Morphology, Structure and Mechanical Properties of Copper Coatings Electrodeposited by Pulsating Current (PC) Regime on Si(111)

: Copper electrodeposition on (111)-oriented Si substrate was performed by the pulsating current (PC) regime at various average current densities in the range of 15–70 mA · cm − 2 , obtained by varying either the frequency (30, 50, 80 and 100 Hz for the current density amplitude of 100 mA · cm − 2 ) or the current density amplitude (120 and 140 mA · cm − 2 at 100 Hz). The produced Cu coatings were examined by SEM, AFM and XRD techniques. The morphology of the coatings changed from those with large grains to ﬁne-grained and globular, while the crystal structure changed from the strong (220) to the strong (111) preferred orientation by increasing the average current density. The mechanical characteristics of coatings were examined using Vickers micro-indentation tests, applying the Chicot–Lesage (C–L) composite hardness model for the analysis of microhardness. The maximum microhardness was obtained for the Cu coating produced at an average current density of 50 mA · cm − 2 , with a current density amplitude of 100 mA · cm − 2 and a frequency of 100 Hz. This copper coating was ﬁne-grained and showed the smallest roughness in relation to the other coatings, and it was obtained in the mixed activation–di ﬀ usion control between the end of the e ﬀ ect of the activation control and the beginning of the dominant e ﬀ ect of di ﬀ usion control.


Introduction
Nanocrystalline materials, and in particular metals, whose grain sizes do not exceed 100 nm, have become attractive for use in various industries due to their specific physicochemical and mechanical properties. Several techniques are known for the synthesis of nanocrystalline materials in the form of thin films or coatings on various substrates: chemical vapor deposition (CVD), physical vapor deposition (PVD), electrochemical deposition (ED), electroless deposition (EL), etc. [1]. Physical methods for deposition of thin films, such as sputtering or evaporation, are limited in terms of film thickness, intended for thin films of less than 1-2 µm [2]. Unlike physical methods, there are no restrictions on the thickness of the film during the application of electrodeposition methods.
For application in Micro-Electromechanical Systems (MEMS) technologies, thin films and coatings must have good adhesion to the substrate, good corrosion resistance and good wear resistance, while maintaining satisfactory mechanical properties [3][4][5][6][7]. In MEMS technologies, the processes of the formation of uniform and compact Cu films and coatings are applied in the production of inductive copper micro-coils for magnetic particles detection [8], in combination with micro-machining techniques to obtain micro-gear [9], for wiring on printed circuit boards (PCBs) and bottom-up filling or superfilling techniques for fabrication of Through Silicon Via (TSV) structures [10]. In addition, copper coatings are used as sacrificial layers for the production of different laminar composite structures [11]. Aside from MEMS technologies, various processes of Cu deposition also found a wide application in microelectronic packaging and interconnects [12,13].
For all the above-mentioned applications, good film quality at the micro-or nano-level is required, and electrodeposition processes are very suitable to reach it. In relation to the application of constant regimes of electrolysis, the improvement of the quality of Cu coatings, i.e., their morphological and structural characteristics, can be achieved by the application of electrodeposition at a periodically changing rate [14][15][16], and the addition of specific substances known as additives to the electroplating baths [17][18][19], or simply by the regulation of parameters of electrolysis including mixing of the electrolyte, finding of the optimal temperature for electrodeposition or balanced salt/acid contents when acidic baths are used [20,21].
One of the most important mechanical characteristics of metal films and coatings is microhardness, which is closely dependent on processing parameters used for their production [22,23]. Examining the mechanical response of a composite system constructed from substrate and film or coating on indentation and estimating the absolute film hardness independently from the substrate hardness include knowledge of parameters and phenomena such as type of the composite system [24], applied load, duration of the applied load at indentation (dwell time) and indentation depth [25,26], thickness of the coatings [27], elastic properties of the coatings [28], indentation size effect (ISE) [29][30][31][32], interfacial adhesion [33,34], etc. A large number of mathematical composite models have been developed so far to determine the "true" or absolute hardness of the film [27,[32][33][34][35][36].
In this study, morphological, structural and mechanical characteristics of Cu coatings electrodeposited on Si(111) substrate by the pulsating current (PC) regime were examined. This was done with the aim to define working conditions enabling the formation of uniform and compact coatings of high microhardness. For that purpose, parameters of the PC regime, such as the current density amplitude and frequency (pause duration), were analyzed. The thickness of the coatings was also examined. The composite hardness model of Chicot-Lesage (C-L) was chosen and applied to experimental data in order to analyze the composite systems made [27,35,36]. The basis of the theory of the composite hardness model according to Chicot-Lesage (C-L) is given in Appendix A.

