PNNL

Abstract

Following the Drude model for dielectric constant, ?(E) = ??(E) + i???(E), the plasmonic resonance energy Eres in a semiconductor depends on four parameters: ??(?) (or ??) , effective mass m*, optical mobility µopt, and optical carrier concentration nopt. By solving the Drude equation at ?(Eres) = 0, we obtain a relationship between µopt and nopt at constant Eres [or wavelength ?res(µm) = 1.2395/Eres(eV)]. A family of µopt vs nopt curves covering a range of ?res values (including the limiting wavelength ?res = ?) constitute a plasmonic resonance phase diagram (PRPD) for a semiconductor defined by only ?? and m*. The PRPD is a convenient instrument that allows an immediate prediction of ?res from Hall-effect measurements of µH and nH. Furthermore, if the µH/nH point falls outside the family of µopt vs nopt curves, it shows that no resonance at all is possible. 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 ?C to 600 ?C. The unannealed sample had a resistivity ? = 1.67 x 10-4 ?-cm, n = 1.39 x 1021 cm-3, and µ = 26.8 cm2/V-s, and the 600-?C sample, ? = 1.52 ?-cm, n = 5.03 x 1017 cm-3, and µ = 8.2 cm2/V-s. Each of the ten µH/nH points was plotted on the PRPD. For the samples that were annealed at 550 ?C or lower, the µH/nH points yielded predicted values of ?res that ranged from 1.07 to 2.80 µm, respectively; however, the 575-?C and 600-?C samples were predicted to have no resonances at all. Reflectance curves for the eight samples annealed up to 550 ?C de-creased slowly from 6 eV down to about 1 eV, and then increased rapidly at an energy evidently close to Eres. In contrast, there was no such increase for the 575-?C and 600-?C samples, and thus presumably, no resonance. Satisfactory agreement is found between the reflectance and Hall-effect-predicted values of ?res.