Optimization of the Copper Plating Process Using the Taguchi Experimental Design Method I. Microvia Filling by Copper Plating Using Dual Levelers

Copper electroplating formulas composed of CuSO 4 , H 2 SO 4 , chloride ions, polyethylene glycol (PEG), bis (3-sulfopropyl) disulﬁde (SPS), and different levelers for microvia ﬁlling of a printed circuit board (PCB) were studied. The inﬂuence of the copper electroplating parameters, accelerator and leveler concentrations and cathodic current density on the microvia ﬁlling performance was explored using the Taguchi experimental design method. An L9 orthogonal array with four controlling factors at three levels was employed in the experimental design method. Variance analyses of the mean ﬁlling performance and the signal-to-noise ratio of the controlling factors showed that the most signiﬁcant factor for the microvia ﬁlling performance was the leveler concentration. The other factors exhibited little to no effect on the microvia ﬁlling performance. The contribution of levelers to the ﬁlling performance was characterized using galvanostatic measurement and linear sweep voltammetry (LSV) with a working electrode at different rotational speeds. The experimental results indicated that the inhibiting effect of the levelers on the copper deposition was related to forced convection, which is a key physicochemical interaction for exhibiting good ﬁlling performance.

In recent years, the high-density interconnection (HDI) of printed circuit boards (PCBs) has become an important technology to fabricate multifunctional portable electronic products. Copper plating has become a critical process for fabricating HDI PCBs with high reliability. [1][2][3] Following the multifunction and miniaturization trends in designing electronic products, microvia metallization and stacking have become increasingly important in HDI PCBs. [4][5][6] In the metallization process, microvias are filled using copper electrodeposition, which provides excellent reliability for signal transmission among dielectric layers. Various copper plating additives, such as suppressors, accelerators and levelers, can interact with each other and result in bottom-up filling of a microvia without voids. [7][8] Via-filling with copper was first applied to the Damascene process for IC chip fabrication, in which the copper electrodeposition rate is controlled by the diffusion, adsorption, and consumption fluxes of additives. 9 These fluxes on an electrode surface result in bottom-up copper deposition behavior in vias and trenches. Moffat et al. [10][11][12][13] explained the bottom-up behavior as a result of the accelerator, which contains thiol or disulfide groups, adsorbing and sliding on the electrode surface. The adsorbed accelerator gradually replaces the suppressor and elevates its coverage in the process of the via bottom moving upward, which combines with surface area shrinkage at the via bottom. As a result, the copper deposition rate at the via bottom becomes greater than that in other areas of the via, which leads to bottom-up copper deposition and copper bump formation. Kondo et al. [14][15] demonstrated that cupric ions react with sodium 3-mercapto-1-propanesulfonate (MPS) or bis-(3-sulfopropyl)-disulfide (SPS) to form Cu(I)-thiolate. The Cu(I)-thiolates accumulate in the microvia to locally accelerate the copper electrodeposition and achieve bottomup filling.
For good microvia filling performance, suppressors, accelerators and levelers are added to the copper plating bath. Suppressors are mostly polymers such as polyethylene glycol (PEG), [16][17][18] triblock copolymers, 19 polypropylene glycol (PPG) [20][21][22] or diallylamine-type copolymers. 23 These polymers interact with chloride ions to inhibit copper deposition. Accelerators that are widely used in the copper plating bath include MPS, SPS and 3,3-thiobis (1-propanesulfonate) (TBPS). [24][25][26][27] To improve the filling performance and decrease the surface roughness of the filled microvia, adding a leveler can inhibit the copper deposition at the via opening. Common levelers include Janus Green B (JGB), Diazine Black and Alcian Blue. 18,[28][29][30][31][32] In the copper electroplating of Damascene and submicron features, forced convection is less important for mass transfer [33][34][35][36] because the feature size is smaller than the diffusion boundary layer of a copper ion. In contrast, the influence of forced convection plays an important role in the microvia filling plating of PCBs because the via size is much larger than the diffusion boundary layer. Dow et al. 25,[37][38][39] proposed that the adsorption of chloride ions is related to the strength of the forced convection. They found that JGB, chloride ions, and PEG form a composite suppressor whose adsorption on the copper surface is sensitive to the strength of forced convection, so the filling mechanism caused by the composite suppressor is referred to as convection-dependent adsorption (CDA).
