Temperature- and frequency-dependent optical properties of ultrathin Au films

While the optical properties of thin metal films are well understood in the visible and near-infrared range, little has been done in the midinfrared and far-infrared region. Here we investigate ultrathin gold films prepared on $\text{Si}\left(111\right)\left(7\times 7\right)$ in UHV by measuring in the frequency range between 500 and $7000{\text{cm}}^{-1}$ and for temperatures between 300 and 5 K. The nominal thickness of the gold layers ranges between one monolayer and 9 nm. The frequency and temperature dependences of the thicker films can be well described by the Drude model of a metal when taking into account classical size effects due to surface scattering. The films below the percolation threshold exhibit a nonmetallic behavior; the reflection increases with frequency and decreases with temperature. The frequency dependence can partly be described by a generalized Drude model. The temperature dependence does not follow a simple activation process. For monolayers we observe a transition between surface states around $1100{\text{cm}}^{-1}$.

Figure 1

(Color online) Frequency dependent reflectivity of thin Au films above the percolation threshold measured at various temperatures as indicated. For the 9 nm and the 5 nm thick films the optical behavior can be fitted by a Drude model when classical size effects are considered.

Figure 2

(Color online) Frequency-dependent reflectivity of thin Au-films on Si(111) at 300 K together with the corresponding fits. The 9 nm and the 5 nm films can be fitted purely by the Drude model with the parameters listed in Table . For the 3 nm and the 2 nm film an additional Lorentz oscillator at higher frequencies is needed for reasonable description.

Figure 3

(Color online) Optical conductivity of thin gold films on Si(111) obtained from reflectivity measurements on films with a thickness of $d=3$, 5, and 9 nm, as indicated. The solid lines correspond to the room-temperature data, the dotted lines to $T=5\text{K}$. In addition the bulk data (dashed dotted line) are shown as obtained from Refs. 1, 17.

Figure 4

(Color online) Total optical conductivity of a 2 nm thick Au film on Si at 300 K together with the two contributions: the Drude response of the free electrons at low frequencies and a broad Lorentz oscillator at higher frequencies.

Figure 5

(Color online) Temperature dependence of the scattering rate $\gamma =1/\left(2\pi c\tau \right)$ and resistivity $\rho =1/{\sigma }_1\left(\omega \to 0\right)$ for the 9 and 5 nm gold film. The full symbols correspond to the scattering rate (left scale), the open symbols correspond to the resistivity (right scale).

Figure 6

(Color online) Frequency dependent reflectivity of three Au films (1, 2, and 3 nm) at the percolation threshold. Note the enlarged scale compared to Fig. 1.

Figure 7

(Color online) Reflectivity for ultrathin films below the percolation threshold. Here the temperature dependence is reversed compared to metallic transport. The dash dotted line corresponds to the reflectivity of bare silicon.

Figure 8

(Color online) Conductivity spectra of ultrathin Au films as derived from reflectivity measurements (Figs. 6, 7) with a nominal thickness of 2, 1, and 0.43 nm.

Figure 9

(Color online) Arrhenius plot of the temperature dependence of the optical conductivity of a 1 nm Au film at different frequencies as indicated. No clear indication of a simple activated transport can be found.

Figure 10

(Color online) Fit of the low-frequency conductivity spectra by Eq. (3). The Lorentz contribution was subtracted to focus on the itinerant electrons. The dashed lines are the experimental data taken from Fig. 8; the solid lines correspond to the generalized Drude model which also takes backscattering into account.