Mask blank substrate, mask blank, and methods for manufacturing them, method for manufacturing transfer mask, and method for manufacturing semiconductor device

Abstract

The object is to provide a mask blank substrate, a mask blank, and a transfer mask which can achieve easy correction of a wavefront by a wavefront correction function of an exposure apparatus. The further object is to provide methods for manufacturing them. A virtual surface shape, which is an optically effective flat reference surface shape defined by a Zernike polynomial, is determined, wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order; and the mask blank substrate, in which difference data (PV value) between the maximum value and the minimum value of difference shape between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of two main surfaces is 25 nm or less, is selected.

1 . A mask blank substrate comprising a substrate having two opposite main surfaces,
 wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         2 . The mask blank substrate according to  claim 1 , wherein the composite surface shape is obtained by adding together a surface shape of one of the main surfaces that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the one main surface to the one main surface, and a surface shape of the other main surface that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the other main surface to the other main surface. 
     
     
         3 . The mask blank substrate according to  claim 1 , wherein the composite surface shape has a difference of 90 nm or less between the maximum height and the minimum height in an inner region of a square shape having a side of 132 mm based on the center of the substrate. 
     
     
         4 . A multi-layer reflective film coated substrate comprising:
 a multi-layer reflective film provided on the one main surface of the mask blank substrate, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         5 . A multi-layer reflective film coated substrate comprising
 a multi-layer reflective film on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the multi-layer reflective film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         6 . The multi-layer reflective film coated substrate according to  claim 5 , wherein the composite surface shape is obtained by adding together the surface shape of the multi-layer reflective film that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the multi-layer reflective film to a surface of the multi-layer reflective film, and the surface shape of the conductive film that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the conductive film to a surface of the conductive film. 
     
     
         7 . The multi-layer reflective film coated substrate according to  claim 5 , wherein the composite surface shape has a difference of 90 nm or less between the maximum height and the minimum height in an inner region of a square shape having a side of 132 mm based on the center of the substrate. 
     
     
         8 . A mask blank comprising
 a thin film for transfer pattern formation provided on the one main surface of the mask blank substrate, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   
       wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
     
     
         9 . A mask blank comprising a thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the substrate having two opposite main surfaces,
 wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   
       wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
     
     
         10 . A mask blank comprising
 a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the other main surface is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         11 . The mask blank according to  claim 10 , wherein the composite surface shape is obtained by adding together the surface shape of the thin film that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the thin film to a surface of the thin film, and the surface shape of the other main surface that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the other main surface to the other main surface. 
     
     
         12 . The mask blank according to  claim 10 , wherein the composite surface shape has a difference of 90 nm or less between the maximum height and the minimum height in an inner region of a square shape having a side of 132 mm based on the center of the substrate. 
     
     
         13 . A mask blank comprising
 a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         14 . The mask blank according to  claim 13 , wherein the composite surface shape is obtained by adding together the surface shape of the thin film that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the thin film to a surface of the thin film, and the surface shape of the conductive film that is an in-plane distribution of height from a reference surface acting as a reference for the surface shape of the conductive film to a surface of the conductive film. 
     
     
         15 . The mask blank according to  claim 13 , wherein the composite surface shape has a difference of 90 nm or less between the maximum height and the minimum height in an inner region of a square shape having a side of 132 mm based on the center of the substrate. 
     
     
         16 . The mask blank according to  claim 13 , wherein a multi-layer reflective film is provided between the one main surface and the thin film. 
     
     
         17 . A method for manufacturing a transfer mask comprising
 forming a transfer pattern in the thin film of the mask blank on the one main surface of the mask blank substrate, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         18 - 34 . (canceled) 
     
     
         35 . A method for manufacturing a semiconductor device comprising:
 placing the transfer mask manufactured by the method for manufacturing a transfer mask on a mask stage of an exposure apparatus, and   transferring a transfer pattern of the transfer mask onto a semiconductor substrate by a lithography method, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         36 . A mask blank comprising:
 a thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the multi-layer reflective film on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the multi-layer reflective film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         37 . A method for manufacturing a transfer mask comprising:
 forming a transfer pattern in the thin film of a mask blank, the mask blank comprising a thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   
       wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
     
     
         38 . A method for manufacturing a transfer mask comprising:
 forming a transfer pattern in the thin film of the mask blank, the mask blank further comprising:   a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the other main surface is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         39 . A method for manufacturing a transfer mask comprising:
 forming a transfer pattern in the thin film of the mask blank, the mask blank further comprising:   a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order   
     
     
         40 . A method for manufacturing a transfer mask comprising:
 forming a transfer pattern in a thin film of the mask blank, the thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the multi-layer reflective film on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the multi-layer reflective film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         41 . A method for manufacturing a semiconductor device comprising:
 placing the transfer mask manufactured by the method for manufacturing a transfer mask on a mask stage of an exposure apparatus, and   transferring a transfer pattern of the transfer mask onto a semiconductor substrate by a lithography method, the transfer mask forming a transfer pattern in the thin film of a mask blank, the mask blank comprising a thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the substrate having two opposite main surfaces,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing respective surface shapes of the two main surfaces is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and   wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.   
     
     
         42 . A method for manufacturing a semiconductor device comprising:
 placing the transfer mask manufactured by the method for manufacturing a transfer mask on a mask stage of an exposure apparatus, and   transferring a transfer pattern of the transfer mask onto a semiconductor substrate by a lithography method;   wherein the transfer mask is formed by a transfer pattern in the thin film of a mask blank, the mask blank further comprising:   a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the other main surface is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         43 . A method for manufacturing a semiconductor device comprising:
 placing the transfer mask manufactured by the method for manufacturing a transfer mask on a mask stage of an exposure apparatus, and   transferring a transfer pattern of the transfer mask onto a semiconductor substrate by a lithography method;   forming a transfer pattern in a thin film of the mask blank, the mask blank further comprising:   a thin film for transfer pattern formation on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the thin film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order. 
   
     
     
         44 . A method for manufacturing a semiconductor device comprising:
 placing the transfer mask manufactured by the method for manufacturing a transfer mask on a mask stage of an exposure apparatus, and   transferring a transfer pattern of the transfer mask onto a semiconductor substrate by a lithography method;   wherein the transfer mask is formed by a transfer pattern in the thin film of the mask blank a thin film for transfer pattern formation provided on the multi-layer reflective film of the multi-layer reflective film coated substrate, the multi-layer reflective film on one of two opposite main surfaces of a substrate and a conductive film on the other main surface,   wherein when the shape fitting between a virtual surface shape and a composite surface shape obtained by composing a surface shape of the multi-layer reflective film and a surface shape of the conductive film is performed in a calculation region inside a circle 104 mm in diameter based on the center of the substrate to obtain differential data, a difference between the maximum height and the minimum height within the calculation region in the differential data is 25 nm or less,   wherein the virtual surface shape has a shape defined by a Zernike polynomial expressed in a polar coordinate system, and
 wherein the Zernike polynomial is composed of only terms in which the order of variables related to a radius is second or lower order and includes one or more terms in which the order of the variables related to a radius is second-order.