Taguchi experimental design method was developed by Genichi Taguchi to analyze the influence of experimental parameters and determined optimum process parameters. 40 Taguchi suggested engineers to use orthogonal arrays of controlling factors and levels to design experiments. This method not only can reduce the experimental cost but also enhances the reliability of the analysis results. In the method, signal to noise ratio (S/N ratio) was employed to analyze the contribution of each experimental data. The S/N ratio can be calculated according to the requirements of nominal-the-better, smaller-the-better, and larger-the-better. Besides, the analysis of variance (ANOVA) can indicate the contribution and significance of experimental parameters. Because the bottom-up copper filling behavior of a microvia is complex, Taguchi method is a good tool to figure out the contribution of various plating parameters for the copper plating process control.
In this work, the effect of dual levelers on the microvia filling process was studied. The influence of electroplating parameters such as additive concentrations and cathodic current density on the filling performance of a microvia was investigated. The study was carried out using the Taguchi experimental design method. The factors that significantly affect the quality of the filling performance were also evaluated according to the results of the Taguchi experiment design method.

Experimental
The composition of the base electrolyte was 0. Germany), leveler A and leveler B were additionally added into the base electrolyte for all electrodeposition experiments and electrochemical analyses. Leveler A contains nitro functional groups, while leveler B is a quaternary ammonium compound. The temperature of the plating solution was maintained at 28 • C for all of the plating tests and analyses.
Electrochemical analysis.-Various formulas were characterized with galvanostatic measurements (GMs) and cyclic voltammetry (CV) at different rotational speeds of a rotating disk electrode (RDE). All of the electrochemical analyses were performed in a glass vessel containing 150 mL of electrolyte using a PGSTAT30 potentiostat (AUTO-LAB) with a three-electrode cell system. A platinum RDE with a 3 mm diameter was employed as the working electrode. A phosphoruscontaining copper rod was chosen as a counter electrode (CE), and a saturated mercurous sulfate electrode (SMSE) was used as a reference electrode (RE). To characterize the polarization behavior of various formulas, a thin copper layer of 1 μm thickness was predeposited onto the platinum RDE in a preposition bath that contained 0.88 M CuSO 4 (Riedel-de Haen, ACS) and 0.54 M H 2 SO 4 (Merck, 96%, Ultrapure) before galvanostatic measurements.
100 rpm and 1000 rpm of the Cu RDE were chosen to simulate the fluid flow inside and outside a microvia, respectively. The cathodic current density was fixed at 1.94 A·dm −2 in the GMs. After GMs were performed for 400 seconds, 1 ppm SPS was injected into the base electrolyte. Following the injection of SPS, 1 ml·L −1 leveler was injected into the electrolyte. After 800 seconds, another leveler was injected into the electrolyte. 18 The filling performance of various formulas was characterized by a mean potential difference ( η) between the two polarization curves measured with the Cu RDE that was individually operated at 100 rpm and 1000 rpm. It was showed that if the copper plating formulas can perform bottom-up filling of a microvia, then a positive potential difference (i.e., η = E 100rpm −E 1000rpm > 0) occurs. 25,27 To characterize the impact of forced convection on the filling performance, CV was carried out using four rotational speeds (i.e., 100, 400, 700 and 1000 rpm). The CV was started from an open circuit potential (OCP) to −0.7 V vs. SMSE, followed by a positive sweep from −0.7 V to 0.9 V vs. SMSE for five cycles. The scan rate was 100 mV·s −1 for all of the CV measurements.
