Polymer for resist under layer film composition, resist under layer film composition, and patterning process

A polymer for a resist under layer film composition, comprising a repeating unit shown by the formula (1) and a repeating unit shown by the formula (3),

• wherein R01 independently represents a hydrogen atom or a methyl group;
• R02 represents a group selected from the formulae (1-1) to (1-3);
• R03 represents a saturated or unsaturated tertiary alkyl group having 4 to 20 carbon atoms and optionally containing a group selected from a cyclic ether group, an ether group, a hydroxy group, or an aromatic heterocyclic oxygen containing ring;
• and A2 represents a single bond or a divalent linking group having 2 to 10 carbon atoms and containing an ester group,
• wherein the dotted line represents a bonding arm,
• wherein the repeating unit shown by the formula (3) is a repeating unit shown by the formula (3-1)
• wherein R01 and R03 have the same meanings as above;
• n represents an integer of 1 to 5, and
• the polymer for a resist under layer film composition further comprises a repeating unit shown by the formula (2),
• wherein R01 has the same meaning as above;
• A1 represents a single bond, an ester group, or a divalent linking group having 2 to 10 carbon atoms and containing an ester group;
• Ar1 represents a substituted or unsubstituted aryl group having 6 to 20 carbon atoms.