1,7-dibromo-N,N′-dioctadecyl-3,4,9,10-perylenetetracarboxylic diimide (PTCDI-Br2-C18) was synthesized and employed in the fabrication of n-type organic field-effect transistors (OFETs). Lower operating voltage was achieved by using a bilayer dielectric containing anodized Al2O3 and poly-(methyl methacrylate) (PMMA) layers. We have studied the effect of individual dielectric layer thickness and the roughness on the threshold voltage (VT) as well as on the field-effect carrier mobility (μFE) and achieved a threshold voltage of <1 V with a subthreshold swing of <0.2 V/decade. We observed the reduction in VT while the thickness of Al2O3 layer is reduced. This has been attributed to the reduction of charge trap density present at the active channel and at the interface between active channel and the dielectric layer. The trap states density is apparently influenced by the roughness of the Al2O3 layer. In such cases, gate-field (E) dependent carrier mobility is almost evident. In this work, we have demonstrated gate-field independent carrier mobility, which are about 0.040 cm2 V−1s−1 in the saturation region and 0.035 cm2 V−1s−1 in the linear region. This indicates the significant reduction of trap states, which are completely full at the voltage below VT. As a result, the carrier mobility is relatively unaffected by trap scattering of the mobile charges.