Numerical analysis.-The microvia fillings were plated in a Haring cell with a continuous air bubble flow. To understand the influence of the fluid flow on the function of these additives, the flow field around the microvia was simplified using a two-dimensional model. [33][34][35][36] The continuity equation and the Navier-Stokes equation for an incompressible fluid are as follows, with a steady-state assumption: where u denotes the velocity vector, μ is the viscosity of the fluid (i.e., 1.6 × 10 −3 Pa·S), ρ is the density of the fluid (i.e., 1158 kg·m −3 ) and p is the pressure term of the fluid. Figure 1 shows the boundary conditions. Boundary 1 depicts the average velocity of the continuous air bubble flow at 10 m·s −1 . The lengths of boundaries 2 and 8 represent the distance of 1 cm between the air bubble flow and the cathodic surface; a fully developed velocity profile is assumed on these boundaries. Boundaries 3-7 depict the surface of a microvia and are regarded as non-slip surfaces. The fluid dynamics model was solved numerically using the COMSOL software.
Microvia filling by copper electrodeposition.-The PCB samples for the plating tests were drilled by CO 2 laser ablation to form identical microvias with a diameter of 95 μm and a depth of 85 μm. Following the laser drilling, the PCB samples were subjected to a desmearing process for smear removal, copper electroless deposition for sidewall  metallization of the microvias, and copper electroplating for thickening the sidewall copper to prevent it from oxidation. The dimensions of the samples were 4.5 cm × 6 cm.
Two phosphorus-containing copper plates were employed as anodes and placed directly in the plating bath with a working volume of 700 mL. The electrolyte was constantly agitated by continuously flowing air bubbles with a flow rate of 1.5 L·min −1 during the electroplating. The temperature of the plating electrolyte was maintained at 28 • C. The filling performances of the various plating formulas were defined by H 2 /H 1 × 100%, as illustrated in Fig. 2. 32 The filling performance was assessed according to the cross-section of the microvia, which was examined using an optical microscope (OM, Olympus BX51).
Taguchi experimental design method.-The Taguchi experimental design method 40 was employed to analyze the influence of the experimental parameters on the copper filling performance. Table I shows the controlling factors and levels designed for the microvia filling experiment. An L 9 (3 4 ) orthogonal array with four factors at three levels, as listed in Table II, was used in this study. The S/N ratio was calculated according to the "nominal-the-best" case. The ANOVA of  Experiment  A  B  C  D  1  1  1  1  2  2  1  2  2  3  3  1  3  3  1  4  2  1  2  1  5  2  2  3  2  6  2  3  1  3  7  3  1  3  3  8  3  2  1  1  9  3  3  2  2 the mean filling performance and the S/N ratio were used to determine the significance and contribution of each control factors.

Results and Discussion
Electrochemical analysis.-According to CDA theory, 25,27,39,41 the mass transfer of chloride ions is convection-dominant, rather than diffusion-and migration-controlled and the functions of the suppressor, leveler and accelerator depend on the surface coverage of chloride ions, so the adsorption of the suppressor, leveler and accelerator used for the microvia filling is convection-dependent. The suppressor and leveler dominate copper deposition at a high surface coverage of chloride ions due to a strong convection; on the other hand, the accelerator dominates copper deposition at a low surface coverage of chloride ions due to a weak convection. These phenomena lead to a different copper deposition rate between the mouth and the bottom of a microvia. The CDA mechanism can explain that if a copper plating formula can lead to good filling performance in microvias, then it also exhibits a positive cathodic potential difference ( η = E 100rpm -E 1000rpm > 0) in GM, as was defined in previous works. 25,27 The GM analyses with additives injection are shown in Fig. 3. When 1 ppm SPS was injected into the basic plating electrolyte, the CDA behavior was not observed (i.e., η = 0). After adding leveler A or B of 1 ml·L −1 to the electrolyte, the η was significantly positive (i.e., η 1 = 15 mV and η 2 = 13 mV). These results show that leveler A or B interacts with SPS and PEG-Cl − to exhibit CDA behavior. When both levelers A and B of 1 ml·L −1 were simultaneously present in the electrolyte, the η became larger (i.e., η 3 = 18 mV and η 4 = 25 mV) than η 1 and η 2 . The CDA behavior was obviously enhanced due to simultaneous addition of levelers A and B.  According to the GM analysis, the copper deposition rate decreases upon increasing the forced convection in the presence of levelers. To evaluate the correlation between the copper deposition rate and the convective strength, CV measurements of various plating electrolytes was carried out. The charges of the copper stripping peaks in the CV measurements are shown in Fig. 4. Formula A, containing only PEG, Cl − , and SPS, did not exhibit CDA behavior because the charge of the copper stripping was almost independent of the rotational speed of the Cu-RDE (i.e., C = 0.752 mC). After adding 1 ml·L −1 leveler A or B into the electrolyte (i.e., formula B and formula C), these plating formulas became sensitive to the rotational speed of the Cu-RDE, showing that stronger forced convection resulted in less copper deposition. Hence, the deposition rate at the bottom of the microvia was greater than that outside of the microvia.
