Electrodeposition of copper from cuprous cyanide electrolyte

www.elsevier.nl/locate/jelechem Journal of Electroanalytical Chemistry 474 (1999) 16 – 30

Electrodeposition of copper from cuprous cyanide electrolyte I. Current distribution on a stationary disk David A. Dudek 1, Peter S. Fedkiw * Department of Chemical Engineering, North Carolina State Uni6ersity, Raleigh, NC 27695 -7905, USA Received 30 December 1998; received in revised form 20 May 1999; accepted 22 June 1999

Abstract A model is developed for electrodeposition of copper from cuprous cyanide electrolyte onto a stationary disk electrode. The − 1) − solutions examined are similar to those of copper strike-plating baths, in which cuprous may exist as Cu + and Cu(CN)(n , n n= 1–4. The effects of mass transport by diffusion and migration, multiple electrode reactions, and homogeneous complexation equilibria are considered. The model elucidates the influence of solution composition, transport properties, and kinetic constants on current distribution and polarization characteristics. Because cyanide is released upon discharge of the copper –cyanide complex, the distribution of copper-containing species shifts towards higher-order complexes near the electrode surface. Changes in solution composition which effect a greater percentage of copper complex in the more saturated cyanide state decrease the uniformity of the current distribution at a given fraction of the limiting current, which occurs because higher-order complexes have a lower diffusivity; and, if higher-order species are less electroactive, these changes decrease the current density at a given applied potential. Because copper–cyanide complexes have smaller diffusion coefficients than free cyanide, the concentration gradient of CN − causes the solution potential to increase near the electrode surface, and migration enhances the transport of anionic complexes. In most cases, the current distribution becomes increasingly non-uniform with applied potential; but under some circumstances that are elucidated here, the least non-uniform current distribution may occur at an intermediate fraction of the limiting current. In all studies, the current distribution approaches the highly non-uniform primary-like distribution as the limiting current is approached. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Copper; Electrodeposition; Cyanide; Disk electrode; Current distribution

1. Introduction Plating copper from cyanide electrolytes offers several advantages over other bath compositions: (i) the deposits are highly adherent; (ii) the deposit thickness is relatively uniform [1], and (iii) deposit morphology is fine-grained [2]. Consequently, the majority of copper strike-plating baths use cyanide electrolyte. Fundamental studies of copper deposition from cyanide-containing electrolytes are few in number, for example see Refs. [3–6], and are hampered by concurrent hydrogen evolution. Because copper is present in several potentially electroactive forms, determination of kinetic * Corresponding author. Fax: +1-919-5153465. E-mail address: peter – [email protected] (P.S. Fedkiw) 1 Present address: IBM, Storage Systems Division, San Jose, CA 95193, USA.

parameters for individual complexes is exceedingly difficult and only apparent or observed kinetic quantities based on an assumed single electrochemical reaction have been reported. Katagiri [7] presented a diffusion–migration model for copper deposition from cyanide electrolyte to predict the current distribution on a grooved substrate in which the diffusion coefficients for all species were assumed to be the same. This assumption is not accurate (for example, the diffusion coefficient of Cu(CN)34 − [8] is only 30% of that of CN − [9]), and eliminates the diffusion potential, which is shown here (and by others [10,11]) to change the sign of the electric field within the diffusion layer and, consequently, reverse the direction of the migration flux. Because of health and environmental risks associated with the use of cyanides, alternative electrolyte formulations are used whenever possible. However, the replacement of cyanide in copper strike-plating baths,

0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 2 2 - 0 7 2 8 ( 9 9 ) 0 0 2 9 9 - 5

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

particularly for coating zinc, steel, or aluminum substrates, remains a challenge. Other than cyanide baths, the only non-proprietary strike-plate formulation involves pyrophosphate electrolytes [12] that can be used to coat steel or aluminum, but not zinc substrates due to spontaneous formation of immersion deposits. In comparison to cyanide electrolytes, the only advantage offered by pyrophosphate formulations is that they contain no cyanide. Disadvantages of pyrophosphate baths include: solution composition requires careful monitoring, lack of use may cause a decrease in bath efficacy, and the baths are sensitive to contaminates such as organics, cyanide, and lead [13]. The distribution of current is an important characteristic of any plating operation, but it is particularly important in strike-plating applications, as quality of subsequent deposits depends upon a uniform undercoat. The primary and secondary current distribution on a disk electrode is inherently nonuniform [14]; consequently, this geometry is appropriate for studying the throwing power of particular bath formulations, and is the focus of this series of two papers. We have investigated the influence of complexation and acid–base chemistry, mass-transport, and multiple electrode reactions on the deposition process. Our findings are reported in a two-part series. In this first part, we present a model of copper deposition from cuprous cyanide electrolyte on a stationary disk electrode. The model describes mass transport by diffusion and migration of species in local equilibrium to a cathode upon which multiple charge-transfer reactions are considered to occur. Using this model, the effects of solution composition, transport properties, and kinetic constants on current distribution and polarization characteristics for a copper – cyanide bath are investigated. In the second part, the current distribution on a rotating disk electrode is considered. The convective transport of copper species adds another layer of complexity to the effects of homogeneous complexation equilibria and electrode activity of each.

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2. Cuprous cyanide electrolyte Although formulations vary, the composition of a typical strike-plating bath is 0.2 M CuCN+0.6 M NaCN+0.1 M Na2CO3, and pH 11.2, with the pH adjusted by addition of NaOH [15]. The baths are typically operated at 60°C. Cuprous cyanide salt is the source of copper and provides cyanide to form complexes. Sodium cyanide provides complexing agent for copper, and sodium carbonate buffers the solution. Equilibrium is established between thirteen species in solution: Cu + , CN − , CuCNaq, Cu(CN)2− , Cu(CN)23 − , Cu(CN)34 − , Na + , CO23 − , HCO3− , H2CO3, HCN, H + , and OH − . In other modeling work, the acid–base chemistry of typical cuprous cyanide strike-plating baths was investigated [16], and we concluded that acid–base chemistry has only a minor influence on the concentration profiles of cuprous cyanide complexes. Thus, to reduce the numerical burden, the acid–base chemistry is not considered here. This reduces the number of species that are considered to seven: Cu + , CN − , CuCNaq, Cu(CN)2− , Cu(CN)23 − , and Cu(CN)34 − .

