The layer thickness of polycrystalline silicon grown in a commercial LPCVD reactor at 25-50 Pa and 850-950 K is accurately simulated with a one-dimensional two-zone model without adjusting any model parameter and applying independently determined reaction kinetics. The radial non-uniformity of the layer thickness is limited to 4%. At a surface-to-volume ratio of 200 m(-1) up to 20% of the growth originates from silylene and disilane. This contribution is the cause of the radial non-uniformity.