Simultaneous Seebeck coefficient and resistivity measurements were performed in four contact set-up using LSR-3 (Linseis Messgeraete GmbH, Selb, Germany), at a temperature ranging from 323–723 K. Thermal diffusivity (D) was measured using a LFA-500 (Linseis Messgeraete GmbH, Selb, Germany), equipped with a xenon-flash lamp over a temperature range of 323–723 K. Seebeck and resistivity measurements were performed under an He atmosphere (0.1 bar). However, the diffusivity was measured under a vacuum (~10−3 bar).

After the TE measurements, morphological images of the selected area electron diffraction (SAED) were collected on powder produced by crushing the sample pellets, and EDX spectroscopy was performed using transmission electron microscopy (TEM; HR-S/TEM ThermoFischer TALOS 200 s, Thermo Fischer Scientific, Waltham, MA, USA). Moreover, morphological images and EDX data were collected on pellet samples to investigate the microstructure and bulk chemistry using a Jeol IT300 scanning electron microscope (SEM) equipped with a tungsten source (Jeol, Ltd., Tokyo, Japan).

**Table 1.** Quantitative phase and average crystallite size before and after TE measurements, measured densities, and relative densities.

#### **3. Results and Discussions**

XRD measurements were performed on all of the polycrystalline samples (Figure 1). The diffraction patterns showed fingerprint peaks at *2θ*~28.5◦, 47.3◦, and 56.0◦, and *2θ* ~33.2◦, 55.5◦, and 66.3◦ using Cu *Kα* and Co *Kα* X-ray sources, respectively. These Bragg peaks represent planes (1 1 1), (2 2 0), and (3 1 1), respectively, confirming the disordered cubic CTS structure, which is derived from the zinc-blende structure (SG: *F*-43*m*). A small amount of WC (SG: *P-6m2*) is present in all of the samples due to the use of WC vials for milling. Additionally, a weak peak (*2θ* ~27◦) of SnO2 (SG: *P*42*mnm*) was observed in the pattern of sample TS1 (see Figure S2). XRD patterns of all the ODP sintered samples also showed Bragg peaks representing the disordered cubic CTS phase. Nevertheless, small amounts of WC and SnO/SnO2 phases were also observed in some ODP sintered samples.

Different crystallographic phases were identified, and their respective weight fractions were obtained by the Rietveld method [36,39]. Information provided by powder pattern refinements, including the average crystallite size, is reported in Table 1. The lattice parameters for all the samples are *a* = 5.43 ± 0.01 Å and *α* = *β* = *γ* = 90◦. The average crystallite size for samples TS1, TS2, and TS3 is 40 ± 10, 75 ± 10, and 70 ± 10 nm, respectively. All the samples have a ~1–2% weight of WC. Additionally, sample TS1 has a small quantity (~2% weight) of SnO2, which is possibly formed due to open environment processing. We did not observe the formation of secondary phase oxides in samples TS2 and TS3, produced in a strictly controlled environment. ODP, like spark plasma sintering (SPS), is a fast-sintering technique needing a short sintering time and applying external pressure. The applied pressure during ODP decreases the sintering temperature and time, simultaneously

improving the densification kinetics. Thus, the crystalline domains show limited growth, while reaching full densification. The average domain sizes for the ODP1, ODP2, and ODP3 samples are 42 ± 10, 54 ± 10, and 64 ± 10 nm, respectively. In our recent work, we showed that SPS on as-milled CTS powder can constrain the grain growth below 50 nm [40].

**Figure 1.** XRD data before and after repeated TE measurements on TS and ODP sintered samples. The difference in diffuse background and shifts in Bragg peaks between TS and ODP samples is due to the use of different diffractometers equipped with Cu *Kα* (*λ* = 1.5406 Å) and Co *Kα* (*λ* = 1.7889 Å) sources, respectively. Rietveld refinement on the XRD data with marked phases is shown in Figure S2.

After the repeated TE measurements (discussed in the next section), the XRD data were collected for the second time. All TS samples showed an increase in the weight fraction of SnO2. Samples TS2 and TS3 showed the formation of a new secondary phase, SnO (SG: *Pnm*21), possibly due to an oxygen-deficient production environment. We also observed the presence of SnS (SG: *Pbmn*) in sample TS1, confirming the chemical instability of the sample prepared in an open environment. Samples sintered using ODP were less prone to growth in the secondary phases. We did not observe any grain growth or increase in the weight fraction of secondary phases for ODP1 and ODP2. The applied pressure during sintering seems to better stabilize the samples than traditional sintering. Nevertheless, an increased amount of SnO2 was observed for ODP3, due to its extended sintering time in comparison to ODP2. The densities of ODP3 and ODP2 samples are similar, in spite of the different sintering times of 30 and 10 min, respectively. Therefore, the densification was complete within ~10 min of sintering. Furthermore, extended sintering mainly promotes phase degradation, leading to the formation of SnO2.

As discussed in the Introduction, the loss of nanostructure has adverse effects on the TE properties of the material, which could drive it towards instability. The average crystalline size for the TS1 sample increased from 40 ± 10 to 75 ± 10 nm after repeated TE measurements, whereas samples TS2 and TS3 did not lose their nanostructure, maintaining their average crystallite size of 75 ± 10 and 70 ± 10 nm, respectively. Similarly, the ODP sintered samples maintained their average domain size of 42 ± 10, 54 ± 10, and 68 ± 10 nm for ODP1, ODP2, and ODP3 samples, respectively, after repeated TE measurements.

SEM micrographs at different magnifications collected on TS and ODP sintered sample surfaces are shown in Figure 2. The difference between the two samples is noticeable. Morphological images of the bulk TS samples (Figure 2a,b) reveal an uneven topology and the presence of microscopic pores. As expected, the ODP sintered samples (Figure 2c,d) had a lower porosity compared to TS, with intact grains. It is also evident through the density measurements that the ODP sintered samples were ~20% denser than TS. Here, it is worth mentioning that similar samples sintered via SPS showed almost no porosity and the density was slightly (~2–4%) higher than the ODP sintered samples (morphological images of SPS sintered samples are shown in Figure S3) [40].

The morphological image and SAED using TEM on TS1, shown in Figure S4 (right bottom inset), reveals many small (d~10 nm) grains surrounding the bigger (CTS) grains. EDX was performed, focusing on the surrounding small dark grains. Strong peaks of oxygen and tin can be observed in the EDX spectra of TS1, and the atomic fraction was found to be oxygen and tin-rich (see Table 2), suggesting that these are SnO2 grains, as we observed from the XRD. The evolution of SnO2 grains makes the sample unstable during TE measurements by unbalancing the stoichiometry. For samples TS2 and TS3, no SnO2/SnO grains appeared in the micrographs, although a weak peak for oxygen could be observed by EDX. The chemical composition for the TS2 sample was copper-rich, whereas, for the sulfurized sample (TS3), the stoichiometry was close to the theoretical (see Table 2).

**Table 2.** Atomic fraction for samples TS1, TS2, and TS3 estimated from the TEM-EDX analysis (corresponding EDX spectra are shown in Figure S4).

SEM-EDX analysis was performed on the ODP sintered samples, including chemical maps on large ODP samples to investigate the overall chemical homogeneity. As discussed in the Experimental Methods, ODP was performed on a large quantity (30–40 g) of ballmilled powder, producing large samples (see Figure S1). The SEM chemical maps (shown in Figure 3) revealed non-homogeneous chemistry on the surfaces of the ODP sintered samples. As ODP is a fast-sintering technique and was performed on a large quantity of materials, variations in chemical composition are likely. However, the overall chemistry of the samples was close to theoretical (shown in Table 3). On the contrary, the SPS sintered samples produced in our past work showed a homogeneous chemical distribution and comparatively lower crystalline domain size [40].

**Figure 2.** SEM micrographs collected on the surfaces of bulk TS (**a**,**b**) and ODP (**c**,**d**) sintered samples showing highly intact grains with a lower porosity in comparison with the TS sintered samples at different magnifications.

**Figure 3.** *Cont.*

**Figure 3.** SEM micrographs collected on ODP samples and chemical maps for individual elements Cu (**a**), S (**b**), and Sn (**c**), and simultaneously for all elements (**d**) (corresponding EDX spectra are shown in Figure S5).

**Table 3.** Atomic fraction of samples ODP1, ODP2, and ODP3 samples, estimated using SEM-EDX analysis (corresponding EDX spectra are shown in Figure S6).

Repeated Seebeck and resistivity measurements are shown in Figure 4. All the samples, and TS and ODP batches, showed positive values for the absolute Seebeck coefficient, indicating holes as majority charge carriers, thus confirming a *p*-type semiconducting nature. The trend of resistivity for sample TS1 is increasing with the temperature, whereas it is decreasing for all other samples, typical of degenerate and non-degenerate semiconductors, respectively.

The first measurement on the TS1 sample shows the lowest values of *S* (40–100 μV/K) and *ρ* (0.01–0.03 mΩ-m). However, these measurements are not reproducible during the second and third measurement cycles. The low Seebeck and resistivity with a nondegenerate semiconducting trend suggest the presence of a higher carrier concentration in sample TS1. This could be due to the alteration in chemical composition, as we observed a large amount of SnO2 using TEM-EDX and XRD. The XRD on the same sample after repeated TE measurement cycles revealed the segregation of SnS (see Table 1), making the sample copper-rich or possibly leading to the formation of CuS. In a recent work on non-stoichiometric (copper-rich) CTS [18], lower Seebeck (~50 μV/K at 300 K) and high electrical conductivity were reported. Other than the formation of SnS and SnO2, the nonrepeatability of *S* and *ρ* during the thermal cycles also confirms the instability of sample TS1. Noticeably, after the three measurements cycles, significant grain growth was observed for TS1, with the average domain size increasing from 40 ± 10 to 75 ± 10 nm.

