**4.1. CdS**

We should report that the state-of-the-art E-ALD systems are also commercially available

In this work, we report the intensity with respect to a coordinate system referred to as the pseudohexagonal surface unit cell of the Ag(111) substrate, in which the surface unit-cell parameters (a, b, c, α, β, γ) are defined so that the a and b vectors lay on the sample surface along the standard fcc [1 −1 0] and [−1 1 0] directions, while the c vector is perpendicular to the surface and parallel to the fcc [111] direction. The amplitude of the three vectors is given

> \_\_ 3 *a*<sup>0</sup>

is the lattice parameter of the cubic fcc cell of Ag. In the following, we adopted

a reciprocal space metrics where *h*, *k*, and l are parallel to the a\*, b\*, and c\* vectors of the reciprocal surface cell. In the following, we present two case studies on the CdS and Cu2

comparing the results and the different applications of the SXRD due to different scientific questions that have to be answered for a better understanding of the E-ALD growth of these

, <sup>|</sup>*a*<sup>|</sup> <sup>=</sup> <sup>|</sup>*b*<sup>|</sup> <sup>=</sup> *<sup>a</sup>*

, mainly used for polycrystalline substrates.

\_\_0 √ \_\_

<sup>2</sup> (3)

S

for the deposition of bigger electrode up to 4 cm2

**Figure 3.** Transmission of X-ray at different energy through different surface.

42 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

by the following relation together with the main surface cell angles.

*α* = *β* = 90°, *γ* = 120°, |*c*| = √

where *a*<sup>0</sup>

two materials.

**4. E-ALD and the sulfides structure**

E-ALD (or in this case ECALE) of CdS on Ag(111) has been involved in the testing of the experimental setup for in situ experiments by means of comparison of the structural results with theory and STM measurements. Moreover, the setups enabled structural determinations of the deposited film at different growth stages. In the first experiments at 20 kV performed by Giusti et al. [12], the reported attenuation is 50%, well matching with the attenuation curves reported in this work. The in situ diffraction measurements at controlled potential allowed the analysis of the CTRs for both the Ag(111) substrate and the Ag(111)/S surface. The fit of the CTRs showed that the last Ag layer on the bare metal has a contraction of 0.013 ± 0.008 nm toward the bulk. A vertical relaxation of the surface layer is observed in several (111) surfaces of noble metals and is due to the lack of bonding electrons at one side of low index surfaces [39]. Experimental works carried out on surfaces with a small roughness show an undetectable contraction of the surface layer [40, 41]. However, Ag(111) the contraction of the top layer is expected to strongly depend on the surface roughness [42]. A β-model has been involved in the fitting of the CTRs in order to take into account the surface roughness by means of fractionally occupied layers residing above the topmost complete one. In order to directly express the roughness in a length unit and not with a probability number, we can calculate the rootmean-square roughness *σ*, which can be calculated on the base of the Robinson model [43]. The oxidative absorption of S onto the Ag(111) surface induces strong modification on the shape of the CTRs. In fact, the best fit confirmed the top Ag layer with a site occupancy of 0.47 ± 0.07, in very good agreement with an S monolayer forming the (√7 × √7)R19.1 supercell as determined by STM images under electrochemical control at the same applied potential [44].

Hence, this setup for SXRD measurement has been successfully compared with literature data. In this context, this setup enabled the structural analysis in a straightforward manner. Wurtzite and zincblende have a very similar diffraction pattern, and they differ by the (200) reflection for zincblende and the (101) and (103) reflections for wurtzite. On this ground, X-ray diffraction data collected either in situ or ex situ, revealed that the films always present an ordered wurtzite structure with the *c*-axis perpendicular to the surface, confirming the epitaxial growth of CdS by means of ECALE on the Ag(111) substrate. In plane, different privileged orientations have been observed indicating that the first S layer structure might play a crucial role for the structural order of the grown films. Moreover, the X-ray reflectivity measurements collected in situ during the ECALE deposition of the CdS film, pointed out the correct 1:1 stoichiometric ratio between Cd and S and showed that the film thickness increases proportionally to the number of deposition cycles. Recent in situ SXRD experiment about the growth of CdS on Ag(100) and Ag(110) has been reported by Carlà et al. [13] confirming the epitaxial growth also on these substrates. On Ag(100), CdS has been found to be wurtzite-like, with two domain rotated by 30° with respect to the other and rotated by 15° and 45° with respect to the quadratic surface cell of the Ag(100) facet. While on Ag(110), the growth of CdS involves both zincblende (one domain) and wurtzite structures (two domains). The wurtzite domains on the Ag(110) are rotated by 30° with respect to the other and aligned with the substrate's main axis. Besides, for Ag(111), a different relative orientation of the two wurtzite domains is reported. These works clearly showed the influences of the substrate orientation on the CdS structure. Moreover, electrochemical measurements on Ag(100) and Ag(110) indicate that the charge associated with each CdS and S layer has an average value comparable to that found for films grown on Ag(111). In this context, the XRR data were fitted including a roughness factor in the fitting parameter calculated according to the Névot and Croce formalism [45–47]. The resulting film thickness has been found to be 52.5 ± 0.5 Å on Ag(110) and 46.5 ± 0.5 Å for Ag(100), while the theoretical value is 100.7 Å. To better explain the experiments, the authors suggest that the UPD process can be considered a dynamic process occurring in steps where rearrangements and reordering of the atoms can take place. For a detailed description of this interpretation, the reader should refer to Ref. [13]. Still, these experiments constitute another confirmation that the film thickness and stoichiometry can be controlled by the number of ECALE cycles, even on different facets.

