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 $1~{\rm \mu S}$ 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 $L_{\rm CH} / W_{\rm CH} < 1.2$ and normalized channel size $L_{\rm CH}W_{\rm CH} / l^2_{\rm CNT} > 250$ for a range of CNT lengths $l_{\rm CNT} = 4-20~{\rm \mu m}$.