Calculation of the emission performance of the carbon nanotube array

Because of the excellent field emission performances, the carbon nanotube array has already been used as the cold electron source in the field emission display, the vacuum microwave tube, and the electron microscopy, etc. It is necessary to estimate the emission performance of the carbon nanotube array in the design of these devices. The emission current density of a single carbon nanotube can be estimated with the Fowler-Nordheim formula approximately. Thus, the emission performance of the whole array is obtained by the sum of the current emitted from all carbon nanotubes in the array. However, this calculation is very complex and time consuming due to the large number of carbon nanotubes in the array. This paper proposes a simple model to predict the emission performance of the whole CNT array. The total emission current can be deduced easily with this model if we know the geometrical parameters of the CNT array. A few experiments have been performed to verify this model. With this model, the influences of geometric dimensions of the CNT array on the emission performance are also discussed.