Article pubs.acs.org/crystal
Effect of Anodic Passivation at High Applied Potential Difference on the Crystal Shape and Morphology of Copper Electrodeposits: Thermodynamics and Kinetics of Electrocrystallization Arijit Mitra,† Manila Mallik,† Srijan Sengupta,† Swastika Banthia,‡ Karabi Das,†,‡ and Siddhartha Das*,†,‡ †
Department of Metallurgical and Materials Engineering and ‡School of Nano Science and Technology, Indian Institute of Technology, Kharagpur, West Bengal, India 721302 S Supporting Information *
ABSTRACT: In this paper, we discuss the effect of potential difference and current density on the crystal morphologies of copper electrodeposits. Their individual roles have been identified by creating a passivation layer in situ at the anode during deposition, which instantaneously reduces the current density in the system while maintaining a high potential difference. It is observed that the crystal shape is decided by the potential difference and current density determines the rate at which that shape is achieved. In a copper system, at high overpotentials, coherent twin boundaries are formed due to their low formation energy as compared to high angle grain boundaries, high index surface planes, etc. Without the presence of any foreign species like H2 bubbles during the crystallization process, the slowest growth direction is identified to be . The passivation layer is formed due to a pH distribution in the electrolyte caused by the high electric field. A new methodology to explain the formation of the passivation layer is proposed, which is performed by analyzing the current transients generated using Kirchhoff’s Laws.
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INTRODUCTION The whole domain of materials engineering, and nanoscience and engineering is based on tinkering with the crystallographic aspect and microstructure of the materials to tune the physical, mechanical, electronic, and/or chemical properties of a material. Of the many processing routes, electrodeposition is one of the processes frequently employed to manufacture coatings for the purpose of changing the surface properties of a material. The process of electrodeposition involves reducing individual ions in an electrolyte by passing electric current and hence is a promising technique to manufacture materials which find their applications in energy storage devices, solar cells, corrosion resistant coatings, very large scale integration (VLSI) contact materials, flip chip technology, micropatterning, nanobiosystems, etc.1−8 Electrodeposition is also a feasible technique for fabricating materials with different meso- and nanostructures.9 Face centered cubic copper is one of the elements which is frequently electrodeposited as surface coatings, material for contact in VLSI fabrication, contact material for arcing equipment, etc. The structure−property relationships in an FCC copper system are well-studied and established from the thermal processing point of view. For example, in solidification processing, the nucleation and growth phenomena are wellknown, and by using various heat treatment procedures, the materials can be fabricated to give desirable properties. However, the concept of the evolution of the microstructure © 2017 American Chemical Society
from the electrochemical processing route requires a few more inputs and modification. A lot of work on the nucleation and growth mechanisms of copper electrodeposits has been published which tackle the observations from the chemical thermodynamics and kinetics perspective along with the role of additives on their mechanisms.10−17 In fact, most of the electrochemical theories have been developed based on the knowledge of chemical mass transport, thermodynamics, and kinetics.11,18−21 For example, Mattsson et al. and Bockris et al. studied the kinetics of deposition of copper using galvanostatic depositions and provided a nucleation mechanism of copper.22−24 Grujicic et al. identified the mechanism of nucleation of copper at different pH using chronoamperometry in dilute concentrations of CuSO4.25 In our previous work on Sn−Cu eutectic solder, we have evaluated the morphological aspect of Sn crystals electrodeposited under pulsed galvanostatic conditions.26 A similar shape controlled electrodeposition of Sn crystals was also performed by Müller et al. from Sn(II) fluoroborate solutions.27 A common aspect observed in all these publications is that the thermodynamics of the system is directly related to the kinetics of the system; i.e., an increase in the overpotential for deposition results in the increase in the current density for Received: September 26, 2016 Revised: January 27, 2017 Published: February 9, 2017 1539
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passivation films start forming after 100 cycles of deposition approximately. Hence, for the studies without the formation of passivation films in the anode, the depositions were carried out for 1000 cycles in total while cleaning the anodic surface after every 100 cycles. In all other cases the depositions were run for 5000 cycles. The formation of passivation films at the anode resulted in the drop in current density at the same applied potential differences. Hence, to record the effect of potential difference on the crystal morphologies, pulsed galvanostatic electrodeposition of copper was also performed at the current densities which were recorded after passivation in pulsed potentiostatic deposition case with the same pulse frequency and duration. It is to be noted that the passivation also occurs in a constant DC bias mode. The microstructural aspects of the copper deposits were analyzed using scanning electron microscope (FEI Quanta 250 FEG, FEI, Netherlands) equipped with an energy