Numerical simulation and twinning evolution mechanism of the deep through silicon via electroplated copper

Method and model of numerical simulation

In this study, the electrodeposited module of COMSOL Multiphysics software was used to simulate the deep TSV filling process, employing the Arbitrary Lagrangian-Eulerian (ALE) approach. The finite element model, considering the processes of diffusion, adsorption, and desorption of additives (including the accelerator and suppressor) and Cl^- was developed^[10]. It was assumed that the mass transport of ion, described using the Nernst-Planck equation, was mainly dominated by the diffusion and electro-migration ignoring the convection. Moreover, the current density on the cathode surface could be divided into three parts: the current density i_a from the surface covered by the accelerator, the current density i_s from the surface covered by the suppressor, and the current density i_u from the uncovered surface. The current density was calculated using a Butler-Volmer equation which was taking into consideration the effect of additives to calculate local plating current density^[9]. The numerical simulation was carried out at the current densities of 0.05, 0.07, 0.09, 0.1, 0.15, 0.17, 0.2 Ampere per Square Decimeter(ASD) (1 ASD = 100 A·m^-2) and the ratios of accelerator and suppressor concentration 1:1, 1:5, 1:10. According to the present numerical simulation [Supplementary Figures 1 and 2], the optimal electrodeposited parameters had been confirmed at the ranges from 0.1-0.17 ASD and an optimal ratio of accelerator and suppressor concentration 1:10. The void-free deep TSV filling experiment [Supplementary Figure 3] could be achieved at the optimal electrodeposited parameter ranges that are used to verify the validation of simulation. The experimental results show good agreement with the simulated results described above, which further confirms the reliability of the simulation and the accuracy of the model.

The current density was set at 0.1, 0.15, and 0.17 ASD (1 ASD = 100 A·m^-2) using a direct current power supply. The electrolyte composition consisted of CuSO₄, H₂SO₄, Cl^-, with a fixed accelerator [Bis-(sodium sulfopropyl)-disulfide, SPS]-to-suppressor (polyethylene glycol, PEG) concentration ratio of 1:10. The total deposition time in the simulation was determined by the experimental complete filling time. All simulations were performed at a constant temperature of 25 °C. The geometric model and mesh division for the deep TSV electroplated copper are shown in Figure 1.

Figure 1. (A) Two-dimensional model and (B) grid division model of the deep TSV electroplated copper. TSV: Through silicon via.

In this model, the electrode surface reactions primarily involve three key complexes: PEG-Cl^--Cu²⁺, SPS-Cl^--Cu²⁺, and free Cu²⁺. The model focuses on capturing the behavior of these complexes, with their transport and reaction kinetics governed by mass conservation laws. Furthermore, the influence of current density on their behavior at the electrode surface is analyzed through energy conservation principles. The specific physical framework is presented in the following section.

The substance transport in the electrolyte is governed by the Nernst-Planck equation, and the fluxes of substance (N_i) are expressed as follows^[9]:

where N_i is the fluxes of substance (mol·m^-2·s^-1), D_i is the diffusion coefficient of the additive or ion (m^-2·s^-1), C_i is the concentration of the additive or ion (mol·m^-3), z_i is the number of valence electrons, Φ is the potential in the electrolyte solution (V), µ_i is the mobility constant, F is the Faraday constant, and u is the velocity field governed by the incompressible Navier-Stokes equations (m·s^-1).

The diffusion process is governed by Fick’s second law, with the temporal variation of copper ion concentration due to the concentration gradient at a given location described by Eq. (2). The electromigration process involves the movement of charged copper ions under the influence of an electric field, with the corresponding temporal variation of copper ions given by Eq. (3). The Nernst-Einstein equation relates the diffusion and electromigration of copper ions^[9], as shown in Eq. (4).

where R is the universal gas constant (8.314 J·K^-1·mol^-1), T is the temperature (298 K), ▽² is the Laplace operator, and µ_Cu²⁺ is the electrochemical mobility of copper ions (m²·V^-1·s^-1).

