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Optimizing thermal anneals of Si-implanted $\beta$-Ga$_2$O$_3$ is criticalfor low resistance contacts and selective area doping. We report the impact ofannealing ambient, temperature, and time on activation of room temperatureion-implanted Si in $\beta$-Ga$_2$O$_3$ at concentrations from 5x10$^{18}$ to1x10$^{20}$ cm$^{-3}$, demonstrating full activation (>80% activation,mobilities >70 cm$^{2}$/Vs) with contact resistances below 0.29 $\Omega$-mm.Homoepitaxial $\beta$-Ga$_2$O$_3$ films, grown by plasma assisted MBE onFe-doped (010) substrates, were implanted at multiple energies to yield 100 nmbox profiles of 5x10$^{18}$, 5x10$^{19}$, and 1x10$^{20}$ cm$^{-3}$. Annealswere performed in a UHV-compatible quartz furnace at 1 bar with well-controlledgas composition. To maintain $\beta$-Ga$_2$O$_3$ stability, $p_{O2}$ must begreater than 10$^{-9}$ bar. Anneals up to $p_{O2}$ = 1 bar achieve fullactivation at 5x10$^{18}$ cm$^{-3}$, while 5x10$^{19}$ cm$^{-3}$ must beannealed with $p_{O2}$ <10$^{-4}$ bar and 1x10$^{20}$ cm$^{-3}$ requires$p_{O2}$ <10$^{-6}$ bar. Water vapor prevents activation and must be maintainedbelow 10$^{-8}$ bar. Activation is achieved for anneal temperatures as low as850 {\deg}C with mobility increasing with anneal temperature up to 1050{\deg}C, though Si diffusion has been reported above 950 {\deg}C. At 950{\deg}C, activation is maximized between 5 and 20 minutes with longer timesresulting in decreased carrier activation (over-annealing). This over-annealingis significant for concentrations above 5x10$^{19}$ cm$^{-3}$ and occursrapidly at 1x10$^{20}$ cm$^{-3}$. RBS (channeling) suggests damage recovery isseeded from remnant aligned $\beta$-Ga$_2$O$_3$ that remains afterimplantation; this conclusion is also supported by STEM showing retention ofthe $\beta$-phase with inclusions that resemble the $\gamma$-phase.

Silicon Implantation and Annealing in $\beta$-Ga$_2$O$_3$: Role of Ambient, Temperature, and Time