# Electrical conduction and noise spectroscopy of sodium-alginate gold-covered ultrathin films for flexible green electronics

### Electric transport and noise properties near the non-metallic threshold

As already mentioned, commercially available biopolymers, even if widely used and studied in various fields ranging from packaging to medicine, are poorly investigated in electronics and in particular as innovative green substrates. In this respect, a comparison of SA with a traditional material such as polymethyl-methacrylate (PMMA), whose properties and applications in electronic devices are well-known, can provide interesting information.

Figure 1 shows the temperature dependence of the measured resistance R(T) for SA and PMMA films covered with a 4.5 nm-thick Au layer, representing the previously studied threshold between a non-metallic (below) and a metallic (above) behavior16. Both for a free-standing SA film (Fig. 1a) and SA or PMMA films spin-coated on glass (Fig. 1b,c), similar R(T) curves are observed in the whole range from 300 down to 10 K. More in details, a resistance increase by lowering the temperature is always found below 100 K, while an evident peak, more pronounced for SA films, occurs in a region around 200 K. At 300 K, a rough estimation of the gold layer sheet resistance, made on the unpatterned samples deposited on glass, gives values of ~ 37 Ω/sq for PMMA and of ~ 19 Ω/sq for SA, which are in a good agreement with those of gold nanostructures sputtered on glass20 and on other transparent polymers21.

These results confirm the general framework of the transport mechanisms already reported in literature, described in terms of a fluctuation-induced tunneling process at low temperatures22 and of a conductive region expansion from 300 to 200 K16. However, whether the few differences found in the R(T) curves are related to the role played by the presence of water, whose effect could be different depending on the polymeric matrix considered (PMMA or SA), is the interesting question to unravel. Therefore, in order to extract more information on the conduction mechanisms in working conditions, a more sensitive investigation has been performed by studying the charge carriers fluctuations, using the well-known electric noise spectroscopy technique.

In this type of noise characterizations, the main information is essentially given by the voltage-spectral density function SV and, more in details, by analyzing its amplitude frequency dependence. For the samples here investigated, the best fitting procedure of the spectral traces can be obtained by using a generic expression in the form of

$$S_{V} (f) = \frac{K}{{f^{\gamma } }} + S_{0}$$

(1)

Here, γ is the noise frequency exponent, S0 is a frequency-independent term, while K is the noise amplitude coefficient whose study as a function of external parameters, such as temperature and bias current, allows establishing correlations and relationships with physical properties of the system involved23,24. The green curves in Fig. 2 show a good agreement between Eq. (1) and the experimental noise spectra, both for PMMA (left panel) and SA (right panel) Au coated films in the whole temperature range. As result of the data analysis, varying the temperature from 300 to 10 K, the exponent γ ranges in the interval between 1.2 and 1.4 on both the investigated substrates. This suggests a small number N of active fluctuators as responsible for the noise mechanisms23,25,26. In fact, a large number of Lorentzian fluctuators (N → ∞) would generate a pure 1/f noise component with γ values ranging from 0.8 to 1.223,27,28. The constant term S0 is the “white-noise” component that essentially consists in the Johnson thermal noise (4kBTR) added to a background contribution. Due to the small resistance values measured both for PMMA and for SA films, S0 corresponds to the voltage-spectral density of the experimental setup electronic chain, being ~ 1 × 10−18 V2/Hz. The noise amplitude coefficient K, moreover, can be studied as a function of the applied bias current I, always revealing a quadratic behavior in the whole tested temperature range, as shown in Fig. 3. This is the expected standard behavior when the noise processes are originated by resistivity fluctuations in a random resistance network28,29.

Starting from the quadratic current dependence of K, it is straightforward to evaluate the Noise Level (NL) of Ohmic systems as23

$$NL = \frac{K}{{V^{2} }} = \frac{K}{{R^{2} I^{2} }},$$

(2)

being V the measured DC voltage. As evidenced in Fig. 4, a clear NL peak occurs in the temperature region where an upturn of the resistance is observed. This happens around 128 K for PMMA (green square) and around 112 K for SA (yellow circle). The presence of a peak in the noise level amplitude is usually associated to a change in the electric transport mechanisms30,31,32,33.

