A method for electrofilling large, high aspect ratio recessed features with copper without depositing substantial amounts of copper in the field region is provided. The method allows completely filling recessed features having aspect ratios of at least about 5:1 such as at least about 10:1, and widths of at least about 1 μm in a substantially void-free manner without depositing more than 5% of copper in the field region (relative to the thickness deposited in the recessed feature). The method involves contacting the substrate having one or more large, high aspect ratio recessed features (such as a TSVs) with an electrolyte comprising copper ions and an organic dual state inhibitor (DSI) configured for inhibiting copper deposition in the field region, and electrodepositing copper under potential-controlled conditions, where the potential is controlled not exceed the critical potential of the DSI.