathrm{N}\mathrm{T}}^2>250$ for a range of CNT lengths $l_{\mathrm{C}\mathrm{N}\mathrm{T}}=4-20\mu \mathrm{m}$.