#### **4.2. Cu2 S**

As reported in Section 2, chemical composition, local structure, and stacking sequence suggest that the E-ALD process would require numerous reorganization steps. SXRD experiments showed no Bragg peaks or Debye rings during the first deposition cycles for Cu2 S. A clear difference with respect to the CdS, probably related to the lower scattering factor of Cu with respect to Cd and the more structural complexity that can be found in the Cu-S compositional field. The Cu-S mineralogical system is structurally and compositionally highly complex including five different structures between the two endmembers, CuS (Covellite) and Cu2 S (Chalcocite). Thus, for this material, it is more difficult, though crucial, to understand its crystalline structure. In a recent paper, our group took into consideration the more stable and geometrically suitable structures in this system. Thus, the published structural results are not conclusive, and other experiments and analysis are in progress. However, recent operando SXRD data acquired for a sample of 80 E-ALD cycles show a hexagonal structure, although a low symmetry structure has been reported. Hexagonal planes are present in the structures of both the possible candidates for the interpretation of the SXRD data. Moreover, in both cases, the *c*-axis of the substrate and of the film coordinate system is parallel. Chalcocite structure has layers (not planes) made of distorted hexagons, a perturbation of these distorted hexagons to make them proper hexagons gives a plane with a hexagonal pattern of sulfur atom. In contrast, Covellite has a hexagonal plane with a much shorter bond length than the Ag hexagonal plane leading (see **Table 2**); the expected strain is compressive of −1.1% along the main Ag(111)R30 –3 × 4 reconstruction directions, while for chalcocite, the strain is expansive of 1.0% along the Ag(111)R30 –4 × 5 reconstruction direction. It is also worth noticing that chalcocite is far more stable than Covellite.

We proposed an attempt to map the indices of a chalcocite structure (Cu2 S) grown on Ag(111), based on two different orientation (Ag(111) and Ag(111)R30) with respect to the substrate. Although the chalcocite structure constitutes a suitable model for the Cu2 S, deposited by means of E-ALD, the transformation between the two crystallographic coordinates systems lead to unsatisfactory results.


**Table 2.** Characteristic length of possible CuS /Ag(111) and Cu<sup>2</sup> S /Ag(111) surfaces. The periodicity along the zonal axis (Ag[111]) is reported in **Figure 4** by means of experimental l-scan in situ and ex situ. The periodicity along Ag[111] corresponding to an interplanar distance of 6.75 Å, very close to the half of the periodicity along c is as observed for the chalcocite [48]. The simulated l-scan correspond to a model constituted by the hexagonal compact packing of sulfur atoms with the same periodicity. The comparison between experimental and simulated l-scans confirmed the correspondence between the chalcocite structure and the structure of the sample along the Ag[111] axis when measured in situ, revealing the presence of another structure in the sample when measured ex situ. In order to highlight the origin of this structural evolution, the Bragg peak at (0.73 0.73 1.04) has been acquired in real time. The structure seems to change in a partially reversible manner while reaching the open circuit potential from the last applied potential. Comparing the data with the covellite structure, the periodicity along the *c* axis of the covellite is found to be not matching (16.34 Å). Moreover, the periodicity presented in **Figure 4** corresponds to a distance of 3.37 Å between two adjacent sulfur layer. Since the S–S distance is "modulated" by the presence of copper atoms (Cu:S ratio) in the Cu-S compositional field, according to Bolge, the measured distance should correspond to a stoichiometric ratio of 2:1(Cu:S) [49]. Although the periodicity of the sample along Ag[111] is well reproduced by chalcocite, on the plane covellite and chalcocite have similar expected strains (1%) for Ag(111)R30°. These data suggest chalcocite (Cu<sup>2</sup> S) as a better model than covellite (CuS) for Cu2 S. However, the definition of a new structure forming the chalcocite one is needed to be able to conclusively describe the structure of this material. Even though the crystallographic structure of the sample is not clarified, the diffracted intensity on selected Bragg peaks during the in situ experiment increases monotonically as shown in **Figure 5**, thus confirming the growth of the films during the whole process.