Since the additives are the electro-neutral with the neglection of the electromigration process, and their transport in the electrolyte is governed solely by Fickian diffusion, as described by Eq. (5):

According to the research on the additives by Akolkar et al., the concentration of additives on the electrode surface directly affects their coverage rate on the electrode surface^[22]. Considering the effect of the diffusion, adsorption and desorption of three substances (accelerator, suppressor and Cl^-) on the cathode surface, the surface coverage rates of three substances are expressed using Eqs. (6-8) based on the Langmuir adsorption equation^[9].

Where θ_A, θ_Cl-, and θ_P denote the surface coverages (%) of the accelerator, Cl^-, and suppressor, respectively, $$ k_{A}^{+} $$, $$ k_{C l^{-}}^{+} $$, and $$ k_{P}^{+} $$ are their respective adsorption rate constants, $$ k_{A}^{-} $$, $$ k_{C l^{-}}^{-} $$, and $$ k_{P}^{-} $$ are their respective desorption rate constants, and v is the electrodeposition velocity (m·s^-1).

Based on the behavior of additives at the electrode surface, the adsorption reaction rate (Eq. 9) and the adsorption-desorption kinetics (Eq. 10) are defined to establish the equilibria among the normal fluxes of the accelerator, suppressor, and Cl^- from the electrolyte to the deposition interface:

where R_i is the adsorption reaction rate of the additive (mol·m^-2·s^-1), Rad_i is the net adsorption-desorption reaction rate (mol·m^-2·s^-1), k_i⁺ and k_i^- is the adsorption and desorption rate constant, respectively, and Γ_i is the surface saturation concentration of the additive (mol·m^-2).

In the present model, the current density associated with this process is described by the Butler-Volmer equation and is given by:

where $$ i_{0}^{i} $$ is the exchange current density on the additive-adsorbed surface (A·m^-2), η is the overpotential (V), α_a and α_c is the anodic and cathodic charge transfer coefficient, respectively.

Since the electrodeposition process occurs exclusively at the cathode, the anodic contribution to the current density is neglected. The cathodic current density is therefore governed by Eqs. (12-14), which determines the total deposition rate at the electrode surface.

where $$ i_{0}^{\text {free }} $$ is the exchange current density on the additive-free surface (A·m^-2), α_A and α_P is the charge transfer coefficient of the accelerator and suppressor, respectively, and α_C is the charge transfer coefficient of copper ions.

The total deposition current density is composed of the current contributions from the accelerator-covered surface (i_A), the suppressor-covered surface (i_P), and the additive-free surface (i_free), and is expressed as^[9]:

The deposition rate is governed by the local current density. According to Faraday’s law, the relationship between current density and deposition rate can be described as:

where M_Cu is the molar mass of copper (0.06355 kg·mol^-1), $$ \rho _{Cu} $$ is the density of copper (8,960 kg·m^-3), and n is the number of electrons transferred in the deposition reaction.

The parameters for numerical simulation during the filling process of the deep TSV electroplated copper are summarized in Table 1.

Electrodeposition experiment

A CZ300 machine was utilized as the direct current electrodeposited equipment. As shown in Figure 2A, the sample size was 10 mm × 10 mm for the deep TSV electroplated copper layer. The copper layer was electrodeposited on the silicon substrate. Figure 2B shows the top view of the via arrangement and the via spacing is 60 μm. The size of deep TSV is approximately Φ20 μm × 200 μm with an approximate aspect ratio of 10:1, as shown in Figure 2C. Figure 2D schematically depicts the multilayer material composition of the TSV cross-section. The multilayer structure consists of SiO₂ as the insulating layer, Ti as the barrier layer, and Cu as the seed layer. The seed layer has a thickness of 1 μm, and copper is electroplated to fill the TSV. The essential raw materials for deep TSV electroplated copper include a base electrolyte solution and additives. The primary additive system is a sulfuric acid-based electrolyte system, consisting of an accelerator (SPS), a suppressor (PEG), and Cl^-. According to the optimal electrodeposited parameters (0.1-0.17 ASD and a ratio of accelerator and suppressor concentration 1:10) that are preliminary confirmed by the numerical simulation, the electrodeposition experiment is carried out.

