FIELD EMISSION OF ELECTRONS BY TAKING INTO ACCOUNT THE DISTRIBUTION OF CHARGE ALONG THE LENGTH OF METALLIC CARBON NANOTUBES (CNTS)

Abstract

An mathematical expression has been derived and analysed for total potential energy V and field emission current density function ϕ of emitted electrons by taking into account the distribution of charge along the length of the carbon nanotubes (CNTs), matching to the representation for the tunnelling coefficient. This tunnelling coefficient is obtained from solving of the time independent Schrödinger’s wave equation. Mathematical calculations for the potential energy V, tunnelling coefficient T and current density function ϕ have been worked out for a distinctive set of the CNTs factors. It is concluded that the potential energy in ergs declines with the radial distance r but increases with z coordinate along the length of the CNT. Moreover, the current density function at the spherical CNT tip is substantially larger than along the length of cylindrical metallic CNT. In addition, the field emission current density function decreases with radius of CNTs in both the cases (i.e., cylindrical and spherical tip). Some of our theoretical results are in agreement with the current experimental observations.