The binding energies of bound polarons near the interface of a strained wurtzite GaN/Al_xGa_(1-x)N het-erojunction are studied by using a modified LLP variational method and a simplified coherent potential approximation under hydrostatic pressure and an external electric field.Considering the biaxial strain due to lattice mismatch or epitaxial growth,the uniaxial strain effects and the influences of the electron-phonon interaction as well as impurity-phonon interaction including the effects of interface-optical phonon modes and half-space phonon modes,the binding energies as functions of pressure,the impurity position,areal electron density and the phonon effect on the Stark energy shift are investigated.The numerical result shows that the contributions from the interface optical phonon mode with higher frequency and the LO-like half space mode to the binding energy and the Stark energy shift are important and obviously increase with increasing hydrostatic pressure,whereas the interface optical phonon mode with lower frequency and the TO-like half space mode are extremely small and are insensitive to the impurity position and hydrostatic pressure.It is also shown that the conductive band bending should not be neglected. The binding energies of bound polarons near the interface of a strained wurtzite GaN / Al_xGa_ (1-x) N het-erojunction are studied by using a modified LLP variational method and a simplified coherent potential approximation under hydrostatic pressure and an external electric field. Considering the biaxial strain due to lattice mismatch or epitaxial growth, the uniaxial strain effects and the influences of the electron-phonon interaction as well as impurity-phonon interactions including the effects of interface-optical phonon modes and half-space phonon modes, the binding energies as functions of pressure, the impurity position, areal electron density and the phonon effect on the Stark energy shift are investigated. numerical result shows that the contributions from the interface optical phonon mode with higher frequency and the LO-like half space mode to the binding energy and the Stark energy shift are important and obviously increase with increasing hydrostatic pressure, but the interfac e optical phonon mode with lower frequency and the TO-like half space mode are extremely small and are insensitive to the impurity position and hydrostatic pressure. It is also shown that the conductive band bending should not be neglected.