Figure 2. Deep TSV electroplated copper: (A) TSV sample; (B) via arrangement; (C) section of TSV; (D) schematic diagram of multi-player material for TSV. TSV: Through silicon via.

Microstructure characterization

The surface filling of the deep TSV electroplated copper layer at different magnifications was observed using Leica DMI3000M Optical Microscope (OM). EBSD was performed to quantify the microstructural parameters, including grain size, twin boundary, and the distribution of low-angle and high-angle grain boundaries. The TEM samples were fabricated using Helios G4 CX FIB/SEM, and the FEI Talos F200X field emission high-resolution transmission electron microscope was utilized for TEM observations. The TKD technique was employed to characterize and analyze the morphology of columnar and equiaxed grains of the deep TSV electroplated copper layer.

Effect of current density on the simulated deep TSV filling

Figure 3 shows the numerical simulation results of electrochemical deposition process for the deep TSV electroplated copper with an additive concentration ratio of 1:10 (accelerator concentration: suppressor concentration) and an applied current density of 0.15 ASD. As shown in Figure 3A, the via filled at 0.15 ASD exhibits no detectable electrolyte potential, confirming that defect-free filling is achieved. Each electrolyte potential curve in Figure 3B represents the simulated filling morphology at different electrodeposition times, exhibiting a characteristic V-shaped filling profile during the deposition process. The V-shaped filling profile is corresponding to the defect-free filling confirmed by the electrochemical deposition experiments in the following section.

Figure 3. Simulation results of deep TSV electroplated copper at an additive concentration ratio of 1:10 and a current density of 0.15 ASD: (A) the electrolyte potential distribution after filling showing the defect-free filling result; (B) the electrolyte potential distribution at different electrodeposition times; (C) the current density distribution along the via depth at different electrodeposition times; (D) the distribution of copper ion concentration along the via depth at different electrodeposition times. TSV: Through silicon via; ASD: ampere per square decimeter.

Figure 3C shows the distribution of current density along the via depth direction at different electrodeposition times. It can be observed that the variation trend of current density is different at different electrodeposited stages. In the early stage of electrodeposition, as indicated by the blue and green curves, the highest current density appears at the via mouth, whereas the lowest occurs at the bottom. In contrast, during the later stage, the maximum current density shifts to a depth of 150 µm, as shown by the black curve. This phenomenon implies that the maximum of local current density shifts toward the via middle-top region during TSV electrodeposited copper. Figure 3D shows the evolution of copper ion concentration distribution in the deep TSV electroplated copper at 0.15 ASD. A noticeable concentration gradient develops from the lowest concentration of via bottom to the highest concentration of via mouth with the electrodeposition time. At the beginning of electrodeposition, the copper ion concentration is uniformly maintained at 1,000 mol·m^-3 along the whole via depth. As electrodeposition proceeds, copper ions are gradually consumed, and insufficient copper ions diffuse to the via bottom. Consequently, the copper ion concentration at the via bottom decreases to 882 mol·m^-3 after 2,370 min of deposition, while it remains close to 1,000 mol·m^-3 at the via mouth. Moreover, the suppressor (PEG) predominantly accumulates near the via mouth due to its comparatively low diffusion coefficient. The diffusion coefficient of the accelerator (SPS) is far larger than of the suppressor, preferentially distributing at the via bottom. The reference^[9] has reported that the accelerator coverage and suppressor coverage would change with the applied current density and electrodeposition time, finally affecting the overall electrodeposition dynamics. Similarly, the distribution of current density and copper ion concentration are also observed in the simulation results at 0.1 ASD and 0.17 ASD [Supplementary Figure 4].

