Stacks of hydrogen-lean aluminum oxide, deposited via plasma-assisted atomic-layer-deposition, and hydrogen-rich plasma-enhanced chemical vapor-deposited silicon nitride (SiNx) are applied to boron-doped float-zone silicon wafers. A rapid thermal annealing (RTA) step is performed in an infrared conveyor-belt furnace at different set-peak temperatures. The hydrogen content diffused into the crystalline silicon during the RTA step is quantified by measurements of the silicon resistivity increase due to hydrogen passivation of boron dopant atoms. These experiments indicate that there exists a temperature-dependent maximum in the introduced hydrogen content. The exact position of this maximum depends on the composition of the SiNx layer. The highest total hydrogen content, exceeding 1015 cm−3, is introduced into the silicon bulk from silicon-rich SiNx layers with a refractive index of 2.3 (at λ = 633 nm) at an RTA peak temperature of 800 °C, omitting the Al2O3 interlayer. Adding an Al2O3 interlayer with a thickness of 20 nm reduces the hydrogen content by a factor of four, demonstrating that Al2O3 acts as a highly effective hydrogen diffusion barrier. Measuring the hydrogen content in the silicon bulk as a function of Al2O3 thickness at different RTA peak temperatures provides the hydrogen diffusion length in Al2O3 as a function of measured temperature.