Mask blank transparent substrate manufacturing method, mask blank manufacturing method, and exposure mask manufacturing method

A method of manufacturing a semiconductor device, comprising the steps of:

• setting an exposure mask having a thin film pattern formed on a main surface of a transparent substrate on an operating exposure apparatus;
• and
• transferring the thin film pattern of the exposure mask to a resist film formed on a semiconductor substrate;
• wherein the transparent substrate of the exposure mask has a precision-polished main surface, and
• wherein with respect to the transparent substrate of the exposure mask,
• height information from a reference plane at a plurality of measurement points provided in a predetermined region on the main surface of the transparent substrate that contacts a mask stage of an exposure apparatus has been obtained as surface shape information of the main surface,
• height information from the reference plane at the plurality of measurement points where the transparent substrate is set in the exposure apparatus has been simulated based on the surface shape information and shape information of the mask stage including a region where the mask stage contacts the main surface of the transparent substrate,
• a difference between a maximum value and a minimum value in a predetermined region including a transfer region of the exposure mask has been derived based on the simulated height information from the reference plane to thereby obtain a flatness of the transparent substrate when the transparent substrate is set in the exposure apparatus,
• the flatness has been judged to satisfy a specification, and
• the simulated height information has been determined based upon a deflection differential equation in mechanics of materials, the deflection differential equation comprising at least (1) the height information as the surface shape information, (2) a warp of the transparent substrate along an X-direction with respect to the mask stage as fulcrums, and (3) a deflection of the transparent substrate along the X-direction due to gravity, the X-direction being a direction perpendicular to a longitudinal direction of the mask stage.

A method of manufacturing a semiconductor device, comprising the steps of:

• setting an exposure mask having a mask pattern on an operating exposure apparatus, the exposure mask comprising a transparent substrate;
• and
• transferring the mask pattern of the exposure mask to a resist film formed on a semiconductor substrate;
• wherein the transparent substrate of the exposure mask has a precision-polished main surface, and
• wherein with respect to the transparent substrate of the exposure mask,
• height information from a reference plane at a plurality of measurement points provided in a predetermined region on the main surface of the transparent substrate that contacts a mask stage of an exposure apparatus has been obtained as surface shape information of the main surface,
• height information from the reference plane at the plurality of measurement points where the transparent substrate is set in the exposure apparatus has been simulated based on the surface shape information and shape information of the mask stage including a region where the mask stage contacts the main surface of the transparent substrate,
• a difference between a maximum value and a minimum value in a predetermined region including a transfer region of the exposure mask has been derived based on the simulated height information from the reference plane to thereby obtain a flatness of the transparent substrate when the transparent substrate is set in the exposure apparatus,
• the flatness has been judged to satisfy a specification, and
• the simulated height information has been determined based upon a deflection differential equation in mechanics of materials, the deflection differential equation comprising at least (1) the height information as the surface shape information, (2) a warp of the transparent substrate along an X-direction with respect to the mask stage as fulcrums, and (3) a deflection of the transparent substrate along the X-direction due to gravity, the X-direction being a direction perpendicular to a longitudinal direction of the mask stage.