Effect of current density on the microstructure of the deep TSV electroplated copper

In order to systematically demonstrate the changes in the microstructure during the bottom-up filling process of deep TSV electroplated copper, the electro-deposited copper layer is divided into four distinct regions (I, II, III, IV) along the electrodeposition V-shaped filling process, as shown in the Figure 4. The following analysis describes the evolution of copper grains according to this regional sequence, providing a clear framework for understanding the grain morphology and size distribution from the via bottom to the top. Figure 4 shows the effect of current density on the inverse pole figure (IPF) of the deep TSV electroplated copper at an additive concentration ratio of 1:10. As shown in Figure 4A, a fine-grained layer forms on the via walls (region I) because the pre-deposited copper seed layer provides abundant nucleation sites for subsequent electrodeposition. In the region away from the via wall, the microstructure is consisted of equiaxed and columnar grains (region II). Notably, the grain colors in the IPF map indicate that the grains exhibit random crystallographic orientations without any distinct texture. In the early stage of electrodeposition, the microstructure is mainly consisted of coarse and equiaxed grains at the via bottom. As the electrodeposition goes on, the columnar grain grows along the via diameter direction at the middle region of the via (region III), and the microstructure is composed of fine and equiaxed grains at the via mouth (region IV). Moreover, the microstructure of four distinct regions is quantitatively analyzed, as shown in Figure 5. In Figure 5A and B, the Cu grain size first increases and then decreases along the electrodeposition direction. The result of aspect ratio is good agreement with the observation of microstructure morphology in Figure 4. The observed changes in grain size can be rationalized using electrocrystallization theory, with the electrodeposition kinetics expressed by the following equation^[24]:

Figure 4. Effect of current density on the IPF ||Z of the deep TSV electroplated copper at an additive concentration ratio of 1:10: (A) 0.1 ASD; (B) 0.15 ASD; (C) 0.17 ASD; (D) regional division diagram. IPF: Inverse pole figure; ASD: ampere per square decimeter.

Figure 5. Effect of current density on the microstructure at different regions of deep TSV and an additive concentration ratio of 1:10: (A) average grain size; (B) aspect ratio of grain; (C) frequency of Σ3 twin boundaries; (D) frequency of all twin boundaries. TSV: Through silicon via.

where η is the cathode potential (V), I is the current density (ASD), a and b are the chemical constants, W is the nucleation rate (%), B is a material constant, and T is the temperature (K).

It can be deduced from Eq. (17) that the cathode potential η increases with increasing current density I. From Eq. (18), the nucleation rate W increases exponentially with increasing cathode potential η. Therefore, a higher current density I corresponds to a higher nucleation rate W, finally resulting in finer Cu grains. According to the above simulation results, the current density at the via mouth is 0.4 ASD in the early stage of electrodeposition but it is 0.1 ASD at the via bottom. Therefore, the higher nucleation rate at the via mouth leads to a fine grain distribution in region IV, whereas the lower nucleation rate at the via bottom produces coarser grains in regions II and III. During electrodeposition, the peak current density moves toward the via’s middle-top region, enhancing the growth rate and driving dynamics of Cu grain nuclei along the direction of the steep current density gradient. Concurrently, a higher accelerator (SPS) concentration in the via’s middle-bottom region promotes the formation of columnar grains in the middle region (regions II and III).

From Figure 5A, it can be also seen that the size of Cu grain first decreases and then increases in the middle region (regions II and III) and via wall (region I) as the current density increases, but there is a negligible effect on the size of Cu grain at the mouth region (region IV). Thus, an overall coarsening tendency of Cu grains is observed at a current density of 0.17 ASD. This behavior can be attributed to the fact that increasing current density strengthens the polarization effect, thereby enhancing Cu nucleation and favoring the formation of fine grains. However, when the current density exceeds a critical threshold, the suppressor undergoes desorption from its inhibited state to an uninhibited state, accelerating grain growth and resulting in coarser Cu grains^[25].

