Isotopic mass dependence of the lattice parameter in silicon determined by measurement of strain-induced splitting of impurity bound exciton transitions

The strain-induced splitting of the impurity bound exciton (BE) transitions in epitaxial layers of isotopically enriched ²⁸Si grown on silicon substrates of natural isotopic composition has been studied using high-resolution photoluminescence (PL) spectroscopy. The slight difference in lattice parameter between the ²⁸Si epitaxial layer and the natural silicon substrate induces a biaxial strain in the epitaxial layer, which can be detected with remarkable sensitivity using low-temperature PL. Measurement of the splitting of the BE transitions in these epitaxial layers of ²⁸Si provides us a method for determining the isotopic mass dependence of the lattice parameter in silicon with unprecedented precision. The level of precision achieved is attributed to the fact that the BE no-phonon transitions in isotopically enriched silicon are much sharper than in natural silicon. We find that scaled to an isotopic mass difference (ΔM) of 1 amu, the relative difference in lattice parameter (|Δa/a|) for silicon is 3.3×10-5.