For samples TS2 (*S* ~250–400 μV/K, *ρ* ~1.5–1.1 mΩ-m) and TS3 (*S* ~325–425 μV/K, *ρ* ~3.5–1.5 mΩ-m), the TE measurements were repeatable during the measurement cycles, and the values of *S* and *ρ* were in agreement with the literature [7,15]. Although we observed an increased amount of SnO2 and the formation of a new SnO phase, segregation of SnS was not observed. Similar values of *S* and *ρ* during several measurement cycles confirmed that the CTS samples prepared in a strictly controlled environment were stable. It is known that sulfurization leads to the formation of stoichiometric CTS [41], which could be the case for sample TS3, leading to a higher Seebeck and resistivity.

The repeated TE measurements on ODP sintered samples were reproducible, especially after the first measurement cycle, and for the second and third measurements cycles, the *S* and *ρ* measurements were coherent. The ODP1 sample sintered at 400 ◦C for 30 min showed the lowest values of *S* (180–310 μV/K) and *ρ* (0.55–0.50 mΩ-m). ODP2 and ODP3 samples sintered at 500 ◦C for 10 min and 30 min showed increasing values of *S* and *ρ*. The Seebeck coefficients and resistivities for the ODP2 and ODP3 samples were *S* ~400–550 μV/K and *ρ* ~2.2–1.0 mΩ-mm, and *S* ~550–650 μV/K and *ρ* ~4.0–1.7 mΩ-m, respectively. The increase in *S* and *ρ* have a clear relation with the increased average domain size of the samples. These results are in agreement with our recent work showing the effects of grain growth on SPS sintered CTS samples, owing to the conduction based on the metallic nature of surfaces due to dangling bonds [40]. Moreover, Ming et al. [42] showed a similar effect in Cu2SnSe3.

**Figure 4.** *Cont.*

**Figure 4.** Repeated absolute Seebeck coefficient (*S*) and resistivity (*ρ*) measurements in temperature for the TS and ODP sintered samples. In the figure, markers 1 (red squares), 2 (green circles), and 3 (blue triangles) represent first, second, and third measurements cycles, respectively.

However, it is important to notice here that two different sintering were used for the sample preparation, resulting in significantly different densities, even if we did not observe a significant difference in the resistivity of the same samples. Thus, we put forward that electrical transport is less likely affected by porosity in these systems. However, we noticed that the TS sintered samples had a lower *S* in comparison with the ODP samples. This could be related to the overall chemical composition of the TS samples, where we noticed a large chemical fluctuation in TEM-EDX. Some chemical fluctuations were also present in the ODP samples, but the overall chemistry of ODP samples was close to the theoretical, as observed by means of the chemical maps.

Thermal diffusivity (*D*) was measured using a xenon flash instrument, and the thermal conductivity (*κ*) was calculated as, *κ* = *D* × *d* × *Cp*, where, *d* and *Cp* are the density of the sample and specific heat capacity, respectively. The density was measured using the Archimedes method (see Table 1), and *Cp* obtained on TS samples is discussed elsewhere [4], whereas *Cp* measurements on ODP sintered samples are shown in Figure S7.

All the samples showed a decreasing trend of thermal conductivity with temperature, implying that the phonon–phonon (Umkalpp process) is dominating the phonon transport (see Figure 5). Here, it is worth mentioning that all the samples of this work have a disordered cubic structure with partial occupancies of cations (Cu and Sn), which results

in a comparatively lower thermal conductivity than the ordered or monoclinic CTS polymorph [6]. The thermal conductivity of sample TS1 ranges from 0.70 W/mK to 0.45 W/mK, whereas it is ultra-low for samples TS2 and TS3, with values of 0.40–0.30 W/mK and 0.30–0.20 W/mK, respectively, in the entire measured temperature range of 323–723 K. Samples TS2 and TS3 have a similar *κ* as we recently reported for CTS [4]. However, the unstable sample TS1 has the highest *κ* in the TS batch. The higher thermal conductivity of sample TS1 is due to its higher electrical conductivity, as observed by the degenerate semiconductor trend of resistivity, probably resulting from the formation of Cu-rich CTS or CuS. The thermal conductivity of ODP sintered samples is in the range of other CTS and Cu-Sn-S-based systems [7,18]. A clear correlation between densities and *κ* can be noticed in the ODP samples as well. The densities of ODP samples are similar to the literature for CTS polymorphs [7,12,18]. The difference in *κ* between TS2 and TS3 is also likely to be due to their lower and higher densities, respectively. It is noteworthy that the *κ* of TS samples is ~3-fold lower in the entire temperature range than for the ODP sintered samples. However, we observed a more or less same behavior for the electrical transport, e.g., samples TS2 and ODP2 have *ρ*~1.5–1.0 mΩ-m and ~2.0–1.2 mΩ-m, respectively, but TS2 has a ~3-fold lower *κ* (0.3–0.2 W/mK) than ODP2 (0.8–0.6 W/mK).

**Figure 5.** Thermal conductivity (*κ*) for TS and ODP sintered samples.

The power factor was calculated as *PF* = *S2*/*ρ*, and is shown in Figure 6. The first measurement on Sample TS1 has the highest *PF* ~3.5 μW/K2 cm, above 700 K, which is continuously decreasing with successive measurements. Samples TS2 and TS3 showed PF ~1.25 μW/K2 cm and ~1 μW/K2 cm, respectively, above 700 K, but they are stable over repeated measurements. Due to the reproducibility of *S* and *ρ*, ODP sintered samples showed reproducible PF. Among all the ODP sintered samples, ODP2 has the highest *PF* ~2.75 μW/K2 cm, above 700 K, because of moderate *S* and *ρ*. However, lower *S* and very high *ρ* for samples ODP1 and ODP3, respectively, have an adverse effect on each other, resulting in a comparatively lower *PF* ~1.75 μW/K2 cm and ~2.25 μW/K2 cm, respectively.

**Figure 6.** Repeated power factor (PF) for TS and ODP sintered samples. In the figure, markers 1 (red squares), 2 (green circles), and 3 (blue triangles) represent the power factors during the first, second, and third measurements cycles, respectively.

Concerning the figure of merit, samples TS1, TS2, and TS3 show *zT* ~0.50, 0.45, and 0.27, respectively, above 700 K (Figure 7). Although TS1 has the highest *zT*, it is not stable and *zT* decreases with subsequent measurements. Among the stable TS samples, TS2 has the highest *zT* of ~*0.45*. The competitively high *zT* of TS2 is supported by its lower *κ* and *ρ*. ODP sintered samples present *zT* ranging from 0.25–0.34, around 700 K. The ODP2 sample has the highest *zT* of ~0.34, around 700 K, thanks to the low thermal conductivity throughout the measured temperature span. It is evident from the discussions above that the comparatively higher *zT* of the TS samples is supported by their lower density (high porosity), which blocked the thermal transport effectively. Impotently, the many folds reduction of *κ* due to the pores does not show a significant increase in the resistivity of the TS samples. Furthermore, the porous CTS samples also showed reproducible results during many measurements cycles. Total elimination of secondary phase oxides is not easy due to the low partial pressure of their formations, but a small amount of tin oxides does not seem to affect the TE properties during repeated TE measurements.

**Figure 7.** The repeated figure of merit (*zT*) for TS and ODP samples. In the figure, markers 1 (red star), 2 (green circles), and 3 (blue triangles) represent the first, second, and third measurement cycles, respectively.

#### **4. Conclusions**

The present work shows that porosity leads to a significant suppression of thermal conductivity, and CTS pellets can be stabilized with different fractions of porosity. The low density or TS samples (*κ* ~0.3–0.2 W/mK) showed ~3 times lower thermal conductivity than the high density or ODP sintered samples (*κ* ~0.8–0.6 W/mK). However, we did not observe any significant difference in electrical transport properties between the TS and ODP samples. The best performing stable TS samples present *zT*~0.45, whereas the best performing ODP sample showed *zT* of ~0.34, around 700 K, a result clearly due to the ultra-low thermal conductivity of the traditionally sintered, porous samples.

Due to the low partial pressure of tin oxides formation, it is difficult to produce pure CTS and similar chalcogenides. However, the continuous evolution of secondary phase oxides can be eliminated by using a highly controlled environment, and a small fraction of secondary phase oxides seem to have little effect on the TE properties and stability of the samples. The results presented in this work give a general overview of the effects of different experimental conditions and porosity on the stability and TE performance of CTS samples. Similar considerations should hold for other Cu-Sn/Fe-S/Se-based systems, chalcogenides, colusites, and chalcopyrite, etc., used for various applications, ranging from photovoltaics to thermoelectricity and LED production.

**Supplementary Materials:** The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/ma15030712/s1. Figure S1: Images of as-sintered ODP samples. Figure S2: Rietveld refinement data before and after many Seebeck and resistivity measurements cycles for all the samples. Figure S3: Morphological images of SPS sintered samples. Figure S4: TEM-EDX, morphological images, and SAED on TE samples. Figure S5: SEM-EDX data for chemical maps collected on ODP samples. Figure S6: Various SEM-EDX data collected on ODP samples. Figure S7: Specific heat capacity (*CP*) measurements on ODP samples.

**Author Contributions:** Conceptualization and original draft writing: K.L.; sample production: K.L. and C.F.; data collection: K.L. and C.F.; discussions, editing, and proofreading: K.L., C.F. and P.S.; supervision and funding, P.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Autonomous Province of Trento, within the framework of the programmatic Energy Action 2015–2017.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors are thankful to Himanshu Nautiyal for useful discussions and suggestions. The authors are also grateful to Mirco D'Incau and Narges Ataollahi for support in the experimental work and for useful discussions on the methods.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

### *Article* **Synthesis and Characterization of Al- and SnO2-Doped ZnO Thermoelectric Thin Films**

**Giovanna Latronico 1,\*, Saurabh Singh 2, Paolo Mele 1,\*, Abdalla Darwish 3, Sergey Sarkisov 4, Sian Wei Pan 5, Yukihiro Kawamura 5, Chihiro Sekine 5, Takahiro Baba 6,7, Takao Mori 6,7, Tsunehiro Takeuchi 2, Ataru Ichinose 8 and Simeon Wilson 3**

**Abstract:** The effect of SnO2 addition (0, 1, 2, 4 wt.%) on thermoelectric properties of *c*-axis oriented Al-doped ZnO thin films (AZO) fabricated by pulsed laser deposition on silica and Al2O3 substrates was investigated. The best thermoelectric performance was obtained on the AZO + 2% SnO2 thin film grown on silica, with a power factor (*PF*) of 211.8 μW/m·K2 at 573 K and a room-temperature (300 K) thermal conductivity of 8.56 W/m·K. *PF* was of the same order of magnitude as the value reported for typical AZO bulk material at the same measurement conditions (340 μW/m·K2) while thermal conductivity *κ* was reduced about four times.

