Calculation of the field emission for the CNTs array with normal-gated of cold cathode

Usually there are two methods,floating charge sphere method and solving Laplace equation method,have been used to simulate the carbon nanotubes(CNTs) field emission display(CNT-FED) at present.Although solving Laplace equation is difficult,but it could get the electric field and potential distribution of CNT array FED in the whole space.A hexagon pitch CNTs array vertical to the normal-gated of cold cathode FED which would be useful for future application is simulated by solving Laplace equation in this article.The calculated results show that the intensity of the electric field is very strong near the top of the CNTs,and drops abruptly with the increasing of the distance from CNTs.The field enhancement factor increases with the increasing aspect ratio of the CNTs.For CNTs with definite aspect ratio,there are optimum densities that correspond their best field enhancement factor.Emission current density can be control strongly by the gate voltage in this structure,and get the emission current density around the CNTs with the change of the distance between cathode and anode.The biger the gate voltage,the greater the influence of the emission current,and the emission current density(J) were decreased with distance of anode-cathode(d) increase.