Influence of temperature on the displacement threshold energy in graphene

Abstract

The atomic structure of nanomaterials is often studied using transmission electron microscopy. In addition to image formation, the energetic electrons impinging on the sample may also cause damage. In a good conductor such as graphene, the damage is limited to the knock-on process caused by elastic electron-nucleus scattering. This process is determined by the kinetic energy an atom needs to be sputtered, i.e. its displacement threshold energy Ed. This is typically assumed to have a fixed value for all electron impacts on equivalent atoms within a crystal. Here we show using density functional tight-binding simulations that the displacement threshold energy is affected by thermal perturbations of atoms from their equilibrium positions. This effect can be accounted for in the estimation of the displacement cross section by replacing the constant threshold energy value with a distribution. Our refined model better describes previous precision measurements of graphene knock-on damage, and should be considered also for other low-dimensional materials.

Indirect measurement of the carbon adatom migration barrier on graphene

“…In this study, our initial aim was to determine the temperature-dependence of the electron knock-on damage cross section for pristine graphene, which is in the range of 5-20 mb for 90 keV electrons and 12 C lattice atoms at ambient temperature [24]. Based on a firstprinciples model of the cross section, one should expect to observe tremendously increasing knock-on damage rates for elevated temperatures due to the higher population of out-of-plane phonon modes [24] and the thermal perturbation of the lattice [27]. In stark contrast to that prediction, the detected damage rates do not increase with temperature, but rather decrease.…”

Three-dimensional description of vibration-assisted electron knock-on damage

“…For a complete description of situations including the beam-induced movement of adatoms [12], momentum transfers in all directions must be included. Further, while knock-on damage in pristine graphene can be accurately described from first principles [13,14], there are puzzling discrepancies between the predicted and measured cross-sections for its impurity sites [15]. Until now, it has not been clear if these are due to shortcomings in the elastic model, or arise from unaccounted inelastic effects.…”

“…Finally, we explored including the variation of E d due to thermal perturbations from the equilibrium geometry [14]. Unfortunately, the addition of an energy dimension to the numerical integration of Eq.…”

“…4 proved too demanding, nor is it possible to perform the required thermal sampling at our DFT/MD level of theory. However, this effect is expected to be only a minor correction [14]. Table I.…”

Super-Graphene: The Role of Temperature on Radiation Resistance

“…A recent theoretical study has extended the description of the knock-on process in graphene to include the effects of temperature [11]. The dependence of the displacement barriers on temperature suggests that graphene should be more easily damaged at higher temperatures.…”