In contrast with formula B, the variation in the copper deposition rate caused by various rotational speeds using formula C ( C = 1.173 mC) was smaller than that using formula B ( C = 2.103 mC). Therefore, the acceleration of the copper deposition at the bottom of the microvia using formula C was weaker than that using formula B, leading to a flat copper profile at the upward-moving copper surface, whereas a copper bump profile was formed with formula B. When 1 ml·L −1 of both levelers A and B were simultaneously added to the plating electrolyte (i.e., formula D), the best filling performance was achieved, as shown in Fig. 4. A flat copper profile combined with a thin copper layer was deposited on the board surface, because formula D resulted in the largest C = 2.526 mC.
Numerical analysis.- Figure 5 illustrates the velocity profile in the proximity of the RDE. The flow behavior of the electrolyte on the surface of the RDE is characterized as 42 V r = 0.5ω 3/2 ν −1/2 r Y h [3] where Y h denotes the thickness of the moment boundary layer (i.e., from V r = 0 to V r = V r, max ), ν is the kinetics viscosity of the electrolyte, ω is the rotational speed of the RDE, V r is the tangential velocity on the rotating disk, and r is the distance from the center of the rotating disk. Therefore, if one knows the ratio of V r /Y h , one is able to theoretically calculate ω. The velocity distribution in the microvia as a function of the plating time was simulated as shown in Fig. 6. In the simulation model, the velocity profile on the copper surface of the microvia was assumed to be linear. Additionally, the velocity profile shown in Fig. 5 is linear from the surface of the RDE to the maximum velocity. To correlate the velocity profile on the RDE shown in Fig. 5 with that on the surface of  the PCB during plating shown in Fig. 6, the ratio m r = V r, max /Y h on the RDE at various rotational speeds was compared with the ratio m = V max /Y h on the PCB that was obtained from the simulation model and shown in Fig. 7a. The simulation result shows that 100 rpm and 1000 rpm used in the GMs may represent the flow velocities at the via bottom and mouth, respectively.   Fig. 7b. The flow velocity on the PCB surface was almost fixed at 1180 rpm during plating, as shown in Fig. 7b. A significant enhancement in the filling performance was not observed at the bottom center from 15 minutes to 30 minutes, but occurred at the bottom corner, as shown in Fig. 6c. This result was attributed to the lowest coverage of chloride ions occurring at the corner of the bottom area because both the strongest electrostatic repulsion and the weakest convection occurred there, as confirmed in Fig. 6d. Hence, the suppressor (i.e., PEG-Cl − ) was not easily adsorbed there, 37 and the SPS easily replaced the PEG and adsorbed at the corner to form the V-shaped copper profile in Fig. 6c.
The convection strength at the via bottom continued to weaken with the bottom area shrinkage from 15 minutes to 30 minutes, as predicted in Figs. 6b, 6d and Fig. 7b. The weakest inhibition and strongest acceleration that was caused by the weakest convection and the strongest electrostatic repulsion of chloride ions interacted at the via bottom, so that the fastest copper deposition rate occurred, as shown in Figs. 6c and 6e. When the convective strength between the via mouth and the via bottom approached similar after the fastest bottom-up copper deposition, the bottom-up rate slowed down correspondingly, as shown in Figs. 6e-6h, because the convective strength at the via bottom rapidly approached to that of the via mouth after 30 minutes, as predicted in Figs. 6f, 6h and Fig. 7b.
