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

Abstract

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.

Interpreting nanovoids in atom probe tomography data for accurate local compositional measurements

“…For APT analysis of He bubbles, despite the presence of He inside the bubble, no He peak could be identified in the APT mass spectrum. This can be explained by the pressurized gas state of He inside the bubbles, the pressure of which were found as high as a few GPa in previous studies 30,45 .…”

Evolution of the properties of helium nanobubbles during in situ annealing probed by spectrum imaging in the transmission electron microscope

“…The additional energy barrier represented by ζ (n He ) could then vary from one bubble to another. Secondly, our investigations recently revealed the formation of an highly pressurized region in the silicon matrix, surrounding the bubble, when the helium density in the bubble is greater than 114 He nm −3 [41]. This is expected to impede the diffusion of He atoms, and thus also the helium emission from the bubble.…”

“…Unfortunately, in silicon, the technique is destructive and can not be used to study thermal emission. We have recently developed a spatially resolved EELS approach based on energy-filtered transmission electron microscopy-spectrum imaging (EFTEM-SI) acquisition of the data avoiding helium detrapping under the electron beam and allowing the investigation of a large number of bubbles [40,41]. EFTEM-SI thus appears as a powerful tool to unravel the detail of the evolution of bubbles during thermal annealing as it offers the unique possibility to investigate simultaneously the structural and the chemical modifications of the bubbles during an in situ annealing for instance.…”

Density functional theory calculations of helium clustering in mono‐, di‐, and hexa‐vacancy in silicon

“…There are two such helium atoms in the case of , with atomic volumes equal to 5.82 Å 3 and 6.04 Å 3 . This corresponds to helium densities of 172 and 165 He nm −3 and an internal pressure of about 19 GPa , which is surprisingly close to the range of values measured in nanometric‐sized bubbles .…”

“…The formation of noble gas bubbles in materials has been the focus of numerous investigations, motivated by the will to understand and control the influence of these bubbles on materials properties. Most of the available studies were dedicated to the state of already formed bubbles, and on their evolution during coarsening stages . Another important information regarding these bubbles relates to the very first steps leading to the formation, that is, the aggregation of noble gas impurities and how the latter interact with point defects like vacancies or self‐interstitials.…”