Abstarct: Nanotechnology is one of the most important issues in contemporary scientific societies, which is rapidly expanding in all fields of science and technology. Today, nanotechnology research is working hard to optimize mextal oxides in nanoscale because of its special properties in relation to mass state. Zinc oxide nanoparticles have a much higher quality and performance than conventional zinc oxide due to their very fine particles and, consequently, a high level of performance. Among nanoscale materials, nanotubes, and especially ZnO nanotubes, have been widely used in all aspects of human life because of their interesting electrical, optical, mechanical and thermal properties. These structures are very important because of their high electrical and thermal conductivity, high mechanical strength, high transparency, high visibility, and are the ideal choice for all types of laser and laser diode and displays. In this project, using the density functional theory (DFT) with the generalized gradient approximation of GGA, and using the SIESTA computational code, the stability and electron properties of pure dowble-walled nanotubes (4.4) @ (n, n) (n=14-7), And (5.5) @ (n, n) (n=16-8) and zigzag (6.0) @(n,0) And (7.0) @(n,0) also doped with Lu atom. The results of the study of pure nanotubes show that the most favorable interstitial distance is 4.6Å for nanotubes , the chirality difference for this category is 5. The most favorable intraocular distance for zigzag nanotubes is 4/4 angstroms, and the chirality difference is reported for this category 7. The investigation of their strip structure shows that all of thedowble-walled nanotubes of the semiconductor ZnO pure sheet of semiconductor are straight-gap and increase with the increase in the band gap, and in the pure zigzag type, the semiconductor is straight-gauged and with increasing diameter The bandwidth increases, although these variations are observed in the band gap for even more dowble-walled nanotubes. The results of the release of double-sided CNTs and zigzags showed that their interstitial distances were altered to the pure state, as well as in lower diameter nanotubes, even with the loss of sustainability. So, the results of the sustainability calculations showed that the diffusion of chiral in the nanotubes in nanotubes increased by 2 units in the nanotubes with the Lu atom, and by encapsulating the nanotubes this chirality difference was compared to the pure state for each Two zigzags and one armchair have risen The dowble walled ZnO nanotube , doped and capsulation with the Lu atom, are a phase change from the semiconductor to the mextal.