Modal analysis of resonant and non-resonant optical response in semiconductor nanowire arrays

Nanowire array solar cells have reached efficiencies where it becomes feasible to talk about creating tandem solar cells in order to achieve even higher efficiencies. An example of such a tandem solar cell could be a nanowire array embedded in a membrane and integrated on top of a Si bottom cell. Such a system, however, requires understanding and control of its interaction with light, especially to make sure that the low energy photons are transmitted to the bottom cell. The dependence of the optical response of a nanowire array on the nanowire length, diameter, array pitch, materials surrounding the nanowires, and absorption coefficient of the nanowire material is very strong and possibly resonant, indicating the complexity of the optical response. In this work, we use an eigenmode-based analysis to reveal underlying physics that gives rise to observed resonant and non-resonant behavior. First, we show that an effective refractive index can be defined at long wavelengths, where only a single mode propagates. Second, we analyze the origin of the resonant reflection when the next optical mode becomes propagating and can be 'trapped' in the array and interact with the fundamental mode. Additionally, we define two simple boundaries for the wavelength range of the resonant response: the resonances can only occur if there is more than 1 propagating mode in the array, and they disappear if the 1st diffracted order is propagating in the top or bottom material. Such resonance effects could be detrimental for tandem solar cells. We thus provide recommendations for tuning the geometry of the array and the nanowire materials in order to push the resonant regime to the absorbing regime of the nanowire, where absorption in the nanowires dampens the resonances. Finally, this work demonstrates the strength of an eigenmode-based analysis of the optical response of periodic nanostructures in terms of simplifying the analysis of a complex system.