Materials and Methods
Electrodeposition of copper was performed from 240 g·L −1 CuSO 4 ·5H 2 O in 60 g·L −1 H 2 SO 4 at room temperature by the regime of pulsating current (PC). Analytical grade chemicals and doubly distilled water were used for the preparation of the electrolyte. The parameters of the PC regime used in the electrodeposition processes are given in Table 1.
The working conditions were selected to enable the formation of compact deposits with uniform current density distributions without stirring of the electrolyte. The thickness of all Cu coatings mentioned in Table 1 was 40 µm. The coatings with different thicknesses of 10, 20 and 60 µm were additionally made under the conditions given for Sample 1. In all experiments, Si(111) wafers (2", p-type, thickness 300 ± 15 µm), cut as pieces with a total surface area of 2 cm 2 , were used as the substrate (cathode) for the electrodeposition process. The preparation of Si(111) wafers as a cathode was performed according to the standard MEMS procedure [37], by the formation of thin layers of Cr (30 nm) and Au (100 nm) on Si as adhesion and nucleation layers by the sputtering procedure, using the Perkin Elmer 2400 sputtered system Metals 2020, 10, 488 3 of 21 (PerkinElmer Corporation, Massachusetts, MA, USA). The surface area for Cu electrodeposition was 1 cm 2 . A high purity copper plate was used as the anode. The Si(111) plate prepared for the electrodeposition was situated in the middle of the cell between two parallel Cu plates.
For this electrolyte, the polarization curve was recorded by the potentiostatic method using working, reference and counter electrodes of pure copper [38]. Table 1. The parameters of the pulsating current (PC) regime used in the electrodeposition processes. j A -the current density amplitude, t c -deposition time (on period), t p -pause time (off period), p-the pause-to-pulse ratio, j av -the average current density and ν-frequency.

Characterization of the Produced Cu Coatings
Characterization of the produced Cu coatings was performed by the following techniques: (a) The morphology of the Cu coatings was examined by scanning electron microscope (SEM)-model JEOL JSM-6610LV (JEOL Ltd., Tokyo, Japan).
(b) The X-ray diffraction (XRD) analysis of the Cu coatings was performed applying RIGAKU Ultima IV diffractometer (Rigaku Co. Ltd., Tokyo, Japan) in Bragg-Brentano Geometry with CuKα radiation in a 2θ range from 30 • to 95 • .
The preferred orientation of Cu coatings was estimated by determining the "Texture Coefficient", TC(hkl) and the "Relative Texture Coefficient", RTC(hkl) [39][40][41]. The procedure for the determination of these coefficients is described in Appendix B.
(c) The surface topography of the Cu coatings of 70 × 70 µm 2 scan area was examined using an atomic force microscope (Auto Probe CP Research; TM Microscopes, Veeco Instruments, Santa Barbara, CA, USA) in the contact mode. The values of the arithmetic average of the absolute (R a ) roughness parameters were measured from the mean image data plane, using software SPLab (SPMLab NT Ver. 6.0.2., Veeco Instruments, Santa Barbara, CA, USA).
(d) The mechanical characteristics of the Cu coatings were characterized using Vickers microhardness tester Leitz Kleinert Prufer DURIMET I (Leitz, Oberkochen, Germany) with loads ranging from 2.942 N down to 0.049 N. The dwell time was 25 s. Measurements were performed at room temperature. For each load, three indentations were made and the diagonals of the indents were measured by an optical microscope (Olympus CX41; Olympus Corporation, Tokyo, Japan) connected to the computer. With the mean value of the diagonal of the indent, the value of the composite hardness could be calculated for each load. The Chicot-Lesage (C-L) composite hardness model was used to analyze the obtained experimental data.

Basic Facts Necessary for Understanding of the Presented Results
The square wave pulsating current (PC) regime is defined by Equation (1) [42,43]: or Metals 2020, 10, 488 where j av is the average current density, j A is the current density amplitude, t c is deposition pulse (on period), t p is pause duration in which the system relaxes (off period) and p is the pause-to-pulse ratio. The PC regime is efficient in a frequency range between 10 and 100 Hz, in which the surface concentration of depositing ions is only determined by the average current density [42,43]. In this frequency range, the surface concentration of depositing ions is constant and equal to that of the constant regime at the current density corresponding to the average current density in the PC regime. From the point of view of the application of this regime, it means that the electrodeposition process by the PC regime in the millisecond range occurs at the average current density.
The polarization curve for copper electrodeposition from 240 g·L −1 CuSO 4 ·5H 2 O in 60 g·L −1 H 2 SO 4 is shown in Figure 1. The ends of the activation control and the mixed activation-diffusion control (i.e., the beginning of the plateau of the limiting diffusion current density) are denoted by vertical lines in this Figure. The end of the activation control corresponds to an overpotential of 100 mV, while the end of the mixed activation-diffusion control corresponds to an overpotential of 500 mV.
where jav is the average current density, jA is the current density amplitude, tc is deposition pulse (on period), tp is pause duration in which the system relaxes (off period) and p is the pause-to-pulse ratio.
The PC regime is efficient in a frequency range between 10 and 100 Hz, in which the surface concentration of depositing ions is only determined by the average current density [42,43]. In this frequency range, the surface concentration of depositing ions is constant and equal to that of the constant regime at the current density corresponding to the average current density in the PC regime. From the point of view of the application of this regime, it means that the electrodeposition process by the PC regime in the millisecond range occurs at the average current density.
The polarization curve for copper electrodeposition from 240 g·L −1 CuSO4·5H2O in 60 g·L −1 H2SO4 is shown in Figure 1. The ends of the activation control and the mixed activation-diffusion control (i.e., the beginning of the plateau of the limiting diffusion current density) are denoted by vertical lines in this Figure. The end of the activation control corresponds to an overpotential of 100 mV, while the end of the mixed activation-diffusion control corresponds to an overpotential of 500 mV.   (Figure 2g,h). These frequencies were obtained by a regulation of pause duration keeping a constant amplitude of the current density and the deposition pulse ( Table 1).

Morphology of the Cu Coatings Obtained by Application of the PC Regime
The Cu coating obtained at a frequency of 30 Hz was very coarse, with large and relatively well-defined crystal grains (Figure 2a,b). The Cu crystals up to about 10 µ m in size were formed by this PC regime. The coarseness of the coatings decreased by increasing the frequency, as seen from    (Figure 2g,h). These frequencies were obtained by a regulation of pause duration keeping a constant amplitude of the current density and the deposition pulse ( Table 1).

