Abstract: A positive resist composition comprises a polymer comprising recurring units having a sulfonium salt incorporated therein as a base resin which becomes soluble in alkaline developer under the action of acid. The polymer generates a strong sulfonic acid upon exposure to high-energy radiation so as to facilitate effective scission of acid labile groups in the resist composition.

Abstract: A chemically amplified resist composition, comprising: a resin which includes a structural unit having an acid-labile group in a side chain, a structural unit represented by the formula (I) and a structural unit having a polycyclic lactone structure, and which is soluble in an organic solvent and insoluble or poorly soluble in an alkali aqueous solution but rendered soluble in an alkali aqueous solution by the action of an acid; and an acid generator represented by the formula (II). wherein X1 represents a hydrogen atom, a C1 to C4 alkyl group, etc., Y in each occurrence independently represent a hydrogen atom or an alkyl group, and n is an integer of 1 to 14, R1 to R4 independently represent a hydrogen atom, an alkyl group, etc., and A+ represents an organic counterion, E? represents CF3SO3—, C2F5SO3—, C4F9SO3—, etc., Y1 and Y2 independently represent a fluorine atom or a C1 to C6 perfluoroalkyl group.

Abstract: Carboxyl-containing lactone compounds having formula (1) are novel wherein R1 is H, F, methyl or trifluoromethyl, R2 and R3 are H or monovalent hydrocarbon groups, or R2 and R3 may together form an aliphatic ring, W is CH2, O or S, k1 is an integer of 0 to 4, and k2 is 0 or 1. They are useful as monomers to produce polymers which are transparent to radiation?500 nm. Radiation-sensitive resist compositions comprising the polymers as base resin exhibit excellent properties including resolution, LER, pattern density dependency and exposure margin.

Abstract: A polymer obtained through copolymerization of a monomer having a hexafluoroalcohol pendant and a monomer having a hexafluoroalcohol pendant whose hydroxyl moiety has been protected is useful as an additive to a photoresist composition and as a protective coating material for immersion lithography. When processed by immersion lithography, the resist composition and protective coating composition exhibit good water repellency and water slip and produce few development defects.

Abstract: A polymerizable anion-containing sulfonium salt having formula (1) is provided wherein R1 is H, F, methyl or trifluoromethyl, R2, R3 and R4 are C1-C10 alkyl, alkenyl or oxoalkyl or C6-C18 aryl, aralkyl or aryloxoalkyl, or two of R2, R3 and R4 may bond together to form a ring with S, A is a C1-C20 organic group, and n is 0 or 1. The sulfonium salt generates a very strong sulfonic acid upon exposure to high-energy radiation. A resist composition comprising a polymer derived from the sulfonium salt is also provided.

Abstract: The present invention provides a chemically amplified resist composition comprising: a resin (A) which contains no fluorine atom and a structural unit (a1) having an acid-labile group in a side chain, a resin (B) which contains a structural unit (b2) having a fluorine-containing group in a side chain and at least one structural unit selected from the group consisting of a structural unit (b1) having an acid-labile group, a structural unit (b3) having a hydroxyl group and a structural unit (b4) having a lactone structure in a side chain, and an acid generator, wherein the amount of the resin (B) is 2 parts by weight or less per 100 parts by weight of the resin (A).

Abstract: A hydroxyl-containing monomer of formula (1) is provided wherein R1 is H, F, methyl or trifluoromethyl, R2 and R3 are monovalent C1-C15 hydrocarbon groups, or R2 and R3 may form an aliphatic ring. The monomers are useful for the synthesis of polymers which have high transparency to radiation of up to 500 nm and the effect of controlling acid diffusion so that the polymers may be used as a base resin to formulate radiation-sensitive resist compositions having a high resolution.

Abstract: Photolithography compositions and methods. A first layer of a first photoresist is formed on a substrate. A second layer of a second photoresist is formed directly onto the first layer. The second polymer of the second photoresist includes an absorbing moiety. The second layer is patternwise imaged and developed, resulting in removal of base-soluble regions. A relief pattern from the second layer remains. The relief pattern and the first layer are exposed to a second dose of the radiation. The polymer in the relief pattern absorbs a portion of the second dose. A fraction of the second dose passes through the at least one region of the relief pattern and exposes at least one region of the first layer. The relief pattern and base-soluble regions of the first layer are removed. A relief pattern from the first layer remains. A second photolithography method and a photoresist composition are also included.

