The industry standard advanced SPICE model (ASM)-GaN compact model has been enhanced to model the GaN high electron mobility transistors (HEMTs) at extreme temperature conditions. In particular, the temperature dependence of the trapping behavior has been considered and a simplifying approximation in the temperature modeling of the saturation voltage in the ASM-GaN model has been relaxed. The enhanced model has been validated by comparing the simulation results of the model with the dc I-V measurement results of a GaN HEMT measured with chuck temperatures ranging from 22 • C to 500 • C. A detailed description of the modeling approach is presented. The new formulation of the ASM-GaN compact model can be used to simulate the circuits designed for extreme temperature environments. Index Terms-Compact models, gallium nitride, high electron mobility transistors (HEMTs), high-temperature modeling, physics-based models, semiconductor device measurement, semiconductor device modeling. I. INTRODUCTION G aN-BASED HEMT devices have demonstrated outstanding performance across a wide range of RF and power applications during recent times. The literature [1]-[3] shows increasingly aggressive scaling of GaN devices, which has resulted in very promising high-speed devices with gate lengths as small as 20 nm and f T / f max exceeding 400 GHz [4]. Furthermore, the GaN power devices that can reliably operate with the drain-source voltage (V DS) values of 600-650 V are widely available where they set the current benchmark for commercial GaN power devices.