Annual Report 2007 - The Australian Nanotechnology Network

2.2 Nanotube Array Field Calculations
The package Lorentz3D was used to solve a variety of nanotube electrostatics problems.
Lorentz3D is a combined electromagnetics and trajectory modelling package that can be
used to solve electrostatic and electromagnetic problems in 3D using the boundary
element method (BEM). The boundary element method allows for accurate microscopic
field solutions even when the boundary conditions are macroscopic, allowing the electric
fields near a nanotube to be calculated whilst taking into account the effects of the much
larger substrate and counter-electrode.
The principle model used for the work is illustrated in Figure 6. A 1 micron long
nanotube with a radius of 25 nm was placed at the centre of a rectangular plane section of
varying size. Four ‘walls’ imposing periodic boundary conditions simulate an infinite array
of nanotubes, the nanotube density is thus controlled by the plane section size. The plane
section and the nanotube were raised to 100 V, whilst a grounded counter electrode
formed the other end cap of the closed cell. Simulations were then run to determine the
electric field at the tip of the nanotube where the field ionization is expected to occur. Both
the nanotube density and electrode/counter-electrode spacing were varied.
Figure 7: Approximate variation of nanotube tip electric field with counter-electrode
distance.
For a fixed nanotube density, the nanotube tip field varies with counter-electrode
spacing as illustrated in Figure 7. As can be seen the function peaks at a value that is
typically between 100-300 microns depending on the nanotube density. The existence
of a peak was unexpected as previously it has been assumed that the tiny nanotube tip
size makes all other surrounding macroscopic geometry irrelevant. The result may
explain why the field emission performance of nanotube arrays is far less than what
would be expected if the array simply multiplied the field emission performance of a
single isolated nanotube. In general, it appears that the less dense the array, the higher
the peak field, whereas the counter electrode spacing has a narrow range of values
over which the field is far higher than the applied field between the substrate and the
counter-electrode. For field ionization applications this range is critical as the fields
required for field ionization are very large, of the order of 10 GV/m, and achieving such
fields with practical voltages can only be done with maximum geometric field
enhancement.
3 Outcomes
It is intended that two scientific papers be written as a direct result of the author’s work. The
58