Theoretical studies of the additives for copper electroplating in PCB by DFT and MD simulations

Abstract

As fundamental elements in contemporary electronic systems, printed circuit boards (PCBs) rely on the copper electroplating process, which enables a uniform, dense coating, excellent electrical conductivity, and the capacity to boost the substrate's wear resistance and corrosion resistance. Copper electroplating additives critically affect metallic deposit quality and device stability. This study uses quantum chemical calculations and molecular dynamic simulations to explore additive screening and adsorption mechanisms. By evaluating orbital energy level difference and adsorption energy, optimal organic compounds for additives are identified, providing theoretical guidance for PCB copper electroplating additive research.

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Introduction

As a core component of electronic devices, printed circuit boards (PCBs) integrate multiple disciplines such as optics, electronics, chemistry, mechanical engineering, and materials science.^1–5 Their advantage lies in their ability to efficiently integrate various electronic components and build complex electronic systems. They are now widely used in numerous industries and have become an indispensable basic carrier for electronic products in daily life.^6–13 With the development of electronic devices towards high integration and the impetus of e-commerce, PCB manufacturing technology is constantly innovating, dedicated to achieving efficient interconnection and optimal electrical connection among components, functional units and chips. Against this backdrop, micro-via filling has become a key process in the manufacturing of multi-layer PCBs, and high-density interconnect (HDI) multi-layer boards have thus become an important technology supporting the manufacturing of highly integrated and small-sized electronic devices.^14–20

Copper is an indispensable basic material in the electrical industry, electronic equipment and renewable energy fields. Copper electroplating is the preferred technology for achieving high-reliability and high-performance interconnection of electronic circuits. With its high electrical conductivity, high thermal conductivity, good ductility and excellent deep plating ability, it has become an indispensable basic process in modern electronic manufacturing.^21–24 However, common problems in copper electroplating include uneven coating, roughness, holes, and poor adhesion. The current density decreases from the surface to the bottom in the microvia during the constant direct current electroplating process due to the unsmooth microvia geometry, so the copper preferentially adsorbs on the copper surface, leading to bad filling performance.

Additives are of great importance for copper electroplating.²⁵ According to the functions of copper electroplating additives, they are mainly classified into brighteners, leveling agents, and inhibiting agents.^26–28 Brighteners accelerate copper deposition and refine grains, making the coating dense and bright. The leveling agent preferentially adsorbs on the protruding areas to inhibit deposition, thereby filling the microscopic depressions and achieving a smooth surface. Inhibiting agents act as carriers to form inhibitory films on the surface, balancing the overall deposition rate and providing a basis for the first two. Screening the additives will help improve the production efficiency and quality of PCBs.

DFT study^29–32 and MD simulations^33,34 are useful tools for chemical sciences, especially electrochemical studies.^35,36 Quantum chemical calculations can precisely reveal the fundamental structure and reaction mechanisms of substances at the atomic and electronic levels, and are adept at explaining microscopic mechanisms.^37–41 Molecular dynamics simulation is good at simulating the dynamic evolution process of large systems over time and can effectively predict their macroscopic behavior and statistical properties.^42–46 Both, starting from the perspectives of static essence and dynamic behavior, jointly provide complementary tools for studying the sustained-release behavior of additives on copper surfaces.

A number of studies have utilized computational methods to conduct in-depth research on copper plating additives. These works have widely combined quantum chemical calculations and MD simulations. Tang et al. investigated the copper plating performance of 4,6-dimethyl-2-mercaptopyrimidine (DMP) using quantum chemical calculations and MD simulations. Dianat et al. conducted a study on the action of polyethylene glycol (PEG) and bis-(3-sulfopropyl)-disulfide (SPS) on Cu(111).^47,48 However, current research in this field remains predominantly centered on the performance and mechanisms of individual additives. This narrow focus has led to a significant gap in understanding the synergistic or antagonistic interactions between different types of additives. Consequently, the lack of comprehensive studies on multi-component additive systems hinders the optimization of plating processes for enhanced functional performance and industrial applications.