2.1. Complexation chemistry Cuprous and cyanide form four stable soluble complexes in water, in addition to the uncomplexed ions: CuCNaq, Cu(CN)2− , Cu(CN)23 − , Cu(CN)34 − , Cu + , and CN − . These complexes undergo rapid ligand exchange when free cyanide is available in solution [6,17,18], suggesting that cuprous cyanide solutions attain equilibrium concentrations quickly. Thermodynamic quantities for cuprous cyanide electrolyte are displayed in Table 1. These values were derived from solubility data [19] or standard potentials [20], or were reported to be approximately the same by independent primary sources, as cited by handbooks [21,22]. Equilibrium between cuprous and cyanide ions strongly favors complex formation. The cumulative equilibrium constant bn written for the reaction:

Table 1 Thermodynamic quantities for cuprous cyanide electrolyte components at 25°C Component

DH °/kJ mol−1 f

Cu Cu+ CN− CuCN CuCNaq Cu(CN)− 2 Cu(CN)2− 3 Cu(CN)3− 4 Na+ NaCN

0 71.7 150.7 95.1 NA 274 334 437.8 −240.3 −87.55

DG °/kJ mol−1 f Definition [22] [21] [20] [20] [20] [20] [22] [22]

0 50.0 172.5 108.4 133 258 404 566.9 −262.06 −76.49

DS °f (25)/J mol−1 K−1 Definition [22] [21] [21] [22,19] [21] [21] [21] [22] [22]

33.17 40.6 94.2 90.13 NA 205 243 209 59.0 115.7

[22] [22] [21] [20] [20] [20] [20] [22] [22]

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

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Table 2 Stability constants for cuprous–cyanide complexes at 25 and 60°C

b1/M−1 b2/M−2 b3/M−3 b4/M−4

25°C

60°C

5.0×1015 1.0×1024 4.4×1028 2.1×1029

1.1×1014 1.5×1022 1.4×1025 9.4×1025

CuCN content. The vertical line corresponds to a NaCN concentration of 0.6 M, which is the typical salt concentration in a strike-plating bath. At this composition, 53.7% of copper is in the n=3 complex, 45.9% is in the n= 4 complex, 0.4% exists in n= 2 form, and only 3× 10 − 8% is in n= 1 form. When the stoichiometric concentration of NaCN is less than that of CuCN, (i) CuCN precipitate is present (Ksp,CuCN = 2.25×10 − 18 M2 at 60°C), (ii) the complexes do not account for 100% of the copper because of the precipitate, and (iii) the portion that is in the n= 1 form is at its maximum of 0.13%. Above 13.8 M NaCN, the solubility limit of NaCN is exceeded (Ksp,NaCN = 179 M2 at 60°C), and the distribution of copper complexes does not change with additional NaCN.

3. Model development

− 1) − Fig. 1. Concentration of Cu(CN)(n as a function of stoichiometn ric NaCN concentration for [CuCN]° = 0.2 M at 60°C and pH 11.2. The vertical line at 0.6 M NaCN marks the composition of a typical copper strike-plating bath.

Cu + + nCN − l Cu(CN)(n−1)− n

n=1–4

(1)

is defined as − 1) − bn = [Cu(CN)(n ]/[Cu + ][CN − ]n n

(2)

Table 2 displays the values of these constants at 25 and 60°C. Values at 25°C were calculated from Gibbs energies using [23]: ln(bn )= − DG °/RT n

(3)

where DG °n is the standard change in Gibbs energy upon formation of the complex from cuprous and n cyanide ions (Reaction (1)), R is the ideal gas constant, and T is temperature. Because cuprous cyanide plating baths typically operate at 60°C, bn at this temperature were calculated using [23]:



ln







bn (T2) − DH °n 1 1 = − bn (T1) R T2 T1

(4)

where DH °n is the standard change in enthalpy upon formation of the complex from cuprous and n cyanide ions (Reaction (1)), T1 =298 K, and T2 =333 K. This relationship assumes that DH °n is constant between T1 and T2. Detailed discussion of the thermodynamic quantities and equilibrium calculations is available [16]. Fig. 1 displays the calculated equilibrium concentration of cuprous–cyanide complexes as a function of sodium cyanide concentration for a given pH and

In formulating the model, we assume: (i) steady-state, isothermal conditions; (ii) dilute-solution theory applies; (iii) double-layer effects are unimportant; (iv) local equilibrium of components; (v) 100% current efficiency, and (vi) complex reduction is described by Butler– Volmer (mass-action) kinetics. In practice, cuprous cyanide plating baths experience only 30–60% current efficiency [12], with the remainder of the current going to hydrogen evolution. Because the primary focus of this series is on the current distribution, and we believe that hydrogen evolution has only a secondary effect on the current distribution, this effect is not incorporated into the model.

3.1. Go6erning equations The flux Ni of species i in dilute, stagnant solutions is given by the Nernst–Planck equation Ni = − Di (zi fci 9F +9ci )

(5)

where Di, zi, and ci are the diffusion coefficient, charge number, and concentration of species i, f=F/RT where F is Faraday’s constant, R is the universal gas constant and T is temperature, F is the solution potential, and the Nernst–Einstein relationship has been assumed (Di = RTui ), where ui is the mobility of species i. The steady-state material balance for each species is: 0= − 9·Ni + Ri

(6)

where Ri is the volumetric molar production rate of species i by all homogeneous reactions. For accounting purposes, the seven species considered present in solution are assigned the following indices (1) Cu+ (2) CN−

(3) Na+ (4) CuCNaq

(5) Cu(CN)− (7) Cu(CN)3− 4 (6) Cu(CN)2− 3

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

There are four homogeneous reactions considered: Cu + nCN l Cu(CN) +

−

(n − 1) − n

n =1 – 4

(7)

