Substrate bonding apparatus

A substrate bonding apparatus, comprising:

• an upper chuck on which a first substrate is securable such that the first substrate has a downwardly parabolic surface profile;
• a lower chuck arranged under the upper chuck, a second substrate being securable on the lower chuck and the lower chuck being configured to change a shape of the second substrate from a flat profile to an upwardly parabolic profile;
• and
• a chuck controller that controls the upper chuck and the lower chuck, the chuck controller being configured to:
• generate a shape parameter for changing the shape of the second substrate to the upwardly parabolic profile from the flat profile, and
• move the upper chuck or the lower chuck to bring the first substrate into contact with the second substrate and bond the first substrate with the second substrate,
• wherein the lower chuck includes:
• a lower stage having a flat plate shape,
• a plurality of protrusions arranged on an upper surface of the lower stage and supporting the second substrate,
• a suction controller configured to apply a suction pressure to the second substrate via the plurality of protrusions to thereby secure the second substrate to the plurality of protrusions, and
• a level controller configured to control top surface levels of the plurality of protrusions.