Abstract: A resist composition comprises: (A) a resin capable of increasing its solubility in an alkali developer by action of an acid; (B) a compound capable of generating an acid upon irradiation with actinic ray or radiation; (C) a resin having at least one of a fluorine atom and a silicon atom; and (D) a solvent, wherein the resin (C) has a degree of molecular weight dispersion of 1.3 or less and a weight average molecular weight of 1.0×104 or less.

Abstract: The invention provides novel acid generators which are unproblematic in combustibility and accumulation inside the human body and can generate acids having high acidities and high boiling points and exhibiting properly short diffusion lengths in resist coating films and which permit the formation of resist patterns excellent smoothness with little dependence on the denseness of a mask pattern; sulfonic acids generated from the acid generators; sulfonyl halides useful as raw material in the synthesis of the acid generators; and radiation-sensitive resin compositions containing the acid generators. The acid generators have structures represented by the general formula (I), wherein R1 is a monovalent substituent such as alkoxycarbonyl, alkylsulfonyl, or alkoxysulfonyl; R2 to R4 are each hydrogen or alkyl; k is an integer of 0 or above; and n is an integer of 0 to 5.

Abstract: A positive photosensitive composition ensuring wide exposure latitude and reduced line edge roughness not only in normal exposure (dry exposure) but also in immersion exposure, a pattern forming method using the positive photosensitive composition, and a novel resin contained in the positive photosensitive composition are provided, which are a positive photosensitive composition comprising (A) a resin having a specific lactone structure in the side chain and being capable of increasing the solubility in an alkali developer by the action of an acid and (B) a compound capable of generating an acid upon irradiation with an actinic ray or radiation, a pattern forming method using the positive photosensitive composition, and a novel resin contained in the positive photosensitive composition.

Abstract: To a resist composition comprising a polymer which changes its alkali solubility under the action of an acid as a base resin, is added a copolymer comprising recurring units containing amino and recurring units containing ?-trifluoromethylhydroxy as an additive. The composition is suited for immersion lithography.

Abstract: A negative resist composition for immersion exposure including a fluorine-containing polymeric compound (F) containing a structural unit having a base dissociable group, an alkali-soluble resin component (A) excluding the fluorine-containing polymeric compound (F), an acid generator component (B) that generates acid upon exposure, and a cross-linking component (C); and a method of forming a resist pattern including applying the negative resist composition for immersion exposure to a substrate to form a resist film, subjecting the resist film to immersion exposure, and subjecting the resist film to alkali developing to form a resist pattern.

Abstract: A polymer comprising recurring units of a sulfonium salt represented by formula (1) is provided as well as a chemically amplified resist composition comprising the same. R1 is H, F, methyl or trifluoromethyl, R2 to R4 are C1-C10 alkyl or alkoxy, R5 is C1-C30 alkyl or C6-C14 aryl, k, m and n are 0 to 3. The recurring units generate a sulfonic acid upon exposure to high-energy radiation so as to facilitate effective scission of acid labile groups in the resist composition. The resist composition exhibits excellent resolution and a pattern finish with minimal LER.

Abstract: A pattern forming method includes (a) coating a substrate with a resist composition including a resin that includes a repeating unit represented by a following general formula (NGH-1), and, by the action of an acid, increases the polarity and decreases the solubility in a negative developing solution; (b) exposing; and (d) developing with a negative developing solution: wherein RNGH1 represents a hydrogen atom or an alkyl group; and RNGH2 to RNGH4 each independently represents a hydrogen atom or a hydroxyl group, provided that at least one of RNGH2 to RNGH4 represents a hydroxyl group.

Abstract: A novel resist composition and method of forming a resist pattern that can be used in lithography applications. The resist composition includes a base component (A) that exhibits changed solubility in an alkali developing solution under action of acid, and an acid generator component (B) that generates acid upon exposure, wherein the base component (A) contains a polymer compound (A1) having a structural unit (a0) represented by general formula (a0-1) shown below, wherein R1 represents a hydrogen atom, an alkyl group of 1 to 5 carbon atoms or a fluorinated alkyl group of 1 to 5 carbon atoms, R2 and R3 each independently represents a hydrogen atom or an alkyl group that may include an oxygen atom at an arbitrary position, or R2 and R3 are bonded together to form an alkylene group, and W represents a cyclic alkylene group that may include an oxygen atom at an arbitrary position.

