Urbach rule behavior in strongly absorbing fine particle solids

Abstract

The intrinsic absorption spectrum α(E) of fine particles (<0.2 μm) of PbCrO4, BiVO4, CdS, and ZnS, respectively, was measured in the vicinity of the visible absorption edge from 20 to 300 K by diffuse reflectance. In PbCrO4 and in isoelectronic BiVO4, the edge is exponential and steepens, while remaining fixed in energy, as T is reduced. The edge fits the Urbach behavior: σ=dlnα/dE=(2σ0/ℏΩ0) tanh (ℏΩ 0/2 kBT), where σ0 and Ω0 are constants and σ≂80 eV−1 at 300 K. We find ℏΩ0=25×10−3 eV in PbCrO4, nearly coinciding with the 23×10−3 eV vibration observed in natural crocoite. For the exponential edge in single crystal CdS, σ≂80 eV−1 at 300 K and also increases at low T. However, the edge shifts to higher energy at low T. In fine particles of pure CdS, the energy shift was again found, but σ≂20 eV−1, independent of T. This suggests that in pigmentary CdS, σ is controlled by extrinsic factors such as defects. It behaves as a compensated semiconductor in which color arises from a transition between delocalized states. ZnS behaves similarly. The intrinsic nature of edge broadening in fine particle PbCrO4 and BiVO4 may result from the electronically isolated nature of the chromophore in these solids, wherein the color probably results from a charge transfer transition between localized states.