Consequently, the net volumetric molar rates Ri of generation by chemical reaction are related by

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problems, and it is employed here. The modified oblatespheroidal coordinates (G, u) are related to cylindrical coordinates (R, Z) by R= cos u cosh

  G 1− G

 

Z= sin u sinh

G 1− G

R1 = − R4 − R5 − R6 −R7

(8)

(16)

R2 = − R4 − 2R5 − 3R6 −4R7

(9)

where R and Z are the radial and axial distance from the center of the disk, normalized by the disk radius. The divergence of the flux 9Ni of species i in this modified oblate spheroidal coordinate system is expressed as: −1 G 9·Ni = sin2 u+ sinh2 1− G

R3 = 0

(10)

Eq. (8), for example, states that the rate at which cuprous ion is generated is equal to the sum of the rates at which cuprous disassociates from copper-containing complexes. Combining Eqs. (6) and (8 – 10) to eliminate Ri yields the following conservation equations for total copper, cyanide, and sodium. 9·(N1 + N4 + N5 +N6 +N7) = 0

(12)

9·(N3)= 0

(13)

Finally, the species concentrations satisfy the four equilibrium constraints: − 1) − ] [Cu(CN)(n n + [Cu ][CN − ]n

n =1 – 4

(14)

and electroneutrality 0=% zi ci

× − Di zi

(11)

9·(N2 + N4 + N5 +3N6 +4N7) =0

bn =

!



(15)

i

This system of 15 equations (Eqs. (5 and 11 – 15)) and unknowns (Ni, ci, i=1 – 7, and f) may be reduced to a system of three partial differential equations in three unknowns by substituting Eqs. (5), (14) and (15) into Eqs. (11)–(13). The procedure employed to solve this system is described below. Verbrugge and Baker [24] proposed a modified version of the oblate– spheroidal coordinate system for solving mass-transport problems by diffusion and migration to a stationary disk electrode that greatly improves the numerical efficiency of solving disk-electrode

− Di







 n

#ci #f #ci #f + (1−G)4 #u #u #G #G

#2ci #2ci + (1− G)4 2 #u #G 2

      "

n

n

G #ci −2(1 −G) #G 1−G #ci #2f #2f 4 −tan u −Di zi ci + (1− G) #u 2 #G 2 #u

+ (1−G 2) tanh



+ (1−G)2 tanh

n

G #f − 2(1− G)3 1− G #G

#f (17) #u Fig. 2 displays the domain used for this problem in cylindrical and the modified oblate-spheroidal coordinates. The quarter-ellipse connecting (0, 1000) to ( 1000, 0) in cylindrical coordinates and the corresponding coordinate G= cosh − 1(1000)/[1 + −1 cosh (1000)]: 0.8837 in modified oblate-spheroidal coordinates are located ‘far’ from the electrode surface, that is, where the concentrations of species are bulk values. This distance is essentially infinite in that the disk current distribution is not affected if it is increased. On the insulating surface (u= 0) and axis of symmetry (u= p/2), the net normal fluxes of species contain−tan u

Fig. 2. Model domain in cylindrical (left) and modified oblate-spheroidal (right) coordinates.

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

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potential at bulk solution concentrations. Because the complexes are in equilibrium, the equilibrium potential E and overpotential h are the same for all four complexes. Discussion of the appropriateness of Eq. (22) is presented in Appendix A. The net normal flux of species containing Cu(I) is proportional to the total current density, which is the sum of the reaction current of each complex 4

n¯·(N1 + N4 + N5 + N6 + N7)= F − 1 % jn

(25)

n=1

Fig. 3. Polarization curve for base-case parameters. Applied potential (V−fb) is relative to the equilibrium potential Ebc of the base-case bulk solution. All parameter values are given in Tables 2 and 3.

n¯·(N1 +N4 + N5 + N6 +N7) = 0

(18)

n¯·(N2 +N4 + 2N5 + 3N6 +4N7) = 0

(19)

n¯·(N3)=0

(20)

where n¯ is the unit normal vector to a surface. On the electrode surface (G= 0), the net normal fluxes of species containing cyanide and sodium are zero (Eqs. (19) and (20)), and Faraday’s law relates the molar flux of a species to the weighted sum of the electrochemical reactions in which it participates. In all electrolytes considered in this work, Cu + concentration is extremely small (10 − 24 M or less), consequently, Cu + reduction is not considered to occur. This leaves reduction of the four complexes as electrode reactions kc,n

n =1 – 4

(21)

a,n

where kc and ka are rate constants. If we assume Reaction (21) is reversible and follows mass-action kinetics, the reaction current density jn due to reduction of − 1) − Cu(CN)(n is given by the rate equation [25] n jn = jo,n

! 

"

cCN − s n (1 − ac,n )fh cn,s − ac,n fh e − e cCN − cn

n= 1− 4

(22)

n =1 – 4

(23)

The overpotential h is given by h= V−fs −E

f= fb

(26)

We make the non-linear system of equations dimensionless and solve using PDE2D, a finite-element partial differential equation (PDE) solver [26]. The convergence rate is significantly improved by providing an analytical Jacobian, and MAPLE was used to perform the necessary manipulations. Because the concentrations of some species can be small, we transform concentrations to make the dependent variables the natural log of the dimensionless concentrations, instead of the concentrations themselves.

4. Results and discussion We first consider conditions found in typical copper strike-plating baths (our base-case calculation), and then discuss the effect of stoichiometric NaCN and CuCN concentration, exchange current densities, and transfer coefficients on current distribution and concentration and potential profiles.

4.1. Model of plating bath conditions

where ci is the concentration of species i in the bulk solution, cis is the concentration of species i at the electrode surface, and jo,n is the exchange current density for a complex with n ligands based on bulk solution concentrations n jo,n =Fk 1c,n− ank aa,n (cn )1 − an (cCN – )nan

ci = cib for i= 1−7

3.2. Method of solution

ing copper, cyanide, and sodium are zero.

