
==== Front
Ultrason Sonochem
Ultrason Sonochem
Ultrasonics Sonochemistry
1350-4177
1873-2828
Elsevier

S1350-4177(24)00267-0
10.1016/j.ultsonch.2024.107019
107019
Original Research Article
Study of liquid-phase mass transfer and residual stress in jet electrodeposition process with coaxial megasonic agitation
Zhai Ke kezhai@hbu.edu.cn
a⁎
Zhou Feng a
Wang Yifan a
Ma Shihao a
Fang Lide a
Du Liqun duliqun@dlut.edu.cn
b⁎
a National & Local Joint Engineering Research Center of Metrology Instrument and System, College of Quality and Technical Supervision, Hebei University, Baoding 071002, China
b State Key Laboratory of High-Performance Precision Manufacturing, School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China
⁎ Corresponding authors. kezhai@hbu.edu.cnduliqun@dlut.edu.cn
06 8 2024
10 2024
06 8 2024
109 10701923 1 2024
3 7 2024
5 8 2024
© 2024 The Authors. Published by Elsevier B.V.
2024

https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Graphical abstract

The electrodeposition process confronts significant challenges arising from mass transfer limitation and residual stress. To address these issues, an innovative method, combining megasonic agitation with coaxial jet electrodeposition, is introduced. This approach aims to enhance mass transfer and mitigate residual stress. First, an electrodeposition nozzle device was designed, and the liquid-phase mass transfer during electrodeposition was analyzed through finite element simulation. Simulation results indicate that the mass transfer coefficient increases with rising megasonic power density. Notably, when the megasonic power density reached 20 W/cm2, the mass transfer coefficient increased from 0.45 × 10−7 m/s to 18.63 × 10−7 m/s, compared to electrodeposition without megasonic agitation. Secondly, electrodeposition experiments were conducted both with and without megasonic assistance. X-ray diffraction (XRD) was employed to measure the residual stress values of the electrodeposited layers. The results reveal that samples processed with megasonic assistance exhibit lower residual stress values compared to those without. Specifically, at a megasonic power density of 10 W/cm2, the residual stress was 94.3 MPa, representing a 37.7 % reduction compared to the residual stress of 151.5 MPa observed in samples without megasonic agitation. Overall, the findings demonstrate that coaxial megasonic agitation can effectively enhance the liquid-phase mass transfer capability during electrodeposition and reduce the residual stress of the electroplated layer. This innovative method presents a promising avenue for improving electrodeposition processes and achieving superior material properties.

Keywords

Megasonic agitation
Mass transfer coefficient
Residual stress
Acoustic streaming
Jet electrodeposition
==== Body
pmc1 Introduction

The electrodeposition process has emerged as a pivotal technique for manufacturing metal microdevices due to its advantages of excellent dimensional accuracy, high replication accuracy, controllable mechanical properties, and batch replication capabilities. It finds applications in diverse fields such as aerospace, precision instruments, military equipment, and electronic devices. However, the electrodeposition process is plagued by limitation in electrolyte mass transfer, leading to cathodic concentration polarization and the formation of defects such as pores, bumps, and hydrogen embrittlement [1]. Additionally, the inhomogeneous electro-crystallization phenomenon often results in significant residual stress within the electrodeposited layer, ultimately causing warping, delamination, and deformation [2].

Addressing the issue of insufficient electrolyte mass transfer within confined spaces and mitigating or eliminating electrodeposition defects is a formidable challenge. Various methods have been employed to enhance electrodeposition and improve liquid-phase mass transfer, including mechanical agitation, periodic vacuum-degassing, and optimizing electroforming current parameters. For instance, Wang et al. [3] comprehensively investigated the influencing factors regarding the deeply filled TSV. They found that under low current density experimental conditions, the use of enforced convection decreases the TSV fill percentage but enhances it at higher current densities. In their study of mass transfer characteristics during microcolumn electrodeposition, Jiang et al. [4] found that the level of current density is closely related to the filling rate of the microcolumn. Through their experiments, they reduced the current density from 1 A/dm2 to 0.25 A/dm2, which effectively improved the filling rate of the microcolumn. Zhang et al. [5], [6] greatly facilitated the electrodeposition mass transfer process by introducing cathodic rotation and jet electrodeposition techniques to address the problem of limited liquid-phase mass transfer in electrolyte. Shen et al. [7] optimized the spraying angle and speed through simulation, and the results showed that the diffusion layer thickness could be effectively reduced by about 74 %, with an error within 7 μm. Coleman [8] investigated the effect of lateral ultrasonic vibration on electrodeposition between small gap electrodes. The results showed that the use of ultrasound significantly enhanced mass transfer and increased the limiting current by up to 10.

