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The disordered microscopic structure of amorphous semiconductors causes the formation of band tails in the density of states (DOS) that strongly affect charge transport properties. Such band tail properties are crucial for understanding and optimizing thin-film device performance with immense relevance for large area electronics. Among the available techniques to measure the DOS, Kelvin Probe Force Microscopy (KPFM) is exceptional as it enables precise local electronic investigations combined with microscopic imaging. However, a model to interpret KPFM spectroscopy data on amorphous semiconductors of finite thickness is lacking. To address this issue, we provide an analytical solution to the Poisson equation for a metal–insulator–semiconductor junction interacting with the atomic force microscope tip. The solution enables us to fit experimental data for semiconductors with finite thickness and to obtain DOS parameters, such as band tail width, doping density, and flat band potential. To demonstrate our method, we perform KPFM experiments on Indium–Gallium–Zinc Oxide (IGZO) thin-film transistors (IGZO-TFTs). DOS parameters compare well with values obtained with photocurrent spectroscopy. We demonstrate the relevance of the developed method by investigating the impact of ionizing radiation on DOS parameters and TFT performance. Our results provide clear evidence that the observed shift in threshold voltage is caused by static charge in the gate dielectric, leading to a shift in flat band potential. Band-tails and doping density are not affected by the radiation. The developed methodology can be easily translated to different semiconductor materials and paves the way for quantitative microscopic mapping of local DOS parameters in thin-film devices.