Mask blank substrate, mask blank, transfer mask, and method of manufacturing semiconductor device

A mask blank substrate for use in manufacturing a mask blank provided with a thin film for forming a transfer pattern on one of a pair of opposing principal surfaces of a transparent substrate,

• wherein the principal surface to which the thin film is provided has a surface shape of which, in a case where a shape fitting on a virtual reference surface is carried out and difference data between the principal surface and the virtual reference surface is obtained in a calculation region within an inner side of a circle of 90 mm diameter based on a center of a substrate, a difference between a maximum height and a minimum height within the calculation region of the difference data is λ/8 or less, provided that an exposure wavelength used for transfer is λ, and
• wherein the virtual reference surface has a shape defined by a Zernike polynomial expressed by a polar coordinate system, which is composed of only terms in which an order of a variable related to a radius is a second or lower order, and includes one or more terms in which an order of a variable related to a radius is a second order.

A mask blank provided with a thin film for forming a transfer pattern on one of a pair of opposing principal surfaces of a transparent substrate,

• wherein a surface of the thin film has a surface shape of which, in a case where a shape fitting on a virtual reference surface is carried out and difference data between the principal surface and the virtual reference surface is obtained in a calculation region within an inner side of a circle of 104 mm diameter based on a center of a substrate, a difference between a maximum height and a minimum height within the calculation region of the difference data is λ/8 or less, provided that an exposure wavelength used for transfer is λ, and
• wherein the virtual reference surface has a shape defined by a Zernike polynomial expressed by a polar coordinate system, which is composed of only terms in which an order of a variable related to a radius is a second or lower order, and includes one or more terms in which an order of a variable related to a radius is a second order.

A mask blank provided with a thin film for forming a transfer pattern on one of a pair of opposing principal surfaces of a transparent substrate,

• wherein a surface of the thin film has a surface shape of which, in a case where a shape fitting on a virtual reference surface is carried out and difference data between the principal surface and the virtual reference surface is obtained in a calculation region within an inner side of a circle of 90 mm diameter based on a center of a substrate, a difference between a maximum height and a minimum height within the calculation region of the difference data is λ/8 or less, provided that an exposure wavelength used for transfer is λ, and
• wherein the virtual reference surface has a shape defined by a Zernike polynomial expressed by a polar coordinate system, which is composed of only terms in which an order of a variable related to a radius is a second or lower order, and includes one or more terms in which an order of a variable related to a radius is a second order.

12-22. (canceled)

(canceled)