Cu(CN)(n−1)− + e − k= +nCN n

Far from the electrode surface (G=0.8837), the concentrations of all species and the potential in the bulk solution are set to a constant value:

(24)

where V is electrode potential, fs is the solution potential adjacent to the electrode, and E is the equilibrium

Parameter values required to perform the calculations are listed in Tables 2 and 3 for the base-case calculation. The diffusion coefficient D1 of free cuprous ion is the value tabulated by Marcus [27] at 25°C, but scaled to 60°C by [14]: Di,T 2 = Di,T 2(m1T2/m2T1)

(27)

where m is solution viscosity. The exchange current densities and transfer coefficients for individual complexes are estimates based on apparent (i.e. observed) quantities determined from hydrodynamically-modulated rotating disk voltammetry experiments conducted in our laboratory [16] and literature values of apparent exchange current densities and transfer coefficients [3,4,6].

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

Fig. 3 is a polarization curve for the base-case parameters. The current is normalized with respect to the absolute value of the mass-transport-limited current. The applied potential is measured relative to the potential of a copper reference electrode located in the base-case bulk solution; therefore, an applied potential of zero results in zero current. As the applied potential becomes more negative, the current approaches a limiting value. Because deposition from cuprous cyanide complexes does not occur until well below the potential at which hydrogen evolution ensues, comparisons to experimental currents reveal no useful information, and are not made in this paper. The concentration and potential profiles along the axis of symmetry for the base case at 80% of the limiting current (applied potential = − 176 mV) are presented in Fig. 4. The choice of 80% is arbitrary; it was chosen for illustrative purpose because the current is in the mixed-control regime and concentration gradients are significant. Because the equilibrium formation constants of the complexes are large, and there is more than enough CN − to saturate the available Cu(I), essentially all of the copper is complexed. That is, the concentration of Cu + is extremely low throughout the diffusion layer and is not discernible on the scale of this figure. Each copper atom deposited from the complex releases nCN − ions and, consequently, the concentration of free cyanide is highest at the electrode surface. In the bulk solution, copper is present in both n= 3 and 4 forms, with equilibrium slightly favoring the n=3 state (54% n= 3, 46% n =4). The most prevalent copper-containing species changes from n =3 in the

Fig. 4. Concentration (a) and potential − (V− f− Ebc) (b) profiles on axis of symmetry for base-case parameters at 80% of limiting current. All parameter values are given in Tables 2 and 3.

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bulk to n= 4 near the electrode because of the higher CN − concentration. Finally, the concentration profile of sodium, which does not participate in any reactions, is determined by electroneutrality. Since Na + is the only cation present in an appreciable amount, its concentration is essentially the sum of the concentration of the anionic species times charge number, and decreases from its bulk value of 0.60 to about 0.53 M at the electrode surface. The corresponding potential profile is displayed in Fig. 4(b). The ordinate for the potential scale is − (V− f− Ebc), which is equal to the negative overpotential on the electrode surface, and has the identical qualitative trend as the solution potential f. The potential profile is such that the net flux of sodium is zero. Since the concentration of sodium is higher in the bulk solution than at the electrode surface, sodium transport by diffusion is towards the electrode. The potential profile is established so that the migration flux of sodium exactly counters the diffusion flux. At 80% of the limiting current, the potential rises across the solution by 3.2 mV. The increase in solution potential near the cathode surface is contrary to intuition, and results from the diffusion potential. This potential reversal agrees with the discussion of Hauser and Newman [10,11] regarding the quantity: % i

zi si Di

(28)

where zi, si, and Di are the charge number, stoichiometric coefficient, and diffusion coefficients of species i participating in the electrode reaction. If the value of Eq. (28) is positive, the solution potential increases as the cathode surface is approached. Eq. (28) was derived for a single electrode reaction. When applied to the reduction of all five copper-containing species (Reaction (21), with n= 0–4), it is negative for reduction of Cu(CN)34 − , Cu(CN)23 − , and Cu(CN)23 − , but positive for reduction of CuCNaq and Cu. Because only an extremely small portion ( B 4× 10 − 11%) of the species at the electrode surface under base-case conditions are CuCNaq or Cu + , we conclude that only a very small portion of the current stems from these reactions, and the electric field determined by our model is in agreement with the prediction of Hauser and Newman. In Katagiri’s model [7], diffusion coefficients were set equal, which eliminates the diffusion potential and, as a consequence, the solution potential at the electrode was more negative than in the bulk solution. Thus, Katagiri’s results indicate that the transport of anionic complexes to the electrode surface is hindered by migration, whereas realistic diffusion coefficients result in a current enhancement. The diffusion coefficients of the cuprous–cyanide complexes listed in Table 3 are based on conductivity measurements conducted in our laboratory [8], and indicate that the dimensionless diffusion

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

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Table 3 Parameters for base-case conditions at 60°C Parameter

Value

Units

Ref.

[CuCN]o [NaCN]o D1 D2,1 D3,1 D4,1 D5,1 D6,1 D7,1 jo,1 bc jo,2 bc jo,3 bc jo,4 bc a1 a2 a3 a4

0.2 0.6 2.6×10−5 1.73 1.11 1.1 1.19 0.90 0.52 6.4 × 10−9 0.050 2.7 1.1 0.38 0.38 0.38 0.38

M M cm2 s−1 None None None None None None mA cm−2 mA cm−2 mA cm−2 mA cm−2 None None None None

[15] [15] [14,27] [27] [27] Estimated [8] [8] [8] Estimated Estimated Estimated Estimated Estimated Estimated Estimated Estimated

species towards higher-order complexes at the disk center relative to its edge. The corresponding potential profile, Fig. 5(b), shows that the potential difference between the disk center and edge is small, about 0.74 mV. The dimensionless current distribution for the basecase parameters at 80% of the mass-transport-limited current density is presented in Fig. 6. For reference, the primary current distribution is also shown. The current distribution is nonuniform, with larger current at the disk edge than center. To quantify the uniformity of current distribution, we define a deviation Dcd from uniform current density as:

& ) 1

Dcd =

r

0

)

j (r)− jave dr jave

(29)

where j(r) is the local current density at radial position r. For a uniform current distribution, Dcd is zero, and the other extreme is the primary current distribution, for which Dcd = 1/4. Fig. 7 displays Dcd for the base-case parameters as a function of the fraction of mass-transport-limited current. In general, a uniform distribution results when the

Fig. 6. Current distribution on disk surface for base-case parameters at 80% of limiting current. For reference, the primary current distribution is also shown (dashed line). All parameter values are given in Tables 2 and 3. Fig. 5. Concentration (a) and potential − (V− f− Ebc) (b) profiles on disk surface for base-case parameters at 80% of limiting current. All parameter values are given in Tables 2 and 3.

coefficients D51, D61, and D71 have the values 1.19, 0.9, and 0.52, respectively. Because these values are considerably smaller than that of CN − (D21 =1.73), a significant diffusion potential results. Fig. 5 displays the concentration and potential profiles on the disk for the base-case parameters at 80% of the limiting current. Because the disk edge is more accessible than the disk center for mass transport, the concentration of complexes is highest at the edge. Likewise, because CN − is released at the electrode, the concentration of free cyanide is higher at the disk center than at the edge. The small increase in CN − concentration illustrated results in a minor shift of copper-containing

Fig. 7. Deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current for base-case parameters. All parameter values are given in Tables 2 and 3.

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

Fig. 8. Total and species current distribution on disk surface at 0.4 (a) and 95 (b) percent of limiting current for base-case parameters. All parameter values are given in Tables 2 and 3.

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nonuniform at larger fractions of the limiting current. For the cuprous cyanide system at a stationary disk, the effect of ohmic resistance on the current distribution is much smaller than that of mass-transport resistance; the ratio of diffusion to ohmic resistance k/( fFDCb ) for this system is on the order of 10 to 102. The negligible effect of ohmic resistance is illustrated by figure 9 of Part II of this series [28]: as the disk rotation rate is increased from 0 rpm, ohmic resistance does not alter the shape of the deviation curve until the rotation rate exceeds 5 rpm. Fig. 8 displays the current distribution from reduction of each complex for the base-case parameters at 0.4% (Fig. 8(a)) and 95% (Fig. 8(b)) of the limiting current. In both cases, the majority of current comes from reduction of Cu(CN)23 − and Cu(CN)34 − . At 0.4% of the limiting current (Fig. 8(a)), 72% of the current results from Cu(CN)23 − reduction and 27% results from Cu(CN)34 − reduction. But at 95% of the limiting current (Fig. 8(b)), 38% of the current is due to Cu(CN)23 − reduction and 62% is due to Cu(CN)34 − reduction. Because the surface concentration of CN − increases with current density, higher-order complexes are present in larger amounts and become responsible for a larger fraction of the total current with more negative applied potentials.

4.2. Effect of NaCN concentration

Fig. 9. Polarization curves (a) and deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current (b) for various NaCN concentrations, with all other parameters given in Tables 2 and 3. The base-case polarization and deviation curves (dashed line) are provided for reference.

reaction rate is limited by electrode kinetics, and a highly non-uniform distribution results when the reaction rate is controlled by mass-transport. Thus, we expect to observe less uniform current distributions as the applied potential is made more negative; that is, the normalized current distribution becomes increasingly

To investigate the effect of NaCN concentration on the polarization characteristics and deposit distribution, the NaCN concentration was set to 0.4 and 0.8 M (cyanide:copper molar ratios of 3:1 and 5:1, respectively), which brackets the base-case concentration of 0.6 M, while holding all other parameters constant. Polarization curves for all three NaCN concentrations are presented in Fig. 9(a). As NaCN concentration increases, (i) the equilibrium potential becomes more negative; (ii) the slope of the polarization curve at low overpotentials becomes steeper, and (iii) the limiting current density decreases. The negative shift in equilibrium potential with increasing stoichiometric NaCN concentration is expected from the stoichiometry of the electrode reactions. The equilibrium potential E is related to the potential Ebc measured by a copper electrode located in the base-case solution by [25] E= Ebc +

 

RT c % si,n ln i F i ci,bc

(30)

where si is the stoichiometric coefficient of species i in Reactions (21), defined to be negative for reactants and positive for products. Applying this expression we find Eeq0.4 = Ebc − 229.1 mV and Eeq0.8 = Ebc + 87.1 mV, which correspond to the zero-current intercepts in Fig. 9(a). The change in slope at low overpotentials is caused by the effect of CN − concentration on exchange

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

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Table 4 Base-case, 0.4 and 0.8 M NaCN bulk electrolyte exchange current densities for reduction of all four cuprous–cyanide complexes, 60°C 0.4 M NaCN jo,n /mA cm−2

Base-case jo,n bc/mA cm−2

n=1 n=2 n= 3 n= 4

7.2×10−8 0.045 0.20 0.0062

6.4×10−9 0.050 2.7 1.1

Total

0.25

3.8

0.8 M NaCN jo,n /mA cm−2 2.3×10−9 0.043 5.4 5.0 10.5

increases, the current distribution becomes significantly less uniform. But the difference is less at larger fractions of the limiting current, and, at the limiting current, the primary current distribution results. The increasing nonuniformity of current with NaCN concentration is caused by the decrease of kinetic resistance relative to mass-transfer resistance, a well-known phenomenon in electrochemical systems [14]. Figs. 10 and 11 display the concentration and potential profiles on the axis of symmetry for 0.4 and 0.8 M NaCN electrolyte, respectively, at 50% of the limiting current (applied potentials of − 52 and −159 mV, respectively). The potential profile in the 0.8 M NaCN electrolyte (Fig. 11(b)) is similar to that of the base-case electrolyte (Fig. 4(b)), and increases monotonically by 1.8 mV across the solution. Because the n= 4 complex diffuses much more slowly than free cyanide, a significant diffusion potential results, which causes the solution potential to rise as the electrode surface is approached. In contrast, with 0.4 M NaCN electrolyte (Fig. 10), most of the copper is present in the faster-diffusing n=3 form. Consequently, the solution potential decreases as the electrode surface is approached until the location at which the n=4 complex begins to carry a significant fraction of the current, at which the diffusion potential contribution to the total solution potential again overcomes ohmic drop. Despite the minimum in solution potential, the potential at the electrode surface is lower than that in the bulk solution, and the net effect of migration in this electrolyte is to retard the passage of current. Thus, migration enhances the trans-