Abstract: A positive photosensitive composition comprises: (A) a resin that has an acid decomposable repeating unit represented by formula (I) and increases its solubility in an alkali developer by action of an acid; (B) a compound that generates an acid in irradiation with actinic light or radiation; (C) a resin that has: at least one of a fluorine atom and a silicon atom; and a group selected from the group consisting of groups (x) to (z); and (D) a solvent: (x) an alkali soluble group, (y) a group which decomposes by action of an alkali developer and increases a solubility of the resin (C) in an alkali developer, and (z) a group which decomposes by action of an acid, wherein, Xa1 represents a hydrogen atom, an alkyl group, a cyano group or a halogen atom, Ry1 to Ry3 each independently represents an alkyl group or a cycloalkyl group, and at least two of Ry1 to Ry3 may be coupled to form a ring structure, and Z represents a divalent linking group.

Abstract: The present invention relates to partially fluorinated (meth)acrylic polymers that can be blended with other (meth)acrylic polymers to provide enhanced surface properties.

Abstract: A topcoat material for application on top of a photoresist material is disclosed. The topcoat material comprises an acid-inert compound. The topcoat material also comprises a polymer or an oligomer or a cage structure which shows negligible intermixing with the imaging layer and is soluble in aqueous base developer. A method of forming a patterned material layer on a substrate and a coated substrate comprising the topcoat material is also disclosed.

Abstract: A photosensitive material for use in semiconductor manufacture comprises a copolymer that includes a plurality of photoresist chains and a plurality of hydrophobic chains, each hydrophobic chain attached to the end of one of the photoresist chains. The copolymer in response to externally applied energy will self-assemble to a photoresist layer and a hydrophobic layer.

Abstract: A positive resist composition with a broad DOF and a method for resist pattern formation are provided. This composition is a positive resist composition which includes a resin component (A) that exhibits increased alkali solubility under the action of acid and an acid generator component (B) that generates acid upon exposure, wherein the component (A) is a copolymer that contains n [wherein, n is an integer from 4 to 6] structural units with mutually different structures, and the proportion of each structural unit within the copolymer is greater than 0 mol % but no higher than 100/(n?1) mol %.

Abstract: A radiation-sensitive resin composition includes a resin that includes a repeating unit shown by the following formula (1) and a solvent. The radiation-sensitive resin composition has an excellent performance as a radiation-sensitive acid generator, includes a resin that adversely affects the environment and a human body to only a small extent, and can form a resist film that has a high resolution and forms an excellent resist pattern. wherein R1 represents a hydrogen atom or the like, M+ represents a specific cation, and n represents an integer from 1 to 5.

Abstract: A positive resist composition comprises (A) a resin component which becomes soluble in an alkaline developer under the action of an acid and (B) an acid generator. The resin (A) is a polymer comprising specific recurring units, represented by formula (1). The acid generator (B) is a specific sulfonium salt compound. When processed by lithography, the composition is improved in resolution and forms a pattern with a satisfactory mask fidelity and a minimal LER. Herein R1 is H or methyl, m is 1 or 2, and n is 1 or 2.

Abstract: There is provided a positive resist composition, including a base component (A) which exhibits increased solubility in an alkali developing solution under action of an acid, and an acid generator component (B) which generates an acid upon exposure, wherein the base component (A) includes a polymeric compound (A1) containing a structural unit (a0) represented by the general formula (a0-1) shown below: (wherein, R1 represents a hydrogen atom, a lower alkyl group or a halogenated lower alkyl group; A represents a bivalent linking group; B represents a bivalent linking group; and R2 represents an acid dissociable, dissolution inhibiting group).

Abstract: A polymer compound including a structural unit (a0) represented by general formula (a0-1) shown below: wherein R1 represents a hydrogen atom, an alkyl group of 1 to 5 carbon atoms or a fluorinated alkyl group of 1 to 5 carbon atoms; R2 and R3 each independently represents a hydrogen atom, an alkyl group or an alkoxy group, or R2 and R3 may be bonded together to form an alkylene group that may include an oxygen atom or sulfur atom at an arbitrary position, —O— or —S—; R4 and R5 each independently represents a hydrogen atom, an alkyl group that may include an oxygen atom at an arbitrary position, a cycloalkyl group that may include an oxygen atom at an arbitrary position or an alkoxycarbonyl group.