**Keywords:** thermoelectricity; Seebeck coefficient; thermal conductivity; thin film; oxides

#### **1. Introduction**

The increasing worldwide demand for energy and the resultant depletion of fossil fuels have brought new challenges for the scientific community [1]. One of the major issues is to develop high-efficiency devices for capturing energy from abundant natural sources such as solar, wind and geothermal energy. Another surplus, but mostly unused, source of energy is wasted heat. There are huge waste heat sources in our environments covering a wide range of temperatures (300~1200 K): industrial processes, domestic stoves and radiators, electrical lighting, pipelines, electrical substations, subway networks, automotive exhaust tubes, but also geothermal heat, body heat, and so on: about 66% of the annual world energy consumption is lost as waste heat, and the loss corresponds to the stellar amount of 3·1020 J per year, just considering the past 10 years [2,3]. A highly promising method for energy recovery from such heat sources is the utilization of thermoelectric (TE) materials that can convert various types of waste heat flow into electricity. The possibility of conversion of heat in electricity was discovered in 1821 by Thomas Seebeck [4]: a junction

**Citation:** Latronico, G.; Singh, S.; Mele, P.; Darwish, A.; Sarkisov, S.; Pan, S.W.; Kawamura, Y.; Sekine, C.; Baba, T.; Mori, T.; et al. Synthesis and Characterization of Al- and SnO2-Doped ZnO Thermoelectric Thin Films. *Materials* **2021**, *14*, 6929. https://doi.org/10.3390/ma14226929

Academic Editor: Andres Sotelo

Received: 8 October 2021 Accepted: 10 November 2021 Published: 16 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of two metals generates the thermoelectric voltage Δ*V* when a temperature gradient Δ*T* is created across it. In mathematical form it can be expressed as:

$$
\Delta V = S \cdot \Delta T \tag{1}
$$

where *S* is the material-dependent Seebeck coefficient. The performance of any TE material is quantified by the figure of merit (*ZT*):

$$ZT = \frac{\sigma S^2}{\left(\kappa\_{cl} + \kappa\_{ph}\right)} T \tag{2}$$

where *σ* is the electrical conductivity, *S* the Seebeck coefficient, *T* the absolute temperature, *κel* the electrical thermal conductivity and *κph* the phononic thermal conductivity being *κ* = *κel + κph* the total thermal conductivity.

*ZT* is related to the efficiency *η* of heat/electrical energy conversion by the relation:

$$\eta = \frac{\Delta T}{T\_H} \left( \frac{\sqrt{1 + ZT\_{\text{ave}}} - 1}{\sqrt{1 + ZT\_{\text{ave}}} + \frac{T\_C}{T\_H}} \right) \tag{3}$$

State-of-the-art TE materials for heat conversion can operate at *T* = 300~1200 K, with *ZT* = 0.1~2.6, corresponding to *η* = 1~20%. Therefore, after two centuries, TE devices are seldom utilized in daily life. TE modules have obtained brilliant success, however, in niche applications, for example for powering the space probe Cassini [5], while high-conversion modules to harvest waste heat of car engines remained at the state of prototypes [6]. *ZT* and *η* must be strongly improved to make TE power competitive with the common thermodynamic cycles based on fossil fuel burning, solar conversion and nuclear power plants. The improvement of *ZT* can be obtained by enhancing *σ* and/or *S*, or the product *σS*2 which is called "power factor" (*PF*), and/or by decreasing the total thermal conductivity. However, *κel* = *LTσ*, with *L* = 2.44 × 10−8 W·Ω·K−2 is the Lorentz number while *κph* = 1/3 *Cv*Л where *C* is the heat capacity, *v* is the speed of phonons, Л is the phonon mean free path. It is thus necessary to decouple *σ* and *κel* and work on the depression of *κph*.

Since the discovery of the Seebeck effect, the benefit of TE harvesting has been understood and a wealth of TE materials has been discovered. After the discovery of BiTe with *ZT* = 0.5 [7] in 1954, the *ZT* of TE materials did not improve for a very long time. In 1993, a seminal paper [8] theoretically predicted the drastic depression of *κph* due to reduction of the mean free path of phonons (Л) to a few nanometers, which resulted in substantial improvement of *ZT*. This concept was firstly validated in Bi2Te3/Sb2Te3 multilayer thin films incorporating natural nano-sized precipitates, showing the extremely small *κ* value (0.22 W·m−1 K−1) and a huge value of *ZT* = 2.5 at T = 300 K [9].

These results were due to the scattering of phonons by nano-defects spontaneously formed inside the thin films. However, TE harvesters based on BiTe and related materials cannot be produced on a large scale because they contain rare (Te) and poisonous (Sb, Bi, Pb) elements, and require high-cost processing. Though the last ten years a great progress has been made with *ZT* = 2.6 for SnSe single crystals [10] and 3.1 for polycrystalline SnSe [11], there is still room for finding even more efficient TE materials in a wide T region.

In particular, the attention of researchers has been focused on the development of stable, environmentally benign, abundant, and cost-effective TE materials based on oxides. In the 1990s, extensive research in the area of bulk oxides focused on the enhancement of the TE performance using atomic substitutions and improved grain connection [12–15]. To date, the best TE performance of the currently available oxide materials is *ZT* = 0.64 for *n*-type Zn0.96Al0.02Ga0.02O [13] and 0.74 for *p*-type Ca2.5Tb0.5Co4O9 [14] at 1000 K. The *ZT* of oxides is not yet up to the level of the best conventional TE materials and needs to be drastically improved to be acceptable for practical applications. The bulk oxides also have the main disadvantages of requiring a long time for sintering and fabrication of the

*n*- and *p*- elements and their assembly in modular shape, and mechanical fragility. All these drawbacks can be overcome by using oxide thin films. Thin-films have significant advantages, such as low dimensionality, rapid fabrication, control of strain at the interface with substrates, and the possibility to insert artificial nano-defects to improve the phonon scattering. Thermoelectric thin films are also attractive for their applicative potential for energy harvesting to power Internet of Things (IoT) sensors [15,16].

Recently, our group studied oxide-thin TE films and obtained encouraging preliminary results. First, epitaxial thin films of 2% Al-doped ZnO (AZO) were fabricated by pulsed laser deposition (PLD) on several single crystal (SrTiO3, Al2O3) and amorphous (silica) substrates. Regardless of a particular substrate, the films always showed higher values of *ZT* in comparison with the corresponding bulk AZO: for example, at *T* = 600 K, *ZTAZO-on-STO* = 0.03 while *ZTbulk* = 0.014 [17,18]. The superior performance of films is due to their lower thermal conductivity: *κAZO-on-STO* (300 K) = 6.5 W/m·K [16,17] while *κbulk* (300 K) = 34 W/m·K. In these series, the grain boundaries can be considered as natural nanodefects for an enhanced scattering of phonons and consequent decrease of *κ*. As a demonstration of this effect, the film on fused silica, showing additional grain boundaries at the seed layer on the substrate, had even lower thermal conductivity: *κsilica* (300 K) = 4.89 W/m·K and larger *ZT*: *ZTsilica* (600 K) = 0.045 [18].

The insertion of artificial nanodefects has been subsequently considered with the purpose of further reduction of *κ* and enhancing *ZT*. Several approaches have been tried by our group: insertion of hydroquinone nanolayers in AZO films prepared by atomic layer deposition (ALD): *κALD* (300 K) = 3.56 W/m·K [19]; addition of polymethylmethacrylate (PMMA) particles to AZO films prepared by multi-beam multi-target matrix-assisted PLD (MBMT/MAPLE-PLD): *κMAPLE* (300 K) = 5.9 W/m·K and *ZTMAPLE* (600 K) = 0.0061 [20]; formation of nanopores in AZO films prepared by mist-chemical vapor deposition (mist-CVD): *κporous* (300 K) = 0.60 W/m·K and *ZTporous* (300 K) = 0.057 [21]; dispersion of Al2O3 nanoparticulate in AZO films prepared by surface-modified target PLD: *κnanoAl2O3* (300 K) = 3.98 W/m·K and *ZTnanoAl2O3* (600 K) = 0.0007 [22]. Several groups worldwide have recently obtained excellent results with different kinds of dopant, like the *κ* (300 K) = 1.19 W/m·K and *ZT* (300 K) = 0.1 of magnetron sputtered AZO films by Loureiro et al. [23], *κ* (323 K) = 3.37 W/m·K and *ZT* (423 K) = 0.052 of CNT-added evaporated porous AZO films by Liu et al. [24], the *κ* (300 K) = 1.1 W/m·K and *ZT* (300 K) = 0.042 of amorphous ZnO*x*N*y* PLD films by Hirose et al. [25], the *κ* (300 K) = 1.8 W/m·K and *ZT* (383 K) = 0.019 of dual-doped AlGaZnO PLD films by Nguyen, et al. [26], just to cite the most impressive. All these successful examples highlight the promise of nanostructured doped ZnO films for future energy-harvesting applications.

