Monolayer coverage and channel length set the mobility in self-assembled monolayer field-effect transistors

The mobility of self-assembled monolayer field-effect transistors (SAMFETs) traditionally decreases dramatically with increasing channel length. Recently, however, SAMFETs using liquid-crystalline molecules have been shown to have bulk-like mobilities that are virtually independent of channel length. Here, we reconcile these scaling relations by showing that the mobility in liquid crystalline SAMFETs depends exponentially on the channel length only when the monolayer is incomplete. We explain this dependence both numerically and analytically, and show that charge transport is not affected by carrier injection, grain boundaries or conducting island size. At partial coverage, that is when the monolayer is incomplete, liquid-crystalline SAMFETs thus form a unique model system to study size-dependent conductance originating from charge percolation in two dimensions.