**3.1. Characterization of CIGS films obtained by electrodeposition**

An electrochemical cell system of three horizontal electrodes was installed with a scheme like the one shown in **Figure 4**. A glass substrate covered by an Mo film (1 μm of thickness and 4x10−4 Ω cm of resistivity) was the WE. The RE and AE were made of a platinum mesh. The CIGS films were electrodeposited by applying −1.0-V DC potential to the WE versus the RE, employing an electrolytic solution with copper, indium, gallium, and selenium ions. At the start, it was the electrodeposition process, where a stage of nucleation and electrocrystallization of the CIGS film on the WE electrode was obtained. After the electrodeposition process, the WE with the CIGS film was removed from the electrochemical bath, rinsed with deionized water, and placed vertically for drying. Although copper, indium, gallium, and selenium ions have different reduction potential, a situation that complicates a simultaneous ED process, the CIGS films have been obtained with the composition ratios of Ga/(In+Ga) = 0.31 and Cu/(In+Ga) ≈ 0.9, close to those reported in the high efficiency cells [32, 33]. The film composition was measured by atomic emission spectroscopy (ICP-AES). The current evolution indicates that the steadystate value can be reached after 5 min, with a limiting current density of ≈ 1 mA / cm<sup>2</sup> . The WE surface changes during the film formation affect the limiting current density in the steady state in such a way that it decreases with very slow dynamics. The above also indicates that diffusion layer thickness increases. During the steady stage, the reaction at the WE is affected by the transport of the chemical species from the bulk solution to the charge transfer zone. By increasing the electrodeposition time, the film obtained is more rugged and darker in color; this is due to the lack of ions near to WE and to the increase of the diffusion layer thickness. The stirring of the solution is desirable since it enhances ion transport to the substrate and decreases the thickness of the diffusion layer [34]. However, the agitation method of stirring for a laboratory-scale deposition leads to gradients of thickness in the flow direction of the electrolyte [35].

nucleation [22]. In CuInSe<sup>2</sup>

104 Perturbation Methods with Applications in Science and Engineering

InCl3

, and GaCl3

through the film [31].

(CIS) one-step electrodeposition, it has been established that the

SeO3

[27].

,

. The WE

Cu-Se phase is formed at a low potential, and a reaction path has been established as a function of the potential. The Cu-Se phase acts as a nucleation site for indium incorporation [23, 24]. The CIS film morphology deposited at various potentials has been analyzed [23]. At low polarizations between −0.4 and − 0.5 V, platelets characteristic of the Cu-Se were observed; when the polarization increased, the morphology was nodular. The mechanisms of Ga to CIS incorporation also have been established. It is incorporated as gallium selenide and GaO<sup>3</sup> [25]. The CIGS film morphology obtained by the one-step electrodeposition with potentiostat mode has been described as nodules with a cauliflower-like growth [22, 26]. The as-electrodeposited CIGS film morphology is strongly influenced by the bath composition. Microcracks in the films have been observed when the films were deposited at low concentrations of CuCl<sup>3</sup>

Many studies have examined ways of improving the CIGS film morphology by a one-step electrodeposition. The effect of sodium sulfamate as a complexing agent on the film morphology was evaluated [28]. An improvement on CIGS thin film morphology was obtained when a short electrode pretreatment of a 1-min deposition at −0.5 V was carried out prior to deposition of the film [29]. The pulse electrodeposition process can produce a CIGS film that is more smooth, compact, and homogeneous than the one deposited by the DC potential electrodeposition [30]. Electrochemical studies in CIGS electrodeposition, generally, use an electrochemical cell with electrodes suspended vertically. However, an electrochemical cell with electrodes in a horizontal position has advantages over a cell with vertical electrodes, principally because the ion transport mechanism as well as the natural flow by convection allows a better uniformity on the WE surface; in this way, the composition is homogeneous

An electrochemical cell system of three horizontal electrodes was installed with a scheme like the one shown in **Figure 4**. A glass substrate covered by an Mo film (1 μm of thickness and 4x10−4 Ω cm of resistivity) was the WE. The RE and AE were made of a platinum mesh. The CIGS films were electrodeposited by applying −1.0-V DC potential to the WE versus the RE, employing an electrolytic solution with copper, indium, gallium, and selenium ions. At the start, it was the electrodeposition process, where a stage of nucleation and electrocrystallization of the CIGS film on the WE electrode was obtained. After the electrodeposition process, the WE with the CIGS film was removed from the electrochemical bath, rinsed with deionized water, and placed vertically for drying. Although copper, indium, gallium, and selenium ions have different reduction potential, a situation that complicates a simultaneous ED process, the CIGS films have been obtained with the composition ratios of Ga/(In+Ga) = 0.31 and Cu/(In+Ga) ≈ 0.9, close to those reported in the high efficiency cells [32, 33]. The film composition was measured by atomic emission spectroscopy (ICP-AES). The current evolution indicates that the steady-

state value can be reached after 5 min, with a limiting current density of ≈ 1 mA / cm<sup>2</sup>

surface changes during the film formation affect the limiting current density in the steady state in such a way that it decreases with very slow dynamics. The above also indicates that diffusion layer thickness increases. During the steady stage, the reaction at the WE is affected by the

