Ultrathin solar cells can be a path forward to low-cost photovoltaics due to their reduced material consumption and shorter required deposition times. With excellent surface passivation, such devices may feature higher open-circuit voltages (VOC). However, their short-circuit current density (JSC) may be reduced due to decreased light absorption. This mandates implementation of efficient light-trapping structures. To design efficient ultrathin solar cells that combine surface-passivation and light-trapping features, accurate 3-D modeling is necessary. To this end, a novel 3-D optoelectrical finite-element model is developed to analyze the performance of ultrathin solar cells. The model is applied to the case of ultrathin (<500 nm) chalcogenide solar cells (copper indium gallium (di) selenide, CIGSe), rear-passivated with nanostructured Al2O3 to circumvent optical and electrical losses. It is found that such a nanopatterned dielectric passivation scheme enhances broadband light-trapping with reduced rear-surface recombination, resulting in an absolute power conversion efficiency enhancement of 3.9%, compared to cells without passivation structure. Overall, the work shows how 3-D finite element modeling can aid in analyzing and developing new optical and electrical solar cell designs for ultrathin solar cells such as those based on chalcogenides and perovskites.