Electron knock-on cross section of carbon and boron nitride nanotubes

Abstract

We present a theoretical description of electron irradiation of single-walled carbon and boron nitride nanotubes. In a first step, the anisotropy of the atomic emission energy threshold is obtained within extended molecular-dynamics simulations based on the density-functional tight-binding method. In a second step, we numerically derive the total Mott cross section for different emission sites as a function of the incident electron energy. Two regimes are then described: at low irradiation energies (below $300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$), the atoms are preferentially ejected from the upper and lower parts of the tube, while at high energies (above $300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$), the atoms are preferentially ejected from the side walls. Typical values from a fraction of barn (at side wall for $150\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ electron) up to around $20\phantom{\rule{0.3em}{0ex}}\text{barn}$ (for $1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ electrons) are obtained for the total cross section of knock-on processes for both C and BN nanotubes. These values are smaller than those previously reported using isotropic models and the main reasons for the discrepancies are discussed. Finally, in boron nitride nanotubes, we report that the emission energy threshold maps show boron sputtering to be more favorable for low irradiation energies, while nitrogen sputtering is more favorable at high energies. These calculations of the total knock-on cross section for various nanotubes can be used as a guideline for transmission electron microscopy experimentalists using high energy focused beams to shape nanotubes, and also more generally if electron irradiation is to be used to change nanotube properties such as their optical behavior or conductivity.