Method for producing copolymer for semiconductor lithography containing reduced amount of metal impurities, and method for purifying polymerization initiator for production of copolymer

A method for producing a polymer for semiconductor lithography, said polymer comprising at least one type of repeating units selected from the group consisting of:

• a repeating unit having a hydroxy group or carboxy group (A), a repeating unit having a structure wherein a hydroxy group or carboxy group is protected with a group that suppresses dissolution into an alkaline developer and is dissociable by the action of an acid (B), a repeating unit having a lactone structure (C), and a repeating unit having a cyclic ether structure (D), said method comprising:
• a filtering step, wherein a solution of a polymerization initiator dissolved in an organic solvent is passed through a tilts r having a pore size of not more than 1.0 μm to reduce a sodium content of said polymerization initiator solution to not more than 300 ppb with respect to a weight of said polymerization initiator to produce a purified polymerization initiator;
• and
• a polymerization step wherein said polymer for semiconductor lithography is synthesized, in the presence of said purified polymerization initiator, by a radical polymerization reaction, wherein said polymerization step uses a dropping polymerization method using a polymerization reactor comprising at least
• a storage tank for a solution comprising the polymerization initiator,
• a polymerization reaction vessel, and
• said filter placed in a channel connected from said storage tank to said polymerization reaction vessel.