In addition to limited liquid-phase mass transfer, excessive residual stress within the electrodeposited layer is another major issue in the process. Commonly used methods to reduce residual stress in electrodeposited layer include electrochemical parameter modulation, high temperature treatment, vibration aging, and ultrasonic assistance. Okoro et al. [9] investigated the effect of chemical components on the thermomechanical behavior of different copper deposited layers. They found that the residual stress level of the deposited layer with higher component impurities was three times higher than that of the one with low impurities. In terms of electrical parameter adjustment, compared to DC electrodeposition, which tended to generate larger residual stress, DiBari [10] utilized the pulsed electrodeposition method and selected appropriate electrical parameters to effectively reduce the residual stress in electrodeposited layers. Additionally, Agrawal et al. [11] reduced the residual stresses in microstructures by adjusting the temperature and varying the pulses during the electroplating process. It was shown that by varying the pulsed electroplating parameters, the residual stress in the electroplated layer was reduced from 364 MPa to −194 MPa, indicating a transition from tensile to compressive stress. Cai et al. [12] investigated the annealing behavior of electrodeposited composites using XRD measurements. It was found that after the annealing treatment, the residual stress of the composite deposited layer changed from tensile to compressive and increased with increasing temperature. Sun et al. [13] employed vibrational aging prior to machining of the workpiece and observed that it could reduce the residual stress of the workpiece by approximately 48 %. Using high temperature treatment and vibration aging can reduce residual stress, but these methods are post-processing techniques that often require significant time and have limited impact. Prasad et al. [14] observed that ultrasonic assistance not only effectively reduces tensile stress in nickel plating, but also enhances physical properties such as hardness and fatigue strength.

As a high-frequency ultrasound technique, megasonic with a frequency of megahertz offers several advantages: low cavitation effect, high acoustic intensity, and strong streaming. These advantages make it well-suited for applications in semiconductors and micromanufacturing [15], [16]. The megasonic wave can decrease diffused layer thickness, enhance electrolytic dispersion capacity, and promote ion mass transfer in liquid phase environments. Jet electrodeposition involves spraying electrolyte onto the cathode surface at high speeds, where forced convective agitation accelerates the mass transfer efficiency of the electrolyte. With this in mind, this study introduces a coaxial jet electrodeposition method combined with megasonic agitation, aimed at enhancing mass transfer and reducing residual stress. In order to validate the method, both simulation calculations and electrodeposition experiments were conducted. We developed a simulation model based on mass transfer coefficients to quantitatively investigate mass transfer during electrodeposition. Then, the residual stress in the electroplated layer was measured using XRD and compared with experimental results obtained without the assistance of megasonic. Furthermore, the mechanisms of acoustic streaming and steady-state cavitation induced by megasonic on the residual stress within the electroplated layer were analyzed.

2 Principle of method

The megasonic agitation combined with coaxial jet method is proposed in this paper, and a nozzle device is designed to apply this method in jet electrodeposition. Fig. 1 shows the principle of megasonic agitation combined with coaxial jet electrodeposition. A megasonic transducer with a diameter of 25 mm and a frequency of 1.7 MHz is housed inside the nozzle. The anode is coaxially integrated within the nozzle, and the megasonic liquid stream generated by the piezoelectric oscillator immediately comes into full contact with the anode, thereby maximizing the effect of megasonic agitation to enhance the mass transfer in the microelectroforming liquid phase. The electroforming liquid enters the nozzle, fully contacts the piezoelectric vibrator, and exits the nozzle outlet in a stable flow. In the electrodeposition process, the electrolyte, having superimposed acoustic energy from the nozzle outflow, forms a megasonic flow and comes into full contact with the cathode substrate. Through the electrochemical cathodic reduction reaction, metal atoms are continuously deposited upwards, and the metal layer on the cathodic substrate continues to grow.Fig. 1 Schematic diagram of megasonic agitation combined with coaxial jet electrodeposition.

