Methods and systems disclosed herein can measure thin film stacks, such as film on grating and bandgap on grating in semiconductors. For example, the thin film stack may be a 1D film stack, a 2D film on grating, or a 3D film on grating. One or more effective medium dispersion models are created for the film stack. Each effective medium dispersion model can substitute for one or more layers. A thickness of one or more layers can be determined using the effective medium dispersion based scatterometry model. In an instance, three effective medium dispersion based scatterometry models are developed and used to determine thickness of three layers in a film stack.