Morphological Stability during Electrodeposition

Transcription

1 C708 Journal of The Electrochemical Society, C708-C /2003/15010/C708/9/$7.00 The Electrochemical Society, Inc. Morphological Stability uring Electroeposition II. Aitive Effects Mikko Haataja, a,z Davi J. Srolovitz, a an Anrew B. Bocarsly b, * a Princeton Materials Institute an Department of Mechanical an Aerospace Engineering an b Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA Common experience shows that electroeposite ED metallic films exhibit rough surfaces unless the electrochemical bath contains small quantities of molecular aitives. We evelop a formalism for escribing the effects of aitives on surface morphology evolution, which buils on that in a companion paper for the aitive-free case. We emonstrate that the aitives suppress the morphological instability that leas to roughening by preferentially accumulating near surface protrusions an blocking growth sites. Our chemically base moel shows that aitives which reaily asorb onto the surface an have a strong tenency to complex with the metal cations reuce the riving force for the instability an thus enhance leveling. Furthermore, polar aitives provie an aitional stabilizing effect, in accor with experimental observations. It is also shown that linearly stable growth can be achieve over a wie range of eposition flux at sufficiently large aitive bulk concentrations. We preict the ED conitions necessary for growing flat films an emonstrate that these are in goo agreement with experimental observations The Electrochemical Society. DOI: / All rights reserve. Manuscript submitte January 28, 2003; revise manuscript receive April 7, Available electronically August 18, Extensive experience shows 1,2 that the properties of electroeposite ED metallic films can be effectively controlle by introucing small quantities of aitives into the electrochemical bath. For example, morphological instabilities uring eposition commonly prouce poor quality films with rough surfaces 3-7 in the absence of aitives. Aition of even small quantities of aitives can rastically ecrease the amplitue of the surface roughness as well as increase the characteristic wavelength of the roughness. 7 In aition to controlling the large-scale roughness leveling, aitives have been use to control crystallographic texture an grain size of ED films. The goal of the present paper is to provie a formalism which can be use to evaluate propose mechanisms for surface leveling by the introuction of aitives into the electrochemical baths. We apply this formalism to explicitly evaluate the effects of complex formation between cations an aitives, aitive ipole moments, surface segregation, an aitive incorporation into the growing electroeposit. Typically, aitives consist of organic compouns or small inorganic species that can act as ligans with respect to the metal being eposite. The ionic nature of the aitive along with the exact moe of ligation is extremely variable. Commonly employe aitives can be organic e.g., thiourea, CH 4 N 2 S in nickel plating baths or inorganic e.g., potassium nitrate, KNO 3 in silver plating baths, ionic e.g., soium sulfocyanate, NaSCN in silver electroeposition, or nonionic, polar e.g., naphthoquinone, C 10 H 6 O 2 in lea electrorefining or nonpolar e.g., anthraquinone, C 14 H 9 NO 2 in lea electrorefining. 2 This suggests that the leveling effect of the aitives epens on only a few key physical characteristics. While there are many commercial levelers, a complete unerstaning of their effects an the physical an chemical mechanisms that allow these molecules to effectively reuce the roughness of films remains elusive. This is in contrast with the emerging unerstaning of the role of aitives in vapor phase eposition; e.g., the surfactant effect in semiconuctor growth see Ref. 8 an references cite therein. In Part I 9 we presente a formalism that provies quantitative preictions for the evolution of the surface morphology in the absence of aitives. In this paper we exten the formalism of Part I to the case where ED occurs in the presence of aitives. We present a physically an chemically motivate moel for ED with aitives, then investigate the influence of the aitives on the morphological evolution an stability of surfaces uring ED. A brief account of this work has appeare in Ref. 10. * Electrochemical Society Active Member. z mhaataja@princeton.eu Morphology evolution in the presence of aitives has been previously aresse through both experiments 2,7 an theory Qualitatively, there is some experimental evience suggesting that polar aitives or aitives which ten to form complexes with the metal cations lea to more effective leveling. 1,2 An experimental stuy of the growth of copper films from a copper sulfate bath prouce increasingly rough surfaces uring growth in the absence of aitives, while aing thiourea le to smoother films. 