3 Mass transfer process analysis

3.1 Mass transfer model

Megasonic wave possess concentrated acoustic energy and propagate well along a straight line. The Helmholtz equation can be employed to calculate the propagation of megasonic waves within an electrolyte. This equation describes the distribution of acoustic pressure and is expressed as [17]:(1) ∇·-1ρ∇p-ω2ρcs2p=0

In this equation, p represents the acoustic pressure, ω represents angular frequency (where ω = 2πf), and f refers to acoustic frequency. The variables ρ and cs represent the density and velocity of the medium, respectively.

During megasonic propagation in the electrolyte, the acoustic pressure generates a volumetric force, Ft, which drives the fluid flow. This force is calculated to satisfy the following equation [18]:(2) Ft=2αsp2ρcs2

where p is the instantaneous acoustic pressure at any point in the solution, it can be seen from the formula that the acoustic pressure is positively correlated with the volume force. The volume force generated by the megasonic action causes the electrolyte to flow, and the electrolyte flow can be expressed by the Navier-Stokes equation and continuity equation [19]:(3) ρ∂u∂t+ρu∙∇u=∇∙-PlI→+μ∇u+∇uT=Ft

(4) ∇∙u=0

The solution flow rate is represented by u, while μ represents the solution viscosity. Pl denotes the pressure in the solution, I→ is the unit matrix. The solution flow rate increases under volumetric forces. The electrolyte flow rate increases to promote ion mass transfer in solution. The expression equation is [20]:(5) ∂ci∂t=Di∇2ci-∇uci+ziDiFciRT∇2Φl

The concentration of ions (ci), charge number of ions (zi), and diffusion coefficient of ions (Di) are related by the equation. The effect of the three liquid-phase mass transfer modes, diffusion, convection, and electromigration, on the mass transfer process is shown on the right side of the expression, respectively.

The acoustic pressure model is employed to calculate the distribution of acoustic pressure. This pressure is subsequently converted into a volumetric force, which is then coupled with the fluid model. By calculating the fluid model and integrating it with the mass transfer model, the liquid phase distribution velocity can be derived. The three models are coupled together to obtain the ion concentration distribution. Ultimately, the mass transfer coefficient is calculated, reflecting the deep deposition capability of electrodeposition. The calculation equation for this process is as follows [21], [22]:(6) k=-DcAS-cAdcdxx=0

where, cAS is the cathode surface ion concentration, cA is the solution body metal ion concentration, the diffusion coefficient D=0.7 × 10−9m/s2, dc/dx is the ion concentration perpendicular to the electrodeposited metal surface.

3.2 Numerical simulation

The geometric model and mesh division established within the simulation software are depicted in Fig. 2. Γ1 represents the electrolyte inlet in the geometric model, and the injected electrolyte covers the cathode surface. Γ2 denotes the cavity structure of the substrate where electrochemical reactions take place during the electrodeposition process. Γ3 and Γ4 are designated as the outlet boundaries for the electrolyte. The density and acoustic velocity of the electrolyte have been set to 1330 kg/m3and 1500 m/s, respectively. The primary parameter settings employed during the simulation are presented in Table 1.Fig. 2 Schematic of the simulation geometry model and meshing.

Table 1 Simulation parameter settings.

Parameters	Value	
Temperature（℃）	45	
Density of electroforming liquid（kg/m3）	1330	
Velocity of megasonic（m/s）	1500	
Diffusion coefficient（m2/s）	3.11 × 10−9[23]	
Initial concentration（mol/m3）	1240	
Dynamic viscosity（Pa·s）	7 × 10−4	

Fig. 3 and Fig. 4 show the acoustic pressure distributions and the flow velocity distributions under various megasonic intensities, respectively. It can be seen from the figures that the velocity of acoustic streaming increases with the increase in sound pressure. Without megasonic agitation, there was almost no electrolyte flow in the cavity structure. However, when electrodeposition was performed with megasonic agitation, the megasonic streaming enhanced convection, contributing to the renewal of the electrolyte solution within the cavity structure. Consequently, acoustic streaming can increase the concentration gradients within the cavity structure, which in turn enhances the diffusion efficiency and mass transfer coefficient [24], [25]. Specifically, the concentration gradients were 0.086 × 106 mol/m3, 2.017 × 106 mol/m3, 2.625 × 106 mol/m3and 3.539 × 106 mol/m3 for megasonic intensities of 0 W/cm2, 5 W/cm2, 10 W/cm2and 20 W/cm2, respectively (Fig. 5(a-d)).Fig. 3 Cloud image of sound pressure distribution.

