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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.