In this work, the effect of leveling agents and inhibiting agents on the adsorption on the surface of metallic copper was studied. By consulting the literature and materials, we screened out additive molecules suitable for theoretical calculation. Four leveling agents (diethylene glycol butyl ether, 2-(3-hydroxy-1H-indol-2-yl)indolin-3-one, nitisinone, and sulfathiazole) and eight inhibiting agents (1-(3,5-dichlorophenyl)pyrrolidine-2,5-dione, etoposide, polypropylene glycol, polyethylene glycol, PEG-2000, PEG-4000, PEG-6000, and PEG-8000) were investigated. The selected leveling agents effectively inhibit the deposition of copper ions at the electrode protrusions through methods such as surface adsorption, chelation or steric hindrance, thereby achieving excellent filling effects. The selected inhibiting agents can form adsorption layers on the copper surface through carbonyl groups, ether bonds or aromatic structures, effectively inhibiting the excessive deposition of copper ions. Firstly, based on the molecular orbital and electronic structure information obtained from quantum chemical calculations, the adsorption behavior of molecules on the copper surface was predicted and evaluated. Subsequently, by combining molecular dynamics simulation methods, the adsorption mechanism was further explored, thereby screening out candidate molecules with excellent adsorption performance on the copper surface.

Details of theoretical calculations

DFT calculations

DFT calculations were performed using the DMol³ module to analyze the electronic properties of the additives.^49–57 Within the framework of the Generalized Gradient Approximation (GGA), the Perdew–Burke–Ernzerhof (PBE) functional was employed, which exhibits reliable performance in describing exchange–correlation effects, particularly in systems involving interactions between metal surfaces and molecules.^58,59 In the calculations, the key point set was set to 1 × 1 × 1, the dispersion correction method adopted was DFT-D, and the double numerical basis set with polarization functions (DND 3.5) was selected. Critical electronic properties, including the energies of the HOMO and the LUMO, were calculated to understand the charge transfer potential and reactivity of the additives. Additionally, the electron density distributions of the HOMO and LUMO were analyzed.

MD simulations

MD simulations were performed using the COMPASS force field in Materials Studio software to investigate the adsorption behavior of additives on Cu surfaces in a gas phase environment.^60–63 The COMPASS force field was selected for its extensive quantum-chemical and experimental parametrization, which affords strong condensed-phase transferability and a reliable description of the PEG/PPG conformational statistics and their non-bonded (van der Waals/electrostatic) interactions with Cu surfaces. This choice delivers reasonable accuracy for weak-adsorption interfaces at modest computational cost with sufficient sampling, while potential biases in chemisorptive regimes are cross-checked against PBE-GGA DFT calculations. Copper was used as the substrate, with a (1 1 1) plane cut, and dimensions of 25.56 × 25.56 × 10.43 Å. Cu(111) is chosen as the model surface because it is the most stable, closely packed facet of copper with low surface energy, and its structural and electronic properties are well documented in the literature. This orientation is common in electrodeposited copper and shows minimal reconstruction, which enables reliable adsorption trends for weakly interacting organic additives. Prior to MD simulations, energy minimization and structural optimization were conducted to ensure the stability of the initial configuration. The convergence criteria for these steps were set as follows: a self-consistent field (SCF) energy tolerance of 2.0 × 10⁻⁵ eV per atom, a maximum force tolerance of 0.004 Ha Å⁻¹, and a maximum displacement tolerance of 5.0 × 10⁻³ Å. MD simulations were then carried out in the NVT ensemble at 298 K using the COMPASS force field. A total simulation time of 500 ps was used with a time step of 1.0 fs. During the simulation, the metal substrate was kept fixed to maintain the structural integrity, while the additives were allowed to move freely. The adsorption energies (E_adsorption) of the additives on the Cu surface were calculated by the following equation:

E_adsorption = E_total − E_molecule − E_surface

Among them, the total energy of the system is E_total, the energy of the additive molecules is E_molecule, and the energy of the copper metal surface is E_surface.

Results and discussion

Leveling agents

Classical MD simulation describes the physical adsorption of leveling agents on the Cu surface in dynamic equilibrium. In contrast, the DFT study explains the potential electron transfer process that occurs in the system when leveling agents are chemically adsorbed on the Cu surface. In this work, we evaluate four organic compounds as potential leveling agents for copper electroplating applications: diethylene glycol butyl ether (DB), 2-(3-hydroxy-1H-indol-2-yl)indolin-3-one (indigo), nitisinone (NTBC), and sulfathiazole (ST).

