Hot electrons relax by interacting with phonons, so information about the electron-phonon interaction mechanisms are obtained by examining the cooling processes of hot electrons. In this study, the effect of annealing time on the electron temperature and energy relaxation rates in as-grown and annealed n-type modulation-doped Ga0.68In0.32N0.017As0.983/GaAs quantum well (QW) samples were investigated by comparing the relative amplitudes of Shubnikov-de Haas oscillations as a function of temperature and electric field. The samples were grown by molecular beam epitaxy (MBE) and annealed at 700 degrees C for 60 s and 600 s. Experiments were carried out by applying an electric field between 0.165 and 5.276 kV/m at a temperature range between 1.8 and 40 K under magnetic up to 11 T. The energy-relaxation mechanism is found to be a mixing of piezoelectric and deformation potential scatterings of hot electrons in the low-temperature regime up to 40 K electron temperature. The electron power loss by interacting with phonons is characterized with exponential term gamma, which is found to be in the range from 3.42 to 4.97. The change of gamma showed that the scattering mechanisms are affected by the annealing time. The piezoelectric stress constant (e(14)) chosen as a fit parameter in the theoretical power loss calculations, which was found between 0.129 and 0.134. The crystal quality at low temperatures has been observed to be effective on energy relaxation times.