In this work, we have focused on enhancing the thermoelectric performance of Aldoped ZnO films by the addition of a controlled amount of SnO2 as a secondary dopant. AZO has the same structure of hexagonal ZnO: wurtzite, hexagonal, space group *P63mc*, cell parameters *a* = *b* = 0.3289 nm and *c* = 0.5307 nm, while SnO2 is cassiterite, tetragonal, space group *P42/mnm* with cell parameters *a* = *b* = 0.4832 nm and *c* = 0.3243 nm. Since the mismatch between the *a*-axis of AZO and the *c*-axis of SnO2 is 1.4%, we forecasted the growth of quasi-epitaxial nanostructures (nanoparticles) of SnO2 with *c*SnO2//*a*AZO, dispersed in the AZO matrix.

The motivation of this work is to prove the presence of SnO2 nanoparticulates in the AZO matrix and verify the optimal content of SnO2 for the TE properties of the nanocomposite Al- and SnO2-doped (AZO + SnO2) thin films.

#### **2. Materials and Methods**

Two sets of four thin films were prepared using various compositions and substrate materials. All samples were deposited both on amorphous silica and *c*-axis oriented alumina by pulsed laser deposition (PLD) technique focusing a Nd:YAG (266 nm, 10 Hz) laser on dense pellets. Four commercial targets (Kurt Lesker Ltd., Jefferson Hills, PA, USA) used for film making had different contents of SnO2 (0, 1, 2 and 4 wt.%) dispersed

in the Al-ZnO (AZO) main phase where the Al content was kept as 2 wt.%. Prior to the deposition, the substrates were cleaned at 773 K for 2 h, then glued by conductive silver glue to a rectangular Inconel plate, which was put in direct thermal contact with a cartridge heater and finally inserted into the vacuum chamber. All films were grown with an energy density of about 4.2 J/cm2 for 60 min at 573 K, in the atmosphere of 20 mtorr of oxygen. The samples deposited on silica are named AZO\_xS and the ones deposited on alumina AZO\_xA, with x = 0, 1, 2 and 4 referring to the concentration (wt.%) of the SnO2 in the respective targets.

Electrical conductivity (*σ*) and Seebeck coefficient (*S*) were measured by means of the four-probe method using a ZEM-3 (ULVAC Advance-Riko, Yokohama, Kanagawa, Japan) apparatus under partial He pressure to assure thermal transport between the heater and the sample. Measurements with ZEM-3 were conducted performing three cycles between 353 and 573 K and measuring both heating and cooling processes. The *σ* and *S* curves reported in Section 3.2 for each sample were those obtained from the last cooling cycle, considered as the most stable and reliable. The uncertainties of the ZEM-3 measurements were ±4% for the electrical conductivity and ±3% for the Seebeck coefficient.

For comparison and validation of data, some selected samples were also characterized by a custom-made apparatus whose working principle and measurement protocol are reported elsewhere [27,28]. The error in the thermoelectric coefficients measurements is ±5% in the case of σ, and ±7% for *S*.

The thickness of the thin films (in the range 295–585 nm, as summarized in Table 1) was measured using a Dektak 6M Stylus Profiler (Bruker, Billerica, MA, USA) and a Filmetrics Profilm 3D (KLA, Milpitas, CA, USA).

The X-ray diffraction analysis was conducted using a Bragg-Brentano powder diffractometer (Smart Lab 3, Rigaku Corporation, Tokyo, Japan) using the Cu Kα radiation in the 10–100◦ angular range with an angular step of 0.02◦ (power settings: 40 mA, 40 kV).

The TEM images and EDS analysis were conducted using a JEM-2100F (JEOL, Akishima, Tokyo, Japan) with EDS spectroscopy. The STEM beam size was set to 0.5 nm.

The picosecond time-domain thermo-reflectance (TD-TR) technique using a customized system PicoTR (PicoTherm, Netzsch Japan KK, Tsukuba, Japan) was utilized to measure the thermal conductivity of the samples at room temperature (T = 300 K) in the cross-plane direction.

Measurement of Hall coefficient at room temperature was performed using a standard four-terminal method with a commercial PPMS instrument (Quantum Design, San Diego, CA, USA) at an AC current of 5 mA.

#### **3. Results and Discussion**

#### *3.1. Structural and Morphological Characterization*

The XRD spectra of the thin films fabricated on amorphous silica and single-crystal c-axis oriented Al2O3 are presented in Figure 1a,b, respectively.

On both substrates, the preferred orientation of AZO films was along the c-axis since only (00l) reflection appeared. The presence of SnO2 in the films of both series was undetectable by X-rays even for the highest amount (x = 4).

**Figure 1.** X-ray diffraction (XRD) spectra of Al-doped ZnO (AZO) films deposited (**a**) on silica (series AZO\_xS); (**b**) on Al2O3 (series AZO\_xA). *(hkl)* reflections of AZO [18] are indicated, while ♦ labels the peaks of Al2O3 substrate and asterisks \* the unattributed peaks.

The cross-sectional TEM images (magnification 150,000, Figures 2a and 3a of two representative samples deposited on fused silica without (AZO\_0S) and with the addition of SnO2 (2 wt.%, AZO\_2S) reveal a typical columnar growth along the c-axis of the films as often reported in the literature for AZO PLD thin films [16,17,19,21]. The addition of SnO2 (AZO\_2S) did not affect the morphology of the films. The higher magnification images (300,000×, Figures 2b and 3b for AZO\_0S and AZO\_2S, respectively) show that the columns were well connected without the presence of pores or misoriented grains so that the density of the films could be considered close to the theoretical value.

**Figure 2.** (**a**) Cross-sectional transmission electron microscope (TEM) image (magnification 150,000) of the AZO/silica thin film AZO\_0S; (**b**) double magnification (300,000×) taken in the central zone of Figure 2a.

The TEM-EDS mapping performed on the sample AZO\_2S (Figure 4) reveals a uniform distribution not only of the elements Al, Zn, O, but also of Sn. Contrary to the predictions based on the 1.4% lattice mismatch, Sn did not form nanoscale aggregates in the AZO matrix, but presumably entered as substitutional or interstitial atoms in the AZO elementary cell. According with TEM-EDS analysis, the atomic percentage of Sn in the film prepared with 2 wt.% SnO2-added AZO target is 0.49%. The atom % of oxygen is 33.91%. Since it is not possible to separate the contribution of oxygen from SnO2 and from ZnO, we can only compare the percentage of Sn in the target and in the film. The percentage of Sn in SnO2 is 78.77%, which in 2 wt.% SnO2 corresponds to 1.58%. This means that in the film the amount of Sn is about 1/3 than in the target. Si is not considered in the discussion being part of the substrate only.

**Figure 4.** TEM-EDS (energy-dispersive spectroscopy) elemental maps of the AZO + SnO2 2 wt.% silica thin film (AZO\_2S) for the atoms Sn, Zn, Al, O and Si.

#### *3.2. Transport and Thermoelectric Characterization*

Room temperature Hall measurement was taken to find the carriers' concentration *nH* and mobility *μH* values for the AZO\_xS and AZO\_xA films. The results are in Figure 5, together with room temperature resistivity values from the ZEM-3 analysis.

The resistivity at room temperature has a clear ascending trend with the increase of the content of SnO2 for both substrates. The films on Al2O3 had half the resistivity of those on silica. The range of *nH* was almost the same for two substrates, and of the order of 1020 cm−3, as expected for a typical semiconductor such as AZO. The maximum number of carriers occurred at x = 1 on silica and at x = 2 on Al2O3. The carrier mobility had the maximum at x = 2 on both substrates but was about 20 times larger for AZO\_2A than for AZO\_2S. AZO\_0S had greater mobility than AZO\_0A and this could be explained by the larger misfit dislocations generated on Al2O3, due to a lattice misfit of 15% [18,29]. Surprisingly, by increasing the content of SnO2 doping, there was a reversal trend and the films grown on Al2O3 presented higher mobility, with the maximum value for AZO\_2A-20 times larger than for AZO\_0S.

**Figure 5.** Hall effect measurements of the number of carriers and their mobility for films deposited (**a**) on silica (series AZO\_xS) and (**b**) Al2O3 (series AZO\_xA) plotted versus the % content of SnO2 (x). Note that reported is the absolute value of *nH* with the aim of simplifying the reading. The resistivity of both series was measured at the lowest temperature (348 K) using the ZEM-3 apparatus.

The electrical conductivity (*σ*) for the AZO films is presented in Figure 6 as a function of temperature in the range 300–600 K. Figure 6 shows that *σ* increases with rising temperature, confirming the semiconductor behaviour of the samples. On both substrates, the film grown without additional SnO2 had the largest *σ* followed by the film with x = 2.

**Figure 6.** Electrical conductivity plotted vs. temperature of thin films deposited on (**a**) silica (series AZO\_xS); (**b**) on Al2O3 (series AZO\_xA).

The temperature dependence (300–600 K) of Seebeck coefficient (*S*) of the AZO films is plotted in Figure 7. S had a negative sign, confirming the *n*-type conductivity of AZO. Figure 7 shows that *S* decreases with the rising temperature, a reversal trend with respect to *σ* as commonly expected for semiconductor materials. On both substrates, the pure AZO film had the lowest *S* while the sample fabricated with a target containing 4% of SnO2 presents the largest one.

**Figure 7.** Seebeck coefficient (*S*) plotted vs. temperature of thin films deposited on (**a**) silica (series AZO\_xS); (**b**) on Al2O3 (series AZO\_xA).

The Seebeck coefficient can be expressed as [30]:

$$S = \left(\frac{8\pi^2 k\_B^2}{3eh^2}\right) m^\* T \left(\frac{}{3n}\right)^{2/3} \tag{4}$$

where *kB* is Boltzmann's constant, *h* is Planck's constant, *T* is the absolute temperature, *m\** is the effective mass and *n* is the carrier concentration. The effective mass is also expressed as *m\* = α me,* where *me* is the mass of the electron and *α* is a positive rational number.

