We present a finite-element-based 1-D formalism to solve the Poisson equation for a thin-film transistor with a floating body. We apply our framework to InGaZnO (IGZO)-based devices, taking into account its subgap density of states (DoS), revealing its impact on device electrostatics, which is fundamental for predicting device performance and reliability. Our simple 1-D approach yields identical results as the more computationally intensive 2-D TCAD implementations, and it enables the convenient implementation of physics-based IGZO-specific models. Finally, we apply the new framework to quantify the IGZO deep subgap DoS measured by light-assisted I – V spectroscopy.