Fig. 4 Cloud image of the flow velocity.

Fig. 5 Concentration distribution and mass transfer coefficient.

Furthermore, using the simulation model, we calculated the mass transfer coefficients under various megasonic conditions. Without megasonic agitation, the mass transfer coefficient was 0.45 × 10−7 m/s. When the megasonic power intensities were 5 W/cm2, 10 W/cm2, and 20 W/cm2, the mass transfer coefficients were 10.62 × 10−7 m/s, 13.82 × 10−7 m/s, and 18.63 × 10−7 m/s, respectively (Fig. 5(e)). Moreover, in this study, the trend of the influence of megasonic agitation on mass transfer is consistent with that reported in other literature [26].

4 Residual stress in electrodeposited layer

4.1 Residual stress test

Electrodeposition experiments were carried out to study the residual stress in the electroforming layer. As shown in Fig. 6, the megasonic nozzle was fixed on the three-axis motion platform. The megasonic generator is connected to a direct current power source and produces an electric signal at a frequency of approximately 1.7 MHz. The relative position of the moving platform and the workpiece was controlled by the computer. The workpiece was placed at the bottom of the nozzle. The experiments were conducted using four varying megasonic power intensities: 20 W/cm2, 10 W/cm2, 5 W/cm2, and no megasonic agitation, respectively.Fig. 6 Physical diagram of the experimental device.

The electrolyte employed in the experiments was a nickel sulfamate solution comprising 90 g/L of nickel ions, 20 g/L of nickel chloride, 30 g/L of boric acid, and 0.5 g/L of sodium dodecyl sulfate. The electrolyte was maintained at a constant temperature of 45 (±1) °C, whilst the pH value was regulated to be within the range of 3.5 to 4.0. The pulsed power supply had a frequency of 5 kHz and a duty cycle of 50 %. The electrodeposition process was conducted at a current density of up to 3 A/dm2 and lasted for 1.5 h. A 10 mm x 10 mm layer of electrodeposited nickel was deposited onto the copper substrate. When the experiments were concluded, the surface micromorphology of the electrodeposited layer was observed with a metallographic microscope (Olympus BX53MRF-S), and the macroscopic morphology within the electrodeposited layer was examined using a physical microscope (Feica LEICA S9i). The surface morphologies of the four samples are shown in Fig. 7.Fig. 7 Surface morphology of electrodeposited layer.

The residual stress within the electrodeposited layer was assessed using the XL-640 X-ray stress detector via the XRD method. The conditions for setting the XRD experiment parameters are shown in Table 2. XRD measurements for residual stress are based on Bragg's law of diffraction, which quantifies the change in grain spacing. Consequently, the residual stress can be determined for the samples.Table 2 XRD experiment parameter setting conditions.

Light source	Scanning method	Peak setting method	Diameter of collimated tube	Acceleration
voltage	Tube
current	Count time	
CuKα	Side-inclination
mode	PearsonVII	1.5 mm	28.0 kV	8.0 mA	8 s	

During the measurement, the Ni(4 2 0) plane was chosen as the diffraction crystal plane. The inclination angle ψ was varied using eight angles: 0°, 15.5°, 22°, 27.5°, 32°, 36.5°, 41°, and 45°. The residual stress is calculated using the equations [27]:(11) σ=-[E/2×(1+ν)]×cotθ0×(π/180)×[∂(2θ)/∂(sin2ψ)]

(12) K=-(E/2(1+ν))×(π/180)×cotθ0

(13) M=∂(2θ)/∂(sin2ψ)

(14) σ=K×M

The stress constant, K, and the slope of the variation of 2θ with respect to sin2ψ, denoted as M, are used in the equation. Here, ψ represents the angle between the normal to the diffraction crystal plane and the normal to the surface of the electrodeposited layer, while 2θ is the Bragg angle measurement corresponding to each ψ angle. Additionally, the equation also includes the elastic modulus of the material, E, the Poisson's ratio, υ, and the Bragg angle measured in the absence of stress, denoted as θ0.