and Ag(110) indicate that the charge associated with each CdS and S layer has an average value comparable to that found for films grown on Ag(111). In this context, the XRR data were fitted including a roughness factor in the fitting parameter calculated according to the Névot and Croce formalism [45–47]. The resulting film thickness has been found to be 52.5 ± 0.5 Å on Ag(110) and 46.5 ± 0.5 Å for Ag(100), while the theoretical value is 100.7 Å. To better explain the experiments, the authors suggest that the UPD process can be considered a dynamic process occurring in steps where rearrangements and reordering of the atoms can take place. For a detailed description of this interpretation, the reader should refer to Ref. [13]. Still, these experiments constitute another confirmation that the film thickness and stoichiometry can be controlled by the number

44 X-ray Characterization of Nanostructured Energy Materials by Synchrotron Radiation

As reported in Section 2, chemical composition, local structure, and stacking sequence suggest that the E-ALD process would require numerous reorganization steps. SXRD experiments

ence with respect to the CdS, probably related to the lower scattering factor of Cu with respect to Cd and the more structural complexity that can be found in the Cu-S compositional field. The Cu-S mineralogical system is structurally and compositionally highly complex including

Thus, for this material, it is more difficult, though crucial, to understand its crystalline structure. In a recent paper, our group took into consideration the more stable and geometrically suitable structures in this system. Thus, the published structural results are not conclusive, and other experiments and analysis are in progress. However, recent operando SXRD data acquired for a sample of 80 E-ALD cycles show a hexagonal structure, although a low symmetry structure has been reported. Hexagonal planes are present in the structures of both the possible candidates for the interpretation of the SXRD data. Moreover, in both cases, the *c*-axis of the substrate and of the film coordinate system is parallel. Chalcocite structure has layers (not planes) made of distorted hexagons, a perturbation of these distorted hexagons to make them proper hexagons gives a plane with a hexagonal pattern of sulfur atom. In contrast, Covellite has a hexagonal plane with a much shorter bond length than the Ag hexagonal plane leading (see **Table 2**); the expected strain is compressive of −1.1% along the main Ag(111)R30 –3 × 4 reconstruction directions, while for chalcocite, the strain is expansive of 1.0% along the Ag(111)R30 –4 × 5 reconstruction direction. It is also worth noticing that chalcocite is far more stable than Covellite.

based on two different orientation (Ag(111) and Ag(111)R30) with respect to the substrate.

means of E-ALD, the transformation between the two crystallographic coordinates systems

**S)**

S /Ag(111) surfaces.

S. A clear differ-

S (Chalcocite).

S) grown on Ag(111),

S, deposited by

showed no Bragg peaks or Debye rings during the first deposition cycles for Cu2

five different structures between the two endmembers, CuS (Covellite) and Cu2

We proposed an attempt to map the indices of a chalcocite structure (Cu2

**Ag(111) Covellite (CuS) Chalcocite (Cu2**

**Table 2.** Characteristic length of possible CuS /Ag(111) and Cu<sup>2</sup>

Although the chalcocite structure constitutes a suitable model for the Cu2

2.889 Å 3.794 Å ~3.963 Å (mean of S–S distance of the hexagonal plane)

of ECALE cycles, even on different facets.

lead to unsatisfactory results.

**4.2. Cu2 S**

**Figure 4.** Operando (in situ), ex situ, and simulated l-scans (0.73, 0.73, l).

**Figure 5.** Diffracted intensity during the growth of Cu2 S ultra-thin film.

### **5. Conclusion**

The first systems studied with operando SXRD has been chosen for their simple chemistry and because they had already been widely characterized with standard electrochemical and spectroscopical characterizations. By performing the operando SXRD, we have been able to address several open questions dealing with the effective growth process, the structures, the thicknesses, and the stoichiometry. SXRD has also successfully employed in the case of ultrathin films grown by E-ALD, allowing to detect the surface reconstructions present in the first stages of the growth for CdS. The determination of thickness by means of the crystal truncation rods and reflectivity analysis revealed a very clear picture regarding the growth process of CdS, which is substantially different with respect to a mere layer-by-layer growth. In the case of Cu<sup>2</sup> S, operando SXRD has revealed that the film crystallographic structure evolves as soon as the control potentials are removed from the cell with a time dynamics of few seconds. This structural transition is partially reversible if the applied potential is restored. Eventually, scanning along some selected reciprocal directions and taking advantage of the real-time acquisition of the diffraction intensity during the electrochemical evolution of the system allowed to understand both the structure and the stability of the Cu2 S. This gives the possibility of gathering information concerning the stoichiometry and its assessment by other techniques. In fact, for the Cu-S system, there is a very well-defined relationship between the structure and the Cu:S ratio; its stability revealed why the stoichiometry is coming from ex situ XPS or why stripping voltammetry is not comparable with the stoichiometry coming from operando structural investigations. The unexpected stoichiometry of the film for Cu<sup>2</sup> S raises several questions about the stability of this system. In conclusion, the operando SXRD results concern both CdS and Cu2 S while confirming the possibility of growing highly ordered ultra-thin films with high reproducibility, and they set a new interesting challenge for the fundamental surface science in explaining the complex mechanism, which is behind the growth of crystal by means of E-ALD.
