In this present paper, a comprehensive drain current model incorporating the effects of channel length modulation has been presented for multi-layered gate material engineered trapezoidal recessed channel (MLGME-TRC) MOSFET and the expression for linearity performance metrics, i.e. higher order transconductance coefficients: $g_{m1}$, $g_{m2}$, $g_{m3}$, and figure-of-merit (FOM) metrics; $V_{IP2}$, $V_{IP3}$, IIP3 and 1-dB compression point, has been obtained. It is shown that, the incorporation of multi-layered architecture on gate material engineered trapezoidal recessed channel (GME-TRC) MOSFET leads to improved linearity performance in comparison to its conventional counterparts trapezoidal recessed channel (TRC) and rectangular recessed channel (RRC) MOSFETs, proving its efficiency for low-noise applications and future ULSI production. The impact of various structural parameters such as variation of work function, substrate doping and source/drain junction depth ($X_j$) or negative junction depth (NJD) have been examined for GME-TRC MOSFET and compared its effectiveness with MLGME-TRC MOSFET. The results obtained from proposed model are verified with simulated and experimental results. A good agreement between the results is obtained, thus validating the model.