Influence of Poly (ethylene oxide) on the Process of Copper

Oct 11, 2007 - This allows a decrease in the overpotential associated with the electrodeposition process. The analysis of the j/t transients shows tha...
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16506

J. Phys. Chem. C 2007, 111, 16506-16515

Influence of Poly(ethylene oxide) on the Process of Copper Electrodeposition onto p-Si(100) Eduardo C. Mun˜ oz,†,‡ Ricardo S. Schrebler,*,† Ricardo A. Co´ rdova,† Ricardo E. Marotti,§ and Enrique A. Dalchiele§ Instituto de Quı´mica, Facultad de Ciencias, Pontificia UniVersidad Cato´ lica de Valparaı´so, Casilla 4059, Valparaı´so, Chile, Departamento de Ciencias Ba´ sicas, Escuela de Educacio´ n, UniVersidad de Vin˜ a del Mar, Agua Santa 7255, Vin˜ a del Mar, Chile, and Instituto de Fı´sica, Facultad de Ingenierı´a, UniVersidad de La Repu´ blica, Herrera y Reissig 565, C.C. 30, 11000 MonteVideo, Uruguay ReceiVed: June 20, 2007; In Final Form: August 10, 2007

In this study we examined the influence of the illumination intensity and the presence of poly(ethylene oxide) (PEO) as an additive for the process of copper electrodeposition onto p-Si(100). The study was carried out by means of cyclic voltammetry (CV) and the potential step method from which the corresponding nucleation and growth mechanism (NGM) were determined. Both methods were performed under illumination for the electron’s photogeneration. Likewise, a morphologic analysis of the deposits obtained at different potential values by means of atomic force microscopy (AFM) was carried out. In the first stage, Mott-Schottky measurements were taken to characterize the energetic of the semiconductor/electrolyte interface. The CV results indicated that the presence of PEO inhibits the electrochemical reaction of oxide formation on the surface of the semiconductor. This allows a decrease in the overpotential associated with the electrodeposition process. The analysis of the j/t transients shows that in the absence of additive the NGM corresponds to progressive 3D diffusional controlled (PN3DDIFF), while in the presence of PEO the NGM corresponds to instantaneous 3D diffusional controlled (IN3DDIFF). In both cases analysis by the AFM technique was performed and confirmed these mechanisms. The morphologic analysis by this technique led us to the conclusion that the deposits made in the presence of additive are more homogeneous.

1. Introduction The deposition of metallic films on semiconductors is usually performed in a vacuum from the vapor phase by evaporation or sputter deposition. Electrochemical deposition represents an alternative approach for the deposition of these films on semiconductor surfaces. The formation of these metallic phases requires a study of the nucleation and growth mechanisms and the influence of parameters such as potential and chemical composition of the solution. Considering silicon, there have been studies of electrochemical film growth. The deposition of metals on silicon generally follows a 3D islands growth mode due to the fact that the metal-metal interaction is stronger than the substrate-metal interaction.1-19 The copper nucleation and growth process onto silicon has been confirmed by means different techniques, such as scanning electronic microscopy (SEM), atomic force microscopy (AFM), and scanning tunneling microscopy (STM).1,7,12,13 The microstructure and morphology of electrodeposited thin films are controlled by addition of additives to the plating solution. These additives are widely used to control long length scale roughness (levelers) and to produce a textured, small grain size film (brighteners). In this sense, it has been shown that for the copper electrodeposition on Si, the use of additives, such as poly(ethylene glycol) (PEG), PEO, and bis(3-sulfopropyl) bisulfide, improve the homogeneity and texture of the depos* Corresponding author. Tel./fax: +56-32-273422. E-mail: rschrebl@ ucv.cl. † Pontificia Universidad Cato ´ lica de Valparaı´so. ‡ Universidad de Vin ˜ a del Mar. § Universidad de La Repu ´ blica.

