In this study, we have numerically investigated the conduction band structures, the carrier densities and the electron probability densities of pseudomorphic grown BexZn1-xO/ZnO heterostructures using self-consistent solutions of one-dimensional, non linear Schrodinger-Poisson equations. In the calculations, two-dimensional electron gas (2DEG) formations were observed in the studied heterostructures and the effects of layer thickness and Be-mole fraction (x) of BexZn1-xO barrier layer on 2DEG were described. For possible transistor device applications, 10nm BexZn1-xO barrier layer structure with x=0.08 has been suggested. For this structure, we examined the variation of electron mobility with temperature using analytical calculations. Because of the polarization-induced low carrier densities, we found that the background impurity scattering has a strong effect on total electron mobility even at room temperature.