Temperature-dependent Si29 incorporation during deposition of highly enriched Si28 films

In this study, we examine the mechanisms leading to $²⁹\mathrm{Si}$ incorporation into highly enriched $²⁸\mathrm{Si}$ films deposited by hyperthermal ion beams at elevated temperatures in the dilute presence of natural abundance silane $({\mathrm{SiH}}₄)$ gas. Enriched $²⁸\mathrm{Si}$ is a critical material in the development of quantum information devices because $²⁸\mathrm{Si}$ is free of nuclear spins that cause decoherence in a quantum system. We deposit epitaxial thin films of $²⁸\mathrm{Si}$ enriched in situ beyond 99.999 98% $²⁸\mathrm{Si}$ onto Si(100) using an ion-beam deposition system and seek to develop the ability to systematically vary the enrichment and measure the impact on quantum coherence. We use secondary ion mass spectrometry to measure the residual $²⁹\mathrm{Si}$ isotope fraction in enriched samples deposited from $\ensuremath{\approx}250\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$ up to 800 \ifmmode^\circ\else\textdegree\fi{}C. The $²⁹\mathrm{Si}$ isotope fraction is found to increase from $<1\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{\ensuremath{-}6}$ at the lower temperatures, up to $>4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at around 800 \ifmmode^\circ\else\textdegree\fi{}C. From these data, we estimate the temperature dependence of the incorporation fraction $s$ of ${\mathrm{SiH}}₄$, which increases sharply from about $2.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ at 500 \ifmmode^\circ\else\textdegree\fi{}C to $2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ at 800 \ifmmode^\circ\else\textdegree\fi{}C. We determine an activation energy of 1.00(8) eV associated with the abrupt increase in incorporation and conclude that below 500 \ifmmode^\circ\else\textdegree\fi{}C, a temperature-independent mechanism such as activation from ion collisions with adsorbed ${\mathrm{SiH}}₄$ molecules is the primary incorporation mechanism. Direct incorporation from the adsorbed state is found to be minimal.