During the processing of substrates, the substrate surface may be subjected to a cleaning process using supercritical CO2. Surface matter may remain, for example, because it is only minimally soluble in the supercritical CO2. For example, an oxidation cleaning process causes the substrate structure to cleave at several points leaving smaller fragments of oxidized residue behind. This residue has only minimal solubility in supercritical CO2 due to the polar constituents resulting from oxidation. The method thus further includes processing the substrate with supercritical CO2 and a functionalizing agent that can react with the smaller fragments and/or other less soluble components. These functionalized components are rendered more soluble in supercritical CO2 and are more easily removed than their predecessors.