dispersive spectroscopy system (Bruker XFlash 6|100). The TEM samples were prepared by thinning the substrate by anodic corrosion, followed by cryogenic ion beam milling to eliminate dislocation generation during milling process in the samples. The TEM images of the deposits along with their selected area diffraction pattern (SADP) were obtained using an FEI Tecnai G2 Microscope operating at 200 kV. The artificial crystal morphological studies were performed using WinXMorph.28,29 WinXMorph software can generate the crystals based on the surface planes which are expected to be present in the crystal, governed by the conditions of a 3D volume enclosure by the planes and point group symmetry of the lattice. The crystal shapes can be modified based on the distance of the surface planes from the center of the crystal. To identify a guess shape of the crystal, stereographic projection diagrams pertaining to the point group symmetry of FCC copper were used. As an example, the shape of {1 0 0} planes, when enclosed by {1 1 0} planes will assume the shape of a square, which can be constructed by joining the {1 1 0} poles in a {1 0 0} stereographic projection. If {1 0 0} planes are enclosed by {1 1 1} planes, they will assume a square shape, which can be constructed by joining the {1 1 1} poles in the {1 0 0} stereographic projection. If {1 1 1} planes are enclosed by {1 1 0} planes, they will assume the shape of a hexagon or a triangle (depending on the Miller indices of the planes enclosing it), which can be constructed by joining the {1 1 0} poles in {1 1 1} stereographic projection. If {1 1 1} planes are enclosed by {1 0 0} planes, they will assume a triangular shape. The shapes of the planes usually come from the rotational symmetry of the crystal, defined by the point group. The {1 0 0} set of planes have a 4-fold symmetry, because of which they are present in the crystal surface in the shape of a square, in most cases. The {1 1 1} set of planes have a 3-fold symmetry, because of which they are present in the crystal surface in the shape of a triangle, in most cases. The angular relationships between the planes are automatically maintained by WinXMorph software, based on the point group symmetry. Any impossible solution is automatically rejected by the software if the condition of volume enclosure by the surface planes is not met. SADP analysis was performed using JEMS software.30 Stereographic projection diagrams of different zone axis for FCC copper was also generated using JEMS software. The surface chemistry of the passivating films formed in the copper anode was determined using an X-ray photoelectron spectroscope (PHI Versa Probe II, Ulvac-Phi, USA) with 100 μm 25 W monochromatic Al Kα radiations (1486.6 eV). The work function of the analyzer was 4.26 eV. The pass energy resolution data are provided in the Supporting Information section 3. The passivation films were stable only during pulsed potentiostatic deposition and disappeared when the bias was removed. Hence, the passivating films on anode for surface analyses were prepared by removing the anode while the deposition was ongoing, and the film was rinsed very gently with double deionized water and the films were stored immediately after vacuum drying in a vacuum desiccator prior to surface measurement. Point XPS analysis was performed for the samples by keeping them at 45ο with respect to the analyzer, and charge neutralization was done using a low energy electron gun and low energy ion gun. Depth profiling of the passivating films was done to remove the surface hydrocarbon layer using 2 mm × 2 mm 2 kV an argon gun. The C 1s peak was identified
deposition. This draws a similarity with solidification processing, where temperature controls both the nucleation and growth of the crystal. In the electrochemical deposition route, the free energy calculations involve the potential terms. Any deviation or polarization from the equilibrium potential, derived from the Nernst equation, affects the free energy of the electrochemical reaction which should ideally be reflected in areas like the critical nuclei radius in the heterogeneous nucleation expression. Similarly, the rate of metal ion reduction, determined from the current density flowing through the electrode, should affect the nucleation and growth rates of the crystal. However, the overpotential and current densities in an electrochemical cell are related to each other, in most of the cases by relationships like the Butler−Volmer equation. An individual study varying just the overpotential to identify the regions it affects in the nucleation and growth theory is extremely difficult to perform due to the dependency between the current density and overpotential. This inter-relationship masks the true roles of these two deposition parameters in determining the nucleation and growth process of the crystal from an electrochemical deposition route, mentioned above. The thermodynamics of nucleation and growth, which is governed by the overpotential, can be separately studied from the kinetics of nucleation and growth (governed by the current density) by reducing the current density in the electrochemical cell dynamically with the help of a passivation layer at the anode. The passivation layer at the counter electrode makes the routine nucleation and growth mechanism identification by I− V characteristics of working electrode−electrolyte system impossible, as the traditional analysis requires the counter electrode to be nonpassivating in nature. This paper aims to study the individual effect of thermodynamics and kinetics in determining the shape of the crystal in the electrochemical deposition process from the perspective of materials engineering, electrochemistry, and electrical engineering.
