A method for treating a mold includes grinding an outer metal surface of a mold body of the mold with a first material; lapping the outer metal surface after the grinding with a second material that is finer than the first material; and polishing the outer metal surface after the lapping to achieve an average surface roughness (R.sub.a) less than or equal to about 0.15 m and a waviness height (W.sub.a) less than or equal to about 100 nm. A mold for shaping glass-based material can include a mold body having an outer metal surface, wherein the outer metal surface has an average surface roughness (R.sub.a) less than or equal to about 0.15 m and a waviness height (W.sub.a) less than or equal to about 100 nm.

A flattening method, by utilizing the advantages of the CARE method and making up for the disadvantages, can perform removal processing of a surface of a workpiece at a sufficient processing rate and can provide a processed surface having enhanced flatness without leaving damage in the processed surface. A flattening method comprises at least two surface removal steps and at least two cleaning steps, the final surface removal step being a catalyst-referred etching step comprising immersing a workpiece in a processing solution containing at least one of hydrohalic acid, hydrogen peroxide water and ozone water, and bringing a surface of a catalyst platen into contact with or close proximity to a surface to be processed of the workpiece to process the surface, said catalyst platen having in a surface a catalyst selected from the group consisting of platinum, gold, a ceramic solid catalyst, a transition metal, glass, and an acidic or basic solid catalyst.

A polishing pad includes and upper portion and one or more lower portions. The upper portion has an upper surface for attachment to a pad carrier and a first lateral dimension. The one or more lower portions project downward from the upper portion. A bottom surface of the one or more lower portions provide a contact surface to contact a substrate during chemical mechanical polishing. Each lower portion has a second lateral dimension that is less than the first lateral dimension. A total surface area of the contact surface from the one or more lower portions is no more than 10% of a surface area of the upper surface.

A polishing pad includes and upper portion and one or more lower portions. The upper portion has an upper surface for attachment to a pad carrier and a first lateral dimension. The one or more lower portions project downward from the upper portion. A bottom surface of the one or more lower portions provide a contact surface to contact a substrate during chemical mechanical polishing. Each lower portion has a second lateral dimension that is less than the first lateral dimension. A total surface area of the contact surface from the one or more lower portions is no more than 10% of a surface area of the upper surface.

Chemical mechanical polishing can be used for touch-up polishing in which polishing is performed on a limited area of the front surface of the substrate. The contact area between the polishing pad and the substrate can be substantially smaller than the radius surface of the substrate. During polishing, the polishing pad can undergo an orbital motion. The polishing pad can be maintained in a fixed angular orientation during the orbital motion. The contact area can be arc-shaped. The contact area can be provided by one or more lower portions projecting downward from an upper portion of the polishing pad. A perimeter portion of the polishing pad can be vertically fixed to an annular member and a remainder of the polishing pad within the perimeter portion can be vertically free.

Chemical mechanical polishing can be used for touch-up polishing in which polishing is performed on a limited area of the front surface of the substrate. The contact area between the polishing pad and the substrate can be substantially smaller than the radius surface of the substrate. During polishing, the polishing pad can undergo an orbital motion. The polishing pad can be maintained in a fixed angular orientation during the orbital motion. The contact area can be arc-shaped. The contact area can be provided by one or more lower portions projecting downward from an upper portion of the polishing pad. A perimeter portion of the polishing pad can be vertically fixed to an annular member and a remainder of the polishing pad within the perimeter portion can be vertically free.

Provided are a method for polishing a silicon substrate according to which PID can be reduced and a polishing composition set usable in the polishing method. The silicon substrate polishing method provided by this invention comprises a stock polishing step and a final polishing step. The stock polishing step comprises several stock polishing sub-steps carried out on one same platen. The several stock polishing sub-steps comprise a final stock polishing sub-step carried out while supplying a final stock polishing slurry P.sub.F to the silicon substrate. The total amount of the final stock polishing slurry P.sub.F supplied to the silicon substrate during the final stock polishing sub-step has a total weight of Cu and a total weight of Ni, at least one of which being 1 ?g or less.

Provided are a method for polishing a silicon substrate according to which PID can be reduced and a polishing composition set usable in the polishing method. The silicon substrate polishing method provided by this invention comprises a stock polishing step and a final polishing step. The stock polishing step comprises several stock polishing sub-steps carried out on one same platen. The several stock polishing sub-steps comprise a final stock polishing sub-step carried out while supplying a final stock polishing slurry P.sub.F to the silicon substrate. The total amount of the final stock polishing slurry P.sub.F supplied to the silicon substrate during the final stock polishing sub-step has a total weight of Cu and a total weight of Ni, at least one of which being 1 ?g or less.

Disclosed are electrochemical-mechanical thinning method and apparatus for large-diameter semiconductor wafers. The large-diameter semiconductor wafers are thinned by combining anodizing modification and mechanical grinding. The apparatus includes a grinding tool system, a wafer holding device and a grinding wheel dressing device. The grinding tool system includes a base plate and a cup-shaped grinding wheel. The base plate is taken as a cathode, and the semiconductor wafer is taken as an anode. During thinning, both the cathode and the anode are immersed in an electrolyte. Under the action of an external electric field, the semiconductor wafer is subjected to surface modification and softening. At the same time, an oxide layer and intermediate state products generated by modification are removed together by using the grinding wheel, and the semiconductor wafer is thinned under the combined action of multi-energy fields of electricity, chemistry, machinery and force.

Disclosed are electrochemical-mechanical thinning method and apparatus for large-diameter semiconductor wafers. The large-diameter semiconductor wafers are thinned by combining anodizing modification and mechanical grinding. The apparatus includes a grinding tool system, a wafer holding device and a grinding wheel dressing device. The grinding tool system includes a base plate and a cup-shaped grinding wheel. The base plate is taken as a cathode, and the semiconductor wafer is taken as an anode. During thinning, both the cathode and the anode are immersed in an electrolyte. Under the action of an external electric field, the semiconductor wafer is subjected to surface modification and softening. At the same time, an oxide layer and intermediate state products generated by modification are removed together by using the grinding wheel, and the semiconductor wafer is thinned under the combined action of multi-energy fields of electricity, chemistry, machinery and force.