Morphology of the Cu Coatings Obtained by Application of the PC Regime
The Cu coating obtained at a frequency of 30 Hz was very coarse, with large and relatively well-defined crystal grains (Figure 2a,b). The Cu crystals up to about 10 µm in size were formed by this PC regime. The coarseness of the coatings decreased by increasing the frequency, as seen from Figure 2c-h. The smaller number of larger Cu grains (up to 10 µm in size) was obtained with an applied frequency of 50 Hz relative to 30 Hz (Figure 2c,d). The majority of the grains were about 5 µm. The coatings obtained with frequencies of 80 and 100 Hz (Figure 2e-h) were smoother than those obtained with frequencies of 30 and 50 Hz. A further decrease in crystal size and an increase in the uniformity of the coatings was observed by increasing the frequency. In coatings obtained at 80 and 100 Hz, the average crystal size was below 5 µm. Figure 3 shows the morphologies of Cu coatings obtained with amplitudes of the current density of 120 mA·cm −2 (Figure 3a,b), and 140 mA·cm −2 (Figure 3c,d). In this series of experiments, the frequency of 100 Hz (t c = 5 ms and t p = 5 ms) is kept constant ( Table 1). Please note that the coating shown in Figure 2g,h is obtained with an amplitude of 100 mA·cm −2 at the same frequency. those obtained with frequencies of 30 and 50 Hz. A further decrease in crystal size and an increase in the uniformity of the coatings was observed by increasing the frequency. In coatings obtained at 80 and 100 Hz, the average crystal size was below 5 µ m. Figure 3 shows the morphologies of Cu coatings obtained with amplitudes of the current density of 120 mA·cm −2 (Figure 3a,b), and 140 mA·cm −2 (Figure 3c,d). In this series of experiments, the frequency of 100 Hz (tc = 5 ms and tp = 5 ms) is kept constant ( Table 1). Please note that the coating shown in Figure 2g,h is obtained with an amplitude of 100 mA·cm −2 at the same frequency. those obtained with frequencies of 30 and 50 Hz. A further decrease in crystal size and an increase in the uniformity of the coatings was observed by increasing the frequency. In coatings obtained at 80 and 100 Hz, the average crystal size was below 5 µ m. Figure 3 shows the morphologies of Cu coatings obtained with amplitudes of the current density of 120 mA·cm −2 (Figure 3a,b), and 140 mA·cm −2 (Figure 3c,d). In this series of experiments, the frequency of 100 Hz (tc = 5 ms and tp = 5 ms) is kept constant ( Table 1). Please note that the coating shown in Figure 2g,h is obtained with an amplitude of 100 mA·cm −2 at the same frequency.  At first sight, it can be mentioned that the Cu coating obtained with the amplitude of the current density of 120 mA·cm −2 (Figure 3a,b) was relatively similar to that obtained with the amplitude of the current density of 100 mA·cm −2 (Figure 2g,h). A uniform and compact structure with a Cu crystal size of about 5 µ m and less were obtained. A completely different surface morphology of Cu was obtained with the amplitude of the current density of 140 mA·cm −2 ( Figure  3c,d). Aside from parts with relatively uniform surface areas, the globules with a diameter of about 30 µ m were also formed by this PC regime. At first sight, it can be mentioned that the Cu coating obtained with the amplitude of the current density of 120 mA·cm −2 (Figure 3a,b) was relatively similar to that obtained with the amplitude of the Metals 2020, 10, 488 6 of 21 current density of 100 mA·cm −2 (Figure 2g,h). A uniform and compact structure with a Cu crystal size of about 5 µm and less were obtained. A completely different surface morphology of Cu was obtained with the amplitude of the current density of 140 mA·cm −2 (Figure 3c,d). Aside from parts with relatively uniform surface areas, the globules with a diameter of about 30 µm were also formed by this PC regime.

X-ray Diffraction (XRD) Analysis of the Produced Cu Coatings
The X-ray diffraction patterns of Cu coatings obtained with the frequencies of 30, 50, 80 and 100 Hz are presented in Figure 4, while those obtained with the current density amplitudes of 100, 120 and 140 mA·cm −2 are presented in Figure 5.  At first sight, it can be mentioned that the Cu coating obtained with the amplitude of the current density of 120 mA·cm −2 (Figure 3a,b) was relatively similar to that obtained with the amplitude of the current density of 100 mA·cm −2 (Figure 2g,h). A uniform and compact structure with a Cu crystal size of about 5 µ m and less were obtained. A completely different surface morphology of Cu was obtained with the amplitude of the current density of 140 mA·cm −2 ( Figure  3c,d). Aside from parts with relatively uniform surface areas, the globules with a diameter of about 30 µ m were also formed by this PC regime.

