We report on the direct measurement of two-dimensional sheet charge density dependence of electron transport in AlGaN/GaN high electron mobility transistors (HEMTs). Pulsed IV measurements established increasing electron velocities with decreasing sheet charge densities, resulting in saturation velocity of 1.9 x 10(7) cm/s at a low sheet charge density of 7.8 x 10(11) cm(-2). An optical phonon emission-based electron velocity model for CiaN is also presented. It accommodates stimulated longitudinal optical (LO) phonon emission which clamps the electron velocity with strong electron-phonon interaction and long LO phonon lifetime in GaN. A comparison with the measured density-dependent saturation velocity shows that it captures the dependence rather well, Finally, the experimental result is applied in TCAD-based device simulator to predict DC and small signal characteristics of a reported GaN HEMT. Good agreement between the simulated and reported experimental results validated the measurement presented in this report and established accurate modeling of GaN HEMTs. (C) 2015 AIP Publishing LLC.