Structural Investigation of Photocatalyst Solid Ag 1 − x Cu x InS 2 Quaternary Alloys Sprayed Thin Films Optimized within the Lattice Compatibility Theory ( LCT ) Scope

CuxAg1−xInS2 solid thin films were fabricated through a low-cost process. Particular process-related enhanced properties lead to reaching a minimum of lattice mismatch between absorber and buffer layers within particular solar cell devices. First, copper-less samplesX-ray diffraction analysis depicts the presence ofAgInS 2 ternary compound in chalcopyrite tetragonal phasewith privileged (112) peak (d 112 = 1.70 Å) according to JCPDS 75-0118 card. Second,when x content increases, we note a shift of the samepreferential orientation (112) and its value reaches 1.63 Å corresponding to CuInS 2 chalcopyrite tetragonal material according to JCPDS 89-6095 file. Finally, the formation and stability of these quaternaries have been discussed in terms of the lattice compatibility in relation with silver-copper duality within indium disulfide lattice structure. Plausible explanations for the extent and dynamics of copper incorporation inside AgInS 2 elaborated ternary matrices have been proposed.


Introduction
AgInS 2 and CuInS 2 , which are both chalcopyrite ternary solids belonging to I-III-VI 2 compounds, are attractive materials of photovoltaic cells and optoelectronic devices because of their good stability under solar radiation, their large absorption coefficient, and their band gap energy lying in 1.5−2.1 eV domain.Theoretical calculation regarding solar conversion efficiencies of 27-32% has been made with I-III-VI 2 ternaries as absorbers.Even thin film solar cells of 12% efficiency have been successfully reached [1,2].However, these ternaries solar cells are typically fabricated by means of high-cost techniques, so that low-cost methods demand is noticeably increasing.
Indeed, the spray pyrolysis technique has not been widely used for preparing a large scale of such ternary materials for energy conversion purpose.In the same line, the mixture of both Ag and Cu as precursors of ternary materials in the started spraying solutions could lead to some various alloys having interesting physical characterisations.
In this work, we report for the first time the preparation on glass substrates at 420 ∘ C of quaternaries Cu x Ag 1−x InS 2 thin films using the spray pyrolysis technique from aqueous solutions.Each ternary has been achieved in our laboratory using appropriate conditions [6][7][8].On the other hand, the structures of these films were studied by means of X-ray diffraction apparatus (Panalytical X Pert PROMPD,  = 1.54056Å) within the lattice compatibility theory.The optical properties were obtained from the analysis of the experimental recorded transmission and reflectance spectral data over the wavelength range 300-1800 nm using unpolarized light by means of a spectrophotometer (Shimadzu UV 3100S) [15].The values of  have been calculated using molar concentration data which were obtained via absorbance measurements.The whole protocol is summarized in Figure 1.

Analyses and Structural Patterns.
The XRD spectra of the obtained compounds show in addition to the principle peak (112) the presence of ( 204), (312), and (116) additional peaks corresponding to the tetragonal structure of AgInS 2 with the presence of minor intensity peaks corresponding to AgInS 2 orthorhombic phase (Figure 1).These results have been obtained in other works [5][6][7][8][9][10][11][12].XRD analysis corresponding to Cu x Ag 1−x InS 2 alloys (Figure 2) exhibits a noticeable shift of (112) principle peak from 2 position (27.08 ∘ ), which is assigned to AgInS 2 material, to the angle (28.09 ∘ ) corresponding to CuInS 2 solid compound.This proves the incorporation of copper in the AgInS 2 tetragonal matrix by taking the silver place.

Additional Conjoint Analyses.
To reinforce and explain this interesting trend of Cu ions behavior, some lattice calculations were carried out.First, average crystallite size  values are obtained (Figure 1) from the Scherrer formula, where  is a constant  = 0.9. the length of wave  = 1.5418 Å.  is the full width at half maximum and  is the angle of the strongest peak.and its enhancement for 0.6 <  < 1.0.If criteria of stability are reported to a high bandgap along with reduced crystallite sizes [17][18][19], an optimality zone can be identified (shaded zone in Figure 3) thanks to the established second order fittings.This zone ([0.40; 0.43]) is in good concordance with several recently published values but seems to be more accurate.

Optical Study and Urbach Energy
Analyses.The optical properties of the Cu x Ag 1−x InS 2 thin films were determined from transmission and reflexion spectra in the range of 300-1800 nm wavelength range.Measurements were guides for evaluating Urbach energy   for each sample.In order to understand Urbach tailing alteration following copper ions insertion in the host AgInS 2 structures, Urbach energy   has been determined.This energy has been adopted as a reliable measure of the inhomogeneous disorder and atomic scale dispersion inside structures as it indicates the width of the band tails of the localized states in presence of defects.Figure 4 shows the low values of   corresponding to AgInS 2 and CuInS 2 compounds, which may be, among others (interstitials, antisites, vacancies, etc.), due to a minimum of distortion of the band gap energy.Yet when 0.4 <  < 0.5, the Urbach energy presented a maximum of distortion of the gap due to structure degradation and spin insatiability in the compound.These values are in good agreement with those reported in precedent sections concerning structural properties.They also confirm the nonlinearity of composition dependencies, as recorded, for similar compounds by Korzoun et al. [20].

