Abstract: In a substrate for use as a mask blank including a first main surface, a normal region, a frame-shaped region and inner region are present on the first main surface. The frame-shaped region includes first to fourth corner region and first to fourth middle region. The inner region has a flatness of 100 nm or less, the flatness being determined on the basis of a least-squares plane PP1 of the normal region. When one of the corner regions is referred to as an n-th corner region and two middle regions nearest to the n-th corner region are respectively referred to as a first near middle region and a second near middle region, the specific relationship regarding the surface profile is satisfied in the n-th corner region and the first and second near middle regions.

Abstract: A glass substrate for a mask blank includes a rectangular-shaped main surface on which a film having a circuit pattern is to be formed. The main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the frame. The center area has a longitudinal length of 142 mm and a lateral length of 142 mm. A surface morphology of the center area is expressed by { z ? ( x , y ) = ? k = 0 N 1 ? ? l = 0 N 2 ? a kl ? P k ? ( x ) ? P l ? ( y ) P k ? ( x ) = 1 2 k ? k ! ? d k dx k ? [ ( x 2 - 1 ) k ] P l ? ( y ) = 1 2 l ? l ! ? d l dy l ? [ ( y 2 - 1 ) l ] . A flatness of a sum of compositing all of aklPk(x)Pl(y) is less than or equal to 20 nm when a sum of k and l is greater than or equal to 3 and less than or equal to 9. The flatness is less than or equal to 20 nm when a sum of k and l is greater than or equal to 10 and less than or equal to 30.

Abstract: A glass substrate for a mask blank includes a rectangular-shaped main surface on which a film having a circuit pattern is to be formed. The main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the frame. The center area has a longitudinal length of 142 mm and a lateral length of 142 mm. A surface morphology of the center area is expressed by the following formulas. A flatness of a sum of compositing all of aklPk(x)Pl(y) is less than or equal to 20 nm when a sum of k and l is greater than or equal to 3 and less than or equal to 9. The flatness is less than or equal to 20 nm when a sum of k and l is greater than or equal to 10 and less than or equal to 30.

Abstract: A glass substrate for a mask blank includes a rectangular-shaped main surface on which a film having a circuit pattern is to be formed. The main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the frame. The center area has a longitudinal length of 142 mm and a lateral length of 142 mm. A surface morphology of the center area is expressed by the following formulas. A flatness of a sum of compositing all of aklPk(x)Pl(y) is less than or equal to 20 nm when a sum of k and l is greater than or equal to 3 and less than or equal to 9. The flatness is less than or equal to 20 nm when a sum of k and l is greater than or equal to 10 and less than or equal to 30.

Abstract: In a substrate for use as a mask blank including a first main surface, a normal region, a frame-shaped region and inner region are present on the first main surface. The frame-shaped region includes first to fourth corner region and first to fourth middle region. The inner region has a flatness of 100 nm or less, the flatness being determined on the basis of a least-squares plane PP1 of the normal region. When one of the corner regions is referred to as an n-th corner region and two middle regions nearest to the n-th corner region are respectively referred to as a first near middle region and a second near middle region, the specific relationship regarding the surface profile is satisfied in the n-th corner region and the first and second near middle regions.

Abstract: A glass substrate for a mask blank includes a rectangular-shaped main surface on which a film having a circuit pattern is to be formed. The main surface includes a quadrangular peripheral frame and a square-shaped center area defined by excluding the frame. The center area has a longitudinal length of 142 mm and a lateral length of 142 mm. A surface morphology of the center area is expressed by { z ? ( x , y ) = ? k = 0 N 1 ? ? l = 0 N 2 ? a kl ? P k ? ( x ) ? P l ? ( y ) P k ? ( x ) = 1 2 k ? k ! ? d k dx k ? [ ( x 2 - 1 ) k ] P l ? ( y ) = 1 2 l ? l ! ? d l dy l ? [ ( y 2 - 1 ) l ] . A flatness of a sum of compositing all of aklPk(x)Pl(y) is less than or equal to 20 nm when a sum of k and l is greater than or equal to 3 and less than or equal to 9. The flatness is less than or equal to 20 nm when a sum of k and l is greater than or equal to 10 and less than or equal to 30.