its.1,11 However, when using polymeric additives, the understanding of the influence on the deposition process is still empirical. In a previous work we demonstrated that the presence of poly(ethylene oxide) (PEO) in the copper electrodeposition process on n-Si(100) increased the copper nucleus density due to the adsorption of this molecule at the active sites inhibiting the oxide formation and this way allowing a more homogeneous deposit.1 In this paper we report the influence of the additive PEO on the nucleation and growth mechanism of copper onto p-Si(100), in a sulfuric acid media. This process must be carried out under illumination for the photogeneration of electrons which in this case is necessary for observing the reduction of copper ions. The study was performed by cyclic voltammetry (CV) and the potential step method (PS). In addition, the morphology of the copper deposits was followed by atomic force microscopy (AFM). Also, a discussion about the nucleus density obtained by both methods was achieved. 2. Experimental Section Electrodeposition was performed on monocrystalline p-Si (100) with a resistivity between 0.1 and 0.3 Ω cm (NA = 5 × 1015 cm-3) and B-doped and polished/etched surfaces (Int. Wafer Service, CA). The silicon wafer was cut into squares (1.0 × 1.0 cm2) that were first degreased in boiling acetone for 10 min. Then they were sequentially cleaned ultrasonically for 10 min in acetone, ethanol, and finally water. The water was distilled and deionized (Millipore) and had a resistivity of 18 MΩ cm. Then the electrodes were treated for 10 min with a 1:1 H2SO4-H2O2 mixture heated up to 80 °C to remove any trace of heavy metals and organic species. Afterward, the oxide

10.1021/jp074813m CCC: $37.00 © 2007 American Chemical Society Published on Web 10/11/2007

Copper Electrodeposition onto p-Si(100) film was removed by etching with 2 M HF solution for 2 min and thoroughly rinsed with ultrapure water. The ohmic contact was made with InGa eutectic on the etched face of the samples, and the electrodes were mounted onto a Teflon holder. The silicon area exposed to the solution was 0.16 cm2. Before the electrochemical experiments, the electrode surface was again etched for 2 min in a 2 M HF solution. After this procedure, an atomically smooth and hydrogen-terminated surface has been obtained. For each measurement, a new electrode of p-Si(100) was used, due to the fact that it is well-known that copper can diffuse toward the inside of the silicon.9-20 A platinum wire was used as a counter electrode, and a mercury/mercury sulfate electrode (MSE) (Hg/Hg2SO4, K2SO4 (saturated), 0.640 V vs NHE) was used as a reference electrode. It was positioned close to the silicon samples using a Luggin capillary. All the potentials reported in this study refer to this reference electrode. The electrolytic solutions were prepared from analytical grade reagents with the following compositions: 5 mM CuSO4‚5H2O + 0.1 M H2SO4 + x mg/L [PEO] (0 e × e 100 mg/L). The molecular weight of the additive was 1 000 000. Cyclic voltammetry experiments were carried out at room temperature and at a scan rate of 0.010 V s-1, according to the perturbation programs indicated in the corresponding figures. For the chronoamperometric measurements, the following E/t program was applied to the electrode: the potential was first held for 5 s at a potential value where the copper electrodeposition is not observed and then stepped to the electrodeposition potential Ed. The Ed values varied between -0.350 and -0.650 V. All the measurements were carried out in darkness and illumination conditions. In this last case, a xenon lamp of 75 W (Oriel Instruments 6263) mounted in a lamp holder (Oriel 66902) was connected to the cell through a water filter (Oriel 61945) and a 1 m length optical fiber (Oriel 77578). A power supply of 40-200 W (Oriel 68907) was used to generate the arc in the lamp. The illumination power was quantified inside of the cell with an energy radiant meter (Oriel 70260). The samples were illuminated with different intensities that were of 2 and 3.5 mW cm-2. A pure argon stream was passed through the solution for 30 min before measurements and over the solution when the experiments were under way. The electrochemical measurements (cyclic voltammetry and chronoaperometry) were done using Princeton Applied Research (PAR) model 273 A equipment. The electrochemical impedance spectroscopy (EIS) measurements were done using Zahner model IM6e equipment. All samples used for ex situ AFM were prepared in the electrochemical cell. The AFM images were obtained with a Digital Instrument Nanoscope IIIa Series employed in tapping mode at a scan rate of 0.02 µm/s. 3. Results and Discussion 3.1. Cyclic Voltammetry Analysis of the p-Si(100) in Darkness and Illumination Conditions, in the Absence of Poly(ethylene oxide). Figure 1 shows the potentiodynamic j/E profiles for a p-Si(100) electrode in 0.1 M sulfuric acid in darkness (Figure 1a) and illumination (Figure 1b) conditions, without copper ions (solid curve) and with 5 mM CuSO4 (dot curve). These profiles were measured with the E/t perturbation program indicated in the inset of this figure. In Figure 1a, in the initial negative scan no significant processes are observed. In the presence of copper ions, a slightly cathodic contribution appears at -0.5 V, which is attributed to the copper electrodeposition due to layer inversion in the semiconductor. In the positive scan and in absence of copper,