7 Increases in thiourea concentration le to smoother films an longer wavelength roughness. A range of thiourea concentration exists for which the growth front remains essentially flat. We argue that this is attributable to the complete suppression of growth instability for aitive concentrations larger than a critical value. Several moels have been propose to explain the leveling effects of aitives. They all assume that the aitives asorb onto the growing surface an interfere with the eposition process through a specific mechanism, such as blocking the surface growth sites; 1,2,11 the leveling effect results from preferential growth at surface epressions instea of protrusions. Maore et al. 11 introuce a continuum moel which inclue the blocking effect of charge aitives as well as aitive reuction at the electroe, couple to iffusive transport of the aitives to the surface. They foun that the leveling effect of aitives is controlle by the ratio of the aitive iffusivity to the rate of aitive consumption at the cathoe. Georgiaou et al. 12 stuie the evolution of film morphology uring ED of copper in microtrenches by employing a moel where the aitive suppresses metal eposition an is consume by an electrochemical reaction. By numerically solving the full nonlinear moving bounary problem they emonstrate that the aitives promote voi-free filling of trenches. Similarly, Cao et al. 13 numerically solve a moel in which the asorption of aitives locally inhibits eposition an showe that this leas to effective leveling an voi-free filling of trenches. Recently, Pricer et al. 14 introuce a couple Monte-Carlo/continuum approach for stuying the effect of a blocking aitive in copper ED in rectangular trenches. Finally, Josell et al. 15,16 have recently introuce an accelerator-aitive moel which quantitatively explains superconformal ED in submicrometer features. While the aforementione theoretical approaches have successfully explaine some of the experimental results, they have neglecte several common experimental observations an have base their moels on an oversimplifie picture of transport in the electrolyte. For example, effective aitives are known to ligan to the electroactive metal ions, forming complexes in solution. The aitives alone or in a complex can prouce neutral species which interact with the electric fiel through strong molecular ipole mo-

2 Journal of The Electrochemical Society, C708-C C709 ments. We consier several types of aitive/metal ion interactions an explicitly account for metal cation an aitive rift in the electric fiel within electrolytes that are not fully supporte. Incluing the effects of spectator ions allows us to interpolate between the limiting cases of fully supporte purely iffusive transport an unsupporte electrolytes. The resultant linear stability theory allows us to examine the interplay between aitive an metal ion transport, rift, an iffusive transport an make preictions about the resulting morphology in terms of the external control parameters e.g., aitive bulk concentration, spectator ion concentration, eposition flux an the chemical properties of the metal cations an aitives e.g., charge, ipole moment, heat of segregation, an complex formation. In the next section we very briefly review the relevant aspects of the formalism an the results on growth instabilities in the absence of aitives from the companion paper, Part I. 9 We then escribe several physical an chemical moels for the mechanisms by which the aitives influence the eposition process. Then we perform a self-consistent, uniform steay-state analysis of ED in the presence of aitives incluing the concentration an electrostatic fiels. Morphology evolution is analyze using perturbation theory, where we linearize aroun the uniform steay-state result. The resultant preictions for the wavelength an growth rate of the roughness as a function of chemical an eposition parameters are collecte in the form of a stability map, which shows uner which conitions the surface instability can be entirely suppresse. Finally, we compare our preictions with experimental observations. Moel for Electroeposition in the Absence of Aitives Formalism. We briefly review the relevant aspects of the morphology evolution formalism put forth in Part I. The number ensity for each ionic species obeys a continuity equation C i t j i 0 where i C, A, XC, XA enotes the metal cations, anions, spectator cations, an spectator anions, respectively. The ion fluxes j i (r) follow from 1 j i r D i C i q ied i C i 2 where D i enotes the iffusivity an is the electrostatic potential. is etermine from the Poisson equation 17 2 e ˆ i q i C i r 3 where ˆ enotes the constant local permittivity of the ionic solution. We consier a rectangular system of imensions L x L z W L, where W enotes the linear imension with of the planar surface an L enotes the thickness of the mass-transfer layer over which the concentrations vary. Beyon L the concentrations of all species are very nearly constant. Perioic bounary conitions are employe in the x irection, an the bounary conitions in the z irection become C C (x, L) C A (x, L) C 0, C XC (x, L) C XA (x, L) C 1, an (x, L) 0. At the growing surface (x, 0) V ext, an the ion fluxes i (A,XC,XA) vanish as these species o not coeposit: j i j i nˆ 0, where nˆ is the surface normal pointing into the bath. The magnitue of the local metal cation flux onto the growing surface j C taken to be positive for a growing film is given by the Butler-Volmer B-V equation j C j C nˆ j 0 C C C 0 e 1 F/RT e 2 F/RT 4 where F an R are the Faraay s an gas constants, an ( 1, 2 ) enote the so-calle symmetry factors relate to the potential barrier for metal cation reuction. 