Binding Energies Of Donors In Al_xGa_1-xAs/GaAs Triangular Potential Quantum Wells With Finite Wide Barriers And Their Lo Phonon Effect Under Hydrostatic Pressure

A variational method is used to investigate binding energies of donors in AlxGa1-xAs/GaAs quantum wells with finite width of potential barriers by using a triangular potential to approximate the band bending of the well potential. The relations between the binding energies and well width, impurity position, Al concentration are given and compared with the cases of square quantum wells. The results indicate:Binding energies with the triangular potential approximation are obviously lower than that of square quantum wells and their difference increases with increasing of well width, Al concentration (barrier height) and decreases with increasing of barrier width. The influence from the variation of the impurity position on the difference is insensitive. Furthermore, the effect of hydrostatic pressure on the effective band mass of an electron, dielectric constants and band gaps is considered to demonstrate that the difference of binding energies obtained with the above models increases obviously with increasing hydrostatic pressure. In this way, we emphasize the importance of considering of the conduction band bending in relative theoretical works.Furthermore, the contribution to the impurity binding energies from longitudinal optical (LO) phonon modes are introduced by using a modified LLP variational method to deal with the electron-LO phonon interaction. The pressure effect and varying relations between the binding energies and well width, Al concentration are given and compared with the cases of without phonons. The results indicate:LO phonons decrease the binding energies of impurity states. This effect is more obvious for wide well cases and the pressure effects is also obvious.