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EXPERIMENTAL SECTION
The copper electrodeposits were prepared from an aqueous electrolytic bath containing 1 M copper(II) sulfate (Loba Chemie) and 0.5 M sulfuric acid (Merck) [prepared using 98% conc. sulfuric acid]. The pH of the electrolyte was recorded as 0.12 ± 0.02 at 23.7 °C. Sulfuric acid was added to deionized water followed by copper(II) sulfate. Pulsed potentiostatic electrodeposition was carried out in a two-electrode setup in Autolab PGSTAT 302N (Metrohm, Netherlands) equipped with a 10 A current booster, with rectangular-shaped copper anodes and cathodes substrates (99.9% purity). The dimensions of both the copper anodes and cathodes are 2 cm × 1 cm. Copper anode substrates were prepared using electrodeposition to ensure its purity. The details of the anode preparation are provided in the Supporting Information section 1. The electrical circuit equivalent of the deposition setup was determined using electrochemical impedance spectroscopy (EIS) in the frequency range of 100 kHz to 0.1 Hz at the open circuit potential, and the circuit structure and parameters were estimated using ZSimpWin 3.21. The pulse frequency for the deposition was decided from the impedance spectroscopy of the system, such that it lies in the charge-transfer controlled region. No stirring or agitation was employed during the whole deposition process. The distance between the electrodes was maintained between 4.5 and 4.7 cm during deposition. The temperature was also maintained at room temperature (25−27 °C approximately) throughout the deposition process for all the cases. Each cycle consisted of 5 on and 5 off pulses, having a duration of 0.005 and 0.01 s, respectively, determined from the EIS spectrum. Thus, the pulse frequency and duty cycle applied during the experiment were calculated as 66.67 Hz and 30% respectively. The potential differences chosen for the pulsed potentiostatic depositions are 5 and 9 V. The 1540
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oxy z + + z e− ⇔ red
and shift corrected at 284.6 eV, which primarily came from environmental hydrocarbons. The obtained spectrum was analyzed and quantified using MultiPak Software. Reason for Not Choosing a Three Electrode Setup for Pulsed Potentiostatic Measurements. Potential measurements are tricky in electrochemistry and require an additional reference electrode to accurately measure the potential of the working electrode. I−V characteristics of the working electrode and electrolyte system along with the chrono-amperometric behavior are utilized to assess the nucleation and growth of crystal and also determine their morphological aspects. However, in the presented experiment, the inertness of the auxiliary electrode is not present, which affects the potential measurements of the working electrode. It was observed that the formation of a passivation layer in the auxiliary electrode immediately sent the potentiostat into a state of voltage overload, which caused it to stop the measurement. Hence, the authors were forced to rely on a two electrode setup. Additionally, due to the low pH value of the electrolyte, the passivation layer instantaneously dissolved back, thus making it nearly impossible to restabilize it for three electrode based measurements, without changing the electrolyte composition. Potential measurements can still be made using a two electrode setup by properly identifying the regions where potential drop occurs, which is discussed in detail in Supporting Information section 5.