In the deep TSV electroplated copper, Σ3 and Σ9 twins are present, with Σ3 coincident site lattice (CSL) boundaries dominating. Figure 5C shows the variation trend of Σ3 twin grain boundaries along the deposition direction at different current densities. It is present that the density of Σ3 twin grain boundaries initially increases and then decreases along the deposition direction. Furthermore, as shown in Figure 5D, the density of Σ3 twin grain boundaries first decreases and then increases with increasing current density, which is similar to the size change of Cu grain, and it can be inferred that the twin density is positively correlated with the grain size.

To further investigate the grain morphology characteristics of the deep TSV electroplated copper, a TKD characterization is performed on region II of Figure 4A at a current density 0.1 ASD and an additive concentration ratio of 1:10, as shown in Figure 6. Figure 6A reveals a mixed microstructure with columnar and equiaxed grains. According to the above-mentioned simulation results of this electrodepositing area, the current density at the via wall is 0.6 ASD but it is 0.2 ASD at the via’s middle region, a larger gradient of current density exists between the via wall and the central axis, causing that copper grain growth is dominated over nucleation in the early electrodeposition stage. Consequently, columnar grains form along the electric field lines under these conditions. During electrodeposition, the current density gradient diminishes while the overall current density increases, leading to an enhanced nucleation but suppressed grain growth. As a result, fine equiaxed grains develop along the central axis of the via [Figure 6A]. Figure 6B and C reveals the high density of Σ3 twin boundaries and the local misorientation map, respectively. From Figure 6C, an obvious accumulation of geometrically necessary dislocations (GNDs) occurs at the twin boundaries in region Ⅱ. The observation region can be divided into zone I and zone II based on the density of Σ3 twin boundaries in Figure 6B. As shown in Figure 6D and E, the density of Σ3 twin boundaries, defined as the fraction of Σ3 twin boundary length relative to the total grain boundary length, reaches 36.31% in the columnar-grain region and 34.44% in the equiaxed-grain region. This further verifies the positive correlation between grain size and twin boundary density.

Figure 6. TKD results of region II in Figure 4A at a current density of 0.1 ASD and an additive concentration ratio of 1:10: (A) IPF||Z image; (B) band contrast and boundary distribution map; (C) KAM map;(D) twin boundary distribution of zone I in Figure 6B; (E) twin boundary distribution of zone II in Figure 6B. TKD: Transmission Kikuchi diffraction; IPF: inverse pole figure; KAM: kernel average misorientation; ASD: ampere per square decimeter.

Σ3 twin characteristics in the deep TSV electroplated copper

As mentioned above, the Σ3 twin boundary is frequently observed in the deep TSV electroplated copper. As shown in Supplementary Figure 5, numerous Σ3 twin boundaries are detected near the sidewall of the deep TSV electroplated copper at a current density of 0.1 ASD and an additive concentration ratio of 1:10. Two characteristic twin morphologies are highlighted: one consists of twins partially extending through the grain [Supplementary Figure 5D], and the other consists of twins fully extending through the grain [Supplementary Figure 5E]. These twins are Σ3 twins (i.e. {111}<$$ 11 \overline{2} $$>-type twins), as evidenced by the SAED result shown in Supplementary Figure 5F. These two twin morphologies are analyzed further in Figures 7 and 8.

Figure 7. TEM results of twins with a stepped morphology partially extending through the grain: (A) BF image; (B) HRTEM image; (C) IFFT image of the region marked by the white square in (B); (D) structural distribution map of (B); (E-H) FFT images of the regions marked by white circles 1-4 in (B). BF: Bright field; HRTEM: high-resolution transmission electron microscopy; IFFT: inverse fast Fourier transform; FFT: fast Fourier transform; ITB: incoherent twin boundary; GB: grain boundary; SF: stacking fault; ZA: zone axis; M: matrix.

