1：Experimental Design and Method Selection:

The study employed X-ray photoelectron spectroscopy (XPS) and photoluminescence (PL) spectroscopy to analyze defects and optical properties. Synthesis methods included wet chemistry for cubic Gd2O3 and combustion for monoclinic Gd2O

2：Sample Selection and Data Sources:

Gd2O3 nanoparticles doped with Er3+ ions at concentrations of 0%,

3：25%, 5%, and 1% were synthesized. Data were collected from XRD for structural analysis, XPS for valence band mapping, and PL spectroscopy for optical properties. List of Experimental Equipment and Materials:

Equipment included XPertPro MTD diffractometer for XRD, Thermo Scientific K-Alpha+ XPS spectrometer, McPherson VuVAS PL 1000 spectrometer with deuterium source and Janis CCS-450 cryostat, and Perkin Elmer LS-35 spectrometer with integrating sphere. Materials included gadolinium oxide, erbium dopants, nitric acid, ammonium hydroxide, glycine, urea.

4：Experimental Procedures and Operational Workflow:

Synthesis involved dissolving Gd2O3 in nitric acid, adding ammonium hydroxide, autoclaving at 140°C for 24h, centrifugation, drying at 80°C, and decomposition at 600°C for cubic phase; combustion method with gadolinium nitrate and organic fuels for monoclinic phase. XPS measurements were done under vacuum with Al Kα excitation. PL measurements used excitation and emission spectra at various temperatures.

5：Data Analysis Methods:

XPS data analyzed for valence band spectra to identify defects. PL data analyzed using Mott law and modified functions for activation energy distribution. Phonon frequencies determined from reflection spectra using Kumar's approach for indirect interband transitions.