Method for manufacturing mask blank substrate, method for manufacturing mask blank and method for manufacturing transfer mask

A method for manufacturing a mask blank by creating a transfer pattern forming thin film on a principal surface of a mask blank substrate polished using a polishing solution containing abrasive grains, the method comprising the steps of:

• preparing a mask blank substrate polished using a polishing solution containing abrasive grains, wherein the abrasive grains are chemically modified colloidal silica, or wherein the polishing solution contains colloidal silica, an additive, and alkali compound, the additive being at least one selected from the group consisting of hydroxyethyl cellulose, hydroxypropyl cellulose, polyvinyl alcohol, polyvinylpyrrolidone, and prolan;
• conducting a Catalyst Referred Etching including contacting a processing fluid that under normal conditions does not show solubility to the principal surface of the substrate, and under condition of making a processing reference surface of a catalytic surface plate to be in contact with or to be in close proximity to the principal surface, causing the substrate and the processing reference surface to move relative to each other to subject the principal surface to Catalyst Referred Etching to remove machining-affected portions of the principal surface, wherein the processing reference surface is placed above the principal surface of the substrate so as to face the principal surface, wherein the processing reference surface is formed by creating a film of catalyst on a pad including foaming resin, and wherein the machining-affected portions are generated by the polishing of the mask blank substrate;
• and
• creating a transfer pattern forming thin film wherein, after the Catalyst Referred Etching, a transfer pattern forming thin film is created on the principal surface by a sputtering method.