Figure 8. TEM results of twins fully extending through the grain: (A) BF image; (B) HRTEM image showing steps near the twins; (C) structural distribution map of (B); (D) FFT images of the region marked by white circle 1 in Figure 8B; (E) IFFT and FFT images of the region marked by white circle 2 in Figure 8B; (F) FFT image of the region marked by white circle 3 in Figure 8B. BF: Bright field; HRTEM: high-resolution transmission electron microscopy; FFT: fast Fourier transform; IFFT: inverse fast Fourier transform; GB: grain boundary; ZA: zone axis.

Figure 7 shows twins partially extending through the grain. As shown in Figure 7A, the twins originate from the grain boundary and extend into the interior of the grain. Several steps are observed at the front of the twins. As shown in Figure 7B, the twin consists of two laths with thicknesses of 30 and 12 nm, forming a step, indicating that these two twin segments are formed sequentially from left to right. Besides, a periodic structure appears next to the twin and parallel to (111) and ($$ 11 \overline{2} $$) planes (e.g., in circles 2 and 4), and the corresponding fast Fourier transform (FFT) result [Figure 7F and H] exhibits extra diffraction spots compared with the FFT result of the FCC matrix [Figure 7E]. In addition, the inverse fast Fourier transform (IFFT) result in Figure 7C reveals a periodicity of three atomic planes separated by stacking faults within the periodic structure, in which planes A, B, and C are the stacking sequence along the [111] direction in the FCC crystal structure, as shown in Supplementary Figure 6. These features indicate that the periodic structure corresponds to a 9R structure. Moreover, the incoherent twin boundary (ITB) exists parallel to ($$ 11 \overline{2} $$) plane between matrix and 9R structure as shown in Figure 7B. Based on FFT results, the matrix, twin, 9R and ITB structure are identified, and the corresponding structural distribution map is shown in Figure 7D. It is found that the 9R structure is located between the matrix and the twins, indicating that the twinning process follows the sequence: matrix→9R→twin. Besides, the steps are specifically located within the 9R structure.

The twins fully extending through the grain are shown in Figure 8. The structural distribution map in Figure 8C is also obtained based on the FFT results. In Figure 8A, although no steps are observed in the BF image, both the HRTEM image [Figure 8B] and the structural distribution map [Figure 8C] reveal the presence of steps within the 9R structure. The matrix/9R interface and the 9R/twin interface, both parallel to the (111) plane, together with the steps within the 9R structure, indicate that the 9R structure and twins are formed layer by layer along the (111) plane, and the steps serve as the boundary between the transformed and untransformed regions. As shown in Figure 8E, a dislocation with Burgers vector of $$ \frac{1}{6}[11 \overline{2}] $$, corresponding to a Shockley partial dislocation in the FCC crystal, is identified within the 9R structure using a Burgers circuit. Therefore, the layer-by-layer formation of the 9R structure and twins during the matrix → 9R → twin transformation process is associated with the motion of Shockley partial dislocations.

