Secondary ion mass spectrometry studies have been made of the removal of the degraded layer formed on polymeric materials when cleaning focused ion beam (FIB)-sectioned samples comprising both organic and inorganic materials with a 30-keV Ga + FIB. The degraded layer requires a higher-than-expected Ar gas cluster ion beam (GCIB) dose for its removal, and it is shown that this arises from a significant reduction in the layer sputtering yield compared with that for the undamaged polymer. Stopping and Range of Ions in Matter calculations for many FIB angles of incidence on flat polymer surfaces show the depth of the damage and of the implantation of the Ga + ions, and these are compared with the measured depth profiles for Ga + -implanted flat polymer surfaces at several angles of incidence using an Ar + GCIB. The Stopping and Range of Ions in Matter depth and the measured dose give the sputtering yield volume for this damaged and Ga +implanted layer. These, and literature yield values for Ga + damaged layers, are combined on a plot showing how the changing sputtering yield is related to the implanted Ga density for several polymer materials. This plot contains data from both the model flat poly(styrene) surfaces and FIB-milled sections showing that these 2 surfaces have the same yield reduction. The results show that the damaged and Ga + -implanted layer's sputtering rate,after FIB sectioning, is 50 to 100 times lower than for undamaged polymers and that it is this reduction in sputtering rate, rather than any development of microtopography, that causes the high Ar + GCIB dose required for cleaning these organic surfaces.