78  US 9,152,050 B2  77  In a further embodiment, an acid generator (b) in the form  of an onium salt having polymerizable olefin may be copo› lymerized with the foregoing monomers. JP-A 804-230645,  JP-A 2005-084365, and JP-A 2006-045311 disclose sulfo› nium salts having polymerizable olefin capable of generating  a specific sulfonic acid and similar iodonium salts. JP-A  2006-178317 discloses a sulfonium salt having sulfonic acid  directly attached to the main chain.  In this embodiment, the polymer may have further copo› lymerized therein recurring units (b 1) to (b3) having a sulfo› nium salt, represented by the following formula ( 4). Some› times, units (b 1) to (b3) are collectively referred to as units  (b).  When hydroxyacenaphthylene is copolymerized, an alter- native method is possible. Specifically, acetoxyacenaphtha› lene is used instead of hydroxyacenaphthylene, and after  polymerization, the acetoxy group is deprotected by alkaline  hydrolysis as mentioned above, for thereby converting the  polymer product to hydroxypolyacenaphthalene. For alkaline  hydrolysis, a base such as aqueous ammonia or triethylamine  may be used. The reaction temperature is -20°  C. to 100°  C.,  Examples of the organic solvent which can be used for  polymerization include toluene, benzene, tetrahydrofuran,  diethyl ether and dioxane. Examples of the polymerization  initiator used herein include 2,2’-azobisisobutyronitrile  (AIBN),  2,2’-azobis(2,4-dimethylvaleronitrile ),  dimethyl  2,2-azobis(2-methylpropionate ), benzoyl peroxide, and lau› royl peroxide. Preferably the system is heated at 50 to 80°  C.  for polymerization to take place. The reaction time is 2 to 100  hours, preferably 5 to 20 hours.  There have been described a polymer of formula (1) as  polymeric additive for modifying the resist film surface and  an acid labile group-containing polymer of formula (2) as  base resin. These polymers may be synthesized by any  desired methods, for example, by dissolving one or more  monomers selected from the monomers to form recurring  units (p ),  (q) and (r) or recurring units (a) to (d) in an organic  solvent, adding a radical polymerization initiator thereto, and  effecting heat polymerization.  The meaning of a+b+c= 1, for example, is that in a polymer  comprising recurring units (a), (b ), and (c), the sum ofrecur› ring units (a), (b ), and ( c) is 100 mo! % based on the total  amount of entire recurring units. The meaning of a+b+c<l is  that the sum of recurring units (a), (b ), and (c) is less than 100  mo! % based on the total amount of entire recurring units,  indicating the inclusion of other recurring units.  acid generator is uniformly dispersed.  In the polymer, recurring units (a) to (d) may be incorpo- rated in the following molar fraction:  OsalsO.9, Osa2sO.9, O<al+a2<1.O, preferably OsalsO.8,  Osa2sO.8, O.lsal+a2sO.8, and more preferably OsalsO.7,  Osa2sO.7, O.2sal+a2sO.7;  OsblsO.3, Osb2sO.3, Osb3sO.3, and Osb (=bl+b2+b3)sO.3;  Osc<l .O, preferably OscsO.9, and more preferably OsCsO.8;  OsdsO.5, preferably OsdsO.4, and more preferably OsdsO.3;  O.5sal +a2+bl +b2+b3+csl.O, preferably O.6sal +a2+bl +  b2+b3+csl.O,  more  preferably  O.7sal+a2+bl+b2+b3+  csl.O; and al+a2+bl+b2+b3+c+d=l.  The attachment of an acid generator to the polymer main  chain is effective in restraining acid diffusion, thereby pre› venting a reduction of resolution due to blur by acid diffusion.  Also edge roughness (LER or LWR) is improved since the  Examples of the non-nucleophilic counter ion represented  by M- include halide ions such as chloride and bromide ions;  fluoroalkylsulfonate ions such as triflate, 1,1,1-trifluoroet› hanesulfonate, and nonafluoro butanesulfonate; ary lsulfonate  ions such as tosylate, benzenesulfonate, 4-fluorobenzene› sulfonate, and 1,2,3,4,5-pentafluorobenzenesulfonate; alkyl› sulfonate ions such as mesylate and butanesulfonate; imi› dates  such  as  bis(trifluoromethylsulfonyl)imide,  bis  (perfluoroethylsulfonyl)imide  and  bis  (perfluorobutylsulfonyl)imide;  methidates  such  as  tris  (trifluoromethylsulfonyl)methide  and  tris  (perfluoroethy lsulfony l)methide.  or cyclic C 1  -C 6  alkylene group, alkenylene or phenylene  group, which may contain a carbonyl, ester, ether or hydroxyl  moiety. M- is a non-nucleophilic counter ion. Molar fractions  bl, b2 and b3 are in the range of OsblsO.3, Osb2sO.3,  Osb3sO.3, and Osbl+b2+b3sO.3.  (4) 