Lattice Compatibility Theory (LCT) Analysis
3.1.Theoretical Fundaments.According to the Lattice Compatibility Theory [21][22][23][24][25][26][27][28] and the generalized Simha-Somcynsky theory [28][29][30][31], any host lattice can be considered as a succession of elementary molecules and holes.Each cell in the occupied fraction is either empty or contains the molecule van-der-Waals volume as well as an inherent free volume.The behavior of any doping or introduced element is based on its interaction with existing host edifices.Preludes to this theory have been established by Boubaker et al. [25,26] in the context of analysing Urbach tailing controversial behaviour in some nanocompounds as well as I-III-O 2 ternary oxides instability at low temperatures.It was also confirmed by Boubaker et al. [23,24] on the bases of investigation on some copper-doped compounds.An original formulation of the Lattice Compatibility Theory [25,26] has been established as follows: "The stability of doping agents inside host structures is favorized by geometrical compatibility, expressed in terms of matching patterns between doping agent intrinsic lattice and those of the host." 3.2.Evidence of Optimality Occurrence.In the actually discussed case (Cu x Ag 1−x InS 2 lattice), the nature of the highest occupied bands and the location of holes in both elemental copper and silver ions as well as CuInS 2 and AgInS 2 chalcopyrite lattice structures have been demonstrated to be determinant.In this context, fundamental geometrical observations concerning the structure of CuInS 2 and AgInS 2 ternary solid compounds (Figure 5) along with the host matrix were interpreted in terms of conventional latticelinked parameters.
In this context, main lattice parameters of both CuInS 2 and AgInS 2 have been gathered in Figure 6, as extreme schemes ( = 0 and  = 1, resp.) for the -dependent Cu x Ag 1−x InS 2 .Stoichiometry-related evolution of cooper element incorporation inside the host matrix is equivalent to a gradual reduction of the first lattice parameter (a) along with a more amplified magnification of the third one (c).Under the presumption of a first-order linear x-dependent evolution, in concordance with Vergard's law (in reference to difference in ionic radii between Ag and Cu, which prevents formation of solid solutions in the Cu x Ag 1−x InS 2 system), a critical point could be detected at approximately  = 0.42 (Figure 6).This value is strongly supported by precedent analyses and studies about copper/silver substation kinetics and extents [23,24,[27][28][29][30][31][32][33][34][35] ternary chalcopyrite structures.
The Lattice Compatibility Theory (LCT) may give hence an explanation to the limit of incorporation of copper ions in  the AgInS 2 host matrix by taking silver's place, as confirmed earlier by the recorded XRD peak shift (Section 2.2).

Conclusion
The structural properties of Cu x Ag 1−x InS 2 thin solid films, deposited on glass substrates by the spray pyrolysis technique from aqueous solutions using various ratios x = [Cu]/([Ag]+[Cu]) at 420 ∘ C as the substrate temperature, have been investigated.X-ray diffraction analysis confirms that all obtained solid films consist essentially of Cu x Ag 1−x InS 2 quaternary tetragonal chalcopyrite compounds with (112) strong peak.On the other hand, it was recorded that the physical properties have been influenced by the penetration of the copper in the structure that showed clearly a band gap energy   shift from 1.7 eV of AgInS 2 to 1.51 eV of CuInS 2 .
A confirmed and experimentally supported extent of the cooper-to-silver ratio has been established through structure alteration in the framework of the Lattice Compatibility Theory (LCT) along withSimha-Somcynsky principles.

2. 1 .
Experimental Details.Before copper processing, AgInS 2 thin films were first prepared at a glass substrate temperature of 420 ∘ C using an aqueous solution which contains silver acetate (AgCH 3 CO 2 ), thiourea (SC (NH 2 ) 2 ), and indium chloride (InCl 3 ) as precursors.The precursor's concentrations are [Ag + ]/[In 3+ ] = 1.3 and [S 2− ]/[In 3+ ] = 5.Molar ratios were prepared by mixing appropriate volumes of silver acetate 10 −2 M., indium chloride 1.310 −2 M., and thiourea 510 −2 M.This protocol is considered as an optimal condition for preparing such a p-type compound [6-8].The carrier gas was nitrogen (pressure ≈ 0.35 bar) through a 0.5 mm diameter nozzle.The nozzle-to-substrate plane distance was fixed at the optimal value of 27 cm as demonstrated earlier, for the same disposal, by Boubaker et al. [16].During the whole deposition process, precursor mixture flow rate was approximately 4 mL/min.In a second step, AgInS 2 sprayed thin films were annealed in a copper-rich sealed vacuum medium with different values of x = [Cu 2+ ]/([Ag + ]+[Cu 2+ ]).

Figure 2 Figure 3 :Figure 4 :
Figure 3: Conjoint variation of crystallite size D (nm) and energy band gap   of Cu x Ag 1−x InS 2 with  ratio.