where “oxy ” represents the oxidized species, converted to its reduced species “red” by a transfer of z electrons. The Nernst equation relates the reduction potential of the eq 1 to the reaction quotient and gives a picture of the thermodynamics of the electrochemical reaction. Any deviation from the equilibrium electrode potential, in the form of overpotential, alters the reaction quotient of the system and takes it to a nonequilibrium state. The nonequilibrium state of the reaction will lead to either consumption or ejection of electrons, which will in-turn be observed in the form of current density. Thus, the current density represents the kinetics of the system away from equilibrium. Nucleation and growth processes depend entirely on the overpotential and current density in the electrochemical system, which ultimately governs the shape and morphology of the grown crystals. In this case the oxidized species is the Cu2+ ions and the reduced species is Cu0 atom. The free energy of formation of Cu crystal from Cu2+ ions by reduction can be represented as eq 2
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crystal ΔGform = −zFη +
RESULTS AND DISCUSSION Morphological Aspects of the Electrodeposits. The various input parameters along with the recorded, steady-state output parameters are tabulated in Table 1. A visible, greyish-
deposition type
1
pulsed potentiostatic (non-passivation)
2
pulsed potentiostatic (passivation)
3
pulsed galvanostatic
input parameter
output parameter
5V
0.6 ± 0.03 A·cm−2
9V 5V
1.16 ± 0.02 A·cm−2 0.018 ± 0.006 A·cm−2
9V 0.018 A·cm−2 0.18 A·cm−2
0.18 ± 0.02 A·cm−2 0.27 ± 0.03 V 0.56 ± 0.05 V
∑ Ahkl γhkl + σ
(2)
where η represents the applied overpotential for reduction, γhkl represents the surface energy of the hkl plane present at the surface of the crystal with an area Ahkl, and σ represents the total energy required to create miscellaneous elements like grain boundaries, dislocations, stacking faults, twins, etc. The surface energy can be plotted against the angular relationships between the planes in the form of Gibbs−Wullf Plots.34 The −zFη term in eq 2 represents the energy that is available for generating the crystal, of which ∑Ahklγhkl is used to create the surface of the crystal and σ goes into generating the grain boundaries, dislocations, etc. The rate at which a Cu2+ ion is incorporated into the crystal is equal to the rate of electron consumption (or the current), which determines the growth rate. Thus, the current density is related to the growth rate of the formed nuclei. The current density also determines the nucleation rate and density as the formation of nuclei with a defined critical radius will require a certain number of copper ions to be reduced to their atomic states. From eq 2, a low applied potential difference will lead to a lower free energy pool for crystallization. At lower applied potential differences, the surface of the crystals will be dominated by the presence of the low index planes like {1 1 1}, {1 1 0}, and {1 0 0}, which have lower surface energies. Dislocations and other boundaries will also be present, but their number density will be lower due to the low free energy pool for crystallization. Similarly, a high applied potential difference will lead to a greater free energy pool for crystallization. This allows the presence of higher index planes at surfaces, and a larger number of grain boundaries, dislocations and coherent twin boundaries in the crystal. However, the crystal would like to have the minimum possible free energy by the free energy minimization criteria, and thus there is a trade-off between the occurrence of these additional elements such that the free energy is minimum. In the case of a cubic crystal like FCC copper, higher index planes at the surface of the crystal are highly unfavorable from the energetics point of view and are possible only when the growth rates are uniform in all the directions. On the other hand, the number of grain boundaries and dislocations can increase. Coherent twin boundaries are preferable in FCC copper due to the addition of elements of
Table 1. Input Parameters during Deposition and Their Recorded, Steady-State Output Parameters S. no.
(1)
z+
black layer is observed at the copper anode when the 5000 deposition cycles are run, which is identified as the passivating layer. A photograph of the layer is presented in Supporting Information, section 2. Two significant effects of the passivation layer at the anode are observed in the electrodeposition cell. The first one is the significant drop in the current density flowing through the cell, and the second one is the retardation and subsequent stopping of H2 bubble generation in the cathode. Figure 1 shows the TEM images of the copper electrodeposits deposited with and without the passivation layer under the same applied potential differences (S. No. 1 and 2 in Table 1). It is observed that coherent twin boundaries are present in the electrodeposits with and without the passivation films. Diffraction pattern analysis reveals the twin operation to be (1 1 1) [1 1 2̅], which matches the coherent twin operation observed in FCC copper.31−33 Twins are, however, not observed in the galvanostatic deposition with the same current densities obtained from the passivation cases (S. No. 3 in Table 1). An electrochemical reaction can be expressed as 1541
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Figure 1. TEM micrographs along with selected area diffraction pattern indicating twinning for (a) 5 V applied potential difference deposition with passivating anode, (b) 9 V applied potential difference deposition with passivating anode, (c) 5 V applied potential difference without the passivating anode, and (d) 9 V applied potential difference without the passivating anode. Zone axis identified in (a) and (b) are [1 0 1]̅ and [1̅ 0 1], respectively.