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Figure 1. Potentiodynamic j/E profiles of a p-Si(100) electrode in 0.1 M H2SO4: (a) in darkness without copper ions (s) and in darkness with 5 mM CuSO4 (‚‚‚); (b) under illumination of 2.0 mW cm-2 without copper ions (s), with 5 mM CuSO4 (‚‚‚), and under illumination of 3.5 mW cm-2 with 5 mM CuSO4 (‚ - ‚). The inset shows the applied E/t perturbation program. Scan rate: 0.010 V/s.

from -0.4 V an anodic current is developed. This contribution is associated with the silicon surface oxidation according to the following reaction:

Si + 4h+ + 2H2O f SiO2 + 4H+

(1)

In the presence of copper, this process appears shifted toward more positive potential values because the copper film electrodeposited during the negative potential scan is blocking the more active sites of silicon. When a -0.35 V potential value is attained, the copper clusters are oxidized allowing the substrate oxidation. Under illumination conditions, during the negative scan in the absence of copper the only feature that is observed corresponds to the hydrogen evolution reaction (HER) beginning at -0.9 V. In the presence of copper ions and in both illumination conditions, a complex cathodic peak is developed previous to the HER which is attributed to the copper electrodeposition. Under these conditions, the HER begins at more positive potentials, because, in this case, the reaction is not occurring on the silicon surface but on the previously electrodeposited copper. In the reverse scan, a limit current is observed which is associated with the diffusional-controlled copper electrodeposition process and the proton reduction on these clusters previosly deposited. At -0.4 V is observed a cross-linking of the currents (forward and reverse scans) which can be associated with the increase of the electrode area due to the conductive film electrodeposited. At more positive potentials than -0.4 V and in the absence of copper, the anodic current is less than those observed under darkness conditions. This effect can be explained by considering that at these potential values the band bending of the semiconductor electrode is minima. Therefore, under illumination it is produced by the recombination of the electron/hole charge carriers thereby decreasing the yield of the anodic processes.

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Figure 2. Mott-Schottky plots of p-Si(100) in 0.1 M H2SO4 obtained from measurements done at (a) 100 kHz and (b) 10 kHz. The corresponding flat band potential values are indicated.

The presence of complex peaks as much in the cathodic and anodic hemicycles is in agreement with those observed using n-Si(100).1 However, the processes associated with the copper electrodeposition on p-Si(100) appear at potential values near the reversible potential (∼0.34 V vs MSE). The electrodeposition of copper onto p-Si(100) substrates can be explained by means of the band diagram (BD) of the semiconductor/electrolyte interface. For this reason, the position of the Fermi level and the location of the valence and conduction bands (VB and CB, respectively), which allow the building of the BD, were determined from the corresponding MottSchottky plots. These plots have been obtained in the same electrolytic medium under study. Figure 2 shows the Mott-Schottky plots for the p-Si(100)/ 0.1 M H2SO4 system obtained at 100 kHz (Figure 2a) and 10 kHz (Figure 2b). In both figures, a linear behavior starting from -0.2 V can be observed. The extrapolation of the linear regions in these plots allows us to determine the flat band potential (VFB). The VFB values found at 100 kHz and 10 kHz were -0.016 V (Figure 2a) and -0.018 V (Figure 2b), respectively. These values are in agreement with the ones reported in the literature.21,22 Furthermore, from the slope value of the Mott-Schottky plots and using eq 2, a majority carrier density value, NA ) 7 × 1015 cm-3, was obtained.

