Two-dimensional (2D) semiconductors have been proposed for heterogeneous integration with existing silicon technology; however, their chemical vapor deposition (CVD) growth temperatures are often too high. Here, we demonstrate direct CVD solid-source precursor synthesis of continuous monolayer (1L) MoS$_2$ films at 560 C in 50 min, within the 450-to-600 C, 2 h thermal budget window required for back-end-of-the-line compatibility with modern silicon technology. Transistor measurements reveal on-state current up to ~140 $mathrm{{mu}A/{mu}m}$ at 1 V drain-to-source voltage for 100 nm channel lengths, the highest reported to date for 1L MoS$_2$ grown below 600 C using solid-source precursors. The effective mobility from transfer length method test structures is $mathrm{29 pm 5 cm^2V^{-1}s^{-1}}$ at $mathrm{6.1 times 10^{12} cm^{-2}}$ electron density, which is comparable to mobilities reported from films grown at higher temperatures. The results of this work provide a path toward the realization of high-quality, thermal-budget-compatible 2D semiconductors for heterogeneous integration with silicon manufacturing.
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