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

Abstract

Size-dependent change of the electronic band structure is one of the key features of nanoparticles in the quantum confinement region. CuFeS2 nanoparticles have a strong absorption feature in the visible region that has, controversially, been described as neither an excitonic transition nor a free carrier plasmon oscillation. Instead, the absorption feature in CuFeS2 nanoparticles has been attributed to quasi-static optical resonances from inter-band transitions between the valence band (VB), intermediate band (IB), and conduction band (CB). As such, we hypothesized that the 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 red-shifts and the optical band gap blue-shifts as the particle size decreases. Through density functional theory (DFT) and the tight binding (TB) modeling, we elucidate the size dependence of the band structure, especially focusing on the change in the IB. Using a Lorentzian oscillator optical model to simulate the absorption spectrum with inputs from the DFT-calculated band structure and band shifts from the TB model, we find that the size-dependent shifts of the optical resonance peak position in CuFeS2 are due to a tri-band quantum confinement effect that results in both the VB to IB and IB to CB gap expansion that accompanies a decrease in particle size. We also find that the transitions between the IB and CB play only a minor role in the optical spectrum. Moreover, the linear optical Lorentzian model predicts that the optical resonance peak is tunable across the visible range by partially filling the IB, lowering the CB, or expanding the IB.