48 μA). Now, suppose I max is 10 (7.81 μA), then the fraction ξ of emitters that will burn out at 1 μA is smaller than 0.04% according to Eq. (17). In
this example, I max is constant: otherwise, the calculation of ξ will be more elaborate. If I max is a known function, then ξ must be integrated over I max for a refined estimative. However, we shall not deepen our analysis on ξ in this paper. Conclusions We simulated the behavior of the field emission current from non-uniform arrays of CNTs and obtained correction factors to multiply the current from a perfect CNT array toward the currents of non-uniform arrays. These correction functions are valid if the allowed dispersion in height and radius is kept inside the limits of 50% and 150% of their average values #LEE011 solubility dmso randurls[1|1|,|CHEM1|]# and if the randomization of the CNT position is done inside the designated unit cell. The uneven screening effect in non-uniform arrays causes many CNTs to become idle emitters while
few may become overloaded and burn out. To avoid this, uniformity is desired: however, non-uniformities are always present in some degree, and our model describes how to treat them. This model can also be used in estimating how many CNTs are expected to burn given their SN-38 tolerance and the total current extracted from the array. We like to point out that in a previous work , we showed that the emission from 3D CNT arrays can be simulated in a two-dimensional (2D) rotationally symmetric system with proper boundary conditions. The currents from the 2D and 3D arrays are also related by a factor that is a function of the aspect ratio and spacing of the actual array. The combined correction factor from Eq. (14) and the procedure in  can considerably ease the modeling of FE from non-uniform CNT arrays, as they can be reduced to perfectly uniform arrays, which may be treated in a 2D model. Acknowledgments This work was supported by the National Council of Technological and Scientific Development (CNPq) of Brazil. References 1. Vieira
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