ABSTRACT: In this work we make a predictive study on the binding energy of the ground state for hydrogenic donor impurity in vertically-coupled quantum-dot structure, considering the combined effects of hydrostatic pressure and in growth-direction applied electric field. The approach uses a variational method within the effective mass approximation. The low dimensional structure consists of three cylindrical shaped GaAs quantum-dots, grown in the z-direction and separated by Ga1−xAlxAs barriers. In order to include the pressure dependent Γ −X crossover in the barrier material a phenomenological model is followed. The main findings can be summarized as follows: 1) for symmetrical and asymmetrical dimensions of the structures, the binding energy as a function of the impurity position along the growth direction of the heterostructure has a similar behavior to that shown by the non-correlated electron wave function with maxima for the impurity in the well regions and minima for the impurity in the barrier regions, 2) for increasing radius of the system, the binding energy decreases and for R large enough reaches the limit of the binding energy in a coupled quantum well heterostructure, 3) the binding energy increases for higher Aluminum concentration in the barrier regions, 4) depending of the impurity position and of the structural dimensions of the system (well width and barrier thickness) – and because changing the height of the potential barrier makes possible to induce changes in the degree of symmetry of the carrier-wave function –, the electric field and hydrostatic pressure can cause the impurity binding energy increases or decreases, and finally 5) the line-shape of the binding energy curves are mainly given by the line-shape of the Coulomb interaction.