Discussion

Formation mechanism of Σ3 twin in the deep TSV electroplated copper

The reason for the formation of the 9R structure prior to twinning
According to the above result, the 9R structure forms prior to twinning, and both the 9R structure and twins develop layer by layer. Figure 9 shows the stacking sequence along [111] direction among FCC matrix, twins of different thicknesses and 9R structure. The stacking sequence of the FCC structure is ABC|ABC|ABC (A, B and C respectively represent the arrangement of atoms at different levels on the corresponding crystal planes). As the number of atomic layers increases from 1 to 6, it is observed that the stacking sequence within the twin zone (marked in green in Figure 9) is BAC|BCA. Specifically, in Figure 9A, for twins containing 1-, 3-, 4-, and 6-layer atoms, the stacking sequence above the topmost twin plane differs from that of the FCC matrix. For instance, the stacking sequence above the topmost twin plane of the 6-layer twin is BCA, whereas the corresponding rows in the FCC matrix follow the ABC sequence. This indicates that the formation of twins containing 1-, 3-, 4-, and 6-layer atoms induces lattice distortion in the FCC matrix due to the differing stacking sequences. As shown in Figure 9B, twins containing 2- and 5-layer atoms do not produce stacking sequences different from those of the matrix above the twin zone. In fact, twins containing (2 + 3n) atomic layers do not alter the stacking sequence above the twin zone either, where n is a natural number. However, the layer-by-layer formation of atomic planes during twinning implies that the number of atomic layers in the twin zone cannot be limited to only 2-, 5-, or (2 + 3n). Therefore, a transitional stacking structure is required to accommodate the transformation.

Figure 9. Comparison of stacking sequence along [111] direction among the FCC matrix, twins of different thicknesses and 9R structure: (A) stacking sequence above the twin plane of 1-, 3-, 4-, and 6-layer twins, differing from that of the FCC matrix; (B) stacking sequence above the twin plane of 2- and 5-layer twins or above the faulted planes of the 9R structure, matching that of the FCC matrix. The first row of atoms above the topmost twin plane of the twins or above the topmost faulted plane of the 9R structure, along with the corresponding atoms in the matrix, is marked with horizontal dashed lines. FCC: Face-centered cubic.

The formation of the 9R structure prior to twinning rationalizes this issue. As shown in Figure 9B, the stacking sequence of the 9R structure is ABC|BCA|CAB. The stacking sequence above the 9R zone is ABC, the same as that of the matrix, and does not induce lattice distortion in the matrix above the topmost faulted planes. Thus, the prior formation of the 9R structure ensures that twins can grow with minimal lattice distortion in the surrounding matrix.

The structural transformation process during matrix→9R→twin
During the formation of the 9R structure and twins, Shockley partial dislocations with a Burgers vector of $$ \frac{1}{6}[11 \overline{2}] $$ (as evidenced in Figure 8E) serve as the key mediators. As shown in Supplementary Figure 6B, the movement of Shockley partial dislocation leads to changes in the stacking sequence of the FCC structure, following A→B, B→C and C→A. To illustrate the layer-by-layer formation of twins along the [111] direction and the simultaneous migration of the 9R structure along the same direction, the structural transformation process of matrix→9R→twin is schematically presented in Figure 10. First, the 9R structure forms through the gliding of Shockley partial dislocations b on (111) planes, occurring every three atomic layers. Then, gliding of Shockley partial dislocation occurs in some special (111) planes of 9R structure zone, forming 1-layer, 3-layer, 5layer and 6-layer twin zone. Meanwhile, as the twin thickness increases, the 9R structure simultaneously shifts upward. This cycle repeats, enabling the continuous process of matrix→9R→twin, with the 9R structure always located at the matrix/twin interface and the twin gradually thickening^[26-28]. This process is consistent with the experimental results shown in Figures 7 and 8.

Figure 10. Schematic illustration of the matrix→9R→twin transformation process, showing that under the action of Shockley partial dislocations, the introduction of the 9R structure prior to twinning can lead to twin thickening and upward migration of the 9R structure. FCC: Face-centered cubic.

The observation of an intermediate 9R structure in deep TSV electroplated copper differs markedly from previous reports on electrodeposited or magnetron-sputtered Cu films^[18-21]. The deep TSV electrodeposition involves high aspect ratio, for example, 10:1 in this work. Although the filling quality is good [Supplementary Figure 3B-D], the geometrical confinement induces pronounced overpotential gradient [Supplementary Figures 1 and 2], resulting in highly non-equilibrium condition for crystal growth at different time and locations. This is supported by the different grain size at the different locations in Figure 4. Under the combined effect of overpotential gradients and geometrical confinement, particularly in regions near the upper part of the TSV (indicated by the blue potential profile in Supplementary Figure 2E), grain nucleation occurs more frequently. This leads to finer grains, which are required to accommodate larger local strains owing to strain accommodation among a greater number of grains. In this context, the formation of an intermediate 9R structure provides a new pathway for strain accommodation, enabling its persistence in these regions. This finding enriches the existing twinning theory of copper and demonstrates that highly non-equilibrium conditions under geometrical confinement can activate additional metastable structure.