The room temperature (300 K) "Pisarenko plots" (*S* versus *nH*) for both series of films are presented in Figure 8. According to the graphs, *m\** was (0.3–0.6) *me* and (0.2–0.7) *me* for the films grown on silica and alumina, respectively. The fractional me was consistent with the parabolic band approximation and relatively simple band structure reported for ZnO [31].

**Figure 8.** Pisarenko plot at 300 K for thin films deposited on (**a**) silica (series AZO\_xS) and (**b**) on Al2O3 (series AZO\_xA).

The calculated power factor (*PF*) as a function of temperature is shown in Figure 9. The maximum power factor value was found for sample AZO\_2S at 573K as 211.78 mW/m·K2. This value was of the same order of magnitude as that measured for bulk AZO at the same conditions (−340 mW/m·K2) [32] and was also comparable with the values reported for AZO thin films [17,18,23–26].

**Figure 9.** Power factor *PF* = *σS*2 plotted vs. temperature for thin films deposited on (**a**) silica (series AZO\_xS) and (**b**) on Al2O3 (series AZO\_xA).

The *PF*s of all films at 353 K and 573 K are summarized in Figure 10, making clear that on both substrates, 2% of SnO2 represents the optimal dopant concentration.

**Figure 10.** The trend of power factor with the content of SnO2 for the two series of films on silica and alumina.

For the films AZO\_0S and AZO\_2S deposited on silica the measurements were repeated using two different apparatuses to verify the accuracy of the reproducibility of data. The comparison between the pair sets of data for *σ*, *S* and *PF* is reported in Appendix C. The transport and thermoelectric properties of the films are summarized in Table 1.

**Table 1.** Thickness, electrical and thermoelectric properties of the AZO films deposited on silica (series AZO\_xS) and on Al2O3 (series AZO\_xA) for different concentrations x (%) of SnO2 dopant.

The room temperature (300 K) thermal conductivity (*κ*) of the sample with the highest *PF* (AZO\_2S) and of a reference sample from the same batch (AZO\_0S) was evaluated by the TD-TR method [32–35] according to the details described in Appendix A. The value of *κ* was 8.88 and 8.56 W/m·K for samples AZO\_0S and AZO\_2S, respectively. These values were in the same range as those reported for pure AZO films deposited by PLD [16,17,21]. Therefore, the four-fold decrease of *κ* with respect to bulk [32] must be attributed to the phonon scattering of grain boundaries, and not to the addition of SnO2. The calculation of *ZT* (*T* = 353 K) using Equation (2) gave the following result: *ZT* (AZO\_0S) = 0.003 and *ZT* (AZO\_2S) = 0.004, of the same order as for AZO thin film deposited by PLD on different substrates. Conservative estimates of *ZT* (*T* = 573 K) were *ZT* (AZO\_0S) = 0.009 and *ZT* (AZO\_2S) = 0.014. Since for oxide thin films *κ* is expected to decrease with *T* [33], *ZT* was calculated using a conservative approach from the *PF* values at 353 K or 573 K, *κ* at 300 K, and *T* = 353 K or 573 K.

These values of *ZT* did not surpass the reported performance of bulk AZO at the same conditions and were also of the same or lower level as for other AZO films prepared by PLD. This indicated that SnO2 could not be considered as an optimal dopant for AZO thin films for thermoelectric applications. On the other hand, it could be that the fine dispersion of SnO2 into AZO matrix enhanced the photoelectric response of AZO, as reported for SnO2/ZnO hierarchical nanostructures prepared by the electrospinning method [34], or could be used to fabricate compact gas sensors, as reported for ZnO–SnO2 nanofibers [35].

#### **4. Summary**

In summary, we fabricated using pulsed laser deposition (PLD) two series of thermoelectric thin films of Al-doped ZnO (AZO) doped with various concentrations of SnO2 (x = 0, 1, 2, 4 wt.%) on the substrates made of fused silica and Al2O3 (001) single crystals. The goal was to enhance the thermoelectric performance. All the films were c-axis oriented. The films deposited on silica showed the highest values of Seebeck coefficient (*S*) and power factor *(PF)* in comparison with the films on Al2O3 with the same content of SnO2. The AZO film on silica with x = 2 showed the best performance, with *σ* = 385.0 S/cm, *S* = –74.17 mV/K, and *PF* = 211.8 μW/m·K2 at the maximum operating temperature (573 K). The room temperature (300 K) thermal conductivity of this sample was evaluated as *κ* = 8.56 W/m·K, with a calculated figure of merit *ZT* (353 K) = 0.003 and a projected value of *ZT* (573 K) = 0.014, comparable with *ZT* of the nanostructured PLD AZO films grown on several substrates.

**Author Contributions:** Conceptualization, P.M. and G.L.; Data curation, G.L. and S.S. (Saurabh Singh); formal analysis, G.L.; funding acquisition, T.M. and A.D.; investigation, G.L., S.S. (Saurabh Singh), S.W.P., Y.K., S.W. and T.B.; methodology, G.L. and P.M.; resources, P.M., T.M., T.T., A.I. and A.D.; supervision, P.M.; visualization, G.L.; writing—original draft preparation, G.L. and P.M.; writing review and editing, G.L., S.S. (Saurabh Singh), S.W.P., Y.K., C.S., T.M., S.S. (Sergey Sarkisov), A.D. and P.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** A.D. appreciates the financial support from US Air Force Office of Scientific Research Grant FA9550-18-1-0364 AFOSR, Army Research Office Grant No W911-NF-19-1-0451, and the partial support from Dillard University Minority Health and Health Disparity Research Center MHHDRC. T.B and T.M. acknowledge support from JST Mirai Program JPMJMI19A1 and JSPS KAKENHI JP19H00833.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this research study are available in this article.

**Acknowledgments:** P.M. and G.L. acknowledge the endorsement of the International Research Center for Green Electronics (IRCGE), Shibaura Institute of Technology. P.M. and G.L. appreciate Shrikant Saini (Kyushu Institute of Technology, Kitakyushu, Japan) and Marco Antonio de la Torre Hidalgo (University Castilla-La Mancha, Ciudad Real, Spain) for the insightful discussions. P.M. acknowledges Masami Yamashita of Filmetrics, KLA corporation, for her support on part of the thickness measurements. P.M. and G.L. thank Cristina Artini (University of Genova, Genova, Italy) for the support on XRD data interpretation.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A**

The picosecond time-domain thermo-reflectance (TD-TR) was utilized to measure the thermal conductivity of two samples in the cross-plane direction using the front-heat frontdetect (FF) configuration. Prior to the measurements, a 100 nm layer of Pt was sputtered on the surfaces of the thin films (see Figure A1). As a reference sample, we used 100 nm-thick Pt film deposited on a silica substrate. Rear-heat front-detect (RF) configuration was used for the reference sample (see Figure A1b). Figure A3 shows the thermo-reflectance signal obtained from the reference sample. We determined 1946 [J/(s0.5 m2 K)] as the thermal effusivity of the silica substrate by curve fitting. (see Figure A1b).

**Figure A1.** Diagram of thermo-reflectance measurement with (**a**) front-detect (FF) configuration and (**b**) rear-heat frontdetect (RF) configuration.

After depositing the Pt layer on the surface, samples consisted of three layers (see Figure A2).

**Figure A2.** Diagram of the applied model.

The thermal conductivities of the thin films were determined by the picosecond time-domain thermo-reflectance (TD-TR) technique, using the original focused beam system [36–38].

For the analysis, the mirror image method was used [39]. In the mirror image method, the temperature history of FF configuration could be described as:

$$T\_f(t) = \frac{1}{b\_f \sqrt{\beta t}} \left( 1 + 2 \sum\_{n=1}^{\infty} f^n \exp\left( -n^2 \frac{a\_f}{t} \right) \right) \tag{A1}$$

$$
\sigma\_f = \frac{d\_f^2}{\bar{f}\!f\!\_f} = \left(\frac{\mathbb{C}\_f}{b\_f}\right)^2\tag{A2}
$$

$$\mathcal{H} = \frac{b\_f - b\_s}{b\_f + b\_s} \tag{A3}$$

where *øf* is the heat diffusion time (in Pt layer), *fl* is the dimensionless parameter, *bf* is the thermal effusivity of the Pt layer, *bs* is the thermal effusivity of the sample, *df* is the thickness of the Pt layer and *fff* is the thermal diffusivity of the Pt layer.

We already knew the value of *Cf* , thus we could determine the thermal effusivity of the sample *bs*. We could also determine the thermal conductivity of the samples *κs* using the following equation:

$$\kappa\_s = \frac{b\_s^{\,^2}}{\mathfrak{c}\_s \mathfrak{a}\_s} \tag{A4}$$

where *cS* and *ρS* are the specific heat capacity and density of the AZO layer, respectively.