18 The overpotential is given by 19 V eq V ext RT F ln C C C C eq F qc The equilibrium potential of the metal-solution interface is V eq, an varying the external electroe potential V ext away from V eq leas to either eposition ( 0) or issolution ( 0). The thir term in Eq. 5 accounts for the metal cation concentration epenence of V eq, an the last term escribes the effects of surface curvature an surface tension, i.e., the Gibbs-Thomson effect. The quantity q C ej 0 enotes the exchange current ensity, an enotes the atomic volume of the metal in the eposit. Finally, the local growth velocity in the normal irection nˆ, v n, follows from the massbalance relation v n j C nˆ. Morphology evolution. In Part I we introuce a physically motivate continuum moel for the morphological stability of surfaces uring ED in the absence of aitives. The moel explicitly accounts for the electric fiel in the electrolyte, the metal cations an anions, an any aitional ions from a supporting electrolyte. By explicitly solving the steay-state equations for a planar growth front, we emonstrate that the moel naturally gives rise to the Gouy-Chapman G-C bounary layer an that increasing the concentration of the spectator ions leas to a rapi ecrease in the magnitue of the electric fiel in the bulk. In this limit the metal cation transport is ominate by iffusion in the concentration graient, as expecte. A first unerstaning of the morphology evolution was obtaine by carrying out a perturbation analysis in the surface profile. In agreement with previous stability analysis, the surface was shown always to be linearly unstable against perturbations with a sufficiently large wavelength for any finite external eposition flux. This result hols for both unsupporte an fully supporte baths an can be unerstoo as follows. Consier a small perturbation to the planar surface. Because C C increases away from the growing surface, the metal cation concentration C C is larger smaller near protrusions epressions than near the flat surface. In the absence of surface tension an increase in C C leas to a larger metal cation flux via the B-V equation, Eq. 4. The larger metal cation flux leas to an increase in v n an hence, to faster slower growth at a protrusion epression. This positive feeback leas to unstable growth of the perturbations. Capillarity, however, effectively suppresses perturbations on small scales, an these two competing effects eposition an capillarity set the lateral scale of the surface roughness observe in experiment. In particular, increasing the eposition flux makes the surface rough on smaller scales an leas to faster roughening. Interestingly, for a fixe eposition flux j the system without the supporting electrolyte was foun to be more stable than one with a supporting electrolyte, in agreement with previous stuies. 22 This was shown to be a consequence of the increasing local metal cation concentration graient as more spectator ions are ae into the bath. Moels for Aitive Effects in Electroeposition We now turn to the escription of aitives within the framework introuce in Part I. Qualitatively, there are three main questions that must be consiere in assessing the role of aitives in ED: i how o they interact with the ions in the bulk, (ii) how o they get to the surface, an (iii) once on the surface, how o they moify the eposition of the metal cations. It has been suggeste that a metal cation an an aitive molecule can form a complex in the bulk solution; 1,2 in particular, it has been note that increasing the tenency of metal ions to form complexes with the aitives correlates with their susceptibility to the effect of aitives. 1 The transport of the aitives to the surface is usually assume to be 5

3 C710 Journal of The Electrochemical Society, C708-C iffusion-limite, 2,7,14 although it is conceivable that some of the aitives are brought onto the surface through the motion of the metal cations as a part of a complex. Several moels have been propose to explain the leveling effects of aitives, the most popular of which are i blocking the surface, (ii) changes in the bounary layer potential, an (iii) ion briging. 1,2 The first mechanism, also known as the irt mechanism, is attribute to the tenency of the aitive molecules to asorb onto the surface an interfere with either the attachment of metal cations or their iffusion along the surface to preferential growth sites. This type of aitive causes a ecrease in the rate of the electroe reaction at fixe potential. The leveling effect of such aitives can be unerstoo by consiering the aitive concentration aroun a protrusion: if the protrusion collects more aitives than o epressions e.g., ue to an aitive concentration graient, it tens to grow more slowly than the epressions, implying leveling. 2,7,14 The secon mechanism is base on the iea that the reuction reaction oes not necessarily have to occur at the surface but can take place anywhere within the G-C bounary layer. 2 Therefore, any foreign ions or neutral molecules which asorb onto the surface moify the potential within the G-C bounary layer an thus influence the eposition rate. Finally, the aitives may increase the rate of reuction; 2 this coul apply to aitives which bon to the surface an meiate the charge transfer between the metal cation an the eposit ion briging. It is noteworthy that the effect of a particular aitive species can be a combination of all these mechanisms. Furthermore, there is some evience that the leveling is brought about through the interaction between reaction proucts of the aitive at the surface an the growing eposit. 