Compact, on-chip spectrometers exploiting tailored disorder for broadband light scattering enable high-resolution signal analysis while maintaining a small device footprint. Due to multiple scattering events of light in the disordered medium, the effective path length of the device is significantly enhanced. Here, on-chip spectrometers are realized for visible and near-infrared wavelengths by combining an efficient broadband fiber-to-chip coupling approach with a scattering area in a broadband transparent silicon nitride waveguiding structure. Air holes etched into a structured silicon nitride slab terminated with multiple waveguides enable multipath light scattering in a diffusive regime. Spectral-to-spatial mapping is performed by determining the transmission matrix at the waveguide outputs,
which is then used to reconstruct the probe signals. Direct comparison with theoretical analyses shows that such devices can be used for high-resolution spectroscopy from the visible up to the telecom wavelength regime.