An Attempt to Optimize ZnO-Like TCO Nanolayered Compound Thickness in Terms of a BPES-Related Physical Parameters Pondering

Recently, metal oxide nanolayered semiconductors revealed their increasing usefulness as UV detectors and transparent conductors in optoelectronic devices. In the present paper, a simple fabrication process has been carried out to prepare layered TCO compounds with different controlled thicknesses. Conjoint physical investigations allowed discussion of the validity of optimality in terms of geometrical parameters. A synthetic function based on pondered physical parameters was a practical guide to reach optimality.

In this study, TCO have been prepared by spray pyrolysis technique using, as main precursor, a solution of zinc acetate dissolved in deionized water. Several characterization techniques such as XRD, optical spectra, and hardness investigations have been applied to differently thick obtained samples [23][24][25][26]. The thickness-dependent performance of the different as-grown layers has been additionally investigated in terms of mechanical, optothermal and microhardness behaviours. The existence of an optimal thickness was investigated using the BPES protocol and compared to some recently published results [27].

ZnO Layers Elaboration.
ZnO thin layers have been prepared by the technique of chemical reactive technique in liquid phase spray. The obtained layers' structural and morphological properties, as well as synthesising details, have been recently published [23][24][25][26].
ZnO thin films having different thicknesses were obtained on 20 × 10 × 3 mm 3 Pyrex glass substrates by spraying an aqueous solution (mixture of water and Propanol 2) containing zinc acetate (Zn (CH 3 CO 2 ) 2 ) and a small amount of acetic acid, in order to avoid the precipitation of zinc hydroxide Zn(OH) 2 . The solution and gas (Nitrogen) flow rates were kept constant at 2 cm 3 ·min −1 and 4.0 l min −1 , respectively, corresponding to a minispray pyrolysis. The substrate temperature Ts, of the order of 460 • C (optimal value under the given experimental conditions, as already confirmed by A. Amlouk et al. [23,24]), was used to prepare these films according to in-room precedent successful attempts of deposition by the spray pyrolysis process [28][29][30][31][32][33][34]

Characterization
Techniques. Precedent X-ray diffraction analyses of the prepared layers were performed by a coppersource diffractometer (Analytical X Pert PROMPD), with the wavelength (λ = 1.54056Å). The optical transmission and reflection measures have been achieved using a common spectrophotometer (Shimadzu UV 3100S) equipped with an integrating sphere (LISR 3200). The spectrophotometer consists of double-beam monochromator (UV-2OOS, Shimazdu apparatus) with monochromatization performed by two flat silicon crystals in Laue diffraction on the (111) plane and enough energy to make several types of accurate measures in a wide wave-length range (220-1800 nm). The loadindependent hardness measurements have been performed by a standard Microhardness Vickers (Hv) apparatus.

Already Achieved Analyses and Discussion
XRD diagram analysis ( Figure 1) shows that the thinner layers (d < 0.6 μm) develop an exclusive preferred orientation of the crystallites with respect to the (002) reflection. Differently, the thicker ones, are identified, beyond the (002) peak, by an extra XRD peak: (101). These features correspond to the hexagonal würtzite system (JCPDS card, file n • : 361451 a = 3.24982, c = 5.20661Å ), which is generally associated, as stated by Dubey et al. [35], Kumar et al. [34] and Paraguay et al. [36], with the appearance of irregularly spaced pores. This structure results in an increasing level of surface roughness [37,38]. It seems that a minimal thickness is needed for the stability of a regular hexagonal würtzite system. Beyond this minimal thicknesses, the epitaxial growth seems to occur with no alteration in the lattice parameters, as discussed earlier by Kaeble [38].
The already published reflection R(λ) spectra [27] presented an accurate guide for estimating the thickness of each sample. In fact, the oscillating behavior of the λ-dependent reflection in the visible domain traduces the fact that the reflectance reaches discrete p-indexed maximal values R (p) max for some particular p-indexed values λ p max of the wavelength [39][40][41][42].
These p occurrences are traduced by the following equations: where n s is the substrate optical index (n s ≈ 1.55) and n is the layer λ-dependent optical index deduced from the optical transmission-reflection spectra. The knowledge of two successive couples of maximal values [40,41] allows calculating the film's thickness d:

Additional Mechanical Moh's Hardness and Optothermal Investigations
Hardness is the resistance offered by a material to localized plastic deformation caused by scratching or indentation. Load-independent Moh's hardness (H M ) estimated from the scratch test is on the Moh's scale, which could be calculated out from the Microhardness Vickers (H v ) using the formula [42]:  The set of hardness of measurements has been performed using a common diamond-pyramidal-indenter under a prefixed load. The obtained imprints dimensions have been exploited for yielding the Microhardness Vickers (H v ) of each sample as a synthetic value at room temperature using a Vickers diamond pyramidal indenter equipped with squared pyramid with 136 • as summit angle (Figure 2). During experiment, it has been verified experimentally that the indenter penetration depth was always less than the layer's thickness. The experimental values are gathered in (Figure 3).
The differences noticed in (Figure 3) can be explained, for the thinner layers, by the hardness contribution of the Pyrex substrate. The remaining layers, develop a mean hardness varying in a narrow interval. If the contribution of the substrate can be omitted, it seems that there is a maximum hardness zone situated in the interval of thickness [0.60-0.80 μm]. This noticed feature is probably due to the establishment of the hexagonal würtzite system which is harder to demolish than unorganized structures [33,34,36,37].
The normalized absorbance spectrum α( λ) is deduced from the BPES by establishing a set of N experimental measured values of the transmittance-reflectance vec- ..N . Then the system (5) is set: where β n are the 4n-Boubaker polynomials B 4n minimal positive roots, N 0 is a given integer and ξ n and ξ n are coefficients determined through the Boubaker polynomials expansion scheme (BPES). The normalized absorbance spectrum α( λ) is deuced from the relation: where d is the layer thickness. The obtained value of normalized absorbance spectrum α( λ) is a final guide to the determination of the effective absorptivity α through (4).
The Amlouk-Boubaker optothermal expansivity Ψ AB is a thermophysical parameter defined in precedent studies [35,[43][44][45][46][47][48][49], as a 3D expansion velocity of the transmitted heat inside the material. It is expressed in m 3 s −1 , and calculated by the following: where D is the thermal diffusivity and α is the effective absorptivity. This parameter gathers two totally different parameters: the thermal diffusivity which is a material intrinsic property, and the effective absorptivity which links the material response to the solar spectrum. The Amlouk-Boubaker optothermal expansivity Ψ AB presents the advantage of describing the conjoint thermal-optical response of the material to the whole spectrum, not only to monochromatic excitation.
As optimality is a complex notion when several physical parameters are involved, a synthetic aggregate is proposed on the bases of both Amlouk-Boubaker optothermal expansivity Ψ AB and load-independent Moh's Hardness H M .

Discussion and Perspectives
A study has been recently presented by Lee et al. [48] on the thickness-related optimization inside IZO/ZnO/PET multilayered structures. The authors have prospected the TCO-induced exclusive electrical performance (carriers' concentration, mobility. . .) and conjectured the existence of an eventual optimal thickness. Earlier, Shan and Yu [49] attempted to verify optimality for a thickness around 500 nm. These intriguing observations have been confirmed through the features of Figure 4. In fact, the optimality is obtained for the lowest point (d ≈ 0.61 μm). This optimality is deduced by estimating the thickness which corresponds to a maximum of the load-independent Moh's Hardness conjointly with a minimal value of Amlouk-Boubaker optothermal expansivity Ψ AB . For this purpose, an optimisation protocol has been established for calculating a pondered function F of Moh's Hardness and Amlouk-Boubaker optothermal expansivity Ψ AB with positive weights for Moh's Hardness and negative ones for Ψ AB . For each value of the measured couple (Moh's Sardness, Ψ AB ), the correspondent values of the thickness d along with the test function F were recorded. Optimality was reached for the value of which corresponded to maximum value of F. Moreover, the mechanical study revealed that, in order to reach the intrinsic hardness value of the layer (required for TCO applications in shock circumstances or aggressive mediums. . .), while avoiding substrate effects, one must either use a load as low as possible, or ensure a thickness exceeding the micrometer. Still, these values can be refined by using the nanohardness measurements to obtain the accurate hardness values of such thin films.

Conclusion
In summary, we have discussed the effects of the controlled thickness of TCO thin films prepared using a simplified and ISRN Nanomaterials 5 already optimized spray pyrolysis setup. Besides commonly considered parameters of the obtained layers, new and original characterization protocols have been carried out. It has been stated that an optimal ZnO thin film thickness is required for TCO purposes via simultaneous morphologicalstructural-physical investigations.