Abstract: A positive resist composition comprises (A) a resin component which becomes soluble in an alkaline developer under the action of an acid and (B) an acid generator. The resin (A) is a polymer comprising specific recurring units, represented by formula (1). The acid generator (B) is a specific sulfonium salt compound. When processed by lithography, the composition is improved in resolution and forms a pattern with a minimal LER. Herein R1 is H or methyl, R2 is an acid labile group, R3 is CO2R4 when X is CH2, R3 is H or CO2R4 when X is O, R4 is a monovalent C1-C20 hydrocarbon group, and m is 1 or 2.

Abstract: A positive resist composition for electron beam, X-ray or EUV exposure, including (A) a resin capable of decomposing by the action of an acid to increase the solubility in an alkali developer; and (B) a compound capable of generating a sulfonic acid upon irradiation with an actinic ray or radiation, wherein the resin (A) is a resin having a phenolic hydroxyl group and having a weight average molecular weight of 1,500 to 3,500, the positive resist composition has a property of decomposing by the action of an acid and causing the dissolution rate in an aqueous 2.38 wt % tetramethylammonium hydroxide solution at 23° C. under normal pressure to increase in a range of 200 to 5,000 times, and the positive resist composition has a solid content concentration of from 2.5 to 4.5 mass %.

Abstract: A photosensitive polymer, the photosensitive polymer including repeating units represented by Formulae 1 to 3: wherein R1 and R3 are independently hydrogen or methyl, R2 is a C4 to C20 acid-labile group, R4 is a lactone-derived group, AR is a substituted or unsubstituted phenyl ring, or a substituted or unsubstituted aryl having from two to three fused aromatic rings, carbon CAR is bonded directly to an aromatic ring of AR, l, m, and n are positive integers, l/(l+m+n) is about 0.1 to about 0.5, m/(l+m+n) is about 0.3 to about 0.5, and n/(l+m+n) is about 0.1 to 0.4.

Abstract: A photosensitive composition comprises: (A) a compound capable of generating an acid represented by formula (I) upon irradiation with actinic ray or radiation; and (B) a resin that decomposes by the action of an acid to its increase solubility in an alkali developer wherein Ra represents an alkyl group substituted with a fluorine atom, or an aryl group substituted with a fluorine atom or a group having a fluorine atom; Rb represents an alkyl group not substituted with a fluorine atom on ?-position of the alkyl group, or an aryl group not substituted with a fluorine atom or a group having a fluorine atom.

Abstract: The present invention provides a chemically amplified positive composition comprising: (A) a resin comprising a structural unit having an acid-labile group and being itself insoluble or poorly soluble in an alkali aqueous solution but becoming soluble in an alkali aqueous solution by the action of an acid, (B) a resin comprising a structural unit represented by the formula (I): wherein R1 represents a hydrogen atom, a halogen atom, a C1-C4 alkyl group or a C1-C4 perfluoroalkyl group, Z represents a single bond or —(CH2)k—CO—X4—, k represents an integer of 1 to 4, X1, X2, X3 and X4 each independently represents an oxygen atom or a sulfur atom, m represents an integer of 1 to 3 and n represents an integer of 0 to 3, and a structural unit having a fluorine atom in a side chain, and an acid generator.

Abstract: Novel ester compounds having formulae (1) to (4) wherein A1 is a polymerizable functional group having a carbon-carbon double bond, A2 is oxygen, methylene or ethylene, R1 is a monovalent hydrocarbon group, R2 is H or a monovalent hydrocarbon group, any pair of R1 and/or R2 may form an aliphatic hydrocarbon ring, R3 is a monovalent hydrocarbon group, and n is 0 to 6 are polymerizable into polymers. Resist compositions comprising the polymers as a base resin are thermally stable and sensitive to high-energy radiation, have excellent sensitivity and resolution, and lend themselves to micropatterning with electron beam or deep-UV.

