Due to the restriction of the ZnO buffer layer on the left barrier in a wurtzite asymmetric ZnO/Mg_xZn_(1-x)O single quantum well(QWs) structure with finite barriers, the other factors such as the size of the well and right barrier, and Mg component, etc. will influence the critical value of the left barrier width to form a binary level energy system. By adopting a finite difference method to solve the Schr?dinger equation, the eigenstates and eigenenergies of electrons in a two-dimensional electron gas are...