correlated the twins generation in copper to high current densities and large pH values.36 Since high current densities are usually accompanied by high deposition overpotentials, Lu et al. have failed to correctly identify which parameter was responsible for the twin nucleation. Also, the authors must have encountered low pH near the vicinity of the cathode due to the accumulation of H+ ions under an electric field, even though convective mass transport was present during their experiments. Figure 2 shows the morphologies of the copper electrodeposits deposited under various conditions mentioned in Table 1. It is observed that the crystal shape of the copper deposits from the galvanostatic depositions and potentiostatic depositions with passivating anode are different, as shown in Figure 2a,b and Figure 2e,f. It is well-known that coadsorption
symmetry and thus have lower formation energy as compared to high angle grain boundaries (HAGB). In fact, the formation energy of coherent twins is the least when compared to HAGB, high-index plane surfaces, stacking faults, etc.32,35 Moreover, twins orient the crystal toward favorable growth directions decided by the current density. Thus, the increase in free energy pool due to increase of overpotential by high applied potential difference allows the spending of energy on the formation of high index-plane surface, dislocations, HAGB, twins etc., of which coherent twins are the most favorable ones because of their low formation energy in FCC copper. Coherent twin boundaries are observed in the passivation layer cases in spite of the low current densities flowing through the Electrodeposition cell. This conclusion is partly contradicting with the explanation provided by Lu et al., where they 1542
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Figure 2. Morphologies of the copper deposits deposited under (a) 5 V applied potential difference with a passivating anode; (b) 9 V applied potential difference with a passivating anode; (c) 5 V applied potential difference without a passivating anode; (d) 9 V applied potential difference without a passivating anode; (e) galvanostatic deposition at a current density of 0.018 A·cm−2 (passivating current density at 5 V applied potential difference); and (f) galvanostatic deposition at a current density of 0.18 A·cm−2 (passivating current density at 9 V applied potential difference).
Figure 3. High magnification SEM images showing the morphologies along with the artificial shape in the inset for copper electrodeposits deposited under (a) 5 V applied potential difference with a passivating anode; and (b) 9 V applied potential difference with a passivating anode.
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Figure 4. High magnification SEM images showing the morphologies for copper electrodeposits deposited under (a) 5 V applied potential difference without a passivating anode; (b) 9 V applied potential difference without a passivating anode. Artificial structure generation is impossible due to extensive twinning.
Figure 5. High magnification SEM images showing the morphologies along with artificial shape at inset for copper electrodeposits deposited galvanostatically at (a) current density of 0.018 A·cm−2, (b) current density of 0.18 A·cm−2.
understandable at high magnifications. The shapes of the copper crystals in Figures 3 and 5 are completely different from each other even though the current densities recorded/applied during the deposition are same. It is observed that no high index planes are present at the surfaces of the crystal except for the crystal in Figure 4b, which evolve due to the nonuniform growth rate in all directions leading to a nearly spherical crystal. Extensive twinning also occurred to orient the growing crystal in multiple directions in Figure 4b, which gives the look of a spiral growth in the crystal. The surface planes in Figure 4b cannot be identified due to this. An interesting observation on the growth velocity of the individual planes can be deduced from Figure 5. The artificial morphology in Figure 5a shows a cylindrical crystal with axis along the direction and having {1 1 0} planes at the outer surface. A copper atom with fractional coordinates (0.0, 0.0, 0.0) in a unit cell belongs to {1 0 0}, {1 1 0}, and {1 1 1} planes. Hence, an addition of atom at the surface during growth at a position (l*a, m*a, n*a), where l, m, n ϵ N and a being the lattice parameter of copper, will lead to the said atom becoming a part of the {1 0 0}, {1 1 0}, and {1 1 1} planes. The direction having the fastest growth velocity will eventually get annihilated at the surface, and only the slow growing planes will remain at the surface.26 The crystal indicated by the arrow in Figure 5a can be identified as the
of foreign species like H2 gas affect the growth direction and crystal shape of electrodeposits.26 However, in both cases, no hydrogen evolution was observed. Hence, this proves that the crystal shape is decided by the applied potential difference or the overpotential of the electrocrystallization. Different free energy pool for crystallization, due to the different applied/ recorded voltage, results in different crystal shapes according to eq 2. The deposits under the nonpassivation and passivation cases, shown in Figure 2a,b and Figure 2c,d, also exhibit different crystal shapes. It can be attributed to the higher growth rate and hydrogen evolution in nonpassivation cases. Figures 3, 4, and 5 show the high magnification images highlighting individual crystal along with an artificially generated shape of the crystal at the inset. Ideally, the crystal facets should be identified with the help of crystallographic techniques like EBSD. However, EBSD requires the sample surfaces to be highly polished, preferably electropolished, to obtain good and reliable signals. Electropolishing will destroy the crystal shapes, and hence the EBSD technique is ruled out for identification of crystal shapes. Crystal shapes are generated according to the procedure mentioned in the experimental section. Twinning of crystals in most of the cases makes it difficult to identify individual crystal shapes at low magnifications. However, the shapes of some of the crystals are 1544
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Figure 6. XPS spectra (a) survey scan, (b) core level scan for Cu, (c) core level scan for O, (d) core level scan for S. The presence of both the oxidation states of Cu along with SO42− and O2− indicates that the passivation layer is composed of a mixture of sulfate and oxides of copper.
