Explanation of the Opposing Shifts in the Absorption Edge and the Optical Resonance in CuFeS₂ Nanoparticles

CuFeS₂ nanoparticles are novel intermediate band semiconductors that possess a prominent plasmon-like absorption feature in the visible region (~2.5 eV), giant optical nonlinearity, and have the potential for post-synthetic tuning of their absorption band. Despite having similar optical properties to other semiconductor plasmonic materials, the quasi-static optical resonance in CuFeS₂ is contributed by collective electronic transitions between filled and unfilled states rather than by a free carrier oscillation.<br/>Size-dependent change of the electronic band structure is one of the key features of nanoparticles in the quantum confinement region, but in CuFeS₂ the optical features follow divergent and conflicting trends that have yet to be explained. Namely, when the particle size decreases the optical resonance feature of CuFeS₂ shows a small redshift while the band gap blueshifts. Since the 2.5 eV absorption feature is contributed by collective electronic transition, we hypothesized that this feature should be subject to quantum confinement effects through modification of the electronic bands. In this paper, we show experimentally that the optical resonance absorption peak redshifts and the optical band gap blueshifts as the particle size decreases. Then, through density functional theory (DFT) and a tight binding modeling, we elucidate the size dependence of the band structure, especially focusing on the change in the intermediate band. Using a Lorentzian oscillator optical model to simulate the absorption spectrum with inputs from the DFT calculated band structure and band shifts from the tight binding model, we find the size-dependent shifts of the optical resonance peak position in CuFeS₂ is due to a tri-band quantum confinement effect that results in both the valence band to intermediate band and intermediate band to conduction band gap expansion that accompanies a decrease in particle size. We also find that the transitions between the intermediate band and conduction band play only a minor role in the optical spectrum. Moreover, the linear optical Lorentzian model predicts the optical resonance peak is tunable across the visible range by partially filling the intermediate band, lowering the conduction band, or expanding the intermediate band.<br/>Overall, in this study, we provide fundamental understandings about the origin of the visible quasi-static resonance in CuFeS₂ nanoparticles and elucidate the correlation between the absorption feature shift and the intermediate-band electronic structure. These results are relevant to other quantum-confined intermediate band systems, which have potential use in optical applications as well as photovoltaic devices.