Glass substrate for mask blank, mask blank, photomask, and method for manufacturing glass substrate for mask blank

摘要

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 a_klP_k(x)P_l(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.; $$ \{\begin{array}{c}z\left(x,y\right)=\sum _{k=0}^{N_1}\sum _{l=0}^{N_2}{a}_{\mathrm{kl}}{P}_k\left(x\right)P_l\left(y\right)\\ P_k\left(x\right)=\frac{1}{2^{k}k!}\frac{d^k}{{\mathrm{dx}}^k}\left[{\left(x^2-1\right)}^k\right]\\ P_l\left(y\right)=\frac{1}{2^{i}l!}\frac{d^l}{{\mathrm{dy}}^l}\left[{\left(y^2-1\right)}^l\right]\end{array}\hspace{1em}$$