Fig. 10. Concentration (a) and potential − (V− f− Eeq) (b) profiles on axis of symmetry for 0.4 M NaCN electrolyte at 50% of limiting current, with all other parameters given in Tables 2 and 3.

current density. Eq. (23) determines the exchange current density for non-base-case conditions as: jo,n =jo,nbc

   cn

cn,bc

1 − an

cCN −



cCN − ,bc

nan

(31)

Table 4 lists the resulting exchange current densities jo,n for all four complexes. The total exchange current density is 42 times larger in 0.8 M than in 0.4 M NaCN, and the slope of the polarization curve is correspondingly steeper at low (linear) polarization. The diffusion contribution to the limiting current decreases with increasing NaCN concentration because of the shift towards higher-order complexes that have smaller diffusivities than lower order-complexes. Migration also influences the limiting current, as described in a subsequent discussion. Fig. 9(b) displays the corresponding deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current for all three stoichiometric NaCN concentrations. As NaCN concentration

Fig. 11. Concentration (a) and potential −(V−f − Eeq) (b) profiles on axis of symmetry for 0.8 M NaCN electrolyte at 50% of limiting current, with all other parameters given in Tables 2 and 3.

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

Fig. 12. Polarization curves (a) and deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current (b) for various CuCN concentrations, with all other parameters given in Tables 2 and 3. The base-case polarization and deviation curves (dashed line) are provided for reference. Table 5 Exchange current densities used in this study a Exchange current density/ mA cm−2

jo,1 jo,2 jo,3 jo,4 jo,total a

Most electroactive species n= 1

n= 2

n= 3

n =4

3.7 0.037 0.037 0.037 3.8

0.037 3.7 0.037 0.037 3.8

0.037 0.037 3.7 0.037 3.8

0.037 0.037 0.037 3.7 3.8

All other parameter values are given in Tables 2 and 3.

port of anionic complexes to the electrode surface in 0.8 M NaCN, and retards mass transport in 0.4 M NaCN electrolyte.

4.3. Effect of CuCN concentration To investigate the effect of CuCN concentration on the polarization characteristics and deposit distribution, the CuCN concentration was set to 0.1 and 0.3 M (cyanide:copper molar ratio of 7:1 and 3:1, respectively), which brackets the base-case concentration of

25

0.2 M, while holding all other parameters constant. Polarization curves for all three CuCN concentrations are presented in Fig. 12(a). As CuCN concentration increases, (i) the equilibrium potential becomes more positive; (ii) the slope of the polarization curve at low overpotentials becomes less steep, and (iii) the limiting current density increases. The positive shift in the equilibrium potential occurs because the free cyanide concentration is significantly higher in 0.1 M CuCN solution (0.33 M) than in 0.3 M CuCN solution (0.010 M). Evaluating Eq. (30) for 0.1 and 0.3 M CuCN yields Eeq0.1 = Ebc + 127.8 mV and Eeq0.3 = Ebc − 233.4 mV, which correspond to the zerocurrent intercepts on Fig. 12(a). The slope of the polarization curve at low currents becomes less steep with increasing CuCN concentration because the smaller quantity of free cyanide results in a lower exchange current density. The increase in mass-transport-limited current as the stoichiometric CuCN concentration increases is caused by two factors: (i) more copper is available, and (ii) the composition of the bath shifts towards lower-order, faster-diffusing complexes. The second factor effects a slight increase in current above that expected from the stoichiometric increase in Cu(I). Fig. 12(b) displays the corresponding deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current. As the CuCN concentration increases, the current distribution becomes significantly more uniform at lower currents. Again, the trend can be understood in terms of the concentration of free cyanide: as CuCN is added, cyanide is consumed to form complexes and the concentration of CN − decreases, which lowers the exchange current density and increases kinetic resistance; at larger fractions of the limiting current these kinetic effects become less important, and the deviation functions for the three concentrations converge.

4.4. Effect of exchange current densities The base-case set of exchange current densities is such that reduction of copper from any of the four complexes may occur. However, it is conceivable that the majority of current results from reduction of a single complex that is considerably more electroactive than the other three. To investigate how this possibility would effect the current distribution, the exchange current densities jo,n were changed such that their sum remained the same as that used for the base-case, but the exchange current density for one complex is 100 times as large as the other three. Table 5 displays the parameter values for the four studies discussed below. Polarization curves for the four sets of parameters listed in Table 5 are presented in Fig. 13(a). For reference, the polarization curve for the base-case parameters is also shown. The limiting current is not

26

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

affected, but the approach to it is influenced by which species is most electroactive. Because reduction of a complex results in release of cyanide, the distribution of copper-containing species at the electrode surface shifts towards higher-order complexes. This effect becomes more pronounced with increasing current because cyanide is released at a faster rate. The shift towards higher-order complexes enhances the current when higher-order complexes are most electroactive, and hinders the current when lower-order complexes are most electroactive, as seen in Fig. 13(a). The base-case parameters result in current from primarily the n= 3 and 4 complexes. Thus, the base-case polarization curve falls between the curves when n =3 and 4 are most electroactive. Fig. 13(b) displays the corresponding results for the deviation from uniform current density Dcd. As expected, the four curves converge at 0 and 100% of the limiting current. At intermediate values, the shift towards higher-order complexes at the electrode surface increases the local total exchange current density (i.e. based on surface concentrations) when higher-order

Fig. 13. Polarization curves (a) and deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current (b) when complex n (indicated on figure) is 100 times as electroactive as the other three. Exchange current densities are listed in Table 5, with all other parameters given in Tables 2 and 3. The base-case polarization and deviation curves (dashed lines) are provided for reference.

complexes are most electroactive, and decreases the local total exchange current density when lower-order complexes are most electroactive. Thus, when either CuCNaq or Cu(CN)2− is most electroactive, the kinetic resistance is largest at intermediate fractions of the limiting current and a minimum in the deviation function is observed, a result that is not a priori expected. Because experimental evidence indicates that lower-order complexes are more electroactive than higher-order complexes (Appendix A), this is likely to be a mechanism to distribute the deposit in cuprous–cyanide plating baths more uniformly.