The aforementioned model assumed that the sample consisted of two layers and the second layer (AZO) was semi-infinite. This model could be derived from the relationship 3(*ξ*)

between the temperature and heat density of the sample layers using quadrupole matrix expression [39]:

$$
\begin{bmatrix}
\tilde{q}\_2(\boldsymbol{\xi}) \\
\tilde{\boldsymbol{\Gamma}}\_2(\boldsymbol{\xi})
\end{bmatrix} = \begin{bmatrix}
\cosh\sqrt{\tau\_1 \xi} & -b\_f \sqrt{\xi} \sinh\sqrt{\tau\_1 \xi} \\
\end{bmatrix} \tag{A5}
$$

$$
\begin{bmatrix}
\tilde{q}\_1(\boldsymbol{\xi}) \\
\tilde{\boldsymbol{\Gamma}}\_1(\boldsymbol{\xi})
\end{bmatrix} \tilde{\boldsymbol{\Gamma}}\_2(\boldsymbol{\xi}) = \frac{1}{b\_2 \sqrt{\xi}} \tilde{q}\_2(\boldsymbol{\xi})
$$

However, we found that the effect of the third layer (silica substrate) was significant, so we modified the model in order to account for the substrate. In the three-layered sample, quadrupole matrices were expressed as:

$$= \begin{bmatrix} \tilde{q}\_{2}(\xi) \\ \tilde{T}\_{3}(\xi) \end{bmatrix}$$

$$= \begin{bmatrix} \cosh\sqrt{\tau\_{2}\xi} & -b\_{2}\sqrt{\xi}\sinh\sqrt{\tau\_{2}\xi} \\ -\frac{1}{b\_{2}\sqrt{\xi}}\sinh\sqrt{\tau\_{2}\xi} & \cosh\sqrt{\tau\_{2}\xi} \end{bmatrix} \begin{bmatrix} \cosh\sqrt{\tau\_{1}\xi} & -b\_{1}\sqrt{\xi}\sinh\sqrt{\tau\_{1}\xi} \\ -\frac{1}{b\_{1}\sqrt{\xi}}\sinh\sqrt{\tau\_{1}\xi} & \cosh\sqrt{\tau\_{1}\xi} \end{bmatrix} \begin{bmatrix} \tilde{q}\_{1}(\xi) \\ \tilde{T}\_{1}(\xi) \end{bmatrix} \tag{A6}$$

$$(\xi)\tau\_{2} = \left(\frac{C\_{2}}{b\_{2}}\right)^{2}$$

where *C2* is the heat capacity of the AZO layer, *b3* is the thermal effusivity of the silica substrate. We could derive the temperature response of the three-layered sample by solving this equation. This time we used the thermal diffusivity of the silica substrate determined using the reference sample (*b3* = 1946 J/(s0.5 m2 K).

Figure A3 shows the thermo-reflectance signal obtained from the samples. Table A1 shows the values determined by curve fitting.

**Figure A3.** Thermo-reflectance signals of the silica reference and AZO samples.

**Table A1.** Thermal properties of samples AZO\_0S and AZO\_2S.

#### **Appendix B**

The electrical conductivity *σ* is plotted versus the SnO2 concentration x in Figure B1.

The undoped sample had the highest *σ*, and x = 2 was the optimal dopant concentration.

**Figure B1.** Electrical conductivity plotted versus the concentration of SnO2 for the two series of films on silica and alumina.

The Seebeck coefficient *S* is plotted versus the concentration x of SnO2 in Figure B2. The undoped sample had the lowest *S* while the sample with x = 4 had the largest *S*.

**Figure B2.** Seebeck coefficient plotted versus the concentration of SnO2 for the two series of films on silica and alumina.

#### **Appendix C**

The comparison of *σ*, *S* and *PF* curves obtained for the samples AZO\_0S and AZO\_2S is reported in the Figures C1–C3, respectively. Except for the case of s, the pair of curves are comparable within the experimental errors.

**Figure C1.** Electrical conductivity plotted vs. temperature of AZO\_0S and AZO\_2S obtained with two different setups. Filled symbols are the same as those reported in the plots in the main text, while the open symbols "chk" were obtained with another device.

**Figure C2.** Seebeck coefficient plotted vs. temperature of AZO\_0S and AZO\_2S obtained with two different setups. Filled symbols are the same as those reported in the plots in the main text, while the open symbols "chk" were obtained with another device.

**Figure C3.** Power factor plotted vs. temperature of AZO\_0S and AZO\_2S calculated from experimental data obtained with two different setups. Filled symbols are the same as those reported in the plots in the main text, while the open symbols "chk" were obtained with another device.

#### **References**

MDPI St. Alban-Anlage 66 4052 Basel Switzerland Tel. +41 61 683 77 34 Fax +41 61 302 89 18 www.mdpi.com

*Materials* Editorial Office E-mail<EMAIL_ADDRESS>www.mdpi.com/journal/materials

MDPI St. Alban-Anlage 66 4052 Basel Switzerland

Tel: +41 61 683 77 34 Fax: +41 61 302 89 18

www.mdpi.com

ISBN 978-3-0365-3504-3


**2.2 Advanced Composites Technology (ACT) program**

The objective of the ACT fuselage program was to develop composite primary structure for commercial airplanes with 20–25% less cost and 30–50% less weight than equivalent metallic structure [3]. The Advanced Technology Composite Aircraft Structure (ATCAS) program was performed by Boeing as the prime

**Figure 9.** *F/A-18E/F fuselage structure.*

contractor under the umbrella of NASA's ACT program and focused on fuselage structures. A large team of industry and university partners also supported the program. The primary objective of the ATCAS program was to develop and demonstrate an integrated technology that enables the cost and weight effective use of composite materials in fuselage structures for future aircraft.

The area selected for study was identified as Section 46 on Boeing wide body aircraft (**Figure 10**). This section contains many of the structural details and manufacturing challenges found throughout the fuselage. This includes variations in design details to address high loads at the forward end and lower portions of the fuselage. The loads decrease toward the aft end and the upper portion of the fuselage, allowing for transitions in the thickness of the structure that are tailored to match the structural loading.

A quadrant panel approach was selected for study as shown in **Figure 11**. The cross section is split into four segments, a crown, keel, and left and right side panels. The circumferential, four quadrant panel approach was selected with the idea of reducing assembly costs by reducing the number of longitudinal splices. This builtup assembly approach is baseline to metallic aircraft manufacturing and is similar to the approach Airbus selected for most of the fuselage of the A350.

Manufacturing process development and design trade studies contributed to the development of Cost Optimization Software for Transport Aircraft Design Evaluation (COSTADE) which allowed for defining and evaluating the costeffectiveness and producibility of various designs. Included in the program were assessments of tooling, materials and process controls needed for future full-barrel fabrication like Boeing selected for the 787.

The structural concepts studied included stiffened skin structures achieved by stand alone or combinations of cocuring, cobonding, bonding, and mechanical attachment of stringers and frames to monolithic or sandwich panel skins (**Table 1**). The crown section study selected fiber placed skins laminated on an IML controlled layup mandrel with the skin subsequently cut into individual panels and transferred to OML cure tools. Hat stiffeners used solid silicone mandrels located longitudinally along the IML of the skin panels for cocuring.

The recommended optimized panel design included cobonding of cured frame elements while cocuring the hat stiffeners and the skin. The cured frames were demonstrated using braided textile preforms and resin transfer molding (RTM). One of the main challenges of the crown panel concept was the bond integrity between the precured frames cobonded to a skin panel that is stiffened with cocured hat stringers. Alternative concepts the team considered during the review process included mechanically attached Z-section frames instead of cobonded J's.

**103**

**Table 1.**

*ACT structural concepts [3].*

**Figure 11.**

*ACT quadrant panels [3].*

**Details Process**

Skins AFP (tow, hybrid AS4/S2)

Frames Braiding/resin transfer molding (triaxial 2-D braid)

Panel assembly Cocured/cobonded stringers, cobonded frames

Compression molding

Pultrusion/pull forming

Stringers Hat—ATLM/drape forming (cocured, thickness variation) "J"—pultrusion

*The Evolution of the Composite Fuselage: A Manufacturing Perspective*

The mechanically fastened frame approach greatly reduces the complexity of IML tooling needed to cocure the hat stiffeners and cobond the frames. This is especially true at the intersections of the frame and hat. Flexible caul plates and custom fit reusable bags became part of the tooling system needed to accomplish the fully integrated skin/stringer/frame structure. Producibility issues are complicated by the blind nature of the IML of the skin being completely covered by flexible cauls and the reusable bagging system. The structural arrangement shown in **Figure 12** is very similar to the configurations that ended up on both the 787 and A350 programs. The program studied the pultrusion process for producing skin stringers. Continuous resin transfer molding (CRTM) developed by Ciba-Geigy was one of the more promising technologies studied. Improved process control and reduced waste are among the perceived advantages; process maturity, constant cross-section stringers and costs associated with secondary bonding or cobonding are among the disadvantages.

CTLM (contoured tape lamination machine, 12″ tape)

Stretch forming (thermoplastic, discontinuous fibers)

Cocured/cobonded stringers, fastened frames Sandwich panels, cobonded frames

*DOI: http://dx.doi.org/10.5772/intechopen.82353*

**Figure 10.** *ACT fuselage section [3].*

*The Evolution of the Composite Fuselage: A Manufacturing Perspective DOI: http://dx.doi.org/10.5772/intechopen.82353*

**Figure 11.** *ACT quadrant panels [3].*

*Aerospace Engineering*

to match the structural loading.

fabrication like Boeing selected for the 787.

along the IML of the skin panels for cocuring.

contractor under the umbrella of NASA's ACT program and focused on fuselage structures. A large team of industry and university partners also supported the program. The primary objective of the ATCAS program was to develop and demonstrate an integrated technology that enables the cost and weight effective use of

The area selected for study was identified as Section 46 on Boeing wide body aircraft (**Figure 10**). This section contains many of the structural details and manufacturing challenges found throughout the fuselage. This includes variations in design details to address high loads at the forward end and lower portions of the fuselage. The loads decrease toward the aft end and the upper portion of the fuselage, allowing for transitions in the thickness of the structure that are tailored

A quadrant panel approach was selected for study as shown in **Figure 11**. The cross section is split into four segments, a crown, keel, and left and right side panels. The circumferential, four quadrant panel approach was selected with the idea of reducing assembly costs by reducing the number of longitudinal splices. This builtup assembly approach is baseline to metallic aircraft manufacturing and is similar to

Manufacturing process development and design trade studies contributed to the development of Cost Optimization Software for Transport Aircraft Design Evaluation (COSTADE) which allowed for defining and evaluating the costeffectiveness and producibility of various designs. Included in the program were assessments of tooling, materials and process controls needed for future full-barrel

The structural concepts studied included stiffened skin structures achieved by stand alone or combinations of cocuring, cobonding, bonding, and mechanical attachment of stringers and frames to monolithic or sandwich panel skins (**Table 1**). The crown section study selected fiber placed skins laminated on an IML controlled layup mandrel with the skin subsequently cut into individual panels and transferred to OML cure tools. Hat stiffeners used solid silicone mandrels located longitudinally

The recommended optimized panel design included cobonding of cured frame elements while cocuring the hat stiffeners and the skin. The cured frames were demonstrated using braided textile preforms and resin transfer molding (RTM). One of the main challenges of the crown panel concept was the bond integrity between the precured frames cobonded to a skin panel that is stiffened with cocured hat stringers. Alternative concepts the team considered during the review process included mechanically attached Z-section frames instead of cobonded J's.

composite materials in fuselage structures for future aircraft.

the approach Airbus selected for most of the fuselage of the A350.

