Numerical calculation of the electric field in an electroplating bath with bipolar electrodes

Litovka, Yu. V.; Mikheev, V. V.

doi:10.1134/s0040579506030110

Cited by 9 publications

(5 citation statements)

References 1 publication

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“…The obtained results confirm the effectiveness of the applied numerical method: the quadratic convergence rate of Newton's method gives a 10‐fold time gain in comparison with one of the best numerical