[en] A model is presented which predicts the current flow through and around grain boundaries which have been treated with atomic hydrogen to reduce their trap-state densities. Measurements on hydrogenated silicon grain boundaries are shown to be in agreement with this model and quantitative estimates of hydrogen penetration depth are made. The dependence of this depth on sample temperature, surface preparation, hydrogen pressure, and geometry are systematically investigated. Maximum penetration is achieved in high-pressure discharges for sample temperatures between 350 and 400 ⁰C. The condition of the surface of the polycrystalline silicon is shown to be critically important for the in-diffusion process