After electrodeposition, the residual stress remains at a constant value for an extended period at normal temperature. From equation (13), it can be concluded that the fundamental challenge in measuring residual stress in the electrodeposited layer using X-ray diffraction (XRD) is the determination of the diffraction angle 2θ corresponding to each ψ angle, which necessitates the measurement of multiple ψ angles. Fig. 8 presents the results of the linear fit of the measurement data obtained under the influence of four distinct megasonic power intensities. The residual stress values for the four electrodeposited samples, calculated via equation (14), are tabulated in Table 3. The residual stress for the sample without megasonic agitation is 151.5 MPa. In contrast, the residual stresses of the samples subjected to varying megasonic agitation power intensities are 113.6 MPa, 94.3 MPa, and 136.9 MPa, respectively. It is evident that the residual stress in the samples assisted by megasonic agitation is lower than that in the unassisted sample. The results demonstrate that the combination of megasonic agitation and coaxial jetting can effectively mitigate the residual stress in the electrodeposited layer. At megasonic power intensities of 5 W/cm2, 10 W/cm2, and 20 W/cm2, the residual stresses are reduced by 25.02 %, 37.75 %, and 9.64 %, respectively, compared to the absence of megasonic assistance. Fig. 9 depicts the trend of residual stress at different power intensity levels. The residual stress in the electrodeposited layer displays a continuous decreasing trend as the megasonic power intensity increases from 0 W/cm2 to 10 W/cm2. However, when compared to the 10 W/cm2 power intensity, the residual stress in the electrodeposited layer increases at the 20 W/cm2 megasonic power intensity. This indicates that there exist optimal parameters for the impact of megasonic vibration on reducing the residual stress in the electrodeposited layer.Fig. 8 Results of linear fitting of measurement data.

Table 3 Results of experimental numerical calculations.

Megasonic intensity W/cm2	Value σ/MPa	
Without megasonic	151.5	
5	113.6	
10	94.3	
20	136.9	

Fig. 9 Trend of residual stress.

4.2 Mechanism analysis

During electrodeposition, megasonic agitation can generate both acoustic streaming and steady-state cavitation effects in the electrolyte [28]. Acoustic streaming enhances the efficiency of lattice dislocation motion of nickel metal within the electroplated layer, thereby modifying the microscopic deformation processes of the metallic material in the layer. When megasonic agitation is combined with coaxial jetting during the electrodeposition process, the force exerted by acoustic streaming on the electrocrystallization of the electrodeposited layer surface acts as a cyclic external force. Nickel atoms undergo cyclic external forces during electrocrystallization, resulting in the formation of a nickel electrodeposited layer [29]. The application of this cyclic external force during electrocrystallization enables the newly deposited atoms to bind more tightly to the surface, leading to a denser structure of the electrodeposited layer in the initial nucleation stage. Furthermore, the external force generated by megasonic agitation increases the collective force acting on dislocations, enabling them to overcome blocking positions and improving the microscopic deformation capability within the lattice. As the acoustic streaming continues, the lattice motion repeats, facilitating ongoing microscopic deformation within the atomic lattice, which in turn reduces residual stress within the electrodeposited layer [30].

Then, the surface roughness was measured using a surface roughness measuring instrument (Johoyd SHT-180). As shown in Fig. 10, the results indicate that the surface roughness of the electrodeposited layer is smallest, with an average value of 0.234 μm, when no megasonic agitation is applied. The average surface roughness of the electrodeposited layer increases to 0.281 μm when the megasonic power intensity is 5 W/cm2. In contrast to the electrodeposited layer with megasonic assistance, the surface of the electrodeposited layer without megasonic agitation appears smooth and dense. This is because, during electrodeposition, small bubbles continuously gather on the cathode surface and form larger bubbles under steady-state cavitation. However, the shear force generated by the acoustic streaming is insufficient to displace the bubbles from the cathode surface, as shown in Fig. 11(b). This results in poor surface quality of the electrodeposited layer and increased roughness. When the megasonic power intensity reaches 10 W/cm2, the surface roughness of the electrodeposited layer increases further. This is due to the fact that the force generated by the acoustic streaming exceeds the adsorption force between the bubbles and the cathode surface. Consequently, the bubbles are discharged from the cathode surface by the force of the acoustic streaming, as illustrated in Fig. 11(c). This process effectively provides stress relief points on the surface of the electrodeposited layer, leading to an increase in surface roughness but a reduction in residual stress. When the megasonic power intensity is increased to 20 W/cm2, the surface roughness of the electrodeposited layer decreases to 0.261 μm. This indicates that the intensity of the acoustic streaming is excessively high at this point, causing a significant number of bubbles to be flushed away from the cathode surface before they can adequately adsorb, as shown in Fig. 11(d). This condition is not conducive to reducing residual stress. Nevertheless, when compared to the case without megasonic agitation (Fig. 11(a)), there still exists the issue of roughness being influenced by the adhesion of a small number of cavitation bubbles.Fig. 10 Electrodeposited layer surface roughness and the trend of variation.

