(Invited) Helium in Silicon: From the Atom to the Bubble
Authors: David Marie-Laure , Dérès Julien , Alix Kevin , Hebert Cecile , Alexander Duncan , Pailloux Frédéric , Pizzagalli Laurent 
Published: July 2021

Helium is one of the most inert elements in nature and its solubility in most materials is very low. When introduced by implantation, the energetic helium atoms induce the displacement of a large number of atoms from their lattice position creating excess defects (self-interstitials and vacancies) that may agglomerate to form larger clusters and/or may interact with the implanted atoms as well. In particular, the interaction of vacancies with helium leads to the formation of bubbles that may modify the mechanical and physical properties of materials. This leads to a very active research field in the nuclear domain, where bubbles are responsible for the embrittlement of materials. In covalent materials, helium bubbles can be formed following high fluence implantation as well and the idea to transform bubbles from a liability into an asset has emerged twenty years ago. The most known application is probably the formation of helium and hydrogen disc-like bubbles, the platelets, used to produce silicon-on-insulator wafers. But other potential applications have been demonstrated as well such as proximity gettering of metallic impurities for instance. For all these applications, the control of the bubble formation and evolution is essential. This requires an in-depth understanding of the underlying physical mechanisms.
In this work, a multiscale picture of the formation mechanisms of helium bubbles in silicon and their evolution under annealing is derived from the combination of numerical simulations and Electron Energy Loss Spectroscopy (EELS) in the Transmission Electron Microscope (TEM).
Using molecular dynamics (MD) and rate equation dynamics calculations, we have identified the atomic scale mechanisms involved in the nucleation and early growth steps of the bubbles and followed their dynamics during experimental timescale. For the smallest length scale, the optimal helium filling in small vacancy clusters was determined (Fig. 1a) [1]. Regarding bubble growth, MD simulations (Fig. 1b) suggest that both Ostwald ripening and migration-coalescence mechanisms are jointly activated during bubble growth. We also discover that an original mechanism, based on the splitting of bubbles, could have a significant contribution. Overall, helium atoms are found to delay growth, proportionally to their concentration. This can be clearly observed at the nanosecond timescale. However, for longer timescales, cluster dynamics calculations also reveal periods of accelerated growth for specific helium concentrations [2].
At larger length scales, the physical properties of the bubbles (helium density, pressure, morphology and size) were investigated experimentally using an original approach based on spatially resolved EELS that we have developed [3]. These experiments allow for an accurate determination of size, aspect ratio and helium density for a large number of single bubbles. These bubbles, 6 to 20 nm in diameter, were synthesized by high fluence helium implantation in silicon, followed by annealing. Very high helium densities, from 60 to 180 He/nm3, were measured in the bubbles depending on the conditions, in stark contrast with previous investigations of helium bubbles in metal with similar sizes. These results were confirmed by atomistic calculations performed for helium bubbles in the diameter range 1 to 13 nm [4].
The structural modifications and, simultaneously, the helium emission from individual bubbles were investigated by spectrum imaging during in situ annealing in the transmission electron microscope (Fig. 1c). We show that helium emission surprisingly takes place at temperatures where bubble migration had hardly started. At higher temperatures, the migration (and coalescence) of voids is clearly revealed. For helium density lower than 150 He.nm-3, the Cerofolini's model taking into account the thermodynamical properties of an ultradense fluid reproduces well the helium emission from the bubbles, leading to an activation energy of 1.8 eV. When bubbles exhibit a higher initial helium density, the Cerofolini's model fails to reproduce the helium emission kinetics. We ascribe this to the fact that helium may be in the solid phase and we propose a model to take into account the properties of the solid [5].
[1] L. Pizzagalli, M.-L. David, J. Dérès, Phys. Stat. Solidi A, 1700263 (2017)
[2] L. Pizzagalli, J. Dérès, M.-L. David, T. Jourdan, J. Phys.
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[3] K. Alix, M.-L. David, G. Lucas, D.T.L. Alexander, F. Pailloux, C. Hébert, L. Pizzagalli, Micron 77, p.57 (2015)
[4] J. Dérès, M.-L. David, K. Alix, D.T.L. Alexander, C. Hébert, L. Pizzagalli, Phys. Rev. B 96, p. 014110 (2017)
[5] K. Alix, M.-L. David, J. Dérès, C. Hébert, L. Pizzagalli, Phys. Rev. B 97, p. 104012 (2018)

Figure 1