2 Finally, in some cases the growth of a level an bright eposit requires the simultaneous use of multiple types of aitives. Such synergistic effects are not consiere here. In light of this iscussion it is clear that unraveling the unerlying mechanisms for the leveling effect of a given aitive molecular species is a aunting task. Therefore, the goal of the present work on aitive effects is by necessity somewhat more limite, namely, to construct a minimal moel for aitive effects, to quantify the role of ifferent interactions in the morphology evolution of the surface, an finally, to relate this to leveling. In particular, we consier aitives which i form complexes with the metal cations, (ii) interact with the electric fiel via a ipole moment, an (iii) interfere with the eposition process by blocking surface growth sites. Although some of the microscopic etails are necessarily ignore in this approach, many of the common properties of aitives are accounte for. This approach provies a means to assess the importance of ifferent types of interactions an therefore provies a guie for the evelopment of aitives. Coupling between the aitives an the eposition process. Complex formation. We assume that complex formation between the aitives an the metal cations is local an pairwise. That is, we moel complex formation between cations an aitive in a small volume of space as proportional to the prouct of the concentration of each in this volume. To obtain the contribution of complex formation to the total Helmholtz free energy, we a the contributions of each local volume element as F C C C rc I rr This type of expression is commonly use in statistical mechanics treatments of solution theory. 26 In this equation is a parameter which characterizes the strength of the local attractive interaction between the aitives an the metal cations. A simple relation between the heat of complex formation Q I per aitive molecule an the parameter can be establishe by assuming that one aitive molecule interacts with a single metal cation: Q I /C 0. In this moel any inhomogeneities in the metal cation concentration are accompanie by a variation in the aitive concentration C I (r). 6 Equation 6 accurately escribes the interaction between the aitives an the metal cations through complex formation, given that the complexes are relatively weakly boun, which implies that Q I. Polar aitives. There is experimental evience 2 that polarity of the aitives enhances the stability of the growing surface. It has been observe in lea electrorefining that naphthoquinone, which has a molecular ipole moment, is a very goo leveler, while a chemically similar complex molecule anthraquinone with very small molecular ipole moment has a very small leveling effect. Hence, it has been hypothesize 2 that the leveling capacity of naphthoquinone can be attribute to the finite molecular ipole moment which allows the aitives to interact with the inhomogeneous electric fiel at the metal/solution interface. The energy of a ipole in an electric fiel is simply the ot prouct of the ipole moment vector an the local electric fiel. 17 The total interaction energy of the ipole moment on the aitives an the electric fiel F E is proportional to the local concentration of ipoles aitives an the local electric fiel summe over all small volume elements F E C I p r C I pr rc I pr r 7 where p is the molecular ipole vector of the aitives, an the last two equalities assume that the molecules quickly orient with their ipoles along the fiel. Note that this coupling enhances the concentration of aitives in regions where the magnitue of the electric fiel is large. Transport equations an fluxes. Base on the aitional interaction terms introuce we rewrite the metal cation flux as j C r D C C C qed CC C D CC C C I 8 The last term is ue to the coupling between the aitives an the metal cations, as escribe by Eq. 6. Because the anions are assume not to form complexes with the aitives their flux is still written as Finally, the aitive flux reas j A r D A C A qed AC A j I r D I C I D IpC I D IC I C C 10 The aitive flux has contributions from iffusion, graients in the electric fiel if the molecules are polar (p 0), asorption to the surface, an complex formation with the metal cations. Diffusion tens to smooth out the inhomogeneities in the concentration profile, whereas the aitives ten to accumulate in regions of large electric fiel graients because the aitives are polar, large metal cation concentration, or both. Aitives an surface site blocking. We incorporate the effect of aitives in blocking potential surface growth sites by aopting a moifie B-V equation for the local metal cation flux j C which satisfies j C D C C C D CqeC C nˆ j 0 1 I D CC C I C FRT e 1 F/RT e 2 C 0 C C 9 11

4 Journal of The Electrochemical Society, C708-C C711 where I enotes the aitive surface coverage. We escribe the surface coverage using a Langmuir isotherm I KC I 1 KC I 12 where the asorption equilibrium constant K exp(q/) an Q enotes the heat of asorption. The tenency of the aitives to locally block some of the available growth sites on the surface thus leaing to slower eposition rates for high local aitive coverage is phenomenologically incorporate by the multiplicative term (1 I ) in the local flux. In particular, we assume that a sufficiently high aitive concentration can lea to a total saturation of the growth sites on the surface, an hence to a suppression of eposition. This moel qualitatively captures the salient features of the interaction between aitives an the metal cations at the growth surface. We also consier the possibility that the aitives on the surface may be incorporate into the growing film by coeposition along with the metal cations. This coeposition is moele by imposing a imensionless aitive flux at the surface which is proportional to the local metal cation flux: j I C I j, where the proportionality constant escribes the extent of coeposition an C I enotes the imensionless aitive bulk concentration. While this amittely constitutes an oversimplification of the true surface physics, it is consistent with experimental observations an allows us to assess the importance of coeposition on the growth of ED films, of which little is generally known. Note that 1 implies that metal cations an