Fig. 11 Bubble changes on the electrodeposited layer under different megasonic power.

The above results show that the residual stress in the electrodeposited layer follows a trend of decreasing and then increasing, and also indicate that megasonic acoustic streaming and steady-state cavitation effect are beneficial in releasing residual stress within the electrodeposited layer.

5 Conclusion

In this paper, a new method combining megasonic agitation with coaxial jet electrodeposition is proposed for enhancing the mass transfer capability of the electrolyte and reducing residual stress in the electroplated layer. On the one hand, the mass transfer of the combined megasonic agitation and coaxial jet electrodeposition process was quantitatively investigated through finite element simulation. The simulation results demonstrate that megasonic agitation can significantly enhance the mass transfer of electrodeposition. Specifically, with megasonic assistance at 20 W/cm2, the mass transfer coefficient increased from 0.452 × 10−7 m/s to 18.63 × 10−7 m/s, compared to the electrodeposition process without megasonic assistance. Therefore, the method of combining megasonic agitation with coaxial jet electrodeposition can significantly improve the electrodeposition process. On the other hand, the properties of the electroplated layer under four different megasonic power densities were investigated through experiments involving the combined megasonic agitation and coaxial jet electrodeposition. The results indicate that this combined method can effectively reduce the residual stress of electrodeposition. In this paper, the best residual stress reduction was achieved at a megasonic power density of 10 W/cm2, with a reduction of 37.75 % compared to the sample without megasonic agitation. This method provides a new reference for reducing the residual stress generated in fabricated metal structure devices, thereby increasing the success rate of device fabrication.

CRediT authorship contribution statement

Ke Zhai: Writing – review & editing, Supervision, Funding acquisition, Conceptualization. Feng Zhou: Writing – original draft, Methodology. Yifan Wang: Investigation, Data curation. Shihao Ma: Validation, Investigation. Lide Fang: Supervision, Project administration. Liqun Du: Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (No. 2022YFB4601602), the Natural Science Foundation of Hebei Province (No. E2022201028).
==== Refs
References

