  We present a comprehensive investigation of self-heating in gallium nitride
(GaN) high-electron-mobility transistors (HEMTs) through technology
computer-aided design (TCAD) simulations and phonon Monte Carlo (MC)
simulations. With microscopic phonon-based electrothermal simulations, we
scrutinize both the temperature profiles and electrothermal coupling effect
within GaN HEMTs. Two metrics, maximum channel temperature ($T_\text{max}$) and
equivalent channel temperature ($T_\text{eq}$), are introduced to measure the
reliability and electrical performance degradation of the device, respectively.
The influence of bias-dependent heat generation and phonon ballistic transport
on the two indicators is thoroughly examined.