X-ray Diffraction (XRD) Analysis of the Produced Cu Coatings
The X-ray diffraction patterns of Cu coatings obtained with the frequencies of 30, 50, 80 and 100 Hz are presented in Figure 4, while those obtained with the current density amplitudes of 100, 120 and 140 mA·cm −2 are presented in Figure 5.  Aside from the Cu coating obtained at a frequency of 30 Hz, in all other XRD patterns, Cu crystallites were predominantly oriented in the (111) plane. In the XRD pattern of the Cu coating electrodeposited with a frequency of 30 Hz, the predominant orientation of Cu crystallites in the (220) crystal plane was observed. The preferred orientation of Cu coatings was estimated by determination of the "Texture Coefficient" (TC(hkl)) and "Relative Texture Coefficient" (RTC(hkl)) 40,41. It is necessary to note that the TC(hkl) values larger than 1.00 indicate the existence of the preferred orientation in the (hkl) plane. Simultaneously, since four reflections in the 2 range between 30° and 95° were recorded, the values of RTC(hkl) coefficients larger than 25% indicate the existence of the preferred orientation 40,41. The values of TC(hkl) and RTC(hkl) coefficients obtained for Cu coatings produced with frequencies of 30, 50, 80 and 100 Hz are given in Tables 2 and 3, respectively.  Please note that the XRD pattern obtained with the current density amplitude of 100 mA·cm −2 ( Figure 5) is given again and corresponds to that obtained with a frequency of 100 Hz in Figure 4.  [41]. Aside from the Cu coating obtained at a frequency of 30 Hz, in all other XRD patterns, Cu crystallites were predominantly oriented in the (111) plane. In the XRD pattern of the Cu coating electrodeposited with a frequency of 30 Hz, the predominant orientation of Cu crystallites in the (220) crystal plane was observed. The preferred orientation of Cu coatings was estimated by determination of the "Texture Coefficient" (TC(hkl)) and "Relative Texture Coefficient" (RTC(hkl)) [40,41]. It is necessary to note that the TC(hkl) values larger than 1.00 indicate the existence of the preferred orientation in the (hkl) plane. Simultaneously, since four reflections in the 2θ range between 30 • and 95 • were recorded, the values of RTC(hkl) coefficients larger than 25% indicate the existence of the preferred orientation [40,41].
The values of TC(hkl) and RTC(hkl) coefficients obtained for Cu coatings produced with frequencies of 30, 50, 80 and 100 Hz are given in Tables 2 and 3, respectively. From Table 2, it can be seen that the Cu coating obtained with a frequency of 30 Hz possesses the strong (220) preferred orientation. According to the same table, the Cu coating obtained at a frequency of 50 Hz showed a (220) preferred orientation with considerably larger ratios of Cu crystallites oriented in the (111) and (311) planes than in the XRD pattern obtained at 30 Hz.
The Cu coatings obtained at frequencies of 80 and 100 Hz showed (311) and (111) preferred orientations ( Table 3). Analysis of TC and RTC coefficients indicated larger ratios of Cu crystallites oriented in the (311) plane than in the (111) plane. Simultaneously, increasing the applied frequency from 80 to 100 Hz led to a decrease of Cu crystallites oriented in the (311) plane and an increase of those oriented in the (111) plane. As indicated in Table 1, the increase in frequency from 30 to 100 Hz is a result of the increase in the average current density from 15 to 50 mA·cm −2 .
The TC(hkl) and RTC(hkl) coefficients calculated for the Cu coatings obtained with a j A of 120 and 140 mA·cm −2 are given in Table 4.
Similar to the Cu coating obtained with an amplitude of 100 mA·cm −2 (100 Hz), the copper coating obtained with an amplitude of 120 mA·cm −2 showed (111) and (311) preferred orientations, with the further decrease of ratios of Cu crystallites oriented in the (311) plane and the increase of ratios of Cu crystallites oriented in the (111) plane. Finally, the strong (111) preferred orientation was observed in the Cu coating obtained with an amplitude of 140 mA·cm −2 .
Anyway, it follows that increasing the average current density of the electrodeposition from 15 to 70 mA·cm −2 led to the strong change in the structure of coatings from the strong (220) to the strong (111) preferred orientation, and it will be explained later in Section 4.

The Roughness Analysis of the Cu Coatings
The AFM surface areas of Cu coatings produced at different frequencies and their line section analyses are shown in Figure 6.   The corresponding values of the arithmetic average of the absolute (R a ) roughness obtained by application of the AFM software are given in Table 5. The decrease of roughness by increasing the frequency is clearly visible from Figure 6 and Table 5. This decrease was about three times with the change of frequency from 30 to 100 Hz.  The Ra values of these Cu coatings are added to Table 5. The surface topographies of the shown AFM images were similar to those obtained with a jA of 100 mA·cm −2 (Figure 6d), while their Ra values were slightly higher than the value obtained with a jA of 100 mA·cm −2 . Please note that analysis of the part of the surface area among globules in the Cu coating obtained with a jA of 140 mA·cm −2 was performed. This is the reason for the similarity of its surface topography and Ra value with those obtained with a jA of 100 and 120 mA·cm −2 . For a comprehensive analysis of the effect of the parameters of PC regimes on the formation of uniform and compact Cu coatings, the presence of globules (Figure 3c) must not be excluded.
The morphology of metal deposits is primarily determined by either condition of electrolysis, such as type and composition of electrolytes, temperature, stirring of electrolyte, the type of cathode material, the presence of additives to electroplating bath, etc., or parameters defining periodically changing regimes of electrolysis [43], while the effect of the time of electrolysis (i.e., the thickness of The R a values of these Cu coatings are added to Table 5. The surface topographies of the shown AFM images were similar to those obtained with a j A of 100 mA·cm −2 (Figure 6d), while their R a values were slightly higher than the value obtained with a j A of 100 mA·cm −2 . Please note that analysis of the part of the surface area among globules in the Cu coating obtained with a j A of 140 mA·cm −2 was performed. This is the reason for the similarity of its surface topography and R a value with those obtained with a j A of 100 and 120 mA·cm −2 . For a comprehensive analysis of the effect of the parameters of PC regimes on the formation of uniform and compact Cu coatings, the presence of globules (Figure 3c) must not be excluded.
The morphology of metal deposits is primarily determined by either condition of electrolysis, such as type and composition of electrolytes, temperature, stirring of electrolyte, the type of cathode material, the presence of additives to electroplating bath, etc., or parameters defining periodically changing regimes of electrolysis [43], while the effect of the time of electrolysis (i.e., the thickness of the coating) on the morphology of coatings is less pronounced. However, it is well known that the value of the microhardness of coatings strongly depends on its thickness. For that reason, the Cu coating which had a fine-grained structure (Figure 2g,h) and showed minimal roughness (Figure 6d; Table 5), obtained with a j A of 100 mA·cm −2 at 100 Hz, was additionally analyzed by varying its thickness. The AFM surface areas and the corresponding line section analyses of the Cu coatings produced under the given conditions with thicknesses of 10, 20 and 60 µm are shown in Figure 8, while the values of R a roughness are added to Table 5. The increase of roughness by increasing the thickness of coatings is clearly visible from Figure 8 and Table 5.

