2  US 7,232,640 Bl  1  POSITIVE RESIST COMPOSITION  FIELD OF THE INVENTION  BACKGROUND OF THE INVENTION  SUMMARY OF THE INVENTION  Patent Document 3 (JP-A-2002-49156) discloses the  positive photoresist composition containing a polymer  obtained by replacing phenolic hydroxyl groups of poly(p› hydroxystyrene) with acetal groups of two different kinds  and thereby giving excellent performances in terms of $_{55 }$ resolution, development defect, linearity and dry-etching  resistance.  Patent Document 2 (JP-A-4-219757) discloses the resist  composition containing a polymer obtained by replacing 20  to 70% of the phenolic hydroxyl groups in poly(p-hydroxy› styrene) with acetal groups.  The present invention relates to a positive resist compo› sition suitable for use in nanolithography processes for  manufacturing VLSI and high-capacity microchips, or other  photo-fabrication processes. More specifically, the invention  is concerned with a positive resist composition capable of  forming finer-resolution patterns by using electron beams,  X-rays or EUV rays. In particular, the invention relates to a  positive resist composition highly suitable for use in super  minute patterning for semiconductor devices by utilizing  high-energy beams, such as electron beams.  In manufacturing processes of semiconductor devices,  such as ICs and LSI circuits, fine patterning by photolithog› raphy using resist compositions has hitherto been carried  out. In recent years, demand for superfine patterning in a  submicron region or a quarter-micron region has grown as  integrated circuits have increased in packing density. In  order to meet such a demand, exposure light sources used in  photolithography have been changed to those of shorter  wavelengths, specifically from g-ray to i-ray, further to KrF  excimer laser light. In addition to photolithography using  excimer laser light, developments of lithography processes  using either electron beams, or X-rays, or EUV light are  proceeding now, too.  As resists suitable for the lithography processes using  electron beams, X-rays and EUV light, respectively, chemi- cal amplification resists utilizing acid-catalyzed reaction are  mainly used from the viewpoint of increases in sensitivity.  With respect to positive resists, chemically amplified resist  compositions whose main components are polymers having  properties of being insoluble or slightly soluble in alkaline  aqueous solutions and becoming soluble therein under the  action of acids (hereinafter referred to as acid-decomposable  resins, too) and acid generators are used effectively.  Transfer of resist techniques for KrF excimer laser to  positive resists for electron-beam lithography or X-ray  lithography have been mainly tried so far, and feasibility  thereof has been contemplated. For instance, Patent Docu› ment  1  (JP-A-2-19847) discloses the resist composition  containing  poly(p-hydroxystyrene)  whose  phenolic  hydroxyl groups are totally or partially protected by tetrahy- dropyranyl groups.  Patent Document  4  (JP-A-2002-323768) discloses the  resist composition ensuring improved line-width stability in  patterns formed under a condition that the resist coating is  left standing in vacuo after exposure.  However, the present state is that high resolution, slight  line edge roughness and in-vacuo PED (Post Exposure  Delay) characteristic requirements cannot be satisfied con› currently even by the foregoing art.  The term "line edge roughness" refers to a condition that,  owing to characteristics of a resist composition used, the  edges of the interface between each resist line pattern and a  substrate have such a shape as to fluctuate in a direction  perpendicular to the line direction. When this line pattern is  observed from the position right above, the edges look rough  (to an extent of– dozens nm). This roughness is transferred  to the substrate through an etching process, and too rough  edges cause impairment of electric characteristics and  reduce yield. Thus, the desire to improve line edge rough› ness is growing as the pattern size is reduced to a quarter  micron or below.  Further, the line-width stability of patterns formed under  a condition that the resist coating is left standing in vacuo  after exposure (in-vacuo PED) is a very important property  because exposure is carried out in vacuo when electron  beams or X-rays are used as exposure source. Inferiority of  in-vacuo PED characteristic causes great variations in resist  properties between the beginning and the end of drawing  with electron beams or X-rays; as a result, line widths of the  drawn patterns seriously lack in-plane uniformity and a  considerable reduction in yield occurs.  In addition, there is a problem that the line edge roughness  also becomes worse by leaving the resist coating standing in  vacuo.  On the other hand, the use of EUV as light source causes  a problem that the contrast is lowered by concerted photo› chemical reaction, such as positive-to-negative conversion,  ascribable to EUV light, because the wavelengths of the  light source are included in the extreme ultraviolet region  and the EUV light has high energy.  It is difficult for the combinations of hitherto known arts  to ensure both very acceptable line edge roughness and  favorable in-vacuo PED characteristic (variations in line  width and line edge roughness) under irradiation with elec› tron beams or X-rays, so it has been desired to attain  compatibility between those two performances. Addition› ally, it has also been desired to achieve both sufficiently high  sensitivity and contrast even under EUV irradiation.  [Patent Document  1]  JP-A-2-19847  [Patent Document 2] JP-A-4-219757  [Patent Document 3] JP-A-2002-49156  [Patent Document  4]  JP-A-2002-323768  An object of the invention is to solve problems of per› formance-enhancement techniques in fine patterning for  semiconductor devices by use of high-energy beams, espe› cially electron beams, X-rays or EUV light. More specifi- cally, an object of the invention is to provide a positive resist  composition capable of satisfying both requirements for  in-vacuo PED characteristic and line edge roughness when  electron beams are used as an irradiation source and having  excellent sensitivity and dissolution contrast when EUV  light is used as an irradiation source.  The following positive resist compositions responsive to  electron beams, X-rays or EUV are embodiments of the  invention.  (1)  A positive resist composition for electron-beam, X-ray  or EUV, comprising:  (a) a polymer capable of increasing its solubility in an  alkali developer under action of an acid,  wherein the polymer has repeating units represented by  formula  (I), repeating units represented by formula (II) and  repeating units represented by formula (III),  (b) a compound capable of generating an acid upon  irradiation with an actinic ray or radiation, and 