The orbital and energy information was calculated after configuration optimization to obtain the intrinsic adsorption characteristics of the leveling agents. The energy and distribution of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and the difference between the E_HOMO and E_LUMO(ΔE) of the four leveling agents are summarized in Table S1 (SI) and Fig. 1–3. In Fig. 1 and 2, the yellow and blue colors denote the positive and negative phases of the orbital wave function, respectively. Bonding orbitals form when regions of like phase (e.g., yellow–yellow or blue–blue) overlap constructively, whereas antibonding orbitals arise from the overlap of opposite phases (yellow–blue), which leads to destructive interference. Furthermore, the extent of phase compatibility between the HOMO of one molecule and the LUMO of another critically influences the probability of electron transfer occurring between them.

Fig. 1 The HOMO energy density distribution of four kinds of leveling agent molecules: (a) DB, (b) indigo, (c) NTBC, and (d) ST.

Fig. 2 The LUMO energy density distribution of four kinds of leveling agent molecules: (a) DB, (b) indigo, (c) NTBC and (d) ST.

Fig. 3 The ΔE diagram of leveling agent molecules: (a) DB, (b) indigo, (c) NTBC, and (d) ST.

As can be seen, the adsorption ability of organic molecules on the metal surface increases with the increase of E_HOMO or the decrease of E_LUMO. Meanwhile, the stability of the adsorption layers of the leveling agents on the metal surface depends on the energy gap (ΔE = E_LUMO − E_HOMO). Thus, smaller ΔE values lead to strong adsorption stability. As illustrated in Fig. 1 and 2, the HOMO orbital is mainly concentrated on the oxygen atoms and aromatic rings, while the LUMO orbital is concentrated on the carbonyl carbons and carbon chain termini. Comparative analysis in Fig. 3 reveals that indigo exhibits the smallest ΔE (0.800 eV) among the four investigated leveling agents, suggesting superior adsorption performance on copper surfaces. This conclusion aligns with the established inverse relationship between ΔE magnitude and adsorption capability, where E_HOMO reflects electron-donating capacity (lower values indicate reduced donation) and E_LUMO corresponds to electron affinity (lower values signify stronger acceptance). Detailed numerical data are compiled in Table S1.

MD simulations effectively characterize the physical adsorption mechanisms of leveling agents on Cu(1 1 1) surfaces under equilibrium conditions. The energy calculation needs to be performed after the system reaches the equilibrium state in all cases. When the deviation between the temperature and energy (E_potential, E_kinetic, E_nonbond, and E_total) changes is lower than 10%. As demonstrated in Fig. S1, all four investigated systems attained equilibrium within 50 ps of simulation. The configurations in Fig. 4 reveal enhanced molecular proximity to the copper substrate with optimized intermolecular packing, confirming spontaneous adsorption and the formation of dense protective layers on the copper surface. The computational analysis enables quantitative determination of system energetics through four principal components: E_total, E_molecule, E_surface and E_adsorption.

Fig. 4 Configuration diagrams of leveling agent molecules before and after MD simulation. (a)–(d) refer to DB, indigo, NTBC, and ST before the simulation. (a′)–(d′) refer to DB, indigo, NTBC, and ST after the simulation.

DB molecules adsorb onto the high current density area of the copper surface through ether bonds and hydroxyl groups, forming an inhibition film to slow down copper deposition. Indigo, with its large conjugated planar structure, is adsorbed by π–π or van der Waals forces to form a dense and stable barrier layer. NTBC undergoes strong coordination with copper through its triketone structure, significantly altering the deposition kinetics. ST effectively inhibits high-level point deposition by chemically adsorbing sulfur and nitrogen atoms in the sulfonamide group and thiazole ring with the copper surface, jointly exerting a leveling effect.

Since the leveling effect of molecules is directly related to the adsorption energy, E_adsorption is an important index for evaluating the inhibition effect. It can be seen from Table 1 that all the adsorption energies are negative, indicating that the adsorption is spontaneous. The comparative analysis identifies indigo as the optimal candidate, demonstrating the highest absolute E_adsorption (−154.288 kJ mol⁻¹) and thus superior surface affinity. Fig. 5 illustrates the inverse proportionality between ΔE and E_adsorption across the tested molecules, revealing methodological concordance between DFT and MD computational frameworks. This synergistic validation underscores the reliability of dual computational approaches in elucidating structure–activity relationships for additive design.

Table 1 The adsorption energy data of the four kinds of leveling agent molecules

Leveling agent	E total (kJ mol^−1)	E s (kJ mol^−1)	E molecule (kJ mol^−1)	E adsorption (kJ mol^−1)
DB	329 337.399	329 343.643	99.052	−105.296
Indigo	336 256.631	336 529.792	−118.873	−154.288
NTBC	350 896.765	344 871.973	6036.496	−11.704
ST	347 113.925	344 863.377	2270.124	−19.576

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Fig. 5 Comparison diagram of ΔE and adsorption energy of the leveling agent molecules.