Absolute Hardness of the Substrate
Microhardness testing was performed first on the substrate of Si(111) covered with the adhesion and nucleation layers of Cr/Au (30/100 nm) in order to observe their hardness response and to determine the absolute hardness of the substrate. Due to the brittleness of Si, it was not possible to apply all the mentioned loads, but measurements in the load range from 0.245 N to 0.98 N were acceptable for diagonal readings. Based on the Proportional Specimen Resistance (PSR) model [44] and Equation (2) from Appendix A, the hardness of the substrate which is load-independent was obtained. This is shown in Figure 9. The calculated absolute hardness of the

Absolute Hardness of the Substrate
Microhardness testing was performed first on the substrate of Si(111) covered with the adhesion and nucleation layers of Cr/Au (30/100 nm) in order to observe their hardness response and to determine the absolute hardness of the substrate. Due to the brittleness of Si, it was not possible to apply all the mentioned loads, but measurements in the load range from 0.245 N to 0.98 N were acceptable for diagonal readings. Based on the Proportional Specimen Resistance (PSR) model [44] and Equation (2) from Appendix A, the hardness of the substrate which is load-independent was obtained. This is shown in Figure 9. The calculated absolute hardness of the substrate was 7.42 GPa.

The Composite and the Coating Hardness
The copper coatings on Si substrates can be considered as a "soft film on a hard substrate" type of composite system [24,45]. Composite and coating hardness values obtained at different frequencies, different amplitudes of the current density and different coating thicknesses were measured and calculated. Changes in the microstructure of the coating will directly affect the values of composite hardness and coating microhardness.
When analyzing the hardness of the composite systems, three areas can be distinguished according to the value of the relative indentation depth (RID = h/δ), where h is the indentation depth and δ is the total coating thickness. When the RID is between 0 and 0.1, it is considered that the influence of coating hardness on composite hardness value is dominant [46]. For the relative indentation depths between 0.1 and 1, it was found that the hardness of the composite system depends on both the hardness of the substrate and the coating hardness and their relative difference. The influence of the substrate is dominant for the values of the RID ≥ 1.
The effect of changing the frequency on the composite hardness Hc, and coating microhardness Hcoat, is shown in Figure 10a,b, respectively.
As already mentioned, in this set of experiments, the current density amplitude was maintained at 100 mA cm -2 and the thickness of the coatings was 40 µ m. An increase in frequency led to an increase in the composite hardness of the system. The values of the coating microhardness were calculated according to the C-L model. The highest values of the composite hardness and the coating microhardness were obtained at a frequency of 100 Hz and the lowest values were obtained for a frequency of 30 Hz. The influence of frequency on the microstructure of the coatings and its hardness is best observed for the relative indentation depth between 0 and 0.1, when the influence of the coating on the composite hardness is dominant.
Variations of the composite hardness and coating microhardness with the current density amplitudes are shown in Figure 10c,d. The frequency value was maintained at 100 Hz and the

The Composite and the Coating Hardness
The copper coatings on Si substrates can be considered as a "soft film on a hard substrate" type of composite system [24,45]. Composite and coating hardness values obtained at different frequencies, different amplitudes of the current density and different coating thicknesses were measured and calculated. Changes in the microstructure of the coating will directly affect the values of composite hardness and coating microhardness.
When analyzing the hardness of the composite systems, three areas can be distinguished according to the value of the relative indentation depth (RID = h/δ), where h is the indentation depth and δ is the total coating thickness. When the RID is between 0 and 0.1, it is considered that the influence of coating hardness on composite hardness value is dominant [46]. For the relative indentation depths between 0.1 and 1, it was found that the hardness of the composite system depends on both the hardness of the substrate and the coating hardness and their relative difference. The influence of the substrate is dominant for the values of the RID ≥ 1.
The effect of changing the frequency on the composite hardness H c , and coating microhardness H coat , is shown in Figure 10a,b, respectively.
As already mentioned, in this set of experiments, the current density amplitude was maintained at 100 mA cm −2 and the thickness of the coatings was 40 µm. An increase in frequency led to an increase in the composite hardness of the system. The values of the coating microhardness were calculated according to the C-L model. The highest values of the composite hardness and the coating microhardness were obtained at a frequency of 100 Hz and the lowest values were obtained for a frequency of 30 Hz. The influence of frequency on the microstructure of the coatings and its hardness is best observed for the relative indentation depth between 0 and 0.1, when the influence of the coating on the composite hardness is dominant.
Metals 2020, 10, x FOR PEER REVIEW 13 of 23 coating, and the highest coating microhardness value was obtained for the current density amplitude value of 100 mA·cm −2 (Figure 10d).  Variations of the composite hardness and coating microhardness with the current density amplitudes are shown in Figure 10c,d. The frequency value was maintained at 100 Hz and the thickness of the coatings was 40 µm. Three values of the current density amplitude were selected for analysis: 100, 120 and 140 mA·cm −2 . Please note that values obtained with a j A of 100 mA·cm −2 are repeated and they correspond to those given in Figure 10a,b for 100 Hz. The maximum value of the composite hardness was obtained for the copper coating deposited with the current density amplitude of 100 mA·cm −2 and the minimum value for the amplitude of 140 mA·cm −2 (Figure 10c). The results of the calculated coating microhardness according to the C-L model more clearly indicate the influence of the amplitude change on the microstructure and the hardness of the coating, and the highest coating microhardness value was obtained for the current density amplitude value of 100 mA·cm −2 (Figure 10d).
Coating thickness is a parameter that significantly affects the composite hardness. As the thickness increases, the coating's participation in the composite system increases. Variations of the composite hardness and coating microhardness with the thickness of coatings at optimal deposition parameters (ν = 100 Hz and j A = 100 mA·cm −2 ) are given in Figure 10e