**102**

**Figure 10.**

*ACT fuselage section [3].*

The mechanically fastened frame approach greatly reduces the complexity of IML tooling needed to cocure the hat stiffeners and cobond the frames. This is especially true at the intersections of the frame and hat. Flexible caul plates and custom fit reusable bags became part of the tooling system needed to accomplish the fully integrated skin/stringer/frame structure. Producibility issues are complicated by the blind nature of the IML of the skin being completely covered by flexible cauls and the reusable bagging system. The structural arrangement shown in **Figure 12** is very similar to the configurations that ended up on both the 787 and A350 programs.

The program studied the pultrusion process for producing skin stringers. Continuous resin transfer molding (CRTM) developed by Ciba-Geigy was one of the more promising technologies studied. Improved process control and reduced waste are among the perceived advantages; process maturity, constant cross-section stringers and costs associated with secondary bonding or cobonding are among the disadvantages.

**Table 1.** *ACT structural concepts [3].*

**Figure 12.** *ACT crown panel structural arrangement [3].*

Airbus has studied automating stringer fabrication using both pultrusion and RTM but felt limited by aspects of both processes. As an answer, Airbus developed their version of pultrusion RTM. **Figure 13** shows equipment completed in 2011 that is being used to develop and qualify the process [4]. This hybrid fabrication approach allows the use of preform laminates instead of being limited to unidirectional reinforcements like traditional pultrusion and supports continuous production instead of batch processing associated with the traditional RTM. Instead of dipping the preform stack through a resin bath, it is pulled into an RTM tool that is open on both ends. To overcome resin being pushed out at both ends of the open tool, Airbus worked with resin suppliers to develop an epoxy resin with a parabolic temperature/viscosity curve. At 120°C resin viscosity is very low with high flow characteristics, but at both room temperature and at 180°C and higher, it is very viscous. The tool entry is cooled so the resin is too viscous to flow out; the middle is heated to obtain resin flow and cure; more heat is added at the end to increase resin viscosity to make sure it does not flow out and reduce cure pressure.

**105**

*The Evolution of the Composite Fuselage: A Manufacturing Perspective*

Even in the early days of development, industry leaders believed in the possibility of higher layup rates using AFP than was possible with hand layup, but the capabilities and the scale that the industry has achieved today is astounding. Almost as astounding as how the industry reinvented itself from a raw material cost saving technology to an enabling technology for large aircraft structural components.

In the late 1980s and early 1990s Northrop and ATK/Hercules worked on several joint projects sponsored by the Air Force which included fiber placement development and application. The technology was in its infancy as ATK was developing tow placement (as it was more commonly referred to originally) from its roots in filament winding technology. The main prize in the early days was \$5 per lb. high modulus carbon fiber and \$15 per pound high temperature/high performance resin instead of the \$60+ per pound price of prepreg. A wet process of running fiber through a resin bath prior to placement onto the layup mandrel was never able to realize the quality and consistency required by the design. This same process has been used in the large wind blade manufacturing process and it reminds us of how challenging (and messy!) that approach can be. In addition, the wind blade manufacturing industry has learned some valuable lessons from those early days of "build it as cheap as you can" using the lowest cost material you can deal with. While those early blades were built with lower manufacturing costs, the argument can be made that many of those blades failed very early in their lifecycle and required costly repairs or replacement to generate electricity. If the blade cannot turn because it has delaminated, it is not generating any electricity in addition to

Not only did the technology not realize the cost savings of dry fiber and wet resin, it was forced to adopt prepreg technology into the process—namely dealing with backing paper and ADDING to the cost of unidirectional prepreg tape by requiring it to be slit into prepreg tows. At the time of the ATCAS program, the AFP process was still evolving from what was originally envisioned as a much lower raw material cost build up starting with a dry fiber/wet resin process instead of a costly unidirectional fiber prepreg. The baseline process the ATCAS program selected for fabricating fuselage skins was AFP using prepreg tow. The dry fiber/wet resin tow had evolved to prepreg tow in an attempt to improve process consistency. The process was selected based on several factors including the potential for reduced material cost (compared to prepreg tape), the potential to achieve high lay-up rates over contoured surfaces, and the potential to efficiently support a significant amount of ply tailoring. In addition, the fact that tow material does not require backing paper eliminated a perceived risk of greater machine downtime.

When compared with the quality and consistency of parts made with prepreg tape, tow preg and subsequent prepreg tow, was not acceptable. The variability seen in the quality of the resultant panels would require compensation in the design of the part, resulting in weight penalties. But this did not prove fatal to the technology,

There have been many studies of the AFP process that have helped to shape and refine the characteristics and capabilities that exist in today's equipment offerings. But the ACT program allowed Boeing to better understand, study, define and refine the process to guide the technology development based on the needs of the user community. Everything from tack of the initial plies to the tool surface, to overlaps and gaps in the laminate; the most efficient ways to handle window/door cutouts, laminate thickness transitions, lay-up rates for flat, curved, cylindrical and duct shaped parts, etc., etc. What has ended up on production on the 787 is not the direct result of that ACT program, but the ACT program created the path for subsequent

instead tow placement reinvented itself (**Figure 14**).

AFP development to follow and improve upon.

*DOI: http://dx.doi.org/10.5772/intechopen.82353*

**2.3 Automated fiber placement**

the cost of repair or replacement.

**Figure 13.** *Airbus continuous pultrusion equipment [4]. Source: CTC Stade.*


**1. Introduction**

The fast evolution of electrical and electronic technologies is generating an exponential growth in the use of non-linear loads, such as switch-mode power supplies, electronic lighting ballasts [1], and other harmonic sources whose penetration can be expected to increase substantially in the future [2]. Harmonic distortions coming from new-generation sources and loads are generally larger and less regular than those due to traditional sources and loads, making power and energy more difficult to measure [3,4]. International standards have been developed to define acceptable limits and suitable measurements techniques for power systems' harmonics, e.g., [5,6]. Fourier spectral analysis is the most widely used approach for the evaluation of the harmonic content in power systems, due to its excellent accuracy under stationary conditions. This choice is reflected in the IEC 61000-4-7 [5] standard, which defines harmonics measurements and instrumentation requirements. This standard proposes the use of the Fast Fourier Transform (FFT), a fast and efficient algorithm for performing the Discrete Fourier Transform (DFT). Although the DFT is valid under general conditions, it is well known that limitations arise when it is applied to non-stationary signals, which is the normal situation in modern power systems. When fluctuating harmonics are analyzed with a DFT, the energy contained in the harmonics is distributed across the spectrum, affecting the accuracy [7]. For this reason, the IEC 61000-4-7 standard proposes a grouping strategy in order to improve the accuracy in non-stationary conditions and, at the same time, explicitly mentions the possibility to employ more advanced processing tools. During the last few years, alternatives to DFT have been proposed in the literature. A common workaround is to use the Short Time Fourier Transform (STFT), which assumes the signal to be piecewise stationary, but other methods have been suggested as well [8]. Among them, there is Wavelet Transform (WT), typically in the form of Discrete Wavelet Transform (DWT). The main advantage of DWT is that, while DFT requires a stationary, perfectly periodic sinusoidal signal to work properly, this is not a requirement for DWT. This signal processing tool has a wide range of applications, including power systems, where it proved to be extremely useful in signal denoising, short time predictions, fault detection, and energy management [9–14], as well as for Power Quality [15–19]. From WT, Wavelet Packet Decomposition (WPD) was derived, generalizing the link between wavelets and Multiresolution Analysis (MRA). Thanks to the uniform frequency bands that can be obtained with WPD, its application in Power Quality has been proposed for power calculation [20,21] and harmonic measurements [22–24]. However, the WPD harmonic analyses proposed in the literature do not look complete from the point of view of compliance with international standards and capabilities under stationary conditions, as will be discussed in Section 2.

To complete the current scenario, this paper presents a WPD method for a full harmonic analysis, in contrast with the valuable, but partial work developed in recent years, e.g., [22–25]. The proposed method takes advantage of the superior performance of WPD with fluctuating harmonics with respect to Fourier analysis. On the other hand, it is for the first time compliant with the IEC 61000-4-7 standard. This result, never achieved before, is possible thanks to the accurate selection of the filtering implementation and to the uniform frequency bandwidth division of WPD, as studied by the authors in [26]. To assess the method's implementation and validate its superior performance within the IEC standard requirements, several voltage signals with known harmonic content, both in stationary and fluctuating conditions, were tested. The accurate assessment of individual harmonic values was the main focus of the proposed method, and therefore, they were the objective of the validation. Other indices, like for instance Total Harmonic Distortion (THD), were not considered since they are the result of a further processing stage that can be performed in the same way as for FFT, as explained in Section 2.2. In Section 4.4, a comparison of the computational effort is provided, and finally, in Section 5, the method is tested with real voltage and current signals measured in a high harmonic distortion environment.