4.5. Effect of transfer coefficients The base-case transfer coefficients an for reduction of the four complexes are set to observed transfer coefficients [3,4,6,16]. Because it is impossible to extract transfer coefficients for individual complexes from an observed quantity, the four base-case transfer coefficients were set to a value observed by independent investigators [3,4], an = aobs = 0.38. The study described here endeavors to determine the sensitivity of results to transfer coefficients, and to gain insight as to values that might be desirable in a non-cyanide alternative electrolyte. To achieve this goal, polarization curves were calculated holding all parameters at their basecase values, with the exception of a1, a2, a3, or a4. These values were individually decreased by a factor of 1/2 to 0.19 or increased by a factor of 3/2 to 0.57, in turn, holding the other three transfer coefficients at their base-case values. Changing the transfer coefficients for the n =1 and 2 complexes (a1 and a2) has negligible effects on the polarization curves, concentration profiles, and current distribution because these complexes are responsible for such a small fraction (less than 1%) of the total current. However, changing a3 and a4 has effects that are more discernible, as described below. Fig. 14(a) displays polarization curves for a3 =0.19 and 0.57, with all other parameters at their base-case values. For reference, the polarization curve for the base-case value of a3 (a3 = 0.38) is also shown. The limiting current is not affected by electrode kinetics and thus remains unchanged. As a3 is increased, reducing the n= 3 complex becomes kinetically easier, and the fraction of the limiting current increases for a given applied potential. While the effect that changing a3 has on the polarization curve is relatively minor, its effect on the current distribution is more pronounced. Fig. 14(b) displays the corresponding deviation from uniform current density Dcd as a function of the fraction of the mass-transport-limited current for the three values of a3 under consideration. When the n= 3 complex is more difficult to reduce (i.e. smaller values of a3), a more uniform current distribution results. Similar effects on the polarization and deviation curves are ob-

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

27

tially unchanged across a concentration boundary layer. A typical pyrophosphate plating bath contains 0.25 M Cu2P2O7 + 1.0 M K4P2O7 + 0.40 M K3PO4 + 0.15 M KNO3 + 0.1 M NH3, pH 8.5 [15]. Consequently, the polarization and current distribution of pyrophosphate electrolytes are considerably less sensitive to free ligand concentration than cyanide baths. Because cyanide and pyrophosphate are weak bases, their release at the electrode causes a local pH rise at the surface. However, the pH change caused by CN − is much less significant than that effected by P2O47 − because the typical operating pH of cyanide baths (pH 11.2) is significantly higher than that of pyrophosphate baths (pH 8.5). Finally, because the diffusion coefficient of Cu(CN)34 − is only 30% of that of free cyanide, whereas the diffusion coefficient of Cu(P2O7)62 − is about 70% of that of free pyrophosphate [21], diffusion potentials are more significant in cyanide than in pyrophosphate electrolytes. Neither cyanide nor pyrophosphate baths are well supported, but the concentration of inert species is larger in pyrophosphate electrolytes. As a result, the electric field, and consequently, the migration enhancement to mass-transport, tends to be smaller in pyrophosphate than in cyanide plating baths.

Fig. 14. Polarization curves (a) and deviation from uniform current density Dcd as a function of the fraction of mass-transport-limited current (b) for various a3, with all other parameters given in Tables 2 and 3. The base-case polarization and deviation curves (dashed line) are provided for reference.

served when a4 is changed. Clearly, the current distribution is more sensitive to the value of transfer coefficients than the polarization curve. This suggests that choosing a non-cyanide alternative that has a relatively small cathodic transfer coefficient may result in a more uniform current distribution while paying a small price in terms of reduced deposition rate at a given applied potential.

4.6. Comparison of cyanide and pyrophosphate baths To compare deposition from cuprous cyanide and cupric pyrophosphate baths, a model of similar sophistication to that discussed here was developed for copper discharge onto a stationary disk electrode from a cupric pyrophosphate electrolyte [16]. To conserve space the detailed results are not presented but are available [16]. Several observations regarding the behavior of cuprous cyanide and cupric pyrophosphate baths are made below. Because the composition of cupric pyrophosphate baths is such that the saturated complex, Cu(P2O7)62 − , is essentially the only form of copper in the bulk solution, the distribution of complexes remains essen-

5. Conclusions Several conclusions regarding the behavior of cuprous-cyanide plating baths, and deposition from metal–ligand complexes in general, can be drawn from this work: (1) the distribution of metal-containing species shifts towards higher-order complexes near the electrode surface. The effect is more pronounced at less accessible portions of the cathode (e.g. the disk center), and at larger current densities. If higher-order complexes are less electroactive than lower-order complexes, this effect decreases the current density at a given applied potential. In addition, because higher-order complexes have smaller diffusivities than lower-order complexes, this effect decreases the current-distribution uniformity at a given fraction of the mass-transport-limited current. (2) Because the diffusion coefficient of Cu(CN)34 − is considerably smaller than that of CN − , a diffusion potential results when Cu(CN)34 − carries a significant portion of the total current, as in the base-case calculations presented here. Consequently, the solution potential increases as the cathode is approached, and migration enhances the transport of the anionic complexes to the electrode surface. In bath formulations where the bulk concentration of Cu(CN)34 − is not significant, the shift towards higher-order complexes near the electrode surface may result in a potential minimum within the stagnant solution. Similar results

