Properties of helium bubbles in covalent systems at the nanoscale: A combined numerical and experimental study

The properties of nanometric-sized helium bubbles in silicon have been investigated using both spatially resolved electron-energy-loss spectroscopy combined with a recently developed method, and molecular-dynamics simulations. The experiments allowed for an accurate determination of size, aspect ratio, and helium density for a large number of single bubbles, whose diameters ranged from 6 to 20 nm. Very high helium densities, from 60 to 180 He nm(-3), have been measured depending on the conditions, in stark contrast with previous investigations of helium bubbles in metal with similar sizes. To supplement experiments on a smaller scale, and to obtain insights into the silicon matrix state, atomistic calculations have been performed for helium bubbles in the diameter range 1-13 nm. Molecular-dynamics simulations revealed that the maximum attainable helium density is critically related to the strength of the silicon matrix, which tends to yield by amorphization at the highest density levels. Calculations give helium density values for isolated single bubbles that are typically lower than measurements. However, excellent agreement is recovered when the interactions between bubbles and the presence of helium interstitials in the matrix are taken into account. Both experiments and numerical simulations suggest that the Laplace-Young law cannot be used to predict helium density in nanometric-sized bubbles in a covalent material such as silicon.