The DC and RF assessment of critical barrier-AlGaN/GaN nano channel tri-gate fin-shaped High Electron Mobility Transistor (FinHEMT) is investigated for Enhancement-mode (E-mode) operation. We propose and analyze critical barrier layer (CBL) and critical-strained barrier layer (CSBL) FinHEMT for a fixed fin-shaped channel width (W fin = 160 nm) and height (H fin = 70 nm). The CBL FinHEMT ensures an E-mode operation by depleting two-dimensional electron gas (2DEG) near the channel region between AlGaN and GaN hetero-junction. The extracted threshold voltage (V T ) in CBL FinHEMT is 0.4 V as compared to −0.2 V obtained in CSBL FinHEMT. However, increased gate leakage current density and poor gate voltage swing in CBL FinHEMT is improved through a metal-oxide-semiconductor FinHEMT (FinMOSHEMT) structure by the incorporation of Al2O3 gate oxide layer between the tri-gate and CBL AlGaN layer. It results in a stable positive VT of 0.5 V due to the negatively charged Al2O3/barrier interface fixed charge density ( NAl2O3 ). The proposed CBL FinMOSHEMT has also been studied for different atomic layer deposition Al2O3 process-dependent variations in NAl2O3. The maximum on-state drain current and transconductance of 1.01 A mm−1 and 430 mS/mm have been extracted respectively with NAl2O3 of −9.2 × 1012 cm−2. Further, the RF analysis of the proposed CBL FinMOSHEMT structure with the same dimension exhibits improved f T and f max responses with 27 GHz and 90 GHz respectively over CBL FinHEMT. The results of the frequency responses obtained for the proposed design make it suitable for power electronics applications.