The strength of deuterium bonding to the walls of closed cavities within Si was determined in ion-beam experiments. These studies circumvented an inherent indeterminacy in the analysis of external-surface desorption and thereby achieved a quantitative characterization of Si-H surface bonding. The Si-D bond energy for submonolayer coverages is 2.5{plus minus}0.2 eV. This value has implications for the reaction path of molecular desorption.