We have performed a detailed study of Cu $2p$ core-level spectra in single layer La$_{2-x}$Sr$_{x}$CuO$_{4}$, La doped Bi$_2$Sr$_{1.6}$La$_{0.4}$CuO$_{6+delta}$ (Bi2201) and bilayer Bi$_2$Sr$_{2}$CaCu$_{2}$O$_{8+delta}$ (Bi2212) high-temperature superconductors by using hard x-ray photoemission (HX-PES). We identify the Cu$^{2+}$ derived (i) the Zhang-Rice singlet (ZRS) feature, (ii) the $d^{n+1}underline{L}$ (ligand screened) feature, (iii) the $d^{n}$ satellite feature, as well as the hole-doping derived high binding energy feature in the main peak. In Bi-based cuprates, intensities of the $d^{n}$ satellite features seem to be strongly enhanced compared to La$_{2-x}$Sr$_{x}$CuO$_{4}$. From x-ray photon energy dependent measurements, it is shown that the increased intensity in the satellite region is associated with Bi $4s$ core-level spectral intensity. The corrected $d^{n}$ satellite intensity is independent of the doping content or number of Cu-O layers. Our results suggest a correlation of the relative intensity of ZRS feature and hole-doping induced high binding energy spectral changes in the main peak with superconductivity.
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