[

]

kb T 1 2 ) -V + VFB 2  eN e C 0 A

(2)

Here C corresponds to the space charge layer capacitance, e, , and 0 are the electron charge, the dielectric constant of the semiconductor, and the vacuum permittivity, respectively, NA is the majority carrier density, kT has the usual significance, and V is the applied potential. From these parameters the band diagram for the p-Si(100)/ Cu+2 interface in darkness conditions was drawn (see Figure 3). Figure 3a shows the flat band condition, which has been calculated from the corresponding flat band potential value and from the majority carrier density. Figure 3b shows the BD

corresponding to the equilibrium condition, which was constructed considering that the open circuit potential (Eoc) of the p-Si(100)/5 mM CuSO4 + 0.1 M H2SO4 interface corresponds to -0.480 V. In this situation, the system is under a depletion layer. The thickness of the space charge region (W), determined from the Mott-Schottky equation, yields a value of 294 nm. The Figure 3c shows an inversion layer when a bias on the semiconductor in darkness is applied (-0.8 V as the Figure 1a). The low-density current attained in these conditions for the electrochemical processes is due to a too slow electron generation on the surface of the conduction band. On the other hand, when the semiconductor is illuminated, it produces a high concentration of minority carriers and in open circuit conditions deposition is possible (Figure 3d). This process can occur if we consider that to the initial potential value -0.3 V the p-type semiconductor is in depletion layer for the holes with a thickness of 230 nm or an accumulation layer for the electrons. This is not possible using a n-Si(100) because this material attains a depletion layer for the electrons. In this way, to carry out the electrodeposition process an overpotential must be applied.1 When the bias is slightly shifted to more negative potential values, it produces the massive copper deposition together with the hydrogen evolution reaction (HER) on electrodeposited copper (Figure 3e). Considering the energetic distribution of the redox couple in solution, the accumulated electrons are transferred to the acceptor levels (WOX) of the Cu2+/Cu system. In this way, the reduction process observed is explained. Finally, when a potential more positive than Eoc is applied to the semiconductor substrate (covered with a copper film), it attains an accumulation layer. In this case, two processes are occurring which can be explained considering the band diagram shown in Figure 3f. Here, the positive hole (h+) arrives at the substrate surface; in this way it produces the substrate oxidation and copper film oxidation, which corresponds to

Cu + 2h+ f Cu2+

(3)

3.2. Cyclic Voltammetry Analysis of the p-Si(100): Effect of the Addition of Poly(ethylene oxide) (PEO) under Illumination Conditions. Figure 4 shows the potentiodynamic j/E profiles corresponding to the electrodeposition of copper on p-Si(100) at different PEO concentrations under illumination of different intensities. In Figure 4a,b is possible to observe that the presence of PEO shifted the copper electrodeposition process toward more positive potential values. Furthermore, when the electrode is illuminated with a higher intensity value, an increase in the photocurrent associated with the HER is observed. These facts can be explained by considering that in the absence of additive and at the initial potential (Ei ) -0.3 V) the reaction is occurring (1). This process is inhibited when the PEO is present. Similar results were observed using an n-type semiconductor.1 For this reason, the copper process appears to have more positive potentials. On the other hand, the increase in the HER photocurrent can be explained by considering that a major number of incident photons (3.5 mW cm-2) produce an increase in the minority charge carriers concentration, which are channeled through the copper nucleus for the HER. In the initial reverse scan no significant differences can be found. The current remains cathodic upon reversion of the sweep toward positive potentials, crossing over the current recorded during the negative sweep at -300 mV. This current loop is due to the fact that the deposition of metals onto their own, in this case copper on

Copper Electrodeposition onto p-Si(100)

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Figure 3. Band diagrams in different situations for the system p-Si(100)/electrolyte: (a) flat bands; (b) equilibrium with 0.1 M H2SO4 + 5 mM CuSO4 electrolyte; (c) cathodic polarization at -0.80 V (inversion layer); (d) open circuit under illumination, -0.30 V (start copper deposition); (e) cathodic polarization at -0.80 V (massive copper deposition); (f) accumulation layer under illumination at 0.20 V (copper dissolution and silicon oxide growth).

Figure 4. Potentiodynamic j/E profiles of a p-Si(100) electrode in 0.1 M H2SO4 + 5 mM CuSO4 at different PEO concentrations and different illumination intensities. (a) 2.0 mW cm-2; (b) 3.5 mW cm-2. PEO concentrations: (s) 0 mg L-1; (- - -) 1.0 mg L-1; (‚‚‚) 100 mg L-1. Scan rate: 0.010 V/s.

