Large fraction of crystal directions leads to ion channeling

It is well established that when energetic ions are moving in crystals, they may penetrate much deeper if they happen to be directed in some specific crystal directions. This `channeling' effect is utilized for instance in certain ion beam analysis methods and has been described by analytical theories and atomistic computer simulations. However, there have been very few systematic studies of channeling in directions other than the principal low-index ones. We present here a molecular dynamics-based approach to calculate ion channeling systematically over all crystal directions, providing ion `channeling maps' that easily show in which directions channeling is expected. The results show that channeling effects can be quite significant even at energies below 1 keV, and that in many cases, significant planar channeling occurs also in a wide range of crystal directions between the low-index principal ones. In all of the cases studied, a large fraction (∼20 -60 % ) of all crystal directions show channeling. A practical implication of this is that modern experiments on randomly oriented nanostructures will have a large probability of channeling. It also means that when ion irradiations are carried out on polycrystalline samples, channeling effects on the results cannot a priori be assumed to be negligible. The maps allow for easy selection of good `nonchanneling' directions in experiments or alternatively finding wide channels for beneficial uses of channeling. We implement channeling theory to also give the fraction of channeling directions in a manner directly comparable to the simulations. The comparison shows good qualitative agreement. In particular, channeling theory is very good at predicting which channels are active at a given energy. This is true down to sub-keV energies, provided the penetration depth is not too small.