aitives are incorporate into the growing eposit in proportions given by their bulk concentrations. It is noteworthy that a finite ipole moment effectively increases the equilibrium constant K as the polar aitives are attracte to the surface by the large electric fiel strengths. Unfortunately, it is generally not easy to estimate the contribution of this interaction to K quantitatively because it epens on the etaile atomic structure of the surface an the structure of the aitive in question. However, as a simple estimate we consier a typical electric fiel strength of 0.3 V/nm at the interface an a typical ipole moment of 5e Å for a polar molecular species, the prouct of which is the ipole moment contribution to Q. Using these values we fin that this contribution is ev, which is larger than by a factor of orer 3 or 4 at room temperature. This translates into a change in the value of K by a factor of nearly 25, as compare with its value if no ipole moment were present. A ipole moment on the aitives may also play a minor role on the metal cation-aitive complex formation. However, in orer to assess the significance of the aforementione interactions on the growth front stability, we treat K, p, an as inepenent parameters in the remainer of the paper. Steay-state properties. We again examine the steay-state properties of the moel as a prerequisite to the morphology analysis. In steay state the metal cation flux is constant across the length of the cell, while the anion an spectator ion fluxes vanish, respectively. Therefore, upon measuring all lengths in units of the masstransfer layer thickness L an thus all wavenumbers in units of 1/L), time in units of iffusion time L 2 /D C, ionic an aitive concentrations in units of the bulk metal cation concentration C 0, electric potential in units of the equilibrium voltage V eq, an fluxes in units of the iffusion-limite flux D C C 0 /L as employe in Part I, we may write the new imensionless steay-state equations as z C C C C z C C z C I j z C A C A 0 z z C XC C XC 0 z z C XA C XA 0 z z C I C I z z C I z C C D C I C I j 2 2 z 2 C C C XC C A C XA 13 where D C I D C /D I, an where we have use two important imensionless parameters C 0 /() Q I /() ln K c an V eq p/(l) in the aitive flux. escribes the interaction strength for complex formation an escribes the interaction strength between the aitives an the inhomogeneous electric fiels through the finite molecular ipole moment. Furthermore, K c enotes the equilibrium constant for complex formation between the aitives an the metal cations. In the subsequent calculations we employ L m, appropriate for free convection electroplating conitions. Written in a imensionless form, it can be inferre from the metal cation steay-state equation in Eq. 13 that the term C C C I /z, arising from complex formation, is typically very small in magnitue (10 6 ) compare to the iffusion an rift terms 1, because the bulk aitive concentration C I 10 6 C 0. Therefore, we may rop the last term in the metal cation flux to a very goo approximation. Note, however, that the complexing term cannot be neglecte in the aitive flux an is thus retaine in the following analysis. Because the aitives now affect the metal cation concentration only through the moifie B-V bounary conition, the steay-state solutions for C C an are exactly as given in Part I in the absence of aitives C C 1 C 1 exp C 1 exp z 2 where z, j 1 * ln 1 j 2 2C 1 1 tanh1 4 e 21 C 1 z/ tanh * 4 1 ln 1 j 2 2C 1 jz 2 2C 1 15 an * V ext /V eq. This solution is accurate to lowest orer in everywhere an to lowest orer in j/(1 C 1 ) within the bounary layer 0 z an to all orers in j in the bulk. Similarly, the steay-state solutions for C A, C XA, C XC, an C I are simply C A e, C XC C 1 e, an C XA C 1 e, an C I C I e C C /z 1 D I C j D I C jz 16 appropriate for 1. We note that the aitive concentration at the surface is given by cf. Eq. 16 C I 0 C I e C C 0 0/z 1 D I C j 17 It is noteworthy that the large electric fiels in the bounary layer effectively attract polar aitive particles. In orer to get a better unerstaning of the effects of the various parameters in the aitive concentration profile C I, we plot some representative profiles in steay state in the absence of spectator ions in Fig. 1. In particular, Fig. 1a shows the equilibrium ( j 0) concentration profiles for several values of the interaction parameter that escribes the strength of complex formation. Notice how an

5 C712 Journal of The Electrochemical Society, C708-C Figure 1. Aitive concentration profiles in steay state in the unsupporte electrolyte i.e., no spectator ions for a, top left j 0, 0, 0, an several values of. b, top right Concentration profiles at finite eposition rate j 0.2, 0, 0, an several values of. c, bottom The effect of the ipole moment on the concentration profiles for j 0.2, 0, an 0. increase in the metal cation concentration in the vicinity of the bounary layer leas to a corresponing increase in C I ue to this attractive interaction. Aitionally, the aitive concentration attains a constant value away from the bounary layer. Upon applying an external eposition flux, the aitive concentration profile is influence by the metal cation concentration graient in the bulk, as shown in Fig. 1b for j 0.2, 0, 0, an several values of. In particular, an aitive concentration graient in the bulk evelops in steay state ue to the interaction between the metal cations an aitives. Finally, in Fig. 1c we plot the aitive concentration profiles in the absence of complex formation for j 0.2, 0, 0, an several values of the parameter which escribes the coupling between