Discussion
It is clear from the above consideration that the highest value of copper coating microhardness was achieved with a j A of 100 mA·cm −2 at 100 Hz, i.e., and with a j av of 50 mA·cm −2 (Figure 2g,h). This coating was fine-grained and had the smallest roughness. High coating microhardness values were also achieved at a frequency of 80 Hz (Figure 2e,f), as well as with the current density amplitude j A of 120 mA·cm −2 (Figure 3a,b). These coatings also have fine-grained structure and their roughness was slightly higher than that obtained with a j A of 100 mA·cm −2 at 100 Hz.
For the lowest frequency value of 30 Hz, the obtained coating was coarse-grained with large relatively well-defined grains (Figure 2a,b). The roughness of this coating was considerably higher than those observed at 80 and 100 Hz, as well as with a j A of 120 mA·cm −2 . The direct consequence is the lower coating microhardness value. Similar results to those for 30 Hz were obtained when the 50 Hz frequency was applied (Figure 2c,d). Applying the current density amplitude of 140 mA·cm −2 , a rough structure with globules was obtained (Figure 3c,d), and as a result of this, the decrease of microhardness of this Cu coating was observed.
All the above-mentioned surface morphologies had a thickness of 40 µm. In coatings of 10 and 20 µm thickness, a contribution of the substrate hardness to the composite hardness was significant.
With an increasing thickness of the coatings, the roughness of coatings increased (Figure 8), resulting in a decrease of composite hardness and coating microhardness for the coating electrodeposited with a thickness of 60 µm relative to that of 40 µm.
Due to the strong dependence of morphology and structure of Cu coatings on the microhardness, optimization of the process of the formation of Cu coatings with a compact and uniform structure on Si(111) by the PC regime was done and discussed as follows. Table 6 shows summarized values of overpotential amplitude (η A ) response obtained with analyzed parameters of the PC regime during electrodeposition processes. In the PC regimes, overpotential amplitude responses consist of the activation and diffusion parts, where a contribution of the activation part of the overpotential depends on the pause-to-pulse ratio and increases with it, i.e., a contribution of the activation part increases with an increase of pause duration and a decrease of frequency [47]. The set of equations explaining it is given in Appendix C.
Regarding the fact the that formation of large well-defined grains is a characteristic of the activation control of the electrodeposition [38,43], it is clear that Cu coatings obtained with a p of 5.66 and 3 (30 and 50 Hz; Figure 2a-d) are formed under conditions of the dominant activation control of the electrodeposition. Of course, a contribution of the activation control to the overall control was larger with an applied frequency of 30 Hz (Figure 2a,b) than with 50 Hz (Figure 2c,d). The high contribution of the activation control at 30 Hz is confirmed by an overpotential amplitude response at this frequency of 99−135 mV (Table 6), which corresponds to the end of the activation control and to the beginning of the mixed activation-diffusion control of the electrodeposition (Figure 1).
The formation of globules with an amplitude of 140 mA·cm −2 (Figure 3c) clearly indicates that the contribution of diffusion becomes dominant in the overall control of the electrodeposition process. This is confirmed by an overpotential amplitude response of 380-500 mV corresponding to the end of the mixed activation-diffusion control ( Figure 1).
Hence, optimum conditions for the formation of compact and uniform films of satisfactory microhardness corresponds to the range of overpotential in the mixed activation-diffusion control between the end of the effect of the activation control and the beginning of the dominant effect of diffusion control. For these working conditions, the optimum conditions are in the range of overpotentials between 200 and 400 mV (denoted by vertical dash lines in Figure 1), and they can be achieved in different ways by appropriate selection of parameters of the PC regimes. Of course, one challenge in the future will be to extend this overpotential range.
Aside from the strong effect on the morphology of the Cu coatings, the applied parameters of PC regimes also had a strong effect on the structure of the coatings leading to a change of preferred orientation from the strong (220) to the strong (111), that can be explained in the following way.
For the FCC crystal lattice of Cu, the values of surface energy of crystal planes follow the trend: γ 111 < γ 100 < γ 311 < γ 110 [48,49]. As a result of different surface energy values, rate of electrodeposition is different on crystal planes, following the opposite trend from that for surface energy values [50]. The (100), (110) and (311) crystal planes are situated to the group of fast-growing planes, while the (111) plane belongs to the group of slow-growing crystal planes [51]. It means that during the electrodeposition process, the fast-growing (100), (110) and (311) planes disappear firstly, while the slow-growing (111) plane survives.
The average current density of 15 mA·cm −2 is too low to cause the disappearance of the fast-growing (220) plane, and the coarse Cu coating with large grains obtained at this average current density (i.e., at 30 Hz) showed the strong (220) preferred orientation. Intensification of the electrodeposition process through an increase of j av from 15 to 25 mA·cm −2 led to faster disappearing of Cu crystallites oriented in the (220) plane, and an increase of the ratios of Cu crystallites oriented in the next (311) plane. As a result of this, the Cu coating obtained at a j av of 25 mA·cm −2 (i.e., at 50 Hz) showed a smaller degree of (220) preferred orientation than that obtained at 30 Hz. The further increase of the average current density from 40 mA cm −2 (80 Hz) and 50 mA·cm −2 (100 Hz) to 60·mA·cm −2 (j A = 120 mA·m −2 ) led to the formation of Cu coatings with crystallites preferentially oriented in the (311) and (111) planes. It is necessary to note that the ratio of Cu crystallites oriented in the fast-growing (311) plane decreased, while the ratio of Cu crystallites oriented in the slow-growing (111) plane increased by increasing the average current density from 40 to 60 mA cm −2 . Finally, the Cu coating obtained at the average current density of 70 mA·cm −2 at which diffusion became the dominant process possessed the strong (111) preferred orientation.
Composite hardness values, H c , were calculated from the experimentally measured indentation diagonals according to Equation (1) from Appendix A. The increase of H c for the RID < 0.1 can be explained by strengthening of the coatings by deformation [35,36,52].
The obtained results are in accordance with the Hall−Petch effect [53], predicting the linear dependence of the hardness of the deposits on the reciprocal square root of grain size [54,55]. Namely, it is well known that an increase in the current density of electrodeposition leads to a decrease of grain size causing an increase in the hardness of deposits [53]. This linear dependence is valid up to some value of grain size corresponding to the certain current density, after which the value of the hardness of the deposit begins to decrease. The decrease of hardness after maximum value, i.e., the transition from grain-size strengthening to grain-size softening can be attributed to a change in the triple junction (i.e., intersection of three or more grain boundaries) volume fraction [53]. In our case, it is clear that the increase of hardness with the decrease of grain size can be attributed to the grain-size strengthening effect achieved in the mixed activation-diffusion control, while the grain size softening effect corresponds to the beginning of the dominant diffusion control of electrodeposition when globules forms.
According to the C-L model, it is possible to calculate the hardness of the coating only from the microhardness results (diagonal of the indent), because the values obtained for the coating hardness are influenced by the applied load. How the coating hardness changes according to this model will depend not only on the type of composite system, but also on the hardness of the coating and the substrate and the ratio of their hardness values. Due to the observation of the variation in hardness of the coating with RID, we applied the model to all samples. According to Equation (7) (Appendix A), the largest effects on the coating hardness have coefficients A, B, and C, which are dependent on parameter f. This parameter is a function of δ/d, and the C-L model gives the most reliable results for the δ/d ratios of about 1 [56,57]. In our case, this condition is fulfilled for coating thicknesses of 10 and 20 µm in the whole range of examined loads. For the coating thickness of 40 µm, this condition is fulfilled in the RID range between 0.1 and 1 for the composite hardness and to a greater extent for the coating hardness. Regarding the coating thickness of 60 µm, the δ/d ratio is considerably larger than 1, causing noticeably larger values for the composite and the coating hardness. It is worth noting that such high values of coating hardness have been reported already for the Cu coatings obtained by pulse electrodeposition [52].
The discrepancy between the composite hardness and the calculated coating hardness can be explained as follows: the composite hardness is determined from Equation (1), while the coating hardness is determined from Equation (7) (both equations from Appendix A). As already mentioned, the main parameter affecting the coating hardness is δ/d, where a contribution of this parameter in the calculation of the coating hardness increases by increasing the thickness of the coating. As a result of this, the difference between the composite and the coating hardness increases by increasing the coating thickness, causing a limitation in the application of the C-L model for the thicker coatings. Of course, morphological characteristics of coatings, such as shape and size of grains, roughness of the coatings, as well as substrate type, also affect the final values of the composite and the coating hardness.
Anyway, the high microhardness showed the Cu coatings with Cu crystallites predominantly oriented in the (111) plane, which is the closest-packed crystal plane of the FCC lattice. According to our opinion, similar to mirror bright Cu coatings [58], the (111) plane is not crucial for the enhanced microhardness of coatings, but it plays a significant role in this mechanical characteristic of Cu coatings.

