In this paper the electric field simulation of carbon nanotubes triode field emission devices is investigated. The geometry of CNTs and their arrangement on the substrate affect the screening effect and filed enhancement factor (β). In an array of nanotubes, for a distance smaller than the CNT length the screening effect is observed. The emission current density is related to the gate aperture and CNT shape. In a triode structure the screening effect occurs in the intertube distances about half of the CNT’s length due to the presence of the gate plate. Furthermore, the presence of the metal-oxide gate has a favorable effect to minimize the screening effect and allows one to increase the density of CNT’s in each array spot and to increase the cluster array density on the substrate, hence to increase the density of emission current and emitter sites where a high current density is required.