the electric fiels an the polar aitives. Note the accumulation of aitives within the bounary layer as a consequence of their interaction with the electric fiel. Linear stability analysis: Aitive effects. Next we apply the linear stability analysis to etermine how the surface evolves uring ED in an electrolyte containing aitives. The analysis follows the proceure escribe in Part I in the absence of aitives. In the fully supporte electrolyte case the analysis is carrie out analytically an is vali for all values of the eposition flux j, while in the partially supporte electrolyte case the analysis is carrie out as a perturbation expansion in the flux j, as outline in Appenix B of Part I in the absence of aitives. Physically, the aitives occupy surface sites where metal cations can attach, thus slowing growth. Therefore, if protrusions collect more aitives than epressions they grow more slowly, hence favoring the growth of smooth surfaces. 7,14,18 Increase aitive concentrations occur where the aitive flux to the surface is greatest. This flux is controlle by i aitive-metal cation complexing represente by in which the metal cations rag the aitives to the growth front uring eposition, (ii) interactions between the polar aitives an the inhomogeneous electric fiel associate with the surface perturbation, an by (iii) aitive coeposition represente by which gives rise to an aitive concentration graient. The linear stability analysis shows that the perturbation growth rate in the presence of aitives (k) in a fully supporte electrolyte is given by

6 Journal of The Electrochemical Society, C708-C C713 Figure 2. Linear ispersion relation (k)/ vs. k for a fully supporte electrolyte with a, top left j 0.5, 4.0, 0.0, 1 0.5, an ˆ an several values of KC I an b, top right j 0.5, KC I 0.25, 0.0, 1 0.5, an ˆ an several values of the parameter escribing complex formation. Linear ispersion relation (k)/ vs. k for an unsupporte electrolyte for c, bottom left j 0.5, KC I 0.5, 0.0, 1 0.5, an ˆ an several values of the parameter an, bottom right j 0.5, KC I 0.25, 0.0, 1 0.5, ˆ 0.001, an 1.0, an several values of the parameter which escribes the ipole moment of the aitives. k jk j eff1 1 1 j eff j1 1 1 j 2 ˆ 1 k j1 D C I j k 18 where the effective current j eff (1 1 )/(1 j eff ) j(1 1 )/(1 j) (j D I C j j 2 D I C ), an the aitive effects are conveniently expresse by as KC I e 1j 1 KC I e 1j 1 D I C j 19 Qualitatively, Eq. 18 is very similar to the corresponing result in the absence of aitives, Eq. 17 in Part I. In particular, the growth rate (k) is positive for small k an becomes negative for k k 0, implying stability on scales s 2/k 0, where s enotes the stabilization length. Equation 18 has a very appealing physical interpretation. The presence of aitives gives rise to an effective flux j eff, the magnitue of which epens on the aitive bulk concentration C I, the strength of complex formation, the egree of coeposition, an the susceptibility to segregate onto the surface of the growing film, escribe by the equilibrium constant K. Because j eff is always less than j, the metal cation flux riven instability is reuce by the presence of the aitives. This follows from the key observation in Part I, i.e., that the morphological instability in the absence of aitives is ue to the finite eposition flux j, an ecreasing j makes the surface smoother. In Fig. 2a we plot (k) vs. k, several aitive concentrations C I, an a fixe metal cation eposition flux j. The other parameters were set to j 0.6, 4.0, 0.0, 1 0.5, an ˆ Note that increasing C I leas to reuce k max an instability growth rates, (k). Thus, increasing the aitive concentration increases the range of surface stability implying leveling for the same external eposition flux j. Closer examination of Eq. 18 also reveals that increasing the egree of aitive coeposition (

7 C714 Journal of The Electrochemical Society, C708-C ), the equilibrium aitive surface concentration represente by K, an the egree of coupling between aitives an metal cations all enhance stability, consistent with experimental observations. 2 This is illustrate in Fig. 2b, where we show (k) vs. k for several values of the interaction parameter with j 0.5, KC I 0.25, 0.0, 1 0.5, an ˆ We note that the aitives can increase the surface stability even without aitive incorporation into the growing film as clearly seen from this figure. Let us now explicitly compare our preictions for surface stabilization with existing experimental ata. In particular, in Ref. 7 the growth of copper eposits from a copper sulfate bath in the presence of thiourea was stuie. For example, employing the current ensity J 200 A/m 2 an cation bulk concentration C M from Ref. 7, an employing the reasonable values D C 10 9 m 2 /s, 1.6 J/m 2, K 10 6 I, 1 1, an 0.5, an experimentally etermine value , c appropriate for thiourea-cupric complexes, we fin that an aitive bulk concentration of mm leas to the stabilization length 0.1 mm s 0.2 mm, in goo quantitative agreement with experimental result of s 0.5 mm in Ref. 7. It is noteworthy that the parameter which escribes the strength of the interaction between the polar aitives an the electric fiel oes not explicitly appear in Eq. 18. This is a irect consequence of the fact that for a sufficiently large spectator ion concentration, the electric fiel is almost completely screene in the bulk, an therefore it is practically unaffecte by the surface perturbation. This implies that the electric fiel aroun a protrusion is the same as for a flat part of the surface or a epression, an therefore the interaction between the ipole moment on the