The applications dealing with the processing and detection of extremely weak signals, such as quantum-computing systems as well as the instrumentation in radio-astronomy and space-science fields, require ultimate low-noise performance. High-electron-mobility transistors (HEMTs) are widely used in these applications, operating at cryogenic temperatures in order to reduce the noise and comply with challenging requirements. The gallium nitride (GaN)-based technology emerges as a potential candidate for the low-noise cryogenic applications, given the significant improvements of the material properties at low temperatures. [1,2] Furthermore, the noise performance of the GaN-based low-noise amplifiers (LNAs) was experimentally demonstrated to improve when cooled down to 4 K [3] One of the physical parameters limiting the noise performances of the GaN HEMTs, and more generally those of field-effect transistors (FETs), is related to the resistance of the gate electrode metallization. Indeed, this resistance introduces a thermal noise source,