Conclusions
The conditions enabling the formation of compact and uniform Cu coatings of a high microhardness by the regime of pulsating current (PC) were defined. The Cu coatings were produced in the 15−70 mA·cm -2 range by varying either the frequency (pause duration) or the current density amplitude. The maximal microhardness showed the Cu coating obtained at a frequency of 100 Hz with the current density amplitude of 100 mA·cm −2 and a pause duration of 5 ms. The optimal thickness of the coating was 40 µm.
It was shown the strong dependence of the microhardness of coatings on their morphology and topography. The copper coating with maximal microhardness was fine-grained and showed low roughness. The coatings with large and relatively well-defined Cu crystals and globules had a smaller microhardness from those with the fine-grained structure. Analysis of the overpotential amplitude responses showed that the Cu coatings of the highest microhardness are obtained in the range of overpotentials between the end of the effect of the activation control and the beginning of the dominant effect of diffusion control of electrodeposition.
Aside from the strong influence on morphology, and hence on microhardness of the Cu coatings, parameters of the PC regimes also affect their crystal structure. The preferred orientation of the coatings changed from the strong (220) to the strong (111) preferred orientation by increasing the average current density. This change was caused by the dependence of the rate of electrodeposition on the process parameters, i.e., on selected average current density.
The Chicot-Lesage (C-L) model was applied for a determination of the coating hardness. The most reliable values for the coating hardness are obtained for the thicknesses of coatings from 10 and 20 µm. For the coating thickness from 40 µm, the reliable values are obtained in the RID range between 0.1 and 1. Finally, for the coating thickness of 60 µm, the considerably higher values of coating hardness, but in accordance with those found in the literature, were obtained, making this model less appropriate for thicker coatings of copper. The limitations in the application of the C-L model for the thicker coatings of copper are also discussed. The model suggested by Chicot and al. [27,35] is based on the analogy between the variation of Young's modulus of reinforced composites in the function of the volume fraction of particles and the variation of the composite hardness with the indentation load. The values of the composite hardness are in the range between the hardness of the substrate and the hardness of the film [35,36,56,57,59,60]. The model assumes the use of only those data that can be obtained from micro-indentation tests (measured composite hardness, H c ).
The composite hardness value depends on the measured diagonal size and applied load and it is defined by Equation (A1) [56,57,59]: where P is the applied load (in N), the constant 1.8544 is a geometrical factor for the Vickers pyramid and d is the average diagonal length of the indent (in m). In order to apply a composite hardness model, it is necessary to know the absolute hardness of the substrate before depositing the coating.
The Proportional Specimen Resistance model (PSR) of Li and Bradt [44] is suitable for analyzing the variation of substrate microhardness with the load: Here, P c is the critical applied load above which microhardness becomes load-independent and d 0 is the corresponding diagonal length of the indents. A plot of P/d against d will give a linear plot.
The slope value multiplied by the geometric constant gives the value of the absolute hardness of the substrate (H S ).
The measured composite hardness values of the system are not constant because the hardness is load-dependent. Meyer's law [61] expresses the variation of the diagonal size in the function of the applied load. Meyer's law can be expressed as the relation: P = a * · d n * (A3) The variation of the hardness value with load is presented by the factor n*, characterizing the way of change of the load hardness, as presented by the Equation (A4) [56,57,59]: where δ is the coating thickness, d is average indent diagonal size, and exponent m corresponds to the inverse of Meyer index for composite material. The value of m (composite Mayer's index) is calculated by a linear regression performed on all experimental points for a given film-substrate system as: Then, the composite hardness model can be expressed by Equation (A6) [56,57]: Rewriting this relation as a polynomial in terms of H coat , the coating hardness can be calculated which is thus the positive root of the equation: The parameters A, B and C represent the coefficients of the second-order polynomials in Equation (A7) and the hardness of the coatings is the positive root of this equation. The parameter (δ/d) m , or function f, can be calculated from Equation (A4), and Meyer's index from Equation (A5). With the known value of m, only the hardness of the coatings remains to calculate.

