Thickness of sputtered layers was measured by AFM. Thickness in the initiatory stadium of deposition (sputtering time, 50 s) was determined from the SEM image of the sample cross-section. Dependence of the layer thickness on sputtering time is displayed in Figure 1. Linear dependence between sputtering time and structure thickness is evident even in the initiatory stadium of the layer growth. This finding is in contradiction with results obtained earlier for Au sputtering on polyethyleneterephtalate 25 . In that case, the initiatory stadium of the layer growth was related to a lower deposition rate.

In Figure 2, a SEM picture of the cross-section of the Au layer at its initiatory stadium of growth is shown. It is obvious that after approximately 20 s of Au deposition, flat, discrete Au islands (clusters) appear on the substrate surface. The flatness may indicate preferential growth of gold clusters in a lateral direction. When the surface coverage increases and the clusters get in close contact with each other, a coarsening sets in and becomes the dominant process. After the surface is fully covered, additional adsorption causes only the vertical layer growth, while the lateral growth is dominated by cluster boundary motion 27 .

Figure 3 shows the dependence of the sheet resistance of Au structure on the sputtering time. Precedence was given to the dependence on the sputtering time since the accuracy of AFM thickness determination is limited for short sputtering times. It is well known that a rapid decline of sheet resistance of the sputtered layer indicates a transition from the electrical discontinuous to the electrical continuous layer 28 . One can see that the most pronounced change in the sheet resistance occurs between 20 and 50 s of sputtering times, corresponding to the 5- to 10-nm range of the layer thickness. Thus, the layers with a thickness below 5 nm can be considered as discontinuous ones, while the layers with a thickness above 10 nm are definitely continuous. From the measured sheet resistance (Figure 3) and effective layer thickness, it is possible to calculate the layer resistivity R (Ω cm). One can see that the layer resistivities are about one order of magnitude higher than that reported for metallic bulk gold (R _Au = 2.5 × 10^-6 Ω cm) 29 . The higher resistivity of thin gold layers is due to the size effect, in accord with the Matthiessen rule 8 .

The temperature dependence of the sheet resistance for two particular structure thicknesses is displayed in Figure 4. One can see that the temperature dependence of the sheet resistance strongly depends on the structure thickness. For the layer about 89 nm thick, the resistance is an increasing function of the sample temperature, the behavior expected for metals. For the structure about 6 nm thick, the sheet resistance first decreases rapidly with increasing temperature, but above a temperature of about 250 K, a slight resistance increase is observed. The initial decrease and the final increase of the sheet resistance with increasing temperature are typical of semiconductors and metals, respectively. It has been referred elsewhere 4 that a small metal cluster can exhibit both metal and semiconductor characteristics just by varying the temperature. It is due to temperature-affected evolution of band gap and density of electron states in the systems containing low number of atoms. From the present experimental data, it may be concluded that for the thicknesses above 10 nm, the sputtered gold layers exhibit metal conductivity. In the thickness range from 5 to 10 nm, the semiconductor-like and metal conductivities are observed at low and high temperatures, respectively. Our further measurements showed that the layers thinner than 5 nm exhibit a semiconductive-like characteristic in the whole investigated temperature scale. Except for band gap evolution theory, typical semiconductor-like behavior may also originate from the tunneling effect of electrons through the discontinuous, separated Au clusters during electrical measurements. Since the probability of electron tunneling depends on the temperature, similarly, typical course of sheet resistance and, as will be shown later, CV characteristic may be affected right by this phenomenon.

Figure 5 displays the CV characteristics of the 5.8-nm-thick Au layer measured at room temperature [RT] and at a temperature of 90 K (LN₂). The CV curve at RT is strictly linear so that Ohm's law is valid and the layer exhibits metallic behavior. The CV curve obtained at 90 K grows exponentially so that it has a non-Ohmic characteristic typical of semiconductors. This is in a good accordance with the data of Figure 4 and the theory of band gap occurrence in metal nanostructures. While at RT the thermal excitation is big enough for electrons to overcome band gap, at 90 K, the band gap cannot be overcome. CV dependence measured at RT and 90 K on the 5.8-nm-thick Au layer confirmed former interpretation of the temperature dependence of the sheet resistence, i.e., metallic characteristic of the conductance at RT and the semiconductor one at low temperatures.

From the measurements of sheet resistance and CV characteristics result the semiconductor-like characteristic of Au at specific structure conditions (thickness, temperature). The observed semiconductor-like characteristic (decreasing resistance with increasing temperature, nonlinearity of CV characteristic) of ultrathin Au structures may originate from two undistinguishable phenomena. The first one results from a tunneling effect which occurs at discontinuous structures during resistance measurements 30 . The second one originates from the semiconductor characteristic of the intrinsic cluster itself, which occurs in metal nanostructures of sufficiently small proportions 4 . With respect to the experimental method used, it is impossible to distinguish which phenomenon prevails in prepared structures and contribute to the observed semiconductor-like behavior of Au nanostructures.

