A brush-cleaning apparatus is disclosed for use in cleaning a semiconductor wafer after polishing. Embodiments of the brush-cleaning apparatus implemented with a multi-branch chemical dispensing unit are applied beneficially to clean semiconductor wafers, post-polish, using a hybrid cleaning method. An exemplary hybrid cleaning method employs a two-chemical sequence in which first and second chemical treatment modules are separate from one another, and are followed by a pH-neutralizing—rinse that occurs in a treatment module separate from the first and second chemical treatment modules. Implementation of such hybrid methods is facilitated by the multi-branch chemical dispensing unit, which provides separate chemical lines to different chemical treatment modules, and dispenses chemical to at least four different areas of each wafer during single-wafer processing in an upright orientation. The multi-branch chemical dispensing unit provides a flexible, modular building block for constructing various equipment configurations that use multiple chemical treatments and/or pH neutralization steps.