The essence of E_adsorption is the interaction between molecules and metals, while ΔE is merely a characteristic of the molecules themselves. Therefore, when evaluating the adsorption performance of molecules, the weight of E_adsorption is even more significant. When there are differences between the conclusions obtained from quantum chemical calculations and MD simulations, E_adsorption should be taken as the standard. As illustrated in Fig. 5, among the leveling agents studied, the adsorption performance ranking is: indigo > DB > ST > NTBC.

Inhibiting agents

This investigation systematically evaluates eight organic compounds as potential copper electroplating inhibiting agents: 1-(3,5-dichlorophenyl)pyrrolidine-2,5-dione (DSI), etoposide (EPE), and polypropylene glycol (PPG), along with a polyethylene glycol (PEG) series comprising monomeric PEG and polymeric derivatives of varying molecular weights (PEG-2000, PEG-4000, PEG-6000, and PEG-8000). The selection encompasses structurally diverse molecules to probe molecular weight effects and functional group interactions in corrosion inhibition mechanisms.

A proportional scaling strategy was implemented for polyethylene glycol (PEG) polymers to address computational constraints associated with macromolecular simulations. Molecular models were constructed with reduced polymerization degrees: PEG-2000 (11 ethylene glycol units), PEG-4000 (22 units), PEG-6000 (33 units), and PEG-8000 (44 units). This hierarchical modeling approach enables a systematic investigation of the effects of polymerization degree on adsorption behavior. Fig. 6 and 7 illustrate the orbital distributions of the HOMO and LUMO of the eight kinds of molecules. It can be seen that their HOMO orbital is mainly concentrated on the ether bonds or benzene rings, while the LUMO orbital is primarily concentrated on the methylene groups or double bonds. The HOMO orbital is the main orbital for donating electrons and the LUMO orbital is the main orbital for accepting electrons. The smaller the ΔE, the stronger the adsorption ability. From Table S2, it can be analyzed that among PPG, EPE, and DSI, EPE has the smallest ΔE. In PEG molecules and PEG macromolecules, it can be observed that as the degree of PEG polymerization increases, its adsorption capacity first becomes stronger and then decreases. When the degree of PEG polymerization is 4000, the adsorption performance of the molecule is the strongest. This is because as the molecular chain of PEG extends, the number of ether bonds also increases, leading to an increase in the energy of the HOMO and a decrease in the energy of the LUMO. As a result, a stronger adsorption ability is achieved. As can be seen from Fig. 8, among the eight kinds of inhibitor molecules, PEG 8000 has the smallest ΔE, which is 0.072 eV.

Fig. 6 The HOMO distribution of eight kinds of inhibitor molecules. (a) DSI, (b) EPE, (c) PPG, (d) PEG, (e) PEG 2000, (f) PEG 4000, (g) PEG 6000 and (h) PEG 8000.

Fig. 7 The LUMO energy density distribution of eight kinds of inhibitor molecules. (a) DSI, (b) EPE, (c) PPG, (d) PEG, (e) PEG 2000, (f) PEG 4000, (g) PEG 6000 and (h) PEG 8000.

Fig. 8 The ΔE diagram of the inhibitor molecules. (a) DSI, (b) EPE, (c) PPG, (d) PEG, (e) PEG 2000, (f) PEG 4000, (g) PEG 6000 and (h) PEG 8000.

Fig. S2 confirms that all eight systems achieved equilibrium within 50 fs based on the equilibrium state criterion. Fig. 9 and 10 present comparative molecular configurations before and after copper substrate adsorption. The MD simulations reveal spontaneous molecular migration toward the substrate with subsequent structural compaction, forming dense protective layers that demonstrate effective corrosion inhibition. Table 2 quantitatively verifies this behavior through negative E_adsorption (DSI: −119.075 kJ mol⁻¹, EPE: −268.379 kJ mol⁻¹, PPG: −464.567 kJ mol⁻¹), confirming spontaneous adsorption. As shown in Table 3, PEG derivatives universally demonstrate spontaneous adsorption.

Fig. 9 Configuration diagrams of DSI, EPE and PPG before and after MD simulation. (a)–(c) refer to DSI, EPE and PPG before the simulation. (a′)–(c′) refer to DSI, EPE and PPG after the simulation.

