• Hall effect;
  • plasmons;
  • reflectance;
  • ZnO

The Drude equation for dielectric constant ϵ(E) depends on four parameters: ϵ, effective mass m*, optical mobility µopt, and optical carrier concentration nopt. By solving this equation at ϵ(Eres) = 0, we obtain a relationship between µopt and nopt at constant plasmonic resonance energy Eres [or wavelength λres (µm) = 1.2395/Eres (eV)]. A family of µopt versus nopt curves covering a range of λres values (including the limiting wavelength λres = ∞) constitutes a plasmonic resonance phase diagram (PRPD) for a semiconductor defined by only ϵ and m*. The PRPD is a convenient instrument that allows an immediate prediction of λres from Hall-effect measurements of µH and nH. We apply the PRPD analysis to a series of ten ZnO samples grown by pulsed laser deposition at 200 °C in an ambient of 33%H2:67%Ar and annealed in 25 °C steps for 10 min in air at various temperatures from 400 to 600 °C. For the samples annealed at 550 °C or lower, the µH/nH points yield predicted values of λres that range from 1.07 to 2.80 µm; however, the 575 and 600 °C samples are predicted to have no resonance at all. Reflectance curves for the eight samples annealed up to 550 °C decrease slowly from 6 eV down to about Eres = 0.5–1.15 eV, and then increase rapidly for E < Eres. In contrast, there is no such resonance-related increase for the 575 and 600 °C samples. Satisfactory agreement is found between the reflectance minima and the Hall-effect-predicted values of λres.