To quantitatively evaluate the filling performance with the plating time, a filling fraction is defined as follows: Filling fraction(FF) = A i A t [4] Specific filling fraction = FF n+1 − FF n 15 min . [5] where A t denotes the cross-sectional copper area as the microvia is fully filled with copper, A i is the cross-sectional copper area as the microvia is filled for t n minutes (see Fig. S1), t is the plating time in minutes and n is the number of 15-minute units of plating time. Therefore, the specific FF indicates the filling rate within the n th unit of plating time. The overall plating time was 60 minutes, so the n was 1, 2, 3 and 4. In addition, m is defined as the m difference between the via mouth and the via bottom at the n th unit of plating time. Figure 8 shows that the tendency of m variation is the same as that of the specific FF, indicating that the forced convection difference be- Taguchi experimental design method.-The signal-to-noise (S/N) ratio is important to evaluate the standard deviation of the characteristic quality (i.e., filling performance) using the Taguchi experimental design method. 40 The characteristics of the S/N ratio were considered with the "nominal-the-best" case. The S/N ratio was calculated according to Eq. 6: S/N (db) = −10 log (ȳ i − Q) 2 + S 2 [6] whereȳ i denotes the average value of each variable, Q is the nominal value and S is the standard deviation. The unit of the S/N ratio is in decibels (db). Table III shows that the experiment number 1 exhibited the best S/N ratio; that is, it had the highest FP (%) and the smallest absolute value of the S/N ratio. Figure 9 shows the plots of the S/N ratio versus the various factor levels. The analysis shows that the characteristic quality (i.e., FP %) decreases with increasing leveler A concentration. The other factors result in the best characteristic quality at intermediate levels. The contribution and significance of the variable factors was calculated using variance analysis (ANOVA), as listed in Table IV. Table IV shows that the leveler A, SPS, and current densities are significant factors in the filling performance. In contrast, leveler B has a less-significant contribution to the filling performance. From Fig. 9, the optimum level of each factor is 1 ml·L −1 (A1) for leveler A, 1.5 ml·L −1 (B2) for leveler B, 2 ppm (C2) for SPS, and 16.2 A·dm −2 (D2) for the current density. The combination of the optimal levels, A1-B2-C2-D2, was checked with a plating experiment to confirm its performance. The predicted filling performance of the optimal factor combination of A1-B2-C2-D2 was calculated from Eq. 7:  where y predicted is the estimated S/N ratio, y avg denotes the average S/N ratio of each experiment, y i_opt is the average S/N ratio of the optimal level of each factor and j is the number of parameters affecting the multiple response. The confirmation result is listed in Table V. If the predicted S/N ratio obtained using the optimal level of each factor is very close to the result of the confirmation experiment, then the Taguchi experimental method has succeeded. From Table V, the predicted S/N ratio of the optimal level combination (i.e., A1-B2-C2-D2) is -7.996 db, which is very close to the experimental value of −9.909 db (see Fig. S2).

Conclusions
In this study, the correlation between the rotational speed of the Cu-RDE and the velocity profile of the copper plating solution near a microvia during the plating process was established by combining an analytical solution and a numerical solution of fluid dynamics. The simulation result can reasonably explain the bottom-up filling mechanism in a microvia. The fluid velocity profile determines the chloride ion distribution inside the microvia during plating, such that the suppressor and accelerator unevenly act inside the microvia, which is referred to as convection-dependent adsorption (CDA). The CDA behavior results in a coverage gradient of chloride ions along the sidewall of the microvia due to the gradient of forced convection. Hence, copper is preferentially deposited at the bottom corner in the beginning because SPS-Cl − easily works there, but the PEG-leveler-Cl − does not easily function there due to the small number of adsorbed chloride ions.
When the filled copper profile is turned into a V-shape, the weakest fluid velocity appears again in the microvia, but it moves from the bottom corner to the bottom center of the microvia, such that the CDA mechanism starts up again to strongly enhance the copper deposition at the via center until complete filling. The Taguchi experimental design method identified the contributions of leveler A, SPS and current density as 38.6%, 26.9%, and 26.9%, respectively, whereas leveler B had no significant effect on the filling performance, but leveler B can modify the copper surface profile on the via top area, resulting in a flat copper profile.