(ARL-6)  -continued  US 10,175,578 B2  101  102  (ARL-7)  an initiator in a solvent and heating the solution, thereby  carrying out the polymerization, and a dropwise-addition  polymerization method of adding dropwise a solution con› taining monomer species and an initiator to a heated solvent  for 1 to 10 hours, with the dropwise-addition polymerization  method being preferable. Examples of the reaction solvent  include ethers such as tetrahydrofuran, 1,4-dioxane, and  diisopropyl ether; ketones such as methyl ethyl ketone and  methyl isobutyl ketone; ester solvents such as ethyl acetate,  amide solvents such as dimethyl formamide and dimethyl  acetamide; and solvents which dissolve the composition of  the present invention, such as propylene glycol monomethyl  ether acetate, propylene glycol monomethyl ether, and  cyclohexanone.  It  is more preferable to carry out polymer› ization using the same solvent as the solvent used in the  actinic ray-sensitive or radiation-sensitive resin composition  of the present invention. Thus, generation of the particles  during storage can be suppressed.  It  is preferable that the polymerization reaction is carried  out in an inert gas atmosphere such as nitrogen and argon.  As the polymerization initiator, commercially available radi› cal initiators ( azo-based initiators, peroxides, or the like) are  used to initiate the polymerization. As the radical initiator,  an azo-based initiator is preferable, and the azo-based ini› tiator having an ester group, a cyano group, or a carboxyl  group is preferable. Preferred examples of the initiators  include azobisisobutyronitrile, azobisdimethylvaleronitrile,  and dimethyl 2,2’-azobis(2-methyl propionate). The initiator  is added or added in portionwise, depending on the pur› poses, and after completion of the reaction, the reaction  mixture is poured into a solvent, and then a desired polymer  is recovered by a method such as powder and solid recovery.  The concentration of the reactant is 5% to 50% by mass, and  preferably 10% to 30% by mass. The reaction temperature is  usually 10°  C. to 150°  C., preferably 30°  C. to 120°  C., and  more preferably 60°  C. to 100°  C.  For the purification, the same method as for a resin (C)  which will be described later can be used, and an ordinary  method such as a liquid-liquid extraction method of apply› ing water washing or combining it with an appropriate  solvent to remove the residual monomers or oligomer com› ponents; a purification method in a solution state, such as  ultrafiltration of extracting and removing only the polymers  having a molecular weight no more than a specific molecular  weight; a re-precipitation method of dropwise adding a resin  solution into a poor solvent to solidify the resin in the poor  solvent, thereby removing the residual monomers and the  like: and a purification method in a solid state, such as  cleaning of a resin slurry with a poor solvent after separation  of the slurry by filtration can be applied.  The weight-average molecular weight of the resin accord› ing to the present invention is a value in terms of polystyrene  by means of a GPC method, and is preferably 1,000 to  200,000, more preferably 1,000 to 20,000, and still more  preferably 1,000 to 15,000. By setting the weight-average  molecular weight to 1,000 to 200,000, the heat resistance  and the dry etching resistance can be prevented from being  deteriorated, and the film forming properties can be pre- vented from being deteriorated due to deteriorated develop› ability or increased viscosity.  The resin having a dispersity (molecular weight distribu› tion) in a range of usually 1 to 5, preferably 1 to 3, more  preferably 1.2 to 3.0, and particularly preferably 1.2 to 2.0  is used. As the dispersity is smaller, the resolution and the  resist shape are excellent, the side wall of the resist pattern  is smooth, and the roughness is excellent.  The  alicyclic  hydrocarbon-based acid-decomposable  resin for use in the present invention can be synthesized by  an ordinary method (for example, radical polymerization).  Examples of the general synthesis method include a batch  polymerization method of dissolving monomer species and  (In the formulae,  Rxyl  represents a hydrogen atom or a  methyl group.)  ARH-1 30  ARH-2  ARH-3  ~  HO  ~  lf+OH  HO 