Ultrafast Nonlinear Response of Bulk Plasmons in Highly Doped ZnO Layers

Longitudinal bulk plasmons in an $n$-doped ZnO layer system are studied by two-color femtosecond pump-probe spectroscopy in the midinfrared. The optical bulk plasmon resonance identified in linear reflectivity spectra undergoes a strong redshift and a limited broadening upon intraband excitation of electrons. The nonlinear changes of plasmon absorption decay on a time scale of 2 ps and originate from the intraband redistribution of electrons. Theoretical calculations explain the plasmon redshift by the transient increase of the ensemble-averaged electron mass and the concomitantly reduced plasma frequency in the hot electron plasma. The observed bulk plasmon nonlinearity holds strong potential for applications in plasmonics.

Figure 1

(a) Interaction geometry of $p$-polarized light with the Ga-doped ZnO layer structure. The electron density in the 100 nm thick top layer has a value of $N_e=1.0\times 10^{20}{\mathrm{cm}}^{-3}$ while the “metallic” 400 nm thick bottom layer has a value of $N_e=6.0\times 10^{20}{\mathrm{cm}}^{-3}$. The small arrows represent the electric field distribution as calculated from the Fresnel equations. (b) Linear reflectivity of the sample measured for angles of incidence of 45 deg and 54 deg. The resonance at 360 meV originates from the bulk plasmon of the top layer. The green dashed line is the pump spectrum in the femtosecond experiments. (c) Contour plot of the femtosecond pump-probe data. The change of absorbance $\mathrm{\Delta }A$ is plotted as a function of probe energy (abscissa) and pump-probe delay (ordinate). (d) Cross sections through the contour plot for fixed delay times. At early delay times, one observes a LO phonon sideband up-shifted by approximately 70 meV. (e),(f) Contour plot and spectral cuts of the calculated transient spectra.

Figure 2

Time-resolved absorption changes for the measured $\mathrm{ZnO}:\mathrm{Ga}$ plasmon and reference samples at fixed probe frequencies plotted as a function of pump-probe delay. (a) Measured transients of plasmon absorption for different incident pump fluences with $p/p$ polarization (lines). Symbols represent plasmon kinetics calculated from the theoretical model for an incident pump fluence of $1.8\mu \mathrm{J}$ and convoluted with the finite duration of the probe pulse. The inset shows the measurement geometry based on a Au-coated prism. The slightly noncollinear pump beam (not shown) is also reflected at the prism and spatially overlapped with the probe beam at the sample. (b) Measured transients with $s/s$ pump and probe polarizations. (c) Measured transients from a $\mathrm{ZnO}:\mathrm{Ga}$ monolayer ($N_{\mathrm{e}}=6\times 10^{20}{\mathrm{cm}}^{-3}$, 400 nm thick) and an undoped ZnO epilayer, $p/p$ polarization. (d) Calculated plasma temperature as a function of the delay time.

Figure 3

(a) Black, calculated reflectivity spectrum $R(\hslash \omega )$ of bulk Ga-doped ZnO with an electron concentration of $N_e=6\times 10^{20}{\mathrm{cm}}^{-3}$; green, $R(\hslash \omega )$ of the sample with the additional 100 nm thick ZnO layer [$N_e=1\times 10^{20}{\mathrm{cm}}^{-3}$, structure in Fig. 1] showing clearly its plasmon resonance at $\hslash {\omega }_p(300\mathrm{K})=360\mathrm{meV}$; red dashed line, $R(\hslash \omega )$ for a heated electron gas, i.e., $\hslash {\omega }_p(3500\mathrm{K})=320\mathrm{meV}$. The corresponding absorbance change $\mathrm{\Delta }A=-\log (T/T_0)$ (red solid line) shows the signature of a redshifted plasmon, whereas an increase of its linewidth resulted in the blue $\mathrm{\Delta }A$ curve. (b) Blue, nonparabolic band structure of ZnO at the conduction band minimum (dashed line, parabolic approximation). (c) Cold (black line, 300 K) and hot (red line, 3500 K) Fermi distributions for $N_e=1\times 10^{20}{\mathrm{cm}}^{-3}$. (d) Calculated plasma frequency ${\omega }_p(T_C)$ as a function of the carrier temperature $T_C$.