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

Abstract

The 1 s 2 → 1 s 2 p ( 1 P ) excitation in compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than in the free atom. For bulk helium, energy shifts predicted from non-empirical electronic structure computations are in excellent agreement with 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 analyses of earlier scanning transmission electron microscope measurements that are untrustworthy because the density dependence of the electron impact excitation cross section was neglected. Experimental electron energy loss data from an earlier study of helium encapsulated in silicon are reanalysed and it is shown 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 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.