### **2. The Proposed WPD Method**

### *2.1. Wavelet Transforms in Power Systems*

WT is a mathematical transform that provides a representation of a function by a series of orthonormal functions, generated by scaling and translating a wavelet. It is particularly powerful in the measurement of the time-frequency variations of spectral components, but not suitable for power harmonics analysis because of the non-uniform frequency bands obtained. WPD is an extension of WT where the frequency axis is divided into equally wide intervals, instead of the traditional division in dyadic intervals, whose sizes have an exponential growth [27]. The advantage is that, with an accurate selection of the sampling frequency and the decomposition structure, it can lead to uniform frequency bands of the desired size and can therefore be employed for harmonics analysis. Previous works on WPD based algorithms for harmonics analysis can be found in the literature, but up to this moment, no IEC compliant approach, with complete harmonic analysis, has been proposed. Hamid et al. presented in [21] a WPD method for Root Mean Squared (RMS) and power measurements, from which harmonic distortion can be obtained. However, with this approach, only odd harmonics can be evaluated, and the wide frequency bands that can be obtained are not compliant with IEC standards. Eren et al. proposed a decomposition scheme in [22], but again, only bands centered in odd harmonics were taken into account. Moreover, results were shown only up to the seventh order. A more refined strategy was proposed by Diego and Barros in [24], where the 50 Hz wide frequency bands were compatible with IEC 61000-4-7 [5], but the decomposition was performed only up to the 15th order, far from compliance with the IEC standards.

Additionally, a major drawback of WPD based algorithms is their difficulty to compete with FFT in terms of computational speed. The FFT algorithm is the result of many years of developments and advances of Fourier analysis, while newly proposed methods (such as WPD) are not yet optimized for high performances. However, this gap is reducing, thanks to the constant increase in available computational power and the possibility of hardware implementation. In [23], it was shown that WPD can be efficiently implemented and be employed online for harmonics analysis. However, although the work showed the feasibility of online measurements, the same limitations on the results were found, i.e., the evaluation of only odd harmonics, limited total bandwidth (only up to 15th order), and too wide frequency bands (even harmonics contributions were included in the odd ones).

WPD algorithms continue to be interesting for power system researchers, as suggested by recent works [20,23], but in order to move forward and make WPD a feasible and better alternative to DFT, a complete algorithm for harmonic assessment must be designed. Modern power systems, with the increasing presence of non-linear loads, require a method compatible with the IEC standards, able to measure not only odd harmonics, but also even harmonics, and up to the highest possible order.

### *2.2. Characteristics of the Proposed Method*

The past limitations of WPD arose from the difficulty of adjusting the algorithm to the constraints given in the IEC 61000-4-7 standard, which is not trivial. Among these constraints, there are: a fixed rectangular sampling window of 10 cycles of the fundamental (200 ms at 50 Hz), frequency bands of 50 Hz centered in integer multiples of the fundamental (both even and odd), a bandwidth up to the 50th harmonic order (2500 Hz), and mainly, the fulfillment of the accuracy requirements for the stationary case. Therefore, the implementation of an IEC compliant algorithm is not just an extension of previous studies, since it requires overcoming the previous limitations and keeping the accuracy within the prescribed limits.

In this paper, it is shown that this can be achieved by an accurate study of the WPD implementation. The novel algorithm hereafter presented is the continuation of the work performed by the authors in [26], where a detailed study was conducted to define a methodology for the selection of the most suitable filter and convolution technique for WPD applied to power systems' harmonics. The methodology proposed in [26] is here employed to develop and characterize a complete measurement method. In order to obtain the IEC frequency bands, up to at least the 50th order, a sampling rate of 6400 Hz is necessary, and seven levels of decomposition must be implemented. These necessary features set high requirements on the frequency selectivity of the decomposition filters. The work performed in [26] showed that a maximally-flat Butterworth Infinite Impulse Response (IIR) filter of order 29 was the most suitable choice, and for this reason, it was employed in this paper as the mother wavelet. Its superior behavior in frequency selectivity, number of coefficients, and spectral leakage under realistic conditions, compared with traditional mother wavelet functions (e.g., db20, db10, Vaidyanathan, etc.) provides the high level of accuracy required to comply with the IEC standards in both stationary and non-stationary conditions. It must be noted that, although IIR filters have a non-linear phase, it does not represent a problem because the purpose of the method is to extract the RMS content of each frequency band, and the convolution technique presented in [26] allows preserving this information even with non-linear phase filtering.

In the following, the filtering procedure at each node of the decomposition tree is explained: the input signal *f* is recursively convolved by a pair of Quadrature Mirror Filters (QMFs), high pass and low pass filters (*h*(*n*) and *g*(*n*), respectively), and then, the filtered signals are downsampled by a factor of two, taking into account that the employed filters are half band filters (see Equations (1) and (2)). Thus, the high pass and low pass QMFs used were obtained from the corresponding IIR Butterworth filter of order 29, as discussed before. This WPD scheme was designed and implemented using MATLAB, allowing the authors to speed up the validation and testing procedure under realistic

input conditions, i.e., with the evaluation of real voltage waveforms. The following equations describe the basic filtering stage of the WPD method, in which the wavelet coefficients at level *l*, node *i*, are obtained from the convolution of the input signal at the previous level with the filters' coefficients and subsequent downsampling.

$$D\_1^{2i}(k) = \sum\_{n} g(n) D\_{1-1}^i(2k - n) \tag{1}$$

$$D\_1^{2i+1}(k) = \stackrel{\cdots}{\sum\_n} h(n) D\_{1-1}^i(2k - n) \tag{2}$$

where *i* = 0, 1, ... , 2(*l* − 1) − 1, and *h*(*n*) and *g*(*n*) are the high pass and low pass filter coefficients, respectively. In this regard, Figure 1 shows the decomposition tree scheme employed.

**Figure 1.** Wavelet Packet Decomposition (WPD) filtering and decimation scheme.

Table 1 summarizes the characteristics of the decomposition structure at each node, including information about the number of nodes per level, samples per node, effective time resolution, and bandwidth for every node at each level.

**Table 1.** Decomposition tree summary.

It is possible to observe that nodes at the seventh decomposition level have a bandwidth of 25 Hz. The required 50 Hz bands were obtained by a two-nodal-grouping (7\*, last level in Table 1). Aggregated RMS harmonic values are derived from individual node content as follows [15]:

$$\chi\_{\text{rms}}(j, p+q) = \sqrt{\frac{\sum\_{k} \left(d\_{j,k}^{p}\right)^{2} + \sum\_{k} \left(d\_{j,k}^{q}\right)^{2}}{N}} \tag{3}$$

where *p* and *q* are the two grouped nodes, *N* the total number of data, *k* the index counter, and *j* the level at which the RMS calculation is performed. In order to obtain the correct IEC bands, the grouping must satisfy: *q* = *p* + 1, *p* = 2, 4, 6, ... (the first node is discarded).

Thanks to this two-nodal-grouping, each band corresponded exactly to an IEC harmonic group, and therefore, any further processing stage, e.g., THD calculation or time aggregation according to IEC 61000-4-30, is perfectly possible. The algorithm was indeed designed to represent an alternative to FFT for power quality analyzers, assuming sampled values as input and producing compliant individual harmonic values as output. As a result, the method did not have any additional requirements than those of FFT.

### **3. Compliance with IEC Accuracy Requirements**

This section presents a test of accuracy, showing that the proposed method fulfills the IEC precision requirements for the stationary case and overperforms the IEC standard method for the non-stationary case.

IEC 61000-4-7 prescribes, for Class I accuracy, a maximum error of 5% in the evaluation of harmonic components, in case of single frequency and steady-state signals. In order to test the compliance of the proposed method, fifty steady-state signals *u*i(*t*), of single harmonic frequency ranging from harmonic order one to 50, were generated with a MATLAB script and subsequently analyzed using both the IEC method and the proposed WPD method. The input signals have the following expression:

$$u\_i(t) = 100\sqrt{2}\sin\left(i\,2\pi f\_0 t\right) \tag{4}$$

where *i* is the *i*th test containing the *i*th pure tone, *f*0 is the power frequency (50 Hz), and *t* is the time.

The top graph in Figure 2 shows the errors obtained with the proposed method for each i*th* harmonic order, with respect to the expected values, which in this case was always 100. It can be seen that the errors were well below the limit for Class I instruments for every harmonic order. The slightly higher errors for order 31st and 33rd were due to an intrinsic characteristic of WPD, which affected the central decomposition bands, as explained in [26]. This, however, did not compromise the accuracy, and compliance with IEC 61000-4-7 was proven.

The same test was repeated for non-stationary single frequency signals. To obtain non-stationary signals, the fluctuation pattern proposed in IEC 61000-4-7 Annex C.3 was employed, i.e., a reduction of the RMS of the signal from 100% to 20% at *t* = 85 ms in a 200 ms window. Since FFT is not suitable for measuring fluctuating harmonics, the standard proposes a grouping strategy, where the FFT bins are summed into harmonic groups to reduce the uncertainty. However, no accuracy limits are prescribed for this scenario. The bottom graph in Figure 2 shows the errors obtained in the case of fluctuating signals using the conventional FFT, the grouped IEC strategy, and the proposed WPD method. It can be seen that the conventional FFT produced errors of the order of 20%, while the IEC grouping strategy allowed a reduction of the error below the 5% limit. In this case, the proposed WPD method further reduced the error, for every order but 31 and 33, never exceeding the IEC stationary-state limits. The proposed method was therefore equally valid as the grouped FFT for single frequency signals, both stationary and fluctuating, and significantly superior to standard FFT, as expected.

**Figure 2. Top**: errors of the proposed method with steady-state single frequency signals. **Bottom**: comparison of the error produced by the conventional FFT, the grouped IEC, and the WPD methods in case of single frequency signals, under fluctuating conditions (as explained in the text). The grey lines show the limits provided by IEC 61000-4-7 for stationary conditions.

### **4. Validation of the Method**

The validation of the method required a more complex harmonic content than single frequency signals. Moreover, in order to be able to assess the accuracy of the method and compare it with the accuracy of Fourier analysis, the true harmonic content of the signals needed to be known a priori, i.e., synthetic signals must be employed. For this reason, realistic signals were generated, starting from the National Physics Laboratory (NPL) Power Quality Waveform Library [28], a public repository of waveforms with known harmonic content, representative of voltage signals found in the grid or used for calibration of equipment. This approach allowed obtaining waveforms whose true harmonic content was known and, at the same time, was realistic harmonic content.