The transition to a typical non-metallic transport is confirmed by the increase of the normalized resistance R/R300K below 100 K for Au film thickness ≤ 4.5 nm. A comparison between the behavior on PMMA and SA shows minor differences indicating a minor role of the substrate composition on the Au growth. The ultrathin film can be regarded as a network of discontinuous metal regions instead of a continuous layer15, whose morphology does not depend on PMMA or SA and results in the specific non-metallic features observed. From a technological point of view, the results of fluctuations spectroscopy give the indication of low NL values in the low-temperature region, as expected because of the low charge carriers mobility. Moreover, similar low NL values are observed even at high temperatures, in the range of a typical device use. This last feature, very interesting for the development of room-temperature applications, is clearly evident in Fig. 5 three-dimensional graphs of the amplitude parameter K, both for PMMA (left panel) and SA (right panel). Notice that, while the general behavior of PMMA and SA spin-coated films is similar, the effect of the fluctuation processes on the room temperature electric noise is lower on SA than PMMA, thanks to the peak of NL shifted toward a lower temperature value in SA (see Figs. 4 and 5, for details). This results in another advantage of SA over PMMA, in addition to the flexibility and the non-fossil-oil origin.

### Electric transport and noise properties above the metallic threshold

The evidence of a NL peak, observed in the presence of a non-metallic conduction, completely disappears when the electric transport mechanisms change. In particular, increasing the thickness of the sputtered Au above 4.5 nm, a more metallic behavior is recovered as shown in Fig. 6 for a free-standing SA film covered with a 5 nm-thick Au layer. After a first thermal cycle (black squares, acquired in cooling mode) the polymeric matrix settles (red circles, acquired in warming mode), becoming more stable during the second thermal cycle (blue stars, acquired in cooling mode) and for all the subsequent thermal cyclic tests performed (green triangles, acquired in cooling mode). It is evident that no hysteretic effect occurs, as observed in the whole set of compounds investigated. It is important to underline that, using Au pads (60 nm-thick, deposited onto the sample surface) for the electrical connections, the measurements are usually characterized by strong stability and repeatability. Signs of instability and non-repeatability are, instead, visible in absence of Au pads, as shown in Supplementary Fig. S1 where experimental data taken on Au sputtered SA films with (red diamonds) and without (black circle) Au pads are compared.

Therefore, it is clear that a well-defined geometry of the contact pads allows an accurate evaluation of the intrinsic noise, as evidenced in Fig. 7 for a typical metallized SA free-standing film (Au thickness of 5 nm). More in details, the 1/f noise amplitude shows a decrease by lowering the temperature (see the two-dimensional plot of Fig. 7a). The reduction of K is usually expected in the case of metals, together with a quadratic current dependence of the 1/f noise component23,27, as shown in the three-dimensional plot of Fig. 7b, which can be attributed to random resistance fluctuations.

From the literature it is known that this type of fluctuation processes, for metal or bad-metal compounds, is characterized by a noise level reduction for decreasing temperature34,35. This behavior is shown in Fig. 8 for all the PMMA and SA samples covered with a 5 nm-thick Au layer, both for free-standing and spin-coated films, whose typical metallic conduction is verified in Fig. 8a in terms of the normalized resistance R/R300K. In particular, Fig. 8b clearly evidences a monotonic decrease of NL moving from 300 to 10 K. One possible explanation for the observed noise temperature dependence can be found in a theoretical model which ascribes the origin of resistance fluctuations to vacancy and interstitial diffusion27,36, as already reported for granular and polycrystalline systems37,38. This finding gives an indication that above a certain Au layer thickness, here identified in 4.5 nm, the conducting regions forming the ultrathin films are more uniformly distributed and interconnected, despite the possible presence of structural defects at the points of their closest distance.

From the point of view of applications, also in the case of metallic films as already discussed for non-metallic samples, it is important to stress that the intrinsic noise level is very low and has a weak dependence on the type of substrate used for the device fabrication. As a matter of fact, the free-standing foils seems to generally have a lower NL value compared to the compounds on glass, resulting very promising in the development of a flexible “green electronics”.

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