The density and pressure of helium nano-bubbles encapsulated in silicon

TL;DR

This paper investigates helium nano-bubbles in silicon, demonstrating a new method to accurately determine their densities and pressures, correcting previous overestimations caused by assumptions about electron scattering cross sections.

Contribution

It introduces a graphical method to reliably compare bubble and bulk properties, enabling accurate density and pressure measurements of helium nano-bubbles in silicon.

Findings

Previous density estimates were significantly overestimated due to incorrect scattering assumptions.

The new method shows helium properties in bubbles are similar to bulk helium.

Corrected pressure estimates are much lower, impacting radiation damage studies.

Abstract

The $1s^2->1s2p(^1P)$ excitation in confined and compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than that in the free atom. For bulk helium, the energy shifts predicted from non-empirical electronic structure computations are in excellent agreement with the experimentally determined values. However, there are significant discrepancies both between the results of experiments on different bubbles and between these and the well established descriptions of the bulk. A critique is presented of previous attempts to determine the densities in bubbles by measuring the intensities of the electrons inelastically scattered in STEM experiments. The reported densities are untrustworthy because it was assumed that the cross section for inelastic electron scattering was the same as that of a free atom whilst it is now known that this property is greatly enhanced for atoms confined at significant pressures. It is shown how experimental measurements of bubbles can be combined with data on the bulk using a graphical method to determine whether the behavior of an encapsulated guest differs from that in the bulk material. Experimental electron energy loss data from an earlier study of helium encapsulated in silicon is reanalyzed using this new method to show that the properties of the helium in these bubbles do not differ significantly from those in the bulk thereby enabling the densities in the bubbles to be determined. These enable the bubble pressures to be deduced from a well established experimentally derived equation of state. It is shown that the errors of up to 80% in the incorrectly determined densities are greatly magnified in the predicted pressures which can be too large by factors of over seven. This has major practical implications for the study of radiation damage of materials exposed to $\alpha$ particle bombardment.