copper, occurs at lower overpotentials that the deposition of metal onto different nature subtrates, in this case copper on p-Si(100). This feature has been frequently observed in cyclic voltammograms when nucleation processes onto silicon are involved.1,3,7,9,13 After this, an anodic process is observed. This is attributed to the copper disolution and the substrate oxidation. The charge associated with this process increases when the PEO concentration is increased. This is attributted to the presence of PEO inhibiting the oxide formation which allows a larger copper deposition (more available active sites) and, therefore, the electrodissolution charge also increasing. Also, the increase of

the anodic charge at lower illumination intensity can be explained by considering the band bending of p-Si at this potential value. In fact, the semiconductor reaches a depletion layer (electron accumulation under illumination). At an illumination intensity of 2.0 mW cm-2, the anodic response indicates the holes transfer by tunneling to the copper deposit (stripping) and the silicon surface (oxide formation). Furthermore, at 3.5 mW cm-2, although more photogenerated electrons can be produced, they are recombined with the holes in the surface due to the weak band bending under these conditions. The results imply that, with an increase of the illumination intensity, the recombination increases and the anodic charge decreases. 3.3. Analysis of the j/t Transients: Nucleation and Growth Mechanisms of Copper onto p-Si(100). The j/t transients obtained by the potential step method were performed in the potential region where the copper electrodeposition occurs. In this way, the nucleation and growth mechanisms further deduced from these j/t transients should be sensitive to the presence of PEO or the illumination intensity. The potential steps were carried out from an initial potential Ei ) -0.30 V to a final deposition potential (Ed) ranging as -0.350 V g Ed g -0.650 V. Figure 5 shows the j/t transients where the time is corrected for the induction time. In all the j/t transients it can be seen that after the initial increase in the current a maximum (jmax) is reached, and then current density decays until after a long time, when it reaches an approximately constant value. When the deposition potential is made more negative, the jmax increases and the time corresponding to the current maximum (tmax) decreases. These features are consistent with the nucleation of hemispherical clusters followed by a diffusion-limited growth.1,3,4,7,9,11,23-32 If we consider a constant potential (e.g., -0.500 V) and with an illumination intensity of 2.0 mW cm-2 (Figure 5a-c), an increase in the photocurrent when the concentration of PEO is increased is observed. This fact can be attributed to the inhibition of the silicon oxide formation on the active sites of the semiconductor. When the electrode is illuminated with a illumination intensity of 3.5 mW cm-2 (Figure 5d-f), an increase in the photocurrent under all conditions is observed, compared to those obtained with a lower illumination intensity.

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Figure 5. j/t transients for copper deposition onto a p-Si(100) in 0.1 M H2SO4 + 5 mM CuSO4 at different PEO concentrations, for potential steps from -0.30 V to a deposition potential (Ed) indicated in the figure. Values at 2.0 mW cm-2: (a) 0 mg L-1; (b) 1 mg L-1; (c) 100 mg L-1. Values at 3.5 mW cm-2: (d) 0 mg L-1; (e) 1 mg L-1; (f) 100 mg L-1.

Figure 6. Dimensionless plots for the current transients from Figure 5: (a-c) at 2.0 mW cm-2; (c-e) at 3.5 mW cm-2. In dimensionless plots, dash and dot lines correspond to the calculated curve for the growth laws for 3D diffusional controlled instantaneous and progressive nucleations mechanisms, respectively.

In the same way, a significant effect in the magnitude of the photocurrent when the PEO concentration is increased is not observed. The increase of the photocurrent to a higher illumination intensity can be explained by considering that it produces an increase in the minority carriers concentration in the surface and for this reason more copper is electrodeposited. The slight decrease in the photocurrent when a 100 mg/L PEO concentration is employed could be explained by taking into account that this molecule can be blocking the surface of the semiconductor for the arrival of the copper ions. Therefore, the photogenerated electrons are not transferred to electrolytes and they can be recombined with the holes of the valence band, thereby decreasing the photocurrent value. To determine the nucleation and growth mechanisms of copper on p-Si(100), and in a first approach to distinguish between instantaneous and progressive nucleation, the experimental data have been represented in a nondimensional form. Figure 6a-c represents the 2.0 mW cm-2 condition using 0, 1,

and 100 mg/L PEO concentration, respectively. In the same way, Figure 6d-f represents the 3.5 mW cm-2 condition using 0, 1, and 100 mg/L PEO concentration, respectively. All the figures are plotted in coordinates (I/Im)2 vs t/tm in accordance with the theoretical models of nucleation and diffusioncontrolled growth of hemispherical clusters, where Im and tm represent the current maximum and time at current maximum, respectively.25-28,31,32 It can be seen that in the absence of PEO and under any illumination conditions the experimental data follow the progressive nucleation model relatively well; however, after tmax big deviations in this model emerge. When the additive is present and under any illumination conditions, the experimental data closely follow the instantaneous nucleation model from the initial part (t < tmax); however, a deviation after tmax is observed too. Both variations in the proposed models can be attributed to the presence of a parallel reaction to the copper electrodeposition process. The last can be attributed to