Fig. 10 Configuration diagrams of PEG, PEG 2000, PEG 4000, PEG 6000 and PEG 8000 before and after MD simulation. (a)–(e) refer to PEG, PEG 2000, PEG 4000, PEG 6000 and PEG 8000 before the simulation. (a′)–(e′) refer to PEG, PEG 2000, PEG 4000, PEG 6000 and PEG 8000 after the simulation.

Table 2 The adsorption energy data of DSI, EPE, and PPG molecules

Inhibitor	E total (kJ mol^−1)	E s (kJ mol^−1)	E molecule (kJ mol^−1)	E adsorption (kJ mol^−1)
DSI	344 604.891	344 863.872	−139.906	−119.075
EPE	345 082.940	344 868.324	482.995	−268.379
PPG	341 009.960	341 288.556	185.972	−464.567

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Table 3 The adsorption energy data of PEG, PEG 2000, PEG 4000, PEG 6000, and PEG 8000 molecules

Inhibitor	E total (kJ mol^−1)	E s (kJ mol^−1)	E molecule (kJ mol^−1)	E adsorption (kJ mol^−1)
PEG	21.602	0.000	67.242	−45.640
PEG 2000	344 903.177	344 877.931	327.932	−302.687
PEG 4000	344 548.459	344 888.807	512.287	−852.634
PEG 6000	344 942.889	344 891.755	654.054	−602.920
PEG 8000	345 766.689	344 899.161	881.811	−14.283

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It can be seen from the figures that DSI and EPE, as small molecule inhibitors, can specifically adsorb onto the copper surface through their aromatic rings, carbonyl groups and other functional groups. Polymer-based inhibitors (such as PPG, PEG and their derivatives of different molecular weights) effectively suppress the migration and reduction processes of copper ions by forming steric hindrances at the electrode interface.

The energy gap landscape analysis in Fig. 11 demonstrates an inverse relationship between molecular orbital energy differences and surface adsorption capabilities, suggesting that compounds with smaller orbital energy disparities exhibit stronger interfacial interactions. Since E_adsorption is used as the main indicator for ranking in this article, we can obtain the following ranking of inhibitor performance: PEG 4000 > PEG 6000 > PPG > PEG 2000 > EPE > DSI > PEG > PEG 8000. From the sorting, we can see that the adsorption performance of PEG shows a trend of first increasing and then decreasing with the molecular weight, and usually reaches the optimal value at medium molecular weights (such as PEG 4000).

Fig. 11 Comparison diagram of ΔE and adsorption energy of inhibitor molecules.

Conclusions

In this work, the DFT method and MD simulation are used to study the effects of leveling agents and inhibiting agents on the adsorption behavior on copper surfaces, and the following conclusions can be drawn. In leveling agent analysis, quantum chemical calculations revealed the HOMO, LUMO, and energy gap parameters for four molecular structures. The theoretical analysis identified that indigo exhibits the strongest adsorption capacity (followed by NTBC and ST, with DB showing the weakest interaction), consistent with molecular dynamics simulations. Indigo demonstrated the lowest E_adsorption and optimal copper surface adhesion, indicating superior capability to inhibit copper surface electrodeposition and enhance micropore filling performance. In inhibitor investigations, the quantum chemical evaluation of eight inhibitor molecules showed that EPE has a stronger adsorption capacity than PPG and DSI. PEG polymers exhibited enhanced adsorption with increased polymerization degree. Molecular dynamics simulations confirmed the spontaneous adsorption of all inhibiting agents on copper surfaces. PPG demonstrated the strongest surface adsorption and inhibition effects among the DSI, EPE, and PPG molecular groups. For PEG compounds, PEG 4000 exhibited comparatively superior adsorption performance. This work provides a theoretical basis for design and selection of organic additives. However, due to the limitation of the simulation model itself, there may be a particular discrepancy with the experimental results, and further theoretical and experimental studies are required.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data used to support the paper are included within the article.

Supplementary information is available. Tables S1 and S2 present the energies of the HOMO and LUMO of additive molecules. Fig. S1–S12 are the equilibrium of temperature and energy of additive molecules. See DOI: https://doi.org/10.1039/d5nj02183a.

Acknowledgements

Support from the Fundamental Research Funds for the Central Universities (DUT24BK002), the Undergraduate Innovation and Entrepreneurship Training Program (20241014110423) of the Dalian University of Technology, and the Hefei Advanced Computing Center for this work are gratefully acknowledged.

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