Abstract: The present invention provides a chemically amplified positive composition comprising: a resin comprising a structural unit represented by the formula (I): wherein R1 represents a hydrogen atom, a halogen atom, a C1-C4 alkyl group or a C1-C4 perfluoroalkyl group, Z represents a single bond or —(CH2)k—CO—X4—, k represents an integer of 1 to 4, X1, X2, X3 and X4 each independently represents an oxygen atom or a sulfur atom, m represents an integer of 1 to 3 and n represents an integer of 0 to 3, and an acid generator.

Abstract: A positive resist composition comprises: (A) a resin that has a repeating unit represented by general formula (a1) and increases its solubility in an alkali developer by action of an acid; (B) a compound which generates an acid upon irradiation with an actinic ray or a radiation; and (C) a resin that has at least one of a fluorine atom and a silicon atom and has a group selected from the group consisting of (x), (y) and (z); and (D) a solvent: (x) an alkali-soluble group; (y) a group capable that decomposes by action of an alkali developer to undergo an increase in a solubility of the resin (C) in an alkali developer; and (z) a group that decomposes by action of an acid, wherein R represents a hydrogen atom or a methyl group, Rxa represents an alkyl group or a cycloalkyl group, and n represents an integer of 1 to 8.

Abstract: A positive resist composition comprises (A) a resin component which becomes soluble in an alkaline developer under the action of an acid and (B) an acid generator. The resin (A) is a polymer comprising specific recurring units, represented by formula (1). The acid generator (B) is a specific sulfonium salt compound. When processed by lithography, the composition is improved in resolution and forms a pattern with a satisfactory mask fidelity and a minimal LER. Herein R1 is H or methyl, R2 is an acid labile group, R3 is CO2R4 when X is CH2, R3 is H or CO2R4 when X is O, R4 is a monovalent C1-C20 hydrocarbon group, and m is 1 or 2.

Abstract: A coating material disposed overlying a photo sensitive layer during an immersion lithography process includes a polymer that is substantially insoluble to an immersion fluid and an acid capable of neutralizing a base quencher from the photo sensitive layer.

Abstract: A curable composition, including: a polymerizable compound (a) including an ethylenically unsaturated bond; a binder polymer (b); a radical polymerization initiator (c); and an alicyclic compound (d) including a urea bond is provided.

Abstract: A resist composition includes (A) a resin including: a repeating unit capable of decomposing by the action of an acid to increase solubility in an alkali developing solution and represented by formula (I), and a repeating unit represented by formula (II); and (B) a compound capable of generating an acid upon irradiation with actinic ray or radiation: wherein A represents a hydrogen atom, an alkyl group, a hydroxyl group, an alkoxyl group, a halogen atom, a cyano group, a nitro group, an acyl group, an acyloxy group, a cycloalkyl group, an aryl group, a carboxyl group, an alkyloxycarbonyl group, an alkylcarbonyloxy group, or an aralkyl group; Ra represents a group containing a group capable of decomposing by the action of an acid; Rb represents an alkylene group, a cycloalkylene group, or a group of combining these groups; Y represents a heterocyclic group; and m represents 0 or 1.

Abstract: An image-forming method includes: exposing a negative type image-forming material including a support and an image-recording layer containing a binder polymer containing at least one group capable of being converted to a sulfonate upon a reaction with an aqueous solution containing at least one of a sulfite and a bisulfite, a sensitizing dye, a polymerization initiator, and a compound having an ethylenically unsubstituted bond; and removing an unexposed area of the image-recording layer with an aqueous solution containing at least one of a sulfite and a bisulfite.

Abstract: A positive resist composition comprises (A) a resin component which becomes soluble in an alkaline developer under the action of an acid and (B) an acid generator. The resin (A) is a polymer comprising recurring units containing a non-leaving hydroxyl group represented by formula (1) wherein R1 is H, methyl or trifluoromethyl, m is 1 or 2, and the hydroxyl group attaches to a tertiary carbon atom. The composition is improved in resolution when processed by lithography.

Abstract: Fluorinated monomers of formula (1) are useful in producing polymers for the formulation of radiation-sensitive resist compositions.

Abstract: A positive photosensitive composition comprising (A) an acid generator that generates an acid upon irradiation of an actinic ray or radiation, (B) a resin that has a monocyclic or polycyclic alicyclic hydrocarbon structure and is decomposed by the action of an acid to increase solubility in an alkali developing solution, and (C) a specific basic compound.

