8  US 7,232,640 Bl  7  chromatography (GPC) and calculated in terms of polysty› rene. The suitable Mw of the trunk polymer is from 2,000 to  200,000, particularly from 2,500 to 20,000. When the Mw is  increased beyond 200,000, the solubility becomes poor and  the resolution trends downward.  Since the line edge roughness shows a tendency to  become worse the greater dispersion degree (Mw/Mn) the  polymer has, or the higher-order multidisperse the polymer  is, with respect to the molecular weight distribution, the  suitable molecular-weight dispersion degree is from 1.0 to  3.0, preferably from 1.0 to 1.5, particularly preferably from  1.0 to 1.3.  Polymers having such small molecular-weight dispersion  degrees can be obtained by making various changes in  conditions for polymer synthesis (amounts of solvent and  initiator used for polymerization) and conditions for poly› mer refining (kind and amount of reprecipitation solvent,  and the number of times the reprecipitation operation is  performed). For instance, the molecular weight can be  controlled by properly choosing amounts of polymerization  solvent and initiator used, and the dispersion degree of  polymer can be reduced by selecting a solvent most suitable  for reprecipitation or increasing the number of times the  reprecipitation operation is repeated.  Specifically, it is preferable that a mixture of at least two  kinds of solvents is used as reprecipitation solvent or a  reprecipitation operation is carried out at least two times,  and it is far preferable that a reprecipitation operation is  repeated at least two times by using a mixture of at least two  kinds of solvents as reprecipitation solvent. Alternatively,  the intended polymer can be obtained by synthesizing poly› vinylphenol having a low degree of molecular-weight dis› persion via a living anion, living radical or living cation  polymerization method, and then making the polyvinylphe› nol undergo acetalation with alkyl vinyl ethers.  As the alkyl vinyl ethers used for acetalation reaction,  compounds represented by the following formula (A) are  suitable:  represented by formula (III) contains 20 to 80 mole %  (preferably 40 to 80 mole % ) based on the total repeating  units. Further, other repeating units may be contained in the  acid-decomposable polymer (a) as required.  The suitable ratio of the content of repeating units of 5  formula (I) to the content of repeating units of formula (II)  in the acid-decomposable polymer (a)  ((I): (II)) is from  0.10:1 to 1:0.10, preferably from 0.25:1 to 1:0.25.  The present acid-decomposable polymer (a) can be pre› pared, e.g., as follows: A polymer having phenolic hydroxyl  groups, which is preferably dissolved in an organic solvent,  is dehydrated by using a process of azeotropic distillation,  and then admixed with two or more kinds of alkyl vinyl  ether compounds and an acid catalyst to undergo acetalation  reaction: Thus, the desired acetal groups are introduced into  phenolic hydroxyl groups and the intended polymer is  obtained.  As the polymer having phenolic hydroxyl groups, poly› mers of hydroxystyrenes are suitable, and copolymers of  hydroxystyrenes and acid-decomposable (meth)acrylates 20  ( e.g. t-butyl acrylate or t-butyl methacrylate) are also usable.  For the purpose of adjusting alkali solubility of an acid› decomposable polymer (a) relating to the invention, acid› indecomposable groups can further be introduced into a  polymer  having  phenolic  hydroxyl  groups.  Suitable  examples of a method of introducing acid-indecomposable  groups include a method of copolymerizing hydroxysty› renes and styrenes, acid-indecomposable (meth)acrylates or  acid-indecomposable (meth)acrylamides, and a method of  protecting hydroxyl groups of hydroxystyrenes with acid- indecomposable substituent groups.  Suitable examples of the foregoing acid-indecomposable  substituent group include an acetyl group, a mesyl group and  a toluenesulfonyl group, but not limited to these groups.  Examples of the foregoing styrenes include styrene, chlo- rostyrene, dichlorostyrene, bromostyrene, dibromostyrene,  iodostyrene, methylstyrene, dimethylstyrene, ethylstyrene,  isopropylstyrene, methoxystyrene, ethoxystyrene, phenyl› styrene, t-butylstyrene and t-butoxystyrene. Of these sty› renes, styrene, methylstyrene, t-butylstyrene and t-butoxy- styrene are preferred in particular.  Examples of the foregoing acid-indecomposable (meth)  acrylates include methyl(meth)acrylate, ethyl (meth)acry› late, propyl(meth)acrylate, ally! (meth)acrylate, glycidyl  (meth)acrylate, benzyl (meth)acrylate and hydroxyethyl  (meth)acrylate.  Examples of acid-indecomposable (meth) acrylamides  include (meth)acrylic amide, (meth)acrylic phenylamide  and (meth)acrylic isopropylamide.  Examples of monomers which can further be copolymer- ized include maleic acid derivatives, maleic anhydride  derivatives, (meth)acrylonitrile, vinylpyrrolidone, vinylpy› ridine and vinyl acetate.  As mentioned above, it is possible to introduce copoly› merizing components and/or acid-indecomposable groups  into the polymer having phenolic hydroxyl groups within the  bounds of alkali solubility adjustment for the acid-decom› posable polymer (a) and no impairment of alkali develop› ability.  From the viewpoints of  dry  etching resistance and sensi- tivity, it is generally preferable that the hydroxystyrene  component constitutes at least 60 mole %, favorably at least  70 mole  %, based the components making up the polymer  having phenolic hydroxyl groups.  The weight average molecular weight (Mw) of the afore- mentioned trunk polymer (the polymer having phenolic  hydroxyl groups) can be measured by Gel Permeation  wherein R 1  represents an open-chain alkyl group which  may have a substituent, a cyclic alkyl group which may have  a substituent, an aryl group which may have a substituent, or  an aralkyl group which may have a substituent, and  wherein Rs and Rt each independently represents an  open-chain alkyl group which may have a substituent, a  cyclic alkyl group which may have a substituent.  The open-chain alkyl group suitable as R1, which may  have a substituent, may be a straight-chain or branched alkyl  group containing 1 to 20 carbon atoms, preferably 1 to 18  carbon atoms, with examples including a methyl group, an  ethyl group, an n-propyl group, an i-propyl group, an n-butyl  group, an i-butyl group, at-butyl group, an n-pentyl group,  an i-pentyl group, a t-pentyl group, an n-hexyl group, an  i-hexyl group, a t-hexyl group, an n-heptyl group, an i-heptyl  group, a t-heptyl group, an n-octyl group, an i-octyl group,  a t-octyl group, an n-nonyl group, an i-nonyl group, a  t-nonyl group, an n-decyl group, an i-decyl group, a t-decyl  group, an n-undecyl group, an i-undecyl group, an n-dodecyl  group, an 1-dodecyl group, an n-tridecyl group, an i-tridecyl  group, an n-tetradecyl group, an i-tetradecyl group, an  (A) 