1 Zhang X.M. Li X.C. Ming P.M. Zhang Y.H. Yan L. Qin G. Micro-electroforming high aspect ratio microstructures under magnetic field Microsyst Technol. 25 2019 1401 1411
2 Du L.Q. Zhao M. Wang A. Chen S. Nie W. Fabrication of novel MEMS inertial switch with six layers on a metal substrate Microsyst. Technol. 21 2015 2025 2032
3 Wang F. Liu X. Liu J. Effect of stirring on the defect-free filling of deep throughsilicon vias IEEE Access. 8 2020 108555 108560
4 Dong Y.Z. Jiang B.Y. Drummer D. Zhang L. Mass transfer characteristics at cathode/electrolyte interface during electrodeposition of nickel microcolumns with various aspect ratios J. Micromech. Microeng. 33 2023 105007
5 Zhang H.G. Zhang N. Fang F.Z. Investigation of mass transfer inside micro structures and its effect on replication accuracy in precision micro electroforming Int. J. Mach. Tool. Manuf. 165 2021 103717
6 Zhang H.G. Zhang N. Fang F.Z. Study of ion transportation and electrodeposition under hybrid agitation for electroforming of variable aspect ratios micro structures Precision Eng. 72 2021 122 143
7 Li T.Y. Shen C.J. Zhu Z.W. Li A.X. Xue Z.M. Electroforming of submillimeter scale array structures with a jet-flush mixed flow field J. Manuf. Process. 96 2023 99 109
8 Coleman S. Roy S. Effect of ultrasound on mass transfer during electrodeposition for electrodes separated by a narrow gap Chem Eng Sci. 113 2014 35 44
9 Okoro C. Labie R. Vanstreels K. Franquet A. Gonzalez M. Vandevelde B. Beyne E. Vandepitte D. Verlinden B. Impact of the electrodeposition chemistry used for TSV filling on the microstructural and thermo-mechanical response of Cu J Mater Sci. 46 2011 3868 3882
10 DiBari G.A. Nickel plating Plat. Surf. Finish. 91 2004 23 26
11 Agrawal V. Mitra B. Residual stress tuning in UV-LIGA fabricated microstructures using deposition temperature and reverse pulse plating J Micromech Microeng. 33 2023 034003
12 Cai F. Chen P.F. Zhang S.H. Jiang C.H. Annealing behaviour of electrodeposited Ni–Zr and Ni–Al composite coatings Surf Eng. 35 2019 153 157
13 Sun M.C. Sun Y.H. Wang R.K. The vibratory stress relief of a marine shafting of 35 # bar steel Materi. Lett. 58 2004 299 303
14 Prasad P.B.S.N.V. Vasudevan R. Seshadri S.K. The effect of ultrasonic vibration on nickel electrodeposition Materi. Lett. 17 1993 357 359
15 Zhang L.F. Lu X.C. Busnaina A.A. Non-contact Post-CMP megasonic cleaning of cobalt wafers Mat Sci Semicon Proc. 156 2023 107278
16 Li Y.T. Wang Y. Li H.Y. Jia B. Bai F. Feng J.J. Terahertz rectangular waveguides by UV-LIGA with megasonic agitation Micromachines-Basel. 13 2022 1601 36295954
17 Dähnke S. Swamy K.M. Keil F.J. Modeling of three-dimensional pressure fields in sonochemical reactors with an inhomogeneous density distribution of cavitation bubbles: comparison of theoretical and experimental results Ultrason Sonochem. 6 1999 31 41 11233936
18 K.R. Nightingale, G.E. Trahey, A finite element model for simulating acoustic streaming in cystic breast lesions with experimental validation, IEEE Trans Ultrason Ferroelectrics Freq Contr. 47 (2000) 201-214.
19 Xu Z. Yasuda K. Koda S. Numerical simulation of liquid velocity distribution in a sonochemical reactor Ultrason Sonochem. 20 2013 452 459 22634380
20 Grande W.C. Talbot J.B. Electrodeposition of Thin Films of Nickel-Iron II.Modeling J Electrochem Soc. 140 1993 675
21 Baehr H.D. Stephan K. Heat and Mass Transfer second ed. 2006 Springer Berlin
22 Annesini M.C. Marrelli L. Piemonte V. Turchetti L. Artificial Organ Engineering-Mass transfer 2017 Springer-Verlag London
23 K.R. Nightingale, G.E. Trahey G E. A finite element model for simulating acoustic streaming in cystic breast lesions with experimental validation, IEEE Trans Ultrason Ferroelectr Freq Control. 47(2000) 201-214.
24 Marken F. Akkermans R.P. Compton R.G. Voltammetry in the presence of ultrasound: the limit of acoustic streaming induced diffusion layer thinning and the effect of solvent viscosity J Electroanal Chem. 415 1996 55 63
25 Strusevich N. Desmulliez M.P.Y. Abraham E. Flynn D. Jones T. Patel M. Bailey C. Electroplating for high aspect ratio vias in PCB manufacturing:enhancement capabilities of acoustic streaming Adv Manuf. 1 2013 211 217
26 Zhao M. Du L.Q. Du C.Q. Wei Z.Z. Ji X.C. Bai Z.P. Liu X.Q. Quantitative study of mass transfer in megasonic micro electroforming based on mass transfer coefficient: simulation and experimental validation Electrochim Acta. 297 2019 328 333
27 Song C. Du L.Q. Li X.J. Li Y.Q. Qi L.J. Li Y. Residual stress modeling and analysis for micro electroforming layer Microsyst Technol. 23 2017 4709 4716
28 Liu G. Huang X.L. Xiong Y. Tian Y.C. Fabricating HARMS by using megasonic assisted electroforming Microsyst Technol. 14 2008 1223 1226
29 Nilson R.H. Griffiths S.K. Enhanced transport by acoustic streaming in deep trench-like cavities J. Electrochem. Soc. 149 2002 G286
30 Zhai K. Du L.Q. Wang W.T. Zhu H.Q. Zhao W.J. Zhao W. Research of megasonic electroforming equipment based on the uniformity of electroforming process Ultrason. Sonochem. 42 2018 368 375 29429681