aitives an the perturbe electric fiel oes not moify the aitive efficacy in stabilizing the surface in the fully supporte electrolyte. Increasing the aitive ipole moment effectively increases the equilibrium constant K as the aitives are attracte to the surface by the large electric fiel strengths, an this helps stabilize the surface, as iscusse previously. In the partially supporte electrolyte case, the polar nature of an aitive can play a further stabilizing role, as iscusse shortly. We have also performe a stability analysis for ED in the presence of aitives for the case in which the electrolyte is unsupporte or only partially supporte using the same approach as outline in the previous section an in Appenix B. Figure 2c shows the perturbation growth rate (k)/ as a function of wavenumber for the case of the completely unsupporte electrolyte (C 1 0), for j 0.5, KC I 0.5, 0.0, 1 0.5, ˆ 0.001, an several values of. As in the fully supporte electrolyte case, increasing is beneficial for stability. Increasing the bulk aitive concentration an the surface coverage of the aitives through increasing the equilibrium constant K also increases the surface stability not shown, as in the fully supporte electrolyte case. A novel feature arises in the unsupporte or partially supporte electrolyte case when the ipole moment of the aitives is finite, as anticipate previously. During eposition, a finite electric fiel is set up in the bulk; the presence of this fiel is ue to the absence of spectator ions an it persists for small spectator ion concentrations, as shown in Part I. Consier next the nonzero electric fiel associate with a surface protrusion. Since the growing surface is an equipotential one, it follows that the equipotential lines are crowe together ahea of the protrusion, an the corresponing electric fiel becomes large this is shown explicitly in Part I, Appenix B; the opposite is true for a epression. Because the polar aitives are attracte to regions of large electric fiels, a protrusion collects more aitives, which tens to stabilize the surface. These physical arguments are confirme by calculating the linear stability curves for an c Doona an Stanbury 27 measure the equilibrium constant K c for thiourea-cupric ion complex formation, from which we fin ln K c. Figure 3. A stability map showing fixe sample imensions an experimental conitions for which the ED surface is smooth stable or rough unstable for 4.0, W 1.0, 0.0, ˆ 0.001, an unsupporte electrolyte with polar aitives. The results are shown in Fig. 2, where we plot (k)/ for j 0.5, KC I 0.25, 0.0, 1 0.5, ˆ 0.001, an 1.0, an several values of the parameter which is relate to the ipole moment of the aitives. It can be seen that increasing is beneficial for leveling. However, the main aitional stabilizing effect of ipolar aitives comes from a larger effective equilibrium constant K, as 10 5 for L 10 4 m, appropriate for typical electroplating conitions. Aitive-assiste growth of linearly stable surfaces. The results presente can be use to choose eposition conitions corresponing to the maximum film growth rate for which the surface remains smooth over the requisite length scale, W. To this en, we require that all perturbation moes with wavelengths smaller than W ecay; i.e., (k) 0 for k 2/W. Equation 18 implies j eff (1 1 )/(1 j eff ) ˆ 1 (2/W) 2 for the case of a fully supporte electrolyte. In orer to guie experiment, we express the stability conitions in terms of the experimentally accessible parameters without changing aitives, metal cation flux j which is proportional to the growth rate, an aitive concentration C I. In Fig. 3 we construct a stability map for realistic growth conitions. Such a map conveniently isplays the full range of stable an unstable growth conitions. While introucing aitives can ramatically increase the eposition currents that can be use, the effect saturates at large aitive concentrations. There exists a critical current j* 1 (1 1 )/ above which the aitives are incapable of leveling the surface. This can be unerstoo by incorporating the blocking effect into the secon term of an effective overpotential eff RT/Fln(1 I ), obtaine from the moifie B-V equation. In orer to prouce large eposition fluxes, the metal cation concentration graient ahea of the surface is large an the metal cation concentration is low. To maintain these high fluxes the overpotential must be large, such that RT/Fln(1 I ). This implies that the aitives represente by I ) are incapable of stabilizing the smooth surface. Finally, let us relate the stability map to experiments. The surface is linearly stable at sufficiently small currents j even in the absence of aitives. However, for sufficiently large j, instabilities with wavenumbers greater than 2/W appear, implying roughening. Increasing C I at fixe j j* leas first to slower roughening an then to a transition from a rough to a smooth surface. This behavior