In order to investigate whether the intrinsic Au clusters forming ultrathin Au coverage exhibit semiconductor behavior, indeed we accomplished additional optical UV/Vis analysis.

Thin Au films exhibit structure-dependent UV/Vis optical spectra 28 31 32 . The localized absorption characteristic of Au films is highly sensitive to the surrounding medium, particle size, surface structure, and shape 33 . Transmission spectra from the samples with gold structures of various thicknesses are shown in Figure 6. Only the samples with the gold structure <20 nm thick, transmitting primary light beam enough, were examined. The spectra exhibit an absorption minimum around 500 nm which is slightly red-shifted with increasing film thickness. Pronounced absorption increasing at longer wavelength could be attributed to the surface plasmon resonance 34 . Discontinuous and inhomogeneous layers, with thickness ranging from 2.4 to 9.9 nm and composed of nanometer-sized metal clusters, exhibit absorption in the visible region attributed to the surface plasmon in the metal islands. The surface plasmon peak is shifted from 720 to 590 nm as the nominal layer thickness decreases from 19.5 to 2.4 nm. It is well known that optical absorption of island films of gold is a function of island density 35 . The absorption band resulting from bounded plasma resonance in the particles is shifted to longer wavelengths as the island density increases. As the thickness becomes greater, the absorption band is broadened due to a wider particle size distribution.

Evaluation of the optical spectra was performed using Film Wizard software and a Maxwell-Garnett model was applied. In this model, Au films were described as a heterogeneous mixture of material and voids. With the aim of incorporating nanosize of gold clusters for the aforementioned material, the Lorentz-Drude behavior of the optical parameters was presumed. This approximation is a generalization of both the Lorentz oscillator and the Lorentz-Drude models and includes the effect of the free carrier contribution to the dielectric function and resonant transitions between allowed states. The best fits were obtained in the case of thickness from 2 to 15 nm. Main parameter of the chosen approximation, plasma frequency, is presented in Figure 7A as a function of the film thickness. As was predicted by the theory of Mie, the red shift 36 occurs with increasing cluster size (film thickness). Additionally, it is evident that plasma frequency strongly depends on the film thickness. The plasma frequency increases with increasing layer thickness, and for thicknesses above 15 nm, it reaches typical 'bulk' value of gold, 9.02 eV. It is well known that the plasma frequency is closely related to the concentration of the free carrier 37 . From Figure 5, it can be concluded that the concentration of free carriers is an increasing function of the film thickness. This result is in good agreement with previous studies 30 . Increase of free carrier concentration with increasing nanostructure thickness is a direct evidence of the tunneling effect of electrons between isolated gold clusters 30 .

The UV/Vis spectra were also interpreted in the frame of Tauc's model 24 (see also above) and the optical band gap (E _g ^opt.) calculated as a function of the structure thickness. The E _g ^opt. as a function of the structure thickness is shown in Figure 7B. A non-zero value of E _g ^opt. was detected in the case of Au structure thicknesses ranging from 2 to 30 nm, which corresponds with the sputtering times between 4 and 150 s. Apart from electrical measurements, optical methods do not require any conductive path between separated clusters during measurement. That is why optical-based methods are able to separate the contribution of tunneling effects to the properties of Au nanostructures, which cannot be omitted during electrical measurements of discontinuous metal layers. Optically analyzed evolution of band gap thus unambiguously confirms the semiconductive characteristic of intrinsic clusters forming Au nanolayers. However, even after the electrically continuous layer is formed (sputtering time of approximately 50 s, which corresponds to a structure thickness of approximately 10 nm), which is characterized by the creation of a conductive path between isolated clusters and a rapid decline of sheet resistance (see Figures 1 and 3), there still must exist regions of separated Au clusters in deposited layer which contribute to non-zero E _g ^opt. up to the structure thickness of approximately 30 nm (see Figure 7B).

It has been published elsewhere 5 38 that the lattice parameter of metals prepared in the form of a thin layer by a physical deposition is not a material constant but depends strongly on the layer thickness. Figure 8 displays the dependence of the Au lattice parameter on layer thickness derived from the present XRD measurements. The dependence exhibits a monotonous decline of the lattice parameter with increasing layer thickness. This can be explained by the internal stress relaxation during the growth of gold clusters (see Figure 2 and 39 ).

With the aim of finding how the decline of lattice parameter influences the density of gold structures, we measured the effective thickness and the mass of deposited structures and calculated the effective density in a standard way. In Figure 8, the dependence of the density on the layer thickness is shown. The density increases with increasing layer thickness, and for about a 90-nm-thick layer, it achieves the density of bulk gold. The reduced density of thinner structures is probably due to the higher fraction of free volume in gold nanoclusters. As the gold clusters become greater 27 , the free volume fraction decreases and the gold density gradually increases. It was reported earlier 40 that gold layers with thicknesses above 100 nm prepared on glass substrate exhibit quite a uniform density, with a mean value of 19.3 g cm^-3 typical of bulk material. Theoretical Au density was calculated from the value of lattice parameter 41 .