cylindrical crystal in the same figure with {1 1 1} planes emerging from it during growth. Also, the area of {1 0 0} planes in Figure 5b decreases, while the area of {1 1 1} planes increases. This leads to the conclusion that is the slowest growing direction, without the effect of coadsorption of foreign species like H2 gas. The presence of high index planes and complex structural elements like twins in the crystals for high overpotential depositions is also reported by Mallik et al. and Müller et al. in their results, which are supported from the conclusions drawn above.26,27 The surfactants used for the shape control of copper nanoparticles during electrodeposition, performed by Wen-Yin Ko et al., modulated the surface energy of the atomic planes.37 The conclusions drawn above support the results observed by Wen-Yin Ko et al., where the changes in the surface energy of atomic planes due to the surfactants affects the quasiequilibrium crystal shape and growth rates of the surface planes. Dale et al. performed a real time AFM study of electrodeposition of bismuth, where they observed no new nucleation of bismuth crystals at very low overpotentials, which are consistent with the conclusions drawn above.38 The low overpotentials lead to a lower free energy pool for
crystallization, thereby increasing the critical nuclei radius. On the other hand, the low current densities associated with low overpotentials reduced the nucleation rate. The combination of these two effects resulted in no new nucleation of bismuth crystals, as observed by Dale et al. Chemistry of the Passivation Layer and Its Formation. The passivation layer at the anode plays a very important role in identifying the parameters of thermodynamics and kinetics in nucleation and growth process. The passivation films are characterized using XPS to identify their chemical composition. Figure 6 shows the XPS spectra obtained from the passivation layer. We identify the presence of Cu, O, S, and C peaks from a survey scan until 1100 eV as shown in Figure 6a. Figure 6b−d shows the core level spectrum for Cu, O, and S, respectively. Deconvolution and curve fitting show the presence of CuI and CuII ions in Cu core spectra; the O and S core level spectra indicate the presence of SO42− and O2− ions. Quantification from the deconvolution and curve fitting, presented in Table 2, confirms the presence of CuSO4, Cu2O, and CuO in the passivation layer. CuSO4 has probably formed when the dissolved Cu2+ ions coming out of the copper anode combined with the SO42− ions in the double layers to crystallize into 1545
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toward the cathode and negative ions migrate toward the anode. This creates a depletion of H+ ions in the anode, and hence the local pH at the anode rises. Also, the Cu2+ ions generated from anodic reaction affect the local concentration of H+. Thus, the anode pH now shifts toward the higher pH area in the pourbaix diagram and enters into region where the oxides are stable at the applied anode potential. The oxides provide a high resistance to the current flow in the circuit, which causes a drop in the current density value even though the high deposition potential difference and electric field are provided in the system. Analysis of the Current Transients. In an electrochemical process, the current density and applied potential are related to each other through parameters like electrolyte resistance, double layer capacitance, etc. In a traditional voltammogram, as applied potential difference is increased, the current density also increases. However, an unusual combination of applied potential difference and current density is encountered, where the current density abruptly drops at high potential differences. The chrono-amperometric curves recorded for depositions at 5 and 9 V potential after 2 cycles and after 5000 cycles are presented in Figure 7. Earlier reports and analysis on current transients observed in electrochemical studies have never shown such a sharp drop in current density values within the time frame of the order of milliseconds. The whole electrochemical system can be very well characterized if it is tackled as an electrical engineering problem. The first step would be to identify the equivalent circuit of the whole setup, which can be
Table 2. Atomic Fractions of the Elements in the Passivating Layer Identified from XPS Spectrum along with the Expected Compounds element and line 3/2
Cu 2p O 1s S 2p Cu 2p3/2 O 1s Cu 2p3/2 O 1s
RSF
normalized atom %
expected compound
4.395 0.733 0.717 4.395 0.733 4.395 0.733
11.15 44.6 11.15 4.85 4.85 15.6 7.8
CuSO4
CuO Cu2O
CuSO4. This CuSO4 is unable to redissolve as the water molecules are being depleted due to their splitting reaction at the anode. The chemistry of the passivation layer is very puzzling as the oxides of copper are unstable in such a highly acidic electrolyte. However, a very justifiable reason for its formation and stability during deposition can be provided in this case. In the two electrode setup with copper anode and cathode substrate, the OCP recorded is ∼0 V. When the potential differences are applied, the anode potential moves toward the Cu2+ region, and the cathode potential moves toward the Cu region in the pourbaix diagram. At the initial moment, the pH near both the anode and cathode is equal. Because of the high electric field which is generated in the electrolyte by the potential difference, a charge separation is created wherein the positive ions migrate
Figure 7. Chronoamperometric curves for depositions under 5 and 9 V potential difference, respectively for (a, b) 2 cycles and (c, d) 5000 cycles. 1546
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Figure 8. (a) Nyquist plot for the frequency response of the electrochemical cell along with (b) equivalent circuit representation. (c) Modified circuit structure incorporating the growth resistance of passivation layer.