8 Journal of The Electrochemical Society, C708-C C715 is consistent with experimental observations of Schilari et al. 7 which show that the ominant wavelength of the surface instability increases with increasing aitive concentration up to a critical concentration beyon which the surface of the growing film remains level. Similarly, we preict that increasing the eposition flux j for a fixe aitive bulk concentration C I leas to a transition from planar to rough morphology. Conclusions We have introuce a chemically motivate continuum moel for the morphological stability of surfaces uring ED an the effects of aitives on that stability. The ED moel explicitly accounts for the electric fiel in the electrolyte, the metal cations an anions, the aitives, an the spectator ions from the supporting electrolyte. The moel for aitives employe here accounts for three main chemical/physical phenomena: i the aitives form complexes with the metal cations in the electrolyte, (ii) the aitive molecules have a finite ipole moment an hence interact with inhomogeneities in the electric fiels in the electrolyte, an (iii) the aitives occupy sites on the surface, thereby blocking eposition of metal cations. The stability of the ED surface in the presence of aitives was analyze using perturbation theory. In the fully supporte electrolyte case, we foun that aitives enhance leveling by making the surface stable on longer length scales an ecreasing the rate at which roughness grows; our quantitative preictions for the stabilization length are in very goo agreement with existing experimental observations. The aitives stabilize the surface by ecreasing the effective riving force for the instability. The effective riving force epens on the bulk concentration of the aitives, the tenency of the aitives to segregate onto the surface, the strength of complex formation, an the local aitive flux; increasing the magnitue of any of these terms increases the surface stability. The tenency of the aitives to segregate onto the surface is enhance in the case of polar aitives, which are attracte to the surface ue to the presence of strong electric fiel graients. This occurs for any bath composition. Aitionally, the ipole moment of the aitive may help further stabilize the surface in the case of an unsupporte or partially supporte electrolyte, as the polar aitives also interact with the electric fiels associate with surface protrusions. Uner typical eposition conitions, however, we expect this effect to be small. Leveling is promote by increasing the concentration of the aitives, the tenency for the aitives to thermoynamically segregate to the surface, the tenency for aitive-metal cation complexing, incorporation of the aitives into the growing electroeposit, an the tenency of the aitives on the surface to block metal cation attachment. At a minimum, aitives must be able to segregate to the surface in equilibrium an be able to block surface sites once they get there. In aition, at least one of the following must also be present: aitive-metal cation complexing, aitive incorporation in the growing eposit or, equivalently, aitive reuction at the surface, or a nonzero ipole moment if the electrolyte is not fully supporte. These ifferent effects act in concert in a well-esigne aitive. Much of these results can be summarize in stability maps that show uner which experimental conitions a surface is stable or unstable for a given feature size below which the surface must be flat. We have constructe such a map in metal cation flux j i.e., growth rate an aitive concentration C I space. This map clearly shows the existence of a sharp bounary between the stable an unstable growth regimes as well as ientifies conitions uner which increasing the aitive concentration is unable to suppress this natural instability. The experiments of Schilari et al. 7 show that incresing the aitive concentration leas to first ecrease in roughness rather than an increase in roughness above some critical concentration. Those authors attribute this to a phase transition within an aitive layer. Acknowlegments We thank Dr. Corbett Battaile an Dr. John Hamilton for fruitful iscussions, an Sania National Laboratories for financial support. Princeton University assiste in meeting the publication costs of this article. List of Symbols C i concentration of species i C 0 metal cation bulk concentration C 1 spectator cation bulk concentration, normalize by C 0 C I aitive bulk concentration, normalize by C 0 D i iffusivity of species i F Faraay constant h position of the surface in the lab frame j imensionless steay-state metal cation flux j i flux of the species i j 0 exchange flux ensity k initial perturbation wavenumber, in units of 1/L K equilibrium aitive surface asorption constant k B Boltzmann constant K c equilibrium constant for aitive-metal cation complex formation k max maximally unstable moe k 0 neutral moe L thickness of the mass-transfer layer s stabilization length nˆ surface normal, pointing into the solution p strength of the ipole moment per aitive q i e charge of the species i R gas constant T temperature V eq equilibrium potential of the metal-solution interface V ext electric potential of the metal-solution interface uring growth v n normal velocity of the growth front z istance from the surface Greek imensionless equilibrium potential of the metal-solution interface surface tension of the metal-solution interface ˆ imensionless surface tension of the metal-solution interface imensionless aitive ipole moment C i perturbation of the species i j perturbation of the local metal cation flux ˆ initial surface perturbation amplitue imensionless thickness of the G-C bounary layer ˆ permittivity of the solution overpotential I aitive surface coverage local curvature of the metal-solution interface GC thickness of the G-C bounary layer imensionless strength of complex formation electric potential * potential of the metal-solution interface, normalize by the equilibrium potential parameter escribing the extent of aitive coeposition parameter which escribes the strength of complexing atomic volume of the metal in the eposit imensionless atomic volume of the metal in the eposit (k) growth rate of perturbation with wavenumber k References 1. 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