Copper Electrodeposition onto p-Si(100)

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SCHEME 1: Representation of the Copper Electrodeposition Process in the Presence of PEO: (a) Capture of One Electron of the Si-H Bond for One Hole Present in the Valence Band; (b) Adsorption of the PEO Molecule through the Oxygen Atoms; (c) Displacement of the PEO Molecules and Copper Electrodeposition

the silicon atom. This unpaired electron is captured for a new hole, leaving one site of silicon with a delta positive charge (δ+). This site is a very reactive front to rich electrons molecules such as water. However, when the additive is present, the oxygen atoms that contain unpaired electrons can attack this positive site, displacing the water molecules due to their amphiphilic character36,37 (Scheme 1b). Later, when the electrode potential becomes more negative, the copper ions are attracted by electrostatic interactions toward the electrode. This way, when the potential is suitably negative, the PEO molecules are displaced and the copper is electrodeposited instantaneously on the sites protected by the additive, which possibly are isoenergetic in nature. Last, because of the capture of the electrons of the Si-H bonds, more active sites are produced. On the other hand, according to Scharifker et al.,2,6 the limiting situations in the electrodeposition process are when it produces a slow nucleation on a large number of active sites and fast nucleation on a small number of active sites corresponding to a progressive and instantaneous nucleation, respectively. In the last case, which is observed in presence of PEO, the small number of active sites is in fact due to the PEO adsorption on p-Si. Furthermore, if there exists oxide formation in the initial stages of the process, the number of active sites decreases even more. In accordance with the photocurrent contributions observed (nucleation + HER), the experimental j/t transients were then fitted using a mathematical function sum of two contributions. In the absence of PEO, the best results were found with the following global j(t) equation with the parameters of this equation summarized in Table 1:

j(t) ) j(t)PN3DDiff + j(t)HER

the HER which is favored on previously electrodeposited copper clusters, in line with that was proposed by PalomarPardave et al.34 for the electroreduction of protons during cobalt electrodeposition. Furthermore, the same deviations after tmax were encountered during the copper electrodeposition onto n-Si(100).1 The change of the nucleation mechanism for action of the additive can be explained by considering the following aspects that are summarized in Scheme 1: As has been proposed by Allongue et al.,35 in the first step there is capture of one electron of the Si-H bond for one hole present in the valence band (Scheme 1a). This process releases one proton and it leaves one unpaired electron over

(4)

Here j(t)PN3DDiff is the current contribution corresponding to a 3D progressive nucleation with diffusion controlled growth and j(t)HER corresponds to the density current associated with the HER. In the presence of PEO, the best results were found with the following global j(t) equation (the parameters of this equations are summarized too in Table 1):

j(t) ) j(t)IN3DDiff + j(t)HER

(5)

Here j(t)IN3DDiff is the current contribution corresponding to a 3D progressive nucleation with diffusion controlled growth. Figure 7 shows the experimental and fitted (with the global eqs 4 and 5) j/t transients recorded at Ed ) -0.500 V for the six conditions assayed. At different potentials the fitted error range was 0.1-5%. The separated contributions for each term

TABLE 1: Nucleation and Growth and HER Models Used to Fit j/t Transients contribn

j ) F(t)

PN3DDiff

j ) (a / xt)(1 - exp[ - bt ])

IN3DDiff

j ) (a / xt)(1 - exp[ - ct])

HER

j ) d{1 - exp[ - f(t - 1 - exp( - gt) / g)]}

global eq without PEO global eq with PEO

j(t) ) jPN3DDiff(t) + jHER(t) j(t) ) jIN3DDiff(t) + jHER(t)

2

paramsa

a b a c d f g

) ) ) ) ) ) )

1/2 ∞

nFD C / xπ 1/2 2 / 3 8π3/2C∞D2MN02A2 / F 1/2 ∞ / nFD C xπ N0πD(8πC∞M / F)1/2 (nHERFkHER)(2C∞M / πF)1/2 N0πD(8πC∞ / F)1/2 A

(

)

a nF is the molar charge transferred during the copper electrodeposition process. D, C∞, M, and F are the diffusion coefficients, the concentration in the bulk of solution, the molar mass, and the density of the copper species, respectively. N0 and A are the number density of active sites for nucleation on the electrode surface and the rate of nucleation, respectively. nHERF and kHER are the molar charge transferred and the rate constant during the proton reduction process.

