Method for producing polymer, polymer for lithography, resist composition, and method for producing substrate

1. A polymerization method, the method comprising:

(I) feeding a first solution to a reactor, wherein the feeding (I) occurs before or simultaneously with the start of a dropwise addition of a polymerization initiator to the reactor, and the first solution comprises two or more monomers α 1 to α n in a first composition ratio;

(II) feeding a second solution to the reactor, wherein the feeding (II) occurs after or simultaneously with the start of the feeding (I) of the first solution,

wherein:

n denotes an integer of 2 or more;

the monomers α 1 to α n are polymerized while the monomers α 1 to α n and the polymerization initiator are added dropwise to the reactor to obtain a copolymer comprising constitutional units α′ 1 to α′ n , wherein α′ 1 to α′ n represent constitutional units derived from the monomers α 1 to α n ;

the first composition ratio is such that the monomers α 1 to α n are reacted in a steady state based on respective reaction rates of the monomers α 1 to α n ;

when a target composition ratio (in mol %), which is represented by a constant ratio of the constitutional units α′ 1 to α′ n , of the copolymer is α′ 1 :α′ 2 : . . . :α′ n , the second solution comprises the monomers α 1 to α n having the same composition ratio as the target composition ratio, and

wherein the first composition ratio is determined by:

(i) adding dropwise at a fixed dropping rate, to a reactor containing a solvent,

a dropping solution comprising 100 parts by mass of a monomer mixture having the same monomer composition ratio as the target composition ratio, α′ 1 :α′ 2 : . . . :α′ n , the polymerization initiator; and the solvent,

wherein a composition ratio (in mol %) M 1 :M 2 : . . . :M n of the monomers α 1 to α n remaining in the reactor is calculated when a passage of time from the start of the dropwise addition is t 1 , t 2 , t 3 . . . , and t m , and a ratio (in mol %) P 1 :P 2 : . . . :P n of the constitutional units α′ 1 to α′ n of each polymer formed, between the time t 1 to the time t 2 , time t 2 to the time t 3 , . . . , and time t m to the time t m+1 is calculated;

(ii) determining a time zone from t m to t m+1 when the ratio P 1 :P 2 : . . . :P n becomes nearest to the target composition ratio α′ 1 :α′ 2 : . . . :α′ n , wherein m represents an integer of 1 or more; and

(iii) determining factors F 1 , F 2 , . . . , and F n from the value of the ratio P 1 :P 2 : . . . :P n between t m and t m+1 and the value of the composition ratio M 1 :M 2 : . . . :M n at the passage of time t m based on equations F 1 =P 1 /M 1 , F 2 =P 2 /M 2 , . . . , and F n =P n /M n , wherein:α 1 =α′ 1 /F 1 , α 2 =α′ 2 /F 2 , . . . , α n =α′ n /F n ; and

(III) feeding the polymerization initiator to the reactor,

wherein the polymerization initiator is added dropwise at a rate higher than an average feed rate Vj during a high-rate feeding period which occurs at an early stage of the polymerization,

the average feed rate Vj is defined as a value obtained by dividing a total feed amount of the polymerization initiator by a standard time,

the high-rate feeding period of the polymerization initiator is defined as a period from 0% to j %, wherein j is 5 to 20, of the standard time, and

the standard time is defined as a passage of time from a beginning of the dropwise addition of the polymerization initiator to a completion of a dropwise addition of the second solution (II).

2. The method of claim 1 , wherein:

the feeding (II), which is a dropwise addition of the second solution, is started after or simultaneously with the start of the dropwise addition of the polymerization initiator to the reactor;

α 1 :α 2 : . . . :α n represents the first composition ratio (in mol %);

the feeding of the first solution (I) is completed before 20% of the standard time passes;

the polymerization initiator is fed in an amount of 30 to 90% by mass of a total feed amount thereof during the high-rate feeding period and

the first composition ratio is determined by:

(i) adding dropwise, at a fixed dropping rate, to a reactor containing a solvent:

a dropping solution comprising 100 parts by mass of a monomer mixture having the same monomer composition ratio as the target composition ratio, α′ 1 :α′ 2 : . . . :α′ n ;

the polymerization initiator; and

the solvent,

wherein a composition (in: mol %) M 1 :M 2 : . . . :M n of the monomers α 1 to α n remaining in the reactor is calculated when a passage of time from the start of the dropwise addition is t 1 , t 2 , t 3 . . . , and t m , and a ratio (in: mol %) P 1 :P 2 : . . . :P n of the constitutional units α′ 1 to α′ n of each polymer, formed between the time t 1 to the time t 2 , between the time t 2 to the time t 3 , . . . , and between the time t m to the time t m+1 , is calculated;

(ii) determining a time zone from t m to t m+1 when the ratio P 1 :P 2 : . . . :P n becomes nearest to the target composition ratio α′ 1 :α′ 2 : . . . :α′ n , wherein m represents an integer of 1 or more; and

(iii) determining factors F 1 , F 2 , . . . , and F n from the value of the ratio P 1 :P 2 : . . . :P n between t m and t m+1 and the value of the composition ratio M 1 :M 2 : . . . :M n at the passage of time t m based on equations F 1 =P 1 /M 1 , F 2 =P 2 /M 2 , . . . , and F n =P n /M n , wherein α 1 =α′ 1 /F 1 , α 2 =α′ 2 /F 2 , . . . ,α n =α′ n /F n .

3. The method of claim 1 , wherein the rate of dropwise addition of the polymerization initiator is changed during a course of the high-rate feeding period.

4. The method of claim 1 , wherein the rate of dropwise addition of the polymerization initiator is changed after an end of the high-rate feeding period.

5. The method of claim 1 , wherein the polymerization initiator is added continuously.

6. The method of claim 1 , wherein the polymerization initiator is added intermittently.