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The use of Coincidence Doppler-Broadened (CDB) positron annihilation spectra for surface analysis requires ensuring that a significant fraction of the annihilation signal originates from positrons annihilating at the surface. We present measurements of CDB spectra obtained using a high-purity germanium (HPGe) detector in coincidence with a sodium iodide (NaI) detector for a series of incident positron beam energies ranging from 2 eV to 20 keV on multilayer graphene (6–8 layers) on copper. The CDB data were analyzed by fitting the Doppler spectra using a linear combination of spectra derived from measured data obtained at the incident beam energies mentioned together with a Gaussian function representing the spectrum associated with para-positronium decay. These fits were used to determine the fraction of incident positrons that annihilate at the surface and in the bulk. We compare the results obtained from fitting the full Doppler-broadened spectra with those derived from a VEPFIT analysis of the S parameters as a function of beam energy, using the same set of Doppler spectra. Both approaches indicate that most annihilation events occur at the surface for beam energies below 5 keV. However, the results from full spectrum fitting suggest a significantly larger bulk annihilation fraction than VEPFIT in the 100 eV to 5 keV range, highlighting the importance of accounting for bulk contributions when using CDB for surface analysis at beam energies above 100 eV.