Evolution of grain morphology in the deep TSV electroplated copper

Figure 11 shows the microstructural evolution of the deep TSV electroplated copper at a current density of 0.1 ASD and an additive concentration ratio of 1:10. As shown in Figure 11A, three distinct microstructural regions are identified from sidewall to central axis: (i) surface fine-grained zone (< 500 nm grain size); (ii) intermediate columnar grain zone (1-3 μm width); and (iii) central equiaxed grain zone (2-5 μm diameter). Specifically, fine and columnar grains dominate near the sidewalls, while equiaxed grains predominantly occupy the central region.

Figure 11. Microstructure and morphology of the deep TSV electroplated copper at a current density of 0.1 ASD and an additive concentration ratio of 1:10: (A) IPF||Z image; (B1-B4) local magnification of (A). TSV: Through silicon via; IPF: inverse pole figure; ASD: ampere per square decimeter.

Along electrodeposit direction, four regions with different grain morphology are identified. In Figure 11B (4), the grain morphology in the bottom area of the via is predominantly equiaxed grains, with fine grains near the via sidewall. The grains on the sidewall grow laterally and those in the central area grow vertically upward. In the lower-middle area of the via [Figure 11B (3)], the grains on the sidewall are columnar and exhibit an oblique upward growth trend, while the grains in the central area are equiaxed. In the upper-middle area of the via [Figure 11B (2)], the grains on the sidewall are columnar and grow obliquely upward, and the grains in the central area are fine equiaxed. At the via opening area [Figure 11B (1)], the grains on the sidewall are fine and columnar, growing laterally, and the grains in the central area are fine equiaxed.

This structural gradation originates from the interplay of three electroplating mechanisms: liquid-phase mass transfer, electron transfer, and phase formation. Notably, accelerator and inhibitor additives critically regulate copper grain nucleation and growth dynamics. Accelerators preferentially adsorb at the via bottom, reducing cathodic polarization to enhance Cu²⁺ reduction and grain growth. Conversely, inhibitors concentrate at the via opening, increasing cathodic polarization to suppress both Cu²⁺ reduction and nucleation. Spatial heterogeneity in current density and Cu²⁺ concentration induces coupled electrochemical and concentration polarization effect. Both electrochemical polarization and concentration polarization jointly impact the electrocrystallization process. Electrochemical polarization enhances nucleation density through increased overpotential, yielding refined-grain copper layer. Concentration polarization governs grain growth kinetics by modulating local ion availability, directly affecting coating uniformity and density. As demonstrated in Section 3.1, bottom-to-top deposition progression correlates with current density variation: minimal at the via bottom versus maximal at the opening [Figure 3C]. Consistent with electrocrystallization principles, higher current density at the opening promotes elevated nucleation rates, resulting in dense nuclei formation. Simultaneously, electric field alignment at the bottom facilitates directional growth along field lines, fostering columnar grain development. With prolonged electroplating, inhibitor depletion near the opening shifts the dominant mechanism from growth to nucleation. Spatial confinement coupled with homogenized polarization conditions restricts grain growth in central regions, ultimately stabilizing equiaxed microstructures. Therefore, inhibitor concentration and overpotential emerge as critical parameters governing intraluminal nucleation-growth equilibria. However, the current model does not take into account the influence of convection, which will limit the material transport process and result in low accuracy of the copper ion concentration field. In subsequent research, a convection model will be further incorporated to more clearly elucidate the microstructure evolution mechanism.