Abstract: The present invention provides a photosensitive resin composition comprising (a) an alkali-soluble resin, (b) a silicon compound having a secondary aromatic amino group and an alkoxy group, and (c) at least one selected from a photopolymerization initiator, a photo acid generator and a photo base generator. According to the present invention, it is possible to obtain a photosensitive resin composition which remarkably enhances the adhesion property with a substrate after curing without deteriorating storage stability of a solution, and does not cause peeling of a fine pattern even upon development.

Abstract: Provided are a positive resist composition and a resist pattern forming method having fewer defects and superior lithographic characteristics. The positive resist composition includes a resin component (A) which has on a main chain a structural unit derived from an (?-lower alkyl)acrylate ester and exhibits increased alkali solubility under the action of an acid, and an acid generating component (B) which generates the acid upon irradiation with radiation, in which the resin component (A) is a copolymer having at least two structural units which is obtained by incorporating an acid when polymerizing at least one monomer for the production thereof.

Abstract: A material for use in lithography processing includes a polymer that turns soluble to a base solution in response to reaction with acid and a plurality of magnetically amplified generators (MAGs) each having a magnetic element and each decomposing to form acid bonded with the magnetic element in response to radiation energy.

Abstract: A positive resist composition for immersion exposure including a resin component (A) which has acid dissociable, dissolution inhibiting groups and exhibits increased alkali solubility under action of acid and an acid-generator component (B) which generates acid upon exposure, the resin component (A) including a cyclic principal chain polymer (A1) and a non-cyclic principal chain polymer (A2) having a structural unit (a) derived from acrylic acid as a principal chain, and the non-cyclic principal chain polymer (A2) having a structural unit (a1) derived from an acrylate ester having an acid dissociable, dissolution inhibiting group (p1) represented by general formula (p1) shown below: wherein R1? and R2? each independently represents a hydrogen atom or an alkyl group of 1 to 5 carbon atoms; n represents an integer of 0 to 3; and Y represents an alkyl group of 1 to 5 carbon atoms or an aliphatic cyclic group of 5 to 16 carbon atoms.

Abstract: A photoresist composition for immersion lithography and a method of forming a photoresist pattern using the photoresist composition are disclosed. The photoresist composition includes a photosensitive polymer including a cycloaliphatic group blocked with at least two cyclic acetal groups as a side chain, a photoacid generator and an organic solvent. The hydrophobic photoresist composition may be changed into the hydrophilic photoresist composition by an exposure process. Thus, before the exposure process, the photoresist composition may be insoluble in a liquid for the immersion lithography. After the exposure process, an exposure portion of a photoresist film formed using the photoresist composition may be effectively dissolved in a developing solution to form a uniform photoresist pattern.

Abstract: A positive resist composition including a resin component (A) which exhibits increased alkali solubility under action of acid and an acid-generator component (B) which generates acid upon exposure, the resin component (A) including: a polymer (A1) including a structural unit (a0) represented by general formula (a0) shown below and no structural unit (a1) derived from an acrylate ester containing an acetal-type acid dissociable, dissolution inhibiting group, exclusive of the structural unit (a0), and a polymer (A2) including the structural unit (a1) and no structural unit (a0).

Abstract: Photoresist additive polymers and photoresist formulations that can be used in immersion lithography without the use of an additional topcoat. The resist compositions include a photoresist polymer, at least one photoacid generator, a solvent; and a photoresist additive polymer. Also a method of forming using photoresist formulations including photoresist additive polymers.

Abstract: A positive resist composition for immersion exposure comprising: (A) a resin having an alicyclic hydrocarbon structure, wherein the resin is capable of increasing a solubility of the resin (A) in an alkaline developer by an action of an acid; and (B) a compound capable of generating an acid upon irradiation with one of an actinic ray and radiation, wherein the resin (A) includes a component having a molecular weight of 1,000 or less in an area ration of 20% or less to an entire area in a pattern area by gel permeation chromatography, and a pattern-forming method using the same.

Abstract: A resist composition including a base resin component (A) and an acid-generator component (B) which generates acid upon exposure, the component (A) including a resin (A1) which has a structural unit (a0) represented by general formula (a-0) shown below: wherein R represents a hydrogen atom, a halogen atom, a lower alkyl group or a halogenated lower alkyl group; a represents an integer of 0 to 2; b represents an integer of 1 to 3; c represents an integer of 1 to 2; and a+b is an integer of 2 or more.