28

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

are expected for deposition from any metal-ligand complex that (i) diffuses at a slower rate than its free ligands and (ii) carries a significant portion of the current. (3) Decreasing the ligand concentration, while holding the total metal concentration constant, decreases the exchange current density but increases the equilibrium potential. In cuprous – cyanide baths, decreasing the stoichiometric NaCN concentration increases the current at a given applied potential, and causes the current distribution to become more uniform at a given fraction of the limiting current. (4) Parameter studies reveal that if the exchange current density of lower-order complexes is increased relative to higher-order complexes, the current distribution becomes more uniform at a given fraction of the limiting current. If this is done while holding constant the sum of the exchange current densities of all complexes, a smaller current results at a given applied potential. A similar effect is observed if the cathodic transfer coefficients of electroactive components are decreased, but to a lesser extent. These results suggest that to obtain relatively uniform current distributions, two criteria in the search for non-cyanide alternatives for copper strike-plating applications are: (i) the electroactive species must not be the highest-order complex, and (ii) the solution composition must be such that the release of ligands at the electrode surface shifts the local equilibrium towards less electroactive complexes. (5) Under some circumstances, a minimum in the deviation from uniform current density is observed at intermediate fractions of the limiting current. This unexpected observation occurs only when lower-order complexes are significantly more electroactive than higher-order complexes. (6) As expected, the current distribution on a stationary disk approaches that of the highly non-uniform primary current distribution as the limiting current is approached.

Acknowledgements This work was supported by the American Electroplaters and Surface Finishers Society, AESF Research Grant No. 91.

Appendix A A comprehensive treatment of the electrochemical kinetics of copper reduction from cyanide complexes has not appeared in the literature. Other modeling efforts [29,30] have applied a single current – potential relationship to describe the behavior of cuprous cyanide systems, which is not consistent with experimental ob-

servations, as discussed below. The kinetic expression used in the present work describes reversible reduction of any of the four complexes. As such, each complex has its own transfer coefficients and exchange current density. While is it unlikely that reduction of all complexes follows simple mass-action kinetics, kinetic expressions formulated in this manner result in an apparent exchange current density and cathodic transfer coefficient that vary with solution composition, in accordance with experimental results. The mechanism by which copper moves from complexed form in solution to reduced metal on the surface is not well understood, but several have been proposed. Costa [3] concluded that copper deposition is a twostep process: Cu(CN)23 − “ CuCNad + 2CN −

(A1)

CuCNad + e “ Cu+ CN

(A2)

−

−

Raub and Mu¨ller [31] propose that copper is deposited from Cu(CN)2− (Reaction (21), n= 2) even though Cu(CN)3 is most prevalent in the electrolytes they describe. Steponvic' ius et al. [6] also studied solutions in which Cu(CN)23 − is the most common copper complex, and concluded that a chemical-electrochemical (CE) mechanism best explains the data, where dissociation of Cu(CN)23 − to Cu(CN)2− precedes Reaction (21), n=2. Bek and Zhukov [30] studied solutions in which Cu(CN)3 and Cu(CN)4 are the most common forms of copper, and reported a similar CE mechanism, where Reaction (21), n= 2 is the electrochemical step. Chu and Fedkiw [5] concluded that Cu(CN)3 is the electroactive species (Reaction (21), n=3) under conditions where Cu(CN)4 is the dominant species in the electrolyte. Several investigators have explored the nature of adsorbed species during copper deposition from cyanide electrolyte [32–36]. The results of these investigators indicate that CuCN and all four complexes can be adsorbed on copper electrode surfaces, depending on solution concentrations and electrode potential. The common observation among the experiments is that lower-order complexes tend to be more electroactive than higher-order complexes. The kinetic constants used for the base-case conditions reflect this common theme. In addition to studies of copper deposition from cyanide electrolyte [3–6,29–36], numerous workers have investigated electrodeposition of other metals from cyanide complexes, including cadmium [37,38], silver [39–47], and gold [41,48–54]. In the majority of these studies [3,4,6,30,37,38,42,48 –52], deposition is considered to occur from a single electroactive complex, although a mixture of complexes may exist in solution. In studies that examine a wide range of solution compositions, the electroactive species is often dependent upon the CN − concentration [5,39,40,42,50], and a dramatic change in the apparent exchange current den-

D.A. Dudek, P.S. Fedkiw / Journal of Electroanalytical Chemistry 474 (1999) 16–30

sity and transfer coefficient may be observed with varying free cyanide concentration [3,39,40,42]. These observations are consistent with electrode kinetics that are dependent upon the number of ligands in a complex. A.1. Nomenclature concentration of species i/mol l−1 ci Di diffusion coefficient of species i/cm2 s−1 Di, j ratio of diffusion coefficients of species i to species j, dimensionless Dcd deviation from uniform current density (Eq. (29)) E equilibrium or open-circuit potential/mV f F/RT F Faraday’s constant, 96 487 C mol−1 j current density/mA cm−2 jo exchange current density/mA cm−2 k rate constant/s−1 n number of ligands in a complex Ni flux of species i/mol cm−2 s−1 r radial position R universal gas constant/8.314 J mol−1 K−1, or dimensionless radial coordinate Ri rate of generation of species i/mol cm−3 s−1 si stoichiometric coefficient of species i T temperature/K ui mobility of species i/cm2 mol J−1 s−1 V electrode potential/mV zi charge number on species i/equiv mol−1 Z dimensionless axial coordinate a cathodic transfer coefficient, dimensionless bn equilibrium constant for Cu(CN)(n−1)− forman tion, (l mol−1)n, (Eq. (2)) f solution potential/mV G coordinate, (Eq. (16)) h overpotential/mV, (Eq. (24)) m solution viscosity u coordinate, (Eq. (16)) Subscripts a anodic aq aqueous species ave average quantity b evaluated at bulk solution bc base-case quantity c cathodic eq equilibrium quantity i species i j species j mt mass-transport-limited quantity n number of ligands in a complex obs observed or effective value s evaluated at electrode surface Superscript ° stoichiometric value

29

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