The plasma-enhanced chemical-vapor-deposited Si3N4 surface passivation layers with high rf (13.56MHz) and low rf (380KHz), were investigated, using the annealing experiment at 500°C in N2 ambient, for their effectiveness in regard to the stability of the two-dimensional electron gas (2DEG) in GaN∕AlGaN∕GaN high-electron-mobility transistor structures. When the unpassivated sample was annealed, as observation using the Hall and high-resolution x-ray diffraction measurements, an irreversible degradation of the 2DEG behavior and a strain relaxation of the AlGaN epilayer occurred. The Si3N4 deposited with high frequency provided superior long-term stability for the sample and showed no change in the 2DEG conductivity and the strain state in AlGaN epilayer after 170h of aging. However, a significant degradation after deposition and a partial recovery of the 2DEG behavior after annealing due to the Si3N4 densification, was found in sample passivated by low-frequency Si3N4. The enhancement of the long-term stability can be explained as a consequence of the strain solidification of the AlGaN epilayer induced by a denser Si3N4 passivation.