Competition between Depletion Effects and Coupling in the Plasmon Modulation of Doped Metal Oxide Nanocrystals

Degenerately doped semiconductor nanocrystals (NCs) exhibit strong light-matter interactions due to localized surface plasmon resonance (LSPR) in the near- to mid-infrared region. Besides being readily tuned through dopant concentration introduced during synthesis, this LSPR can also be dynamically modulated by applying an external electrochemical potential. This characteristic makes these materials candidates for electro-chromic window applications. Here, using prototypical doped indium oxide NCs as a model system, we find that the extent of electrochemical modulation of LSPR frequency is governed by the depletion width and the extent of inter-NC LSPR coupling, which are indirectly controlled by the dopant density, size, and packing density of the NCs. The depletion layer is a near-surface region with a sharply reduced free carrier population that occurs whenever the surface potential lies below the Fermi level. Changes in the depletion width under applied bias substantially control the spectral modulation of the LSPR of individual NCs and also modify the inter-NC LSPR coupling, which additionally modulates the LSPR absorption on the NC film scale. Here, we show that both of these effects must be considered primary factors in determining the extent of LSPR frequency modulation and that the dominant factor depends on NC size. For a constant doping concentration, depletion effects govern LSPR modulation for smaller NCs, while LSPR coupling is prevalent in larger NCs. Consequently, as the size of the NCs is increased while keeping the doping concentration constant, we observe a reversal in the sign of the LSPR frequency modulation from positive to negative.