and profile fitting of chrono-amperometric curves are provided in Supporting Information section 4. Kirchhoff’s circuit laws are applied on the modified electrical circuit as shown in Figure 8c, with a constant voltage V applied across it. The CPE element corresponds to a capacitor of capacitance Cdl. The capacitive current and the faradaic current are icap and ifaradaic, respectively. The voltage across the capacitor is Vc. Since, the inductance element is very small, it can be neglected from the calculations. Writing the Kirchhoff’s circuit equations:
performed using EIS at open circuit potential (OCP). The EIS spectrum, presented in Figure 8a, reveals the equivalent circuit to be a simple Randle’s circuit as shown in Figure 8b. For simplicity, the CPE element in the circuit can be considered as a capacitor. This is because in a polycrystalline material, each grain will have their own Randle’s circuit, and the overall circuit from the combination of these circuits from individual grains will result in the double layer capacitance being replaced by the constant phase element. The applied pulse frequency for depositions lies in the charge-transfer controlled region. A profile fitting of the chrono-amperometric curves during the on-period shows a sigmoidal nature of the current transient for both the cases of 5000 cycle depositions. This is very different from a typical chrono-amperometic curve which shows an exponential behavior due to RC discharge in a charge transfer controlled process when the R and C values are constants, or follows the Cottrell equation when it is a mass-transfer controlled process. Judging from the steady state current values, it is identified that the resistance value is changing with respect to time. When the passivating layer is forming due to the charge separation under electric field, it increases the resistance of the system which comes off as an additional resistance Rg (growth resistance) in series to the charge transfer resistance RCT. When the electric field is removed during the off period of the pulse, dissolution of this passivating layer begins. The value of this additional resistance is thus time dependent. During the deposition process, the passivating layer forms and dissolves continuously, and therefore this process will reach a steady state at a certain point of time. At this moment, the amount of passivating film formed during the on period is equal to the amount of passivating film dissolved during the off period. The growth process of the passivating film can be deduced by observing the value of this additional resistance with time during the on period of the deposition. A point to remember is that the values of the circuit elements change when external current and voltage are applied, but the basic structure of the circuit remains unaltered. On the basis of this initial structure of the circuit, modeling of the process can be performed and the circuit parameters can be estimated using other electrochemical tests. Details of the EIS spectrum fitting
V = VC + (icap + ifaradaic)R electrolyte
(3)
icap = Cdl
dVC dt
(4)
ifaradaic =
VC R CT + R g
(5)
Substituting eqs 4 and 5 in 3, the final linear differential equation is ⎛ R electrolyte ⎞ dV ⎟⎟ + R electrolyteCdl C V = VC⎜⎜1 + R CT + R g ⎠ dt ⎝
(6)
The electrochemical reaction occurring at the anode is the oxidation of copper atoms under the presence of adsorbed water molecules to form copper oxides, as presented in eq 7. k fCT
Cu + H 2O (ads) ⎯⎯→ copper oxides + 2H+ + 2e−
(7)
In eq 7, the forward reaction is favored during the on period of the pulse as the H+ ions are taken out due to the high electric field, and the backward reaction occurs when the H + concentration is restored during the off period of the pulse. The current is recorded by the potentiostat cum galvanostat for this reaction, as the electrons are generated in this reaction. Note that the above reaction may consist of multiple steps, and the overall rate is governed by the slowest step, whose forward rate constant is kfCT. The water molecule is present both in adsorbed as well as desorbed form. 1547
DOI: 10.1021/acs.cgd.6b01420 Cryst. Growth Des. 2017, 17, 1539−1549
Crystal Growth & Design H 2O (l) ⇔ H 2O (ads)
Article
By analyzing the current transients and treating the electrochemical phenomena from the perspective of an electrical circuit problem, one can indirectly estimate various electrochemical parameters and also ascertain the mechanism of the whole process. An electrochemical process can be treated as the circuit problems solved in electrical engineering and various simplistic models based on the techniques used in electrical engineering can be constructed to evaluate and represent the physical phenomena in the electrochemical process.
