Method of manufacturing a mask blank substrate, method of manufacturing a mask blank, method of manufacturing a transfer mask, and method of manufacturing a semiconductor device

A method of manufacturing a mask blank substrate, comprising:

• a preparation step of preparing a transparent substrate having a precision-polished main surface;
• a shape measurement step of measuring height information of the main surface from a reference plane at a plurality of measurement points set in an actual measurement region of the main surface, thereby obtaining a before-chucking main surface shape;
• a simulation step of obtaining, through simulation, an after-chucking main surface shape which is height information of the main surface from the reference plane at the plurality of measurement points when the transparent substrate is chucked on a mask stage of an exposure apparatus;
• an approximate curved surface calculation step of calculating, based on the after-chucking main surface shape, an approximate curved surface given by a function of several variables expressed by a three-dimensional coordinate system which is obtained by setting an X-coordinate axis and a Y-coordinate axis on the reference plane and setting a Z-coordinate axis in a direction perpendicular to the reference plane;
• a partial differential function calculation step of calculating an X partial differential function by partially differentiating the function of several variables with respect to X and calculating a Y partial differential function by partially differentiating the function of several variables with respect to Y;
• and
• a recording step of recording information of coefficients of the X partial differential function and the Y partial differential function as information of the approximate curved surface in a recording apparatus in association with the transparent substrate.

A method of manufacturing a mask blank, comprising:

• a preparation step of preparing a mask blank having a thin film on a main surface of a transparent substrate;
• a shape measurement step of measuring height information of a main surface of the mask blank from a reference plane at a plurality of measurement points set in an actual measurement region of the main surface, thereby obtaining a before-chucking main surface shape;
• a simulation step of obtaining, through simulation, an after-chucking main surface shape which is height information of the main surface from the reference plane at the plurality of measurement points when the mask blank is chucked on a mask stage of an exposure apparatus;
• an approximate curved surface calculation step of calculating an approximate curved surface based on the after-chucking main surface shape;
• and
• a recording step of recording information of the approximate curved surface in a recording apparatus in association with the mask blank.

A method of manufacturing a mask blank, comprising:

• a preparation step of preparing a mask blank having a thin film on a main surface of a transparent substrate;
• a shape measurement step of measuring height information of a main surface of the mask blank from a reference plane at a plurality of measurement points set in an actual measurement region of the main surface, thereby obtaining a before-chucking main surface shape;
• a simulation step of obtaining, through simulation, an after-chucking main surface shape which is height information of the main surface from the reference plane at the plurality of measurement points when the mask blank is chucked on a mask stage of an exposure apparatus;
• an approximate curved surface calculation step of calculating, based on the after-chucking main surface shape, an approximate curved surface given by a function of several variables expressed by a three-dimensional coordinate system which is obtained by setting an X-coordinate axis and a Y-coordinate axis on the reference plane and setting a Z-coordinate axis in a direction perpendicular to the reference plane;
• a partial differential function calculation step of calculating an X partial differential function by partially differentiating the function of several variables with respect to X and calculating a Y partial differential function by partially differentiating the function of several variables with respect to Y;
• and
• a recording step of recording information of coefficients of the X partial differential function and the Y partial differential function as information of the approximate curved surface in a recording apparatus in association with the transparent substrate.

A method of manufacturing a transfer mask, comprising:

• a preparation step of preparing a mask blank having a thin film on a main surface of a transparent substrate;
• a shape measurement step of measuring height information of a main surface of the mask blank from a reference plane at a plurality of measurement points set in an actual measurement region of the main surface, thereby obtaining a before-chucking main surface shape;
• a simulation step of obtaining, through simulation, an after-chucking main surface shape which is height information of the main surface from the reference plane at the plurality of measurement points when the mask blank is chucked on a mask stage of an exposure apparatus;
• an approximate curved surface calculation step of calculating an approximate curved surface based on the after-chucking main surface shape;
• a resist film forming step of forming a resist film on the pattern-formation thin film of the mask blank;
• a pattern correction step of correcting a transfer pattern, to be formed in the resist film, based on information of the approximate curved surface;
• and
• a resist pattern forming step of forming, in the resist film, the transfer pattern corrected in the pattern correction step.