Appendix B
Determination of the "Texture Coefficient", TC(hkl) and the "Relative Texture Coefficient", RTC(hkl) by analysis of the XRD data The ratio of reflection intensity (hkl) to the sum of all intensities of the recorded reflections, R (hkl), (in %) is given by Equation (A8) [39][40][41]: The "Texture Coefficient", TC(hkl), for every (hkl) reflection is defined by Equation (A9): where R s (hkl) is defined in the same way as given by Equation (A9), but is related to the Cu standard (04-0836). This coefficient gives accurate quantitative information about the absolute reflection intensity. Finally, the "Relative Texture Coefficient", RTC(hkl) is defined by Equation (A10): The RTC (hkl) coefficient defines the reflection intensity (hkl) relative to the standard (included in the TC values).

Appendix C
The dependence of the overpotential amplitude on parameters of the pulsating current regimes In the PC regime, the overpotential amplitude, η A can be presented by Equation (A11) [47]: where b c is the cathodic Tafel slope, j L is the limiting diffusion current density, and j 0 is the exchange current density. The activation part of overpotential, η act is given by Equation (A12): while the diffusion part of overpotential, η diff is given by Equation (A13): Hence, it follows from Equation (A12) that the activation part of the overpotential depends on the pause-to-pulse ratio and increases with it. Equation (A12) can be rewritten in the form: where η const is the overpotential in the constant regime of electrolysis defined by Equation (A15): if j av = j, where j is the current density in the constant regime of electrolysis. From the point of view of the average current density, it means that there is no difference between electrochemical deposition processes in the constant regimes and PC conditions. On the other hand, it is very clear from Equation (A15) that at the fixed value of the average current density the amplitude of overpotential depends on the pause-to-pulse ratio, and it increases with the increasing pause-to-pulse ratio.
According to Popov and Pavlović [62], the degree of diffusion control of electrodeposition process, ω, is defined by Equation (A16): and it represents a contribution of diffusion overpotential to total cathode overpotential. Hence, due to the increase of the activation part of overpotential with the increasing pause-to-pulse ratio, the degree of diffusion control will decrease with the increasing pause-to-pulse ratio, resulting in the possible change of texture of deposit. It is noteworthy that it is valid if j av < j L in the mixed controlled deposition.