(8)
Assuming a first order kinetics for eq 8, then the concentration of adsorbed water molecules can be represented as [H 2O (ads)] = N0(C1 + C2 exp( −Ωt ))
(9)
where C1 =
k bads k fads
+
k bads
; C2 = φ0 − C1; Ω = k fads + k bads
⎛ 2αFη ⎞ d[oxide] ⎟ = k fCT[H 2O (ads)] = k 0CT exp⎜ ⎝ RT ⎠ dt (10)
The resulting current density can be obtained by calculating the rate of generation of electrons from the reaction, which is represented as J = 2F
d[oxide] dt
(11)
Combining eqs 9, 10, and 11, the expression of current density can be rewritten as ⎛ 2αFη ⎞ ⎟(C + C exp( −Ωt )) J = 2FN0k 0CT exp⎜ 2 ⎝ RT ⎠ 1
(12)
An electrical resistance for this phenomenon can be arrived at by differentiating eq 12 with respect to η and taking the inverse, which is Rg. Rg =
CONCLUSIONS
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ASSOCIATED CONTENT
(1) The effect of thermodynamics and kinetics of crystal growth by electrodeposition has been successfully studied by creating a passivation layer in situ at the anode during deposition process. (2) The crystal shape is determined by the overpotential (thermodynamic factor), whereas the current density (kinetic factor) controls the rate at which that shape is achieved. (3) With a big free energy pool for crystallization in cubic systems, creation of elements having a lower formation energy such as twin boundaries is favorable. (4) The slowest growth direction in copper is identified to be , without the effect of any foreign species like H2 bubbles. (5) The electrical resistance encountered during the growth of the passivation layer, consisting of copper(I) oxide, copper(II) oxide, and copper(II) sulfate, follows the sigmoid function. (6) A methodology based on identifying the circuit structure by EIS and applying Kirchhoff’s laws to estimate the circuit parameters has been discussed to model the passivation process.
N0 is the total number of active reaction sites per unit area, and φ0 is the fraction of active reaction sites covered by H2O (ads) at t = 0. The overall rate expression for the electrochemical reaction in 7 is represented as
[H 2O (ads)]
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S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b01420. Detailed discussions on anode preparation, experimental setup, passivation layer chemistry, analysis on the current transients, and the justification for choosing a two electrode setup for potentiostatic measurements (PDF)
⎛ 2αFη ⎞ RT 1 ⎟ exp⎜ − 2 CT ⎝ ⎠ RT (C1 + C2 exp( −Ωt )) 4F N0k 0 α (13)
The net current as well the current density which flows through the modified circuit, shown in Figure 8c, follows the sigmoid function when a constant potential difference is applied across the circuit for the expression of Rg provided in eq 4. The validation of the expression with the experimental data is provided in the Supporting Information section 4. By comparing the expression of Rg with the experimental data, the various parameters in expression can be obtained. However, many parameters in the expression of Rg like the active reaction sites per unit area N0 are statistical in nature. A qualitative overview can still be obtained from this method. For example, the steady state growth resistance value for the 5 V applied potential difference case, calculated from the current density plots, is larger than the 9 V potential difference case, which indicates that the passivation must be electrically breaking down as the applied voltage is increased. Also, the RCT value for the 9 V potential difference case (0.0285 Ω·cm−2) is lower than the 5 V potential difference case (0.649 Ω·cm−2), which is in accordance with the existing charge transfer theories. It is also estimated that the equilibrium constant of adsorption of water molecules is nearly the same for both the applied potential difference cases, which is consistent with existing theories.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Siddhartha Das: 0000-0002-0413-6680 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The authors would like to thank Mr. Arghya Patra for the help during the experimentation process. The authors would also like to thank Mr. Ratul Paul of Icon Analytical for the help in analyzing the XPS data of the passivation film.
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ABBREVIATIONS CPE, constant phase element; RCT, charge-transfer resistance; Rg, growth resistance; EIS, electrochemical impedance spectroscopy 1548
DOI: 10.1021/acs.cgd.6b01420 Cryst. Growth Des. 2017, 17, 1539−1549
Crystal Growth & Design
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Article
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