A model calculation of the tip field distribution for a carbon nanotube array and the optimum intertube distance

In a previous paper, the model of a floating top segment was proposed and used successfully to calculate the field enhancement factor as well as the field distribution on the top surface for a single carbon nanotube (CNT). In this paper, the model is extended to a CNT array. A set of modified linear charge equations has been derived for the CNT array using an approximation of multipole potential expansion. Fictitious charges inside a specific segment can be solved from these equations to calculate the field around the tips. Some numerical calculations of the field enhancement factor have been carried out, quantitatively accounting for the reduction of the factor with decreasing intertube distance. The relative field strength distribution on the top hemisphere of a CNT array is calculated too; it is observed to be close to that of a single CNT. Using the Fowler-Nordheim formula, the field emission intensity of a CNT array is maximized with varying intertube distance. The resulting optimum intertube distance to height ratio decreases gradually with increasing height to radius ratio, and is close to 2 only for height to radius ratio around 3 x 102