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Figure 7. Experimental (O) and fitted (s) j/t transients obtained at Ed ) -0.500 V. Dashed lines 1 (in a and d) correspond to PN3DDIFF. Dashed lines 1 (in b, c, e, and f) correspond to IN3DDIFF. Dotted lines 2 correspond to the HER contributions. Values at 2.0 mW cm-2: (a) 0 mg L-1 PEO; (b) 1 mg L-1 PEO; (c) 100 mg L-1 PEO. Values at 3.5 mW cm-2: (d) 0 mg L-1 PEO; (e) 1 mg L-1 PEO; (f) 100 mg L-1 PEO.

TABLE 2: Electric Charge and Percentage of the Total Charge Associated with the Contributions PN3DDIFF and IN3DDIFF (N3DDiff) and HER Obtained from the j/t Transients Fitted from Figure 7 condition

calcd tot. N3DDIFF exptl tot. HER charge/mC cm-2 charge/mC cm-2 charge/% charge/%

without PEO 1 mg L-1 PEO 100 mg L-1 PEO

6.47 7.94 8.42

2.0 mW cm-2 6.47 8.00 8.48

4.76 7.99 7.12

1.74 0.01 1.36

without PEO 1 mg L-1 PEO 100 mg L-1 PEO

9.62 10.1 8.08

3.5 mW cm-2 9.62 10.0 8.46

8.97 9.26 8.46

0.65 0.79 0.00

are also shown in Figure 7. The electric charge associated with each contribution expressed as percentages of the transient total charge are summarized in Table 2. On the basis of the results shown in Figure 7 and the values presented in Table 2, it can be concluded that the principal contribution in the copper electrodeposition process is NP3DDIFF and NI3DDIFF in the absence and in the presence of PEO, respectively. In cases where the HER appears, this is developed at t > tmax, which indicates that this reaction is revealed after the coalescence of the diffusion zones. The last is due to that the adsorption of hydrogen in the nucleation process product of the diffusion zones growth around of the metallic nucleus is not possible. When the 1D diffusion is attained, the adsorption is possible and this occur after tmax.25,31,34 For a quantitative analysis of the NGM, the nucleation rate in the absence of additive was evaluated using the following equation:26,31-33

(zFc0)2 Jnucl ) knN0 ) 0.2898(8πc0Vm)-1/2 2 3 imax tmax

Figure 8. Semilogarithmic plot of the nucleation rate (a) calculated from eq 6 as a function of the potential in absence of PEO: (O) 2.0 mW cm-2; (0) 3.5 mW cm-2. (b) Nucleus density calculated from eq 9 as a function of the potential in the presence of PEO: values at 2.0 mW cm-2 (0, O), 1.0 and 100 mg L-1 PEO concentrations, respectively; values at 3.5 mW cm-2 (4, 3), 1.0 and 100 mg L-1 PEO concentrations, respectively.

In the kinetic approach, the nucleation rate is given by32,33

JNucl ) knN0 ) A3D exp

(

)

(β + NCrit)e|η| kT

(7)

where Ncrit is the number of atoms required to form a critical nucleus, η is the overpotential, k is the Boltzmann constant, and A3D is a preexponential factor. The preexponential factor and Ncrit are independent of the potential, whereas β depends on the mechanism of attachment. This β parameter can take values ranging from 0 to 1 depending on this attachment mechanism. The potential dependence of the nucleation rate is in a potential range where Ncrit is a constant and is given by33

(6)

Here kn is the nucleation rate constant, N0 is the final nucleus density, Vm is the molar volume, and the other symbols have their usual meanings. Figure 8a shows log(knN0) vs potential for the systems in the absence of PEO at different illumination intensities, and it indicates that the nucleation rate increases exponentially with the applied potential.

d(log JNucl) e ) (β + NCrit) d|η| 2.303kT

(8)

The (β + NCrit)C values found from the slope values of the plots shown in Figure 8a were also