The experimental techniques advances in the formation of artificial crystals based on quantum dots (QD) allow us to think about the possibility of generating novel materials. However, there is a lack of theoretical calculations which permits pre-designing the properties of the new materials. Taking advantage on a theoretical derivation of the electronic dielectric response of semiconductor nano-crystals using a tight binding framework [F. Trani, D. Ninno, G. Iadonisi, Phys. Rev. B 76 (2007) 085326], we calculate the dielectric function of QD arrays of finite size introducing the screening of surface polarization by means of a tuning static electric field. In previous calculations we report drastic geometric effects in the electronic structure of QD super-crystals, as the shape changes in 3D semiconductors, while in 2D the dielectric function peaks correspond to the predicted dipole transitions energies [J.F. Nossa, A.S. Camacho, J.L. Carrillo, Rev. Mex. Fis. 53 (7) (2007) 123]. With the aim of explaining the role of the dimensionality in nanosystems we apply the above method to III–V and II–VI QD 3D supercrystals of several geometries. In this report we study the dielectric behavior of finite 3D supercrystals built up of spherical, cylindrical and conical QD and particularly we discuss the shape dependence of the QD constituents on the response function and therefore on the surface polarization fields of finite arrays. Finally, we compare the results in 3D systems with the 2D systems.