I. Y-function Method for estimating contact resistance. Y-function method, as first demonstrated by Ghibaudo 1 and modified by Chang et.al, 2 to include gate dependent Schottky barrier, was used to evaluate low-field mobility (μ0) and estimate effective contact resistance (RC) in strong inversion region (Vg >> Vd). Detailed derivation of Yfunction method can be found in ref 2. For low-field bias condition (Vg >> 0.5Vd), drain current can be writes as Equation S.I.1, (S.I.1) where all symbols carry their usual meaning and θ is effective attenuation factor, express as θ = θ0 + μ0.RC.Cox.W/L and θ0 is first-order mobility attenuation coefficient. In general case, Y-function, which is defined as Id/√gm (gm is transconductance, ∂Id/∂Vg) is given by Equation S.I.2,