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Illumination stress (IS) and negative bias under illumination stress (NBIS) cause considerable device instability in thin-film transistors based on amorphous In–Ga–Zn–O (a-IGZO). Models using in-gap states are suggested to explain device instability. Therefore, to provide reliably their density of states (DOS), this study investigated the valence band, conduction band, and in-gap states of an a-IGZO thin film. The DOS of in-gap states was directly determined in a dynamic range of six orders of magnitude through constant final state yield spectroscopy (CFS-YS) using low-energy and low-flux photons. Furthermore, light irradiation irreversibly induced extra in-gap states near the Fermi level and shifted the Fermi level to the vacuum level side, which should be related to the device instability due to IS and NBIS. Hard x-ray photoemission spectroscopy and ultraviolet photoemission spectroscopy using synchrotron radiation observed the large DOS of in-gap states near the Fermi level as in previous works. Here, we reveal that they are not intrinsic electronic states of undamaged a-IGZO, but induced by the intense measurement light of synchrotron radiation. This study demonstrates that CFS-YS is useful for determining the reliable DOS of the in-gap states for samples that are sensitive to light irradiation. The absorption spectrum measured through photothermal deflection spectroscopy is interpreted based on DOS directly determined via photoemission spectroscopies. This indicates that the line shape in the energy region below the region assigned to the Urbach tail in previous works actually roughly reflects the DOS of occupied in-gap states. [ABSTRACT FROM AUTHOR]