For the high-electron-mobility transistor(HEMT) terahertz detector with a side-gate structure, a physical model for DC transport and terahertz detection of the device was constructed. Using a self-alignment process, well-shaped and reliable contacts for the side-gate structure were successfully fabricated, effectively solving contact issues between the dual gates and the mesa. Ultimately, terahertz detectors with different gate widths(200 nm, 800 nm, and 1400 nm) of side-gate GaN/AlGaN HEMTs were obtained. DC tests revealed a clear linear relationship between the gate width of different devices and their threshold voltage, confirming the DC transport model of the side-gate HEMT terahertz detector. These results provide experimental verification and guidance for the theoretical model of the complete side-gate HEMT terahertz detector, offering significant support for the development of side-gate HEMT terahertz detectors.