  Amorphous oxide semiconductors are receiving significant attention due to
their relevance for large area electronics. Their disordered microscopic
structure causes the formation of band tails in the density of states (DOS)
that strongly affect charge transport properties. Bandtail properties are
crucial to understand for optimizing thin film device performance. Among the
available techniques to measure the DOS, 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's equation for a
metal-insulator-semiconductor (MIS) junction interacting with the AFM tip. The
solution enables us to fit experimental data for semiconductors with finite
thickness and obtain the DOS parameters, such as band tail width (E_t), doping
density (N_D), 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 to values obtained with photocurrent
spectroscopy. We demonstrate the potentials 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 towards quantitative
microscopic mapping of local DOS parameters in thin film devices.