salts and at high concentrations of H2

**3.1. Characterization of CIGS films obtained by electrodeposition**

The CIGS films characterized by scanning electron microscope (SEM) are shown in **Figure 5**. **Figure 5(a, b)** shows micrographs of surface and cross section. In both cases, the morphology consists of vertical nodules with a well-defined boundary between them. Some nodules are larger than others, which apparently have stopped growing. The stunted nodules increase the boundary between the nodules that have a greater growth. **Figure 5(c)** shows the surface morphology of the vertical nodules with a cauliflower-like growth. The surface morphology among the nodule boundaries is shown in **Figure 5(d)**. The film morphology in the nodule has differences with the one that exists in the boundary. Apparently, the film formed between boundaries is less compact than those formed in the nodule. In general, the CIGS films that were obtained through the one-step electrodeposition are not very compact and have a low crystalline structure, so that they do not have the properties to be used in solar cells. The principal morphology consisted in groups of atoms forming the cauliflowerlike growth. The annealing process in a selenium atmosphere is necessary to transform the as-electrodeposited film into a more crystalline, with large grains and with compact morphology.

The CIGS thin films that were subjected to an annealing process in a selenium atmosphere are shown in **Figure 6**. The selenization temperature was 550°C for 180 min. **Figure 6(a,b)** shows the surface and cross-section micrographs. In the micrographs, there is evidence that the nodules are of different length. On increasing the deposition time, some nodules continue

**Figure 4.** A diagram of an electrolytic cell with three horizontal electrodes.

**Figure 5.** Micrographs of the CIGS film that has been electrodeposited in a conventional mode: (a) surface, (b) cross section, (c) nodule with a cauliflower-like growth, and (d) morphology in the nodule boundary [13].

**4. Conventional electrodeposition plus periodical perturbations**

(c, d) composition ratio Cu/(In + Ga) = 1.18 [13].

In the electrodeposition theory, it is assumed that the WE surface is homogeneous so that the current density in the macroscopic level is uniformly distributed over the WE surface [8]. However, at the microscopic level, if the surface of the WE is considered as a surface with roughness, there will be a greater electric field strength in the peaks than in the surface valleys, as shown in **Figure 7(a)**, where the WE roughness has been amplified. Thus, the electrochemical kinetic is affected. For this reason, the electric load will be concentrated in the crests of the WE. With the formation of the first nodules, the WE roughness increases in such a way that the current density and therefore the mass transport mechanism are concentrated at the nodules. The foregoing has been observed in other studies, where it has been determined that the nonuniformity in the local current densities can exist even when the macroscopic current distribution over a given surface is completely uniform [34]. Assuming that there is a direct relationship between the load transfer ratio and the current density that is demanded during the electrodeposition process, the load transfer process can be analyzed using the current density. The points of greatest intensity of the electric field are the crests of the WE. In this way, they produce a greater current density during the ion reduction process, in such a way that, in the crests, the growth of the film originates grains that grow perpendicularly with respect to the WE. In the valleys, the current density is lower, and therefore, the density of ions is reduced and the growth speed of the film is slower. From the previous results, it can be established that as a consequence of nonuniformity in the local current densities through the WE, due to the diffusion layer growth, the CIGS morphology consists of isolated nodules

**Figure 6.** Micrographs of surface and cross section of the CIGS films with (a, b) composition ratio Cu/(In + Ga) = 0.9 and

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107

to grow and others stop growing. The cross-section film micrograph shows the Mo layer and over it, a CIGS film with a compact morphology with 300 nm of thickness; this layer is also evident from the as-electrodeposited film shown in **Figure 5(b)**. It was noticeable that the compact layer is due to the initial growth when the current density is in a transitory state and the diffusion layer is thin. Over the compact CIGS film, there are only formations of isolated nodules of different sizes with very large boundaries between them; in this stage of formation, the current density and the mechanism of mass transport are not locally uniform. In order to reduce the activation energy and grow large grains during the annealing process, a Cu-rich film was prepared. The film composition ratios were Ga/(In+Ga) = 0.29 and Cu/(In+Ga) = 1.18. The Cu content of the film determines the activation energy for grain boundary motion. It has been determined that by increasing the Cu content of the film from 17.9 to 25.7%, the activation energy decreases from 3.5 to 3.0 eV [36]. The micrographs of annealed films are shown in **Figure 6(c, d)**. From these micrographs, it can be noted that there is also a compact CIGS film over the Mo film, which shows that in the copper-poor and copper-rich films, the films are compact in the first stage of growth, up to a thickness of 300 nm. A nonuniform grain growth is identified. There is only a grain growth in the boundaries indicating that the kinetic of grain growth during selenization process in the nodule boundaries was different, which is believed to be caused by the non-homogeneity in the film composition originated by the nonuniformity of the current density during the one-step electrodeposition process. Copper-rich films were formed in the nodule boundaries. In this way, the atomic composition in the films is not uniform, the nodules are copper-poor, and the boundary nodules are copper-rich. That is, the film locally will have different electrical, structural, and optical characteristics.

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**Figure 6.** Micrographs of surface and cross section of the CIGS films with (a, b) composition ratio Cu/(In + Ga) = 0.9 and (c, d) composition ratio Cu/(In + Ga) = 1.18 [13].
