This analytical modeling study delves into the resonance behavior of plasma waves within the channel of High Electron Mobility Transistors (HEMTs) when subjected to Terahertz (THz) excitation. The core objective is to systematically examine the influence of various HEMT parameters on the dynamics of plasma resonance and the detection of THz signals. A noteworthy finding emerges: the most effective detection of THz signals materializes when both the gate and drain terminals simultaneously receive the THz excitation. Moreover, the modulation of biasing conditions, specifically represented by polarization voltages, exerts a substantial influence on plasma resonance frequencies, offering a promising avenue for tailoring HEMT responses. Further exploration reveals the substantial impact of access region characteristics, including length and doping concentration, on the excitation of 3D plasma waves within the HEMT, with the drain access region demonstrating particular significance. Additionally, we delve into the ramifications of gate geometry, encompassing width and channel-to-gate distance, revealing their capacity to significantly alter 2D plasma resonance frequencies. In extreme cases, the HEMT exhibits behavior akin to a simplified diode configuration, resulting in the absence of 2D plasma resonance. In summation, this research unfolds essential insights for the design and optimization of HEMT-based devices tailored to specific THz frequency applications. It underscores the pivotal roles of biasing conditions, access region properties, and gate geometries in shaping HEMT performance and THz signal detection.