We theoretically study the energy relaxation of hot electrons via LO-phonon emission in two-dimensional GaN systems. We employ a model in which electrons and the lattice are in equilibrium separately, and the effective electron temperature is much larger than the lattice temperature. We include the dynamical screening of electrons, electron-phonon interactions reduced phonon self-energy correction, the hot-phonon, and the finite-size effects. The power loss to acoustic phonons is also considered.In the last few years, a great deal of experimental and theoretical attention has focused on the direct, large band gap III-V nitride semiconductors GaN, AlN and InN. The large band gap leads to high breakdown voltages and electric fields, good thermal conductivity, low noise generation, high power and high temperature operation. All of these properties make these structures desirable for electronic and optoelectronic device applications [1][2][3][4][5][6][7]. These devices work mostly under high electric field, which brings about substantial heating and decrease in their performance. For desired efficiency in device applications and good explanation of the experimental results, the electronic processes behind the transport properties of nitrate heterostructures should be understood clearly.The electrons in a bulk or quantum well become energetic (or hot) when a high electric field is applied, and the thermal equilibrium between the electron gas and the lattice is destroyed. The electrons relax by losing their excess energy to the lattice. This process follows several steps. First, the electrons having enough energy emit longitudinal optical (LO) phonons, Then, the emitted LO phonons decay into acoustic phonons and the excess energy drains out to the lattice. Finally, the electron gas and the lattice reach equilibrium separately at different temperatures, T and T L , respectively, coupled only weakly through electron-phonon interaction. In the steady state the input power is equal to the power loss to the lattice. At high electron temperatures the dominant mechanism for energy relaxation is emitting LO phonons. However, there are several parameters affecting the power loss of hot electrons: the electron-phonon coupling, electronic screening, hot-phonon and finite-thickness effects. Throughout the years, there has been a large amount of theoretical effort to explain the experimental results for the power loss of electrons in semiconductor bulk and lower dimensional structures, especially GaAs based quantum wells [8][9][10][11][12][13][14][15][16][17].In order to understand the power loss mechanism of hot electrons in GaN quantum wells, we made a detailed theoretical investigation. We included the dynamical screening of electrons within the finitetemperature random-phase approximation (RPA). Phonon self-energy renormalization due to the electronphonon coupling, hot-phonon effect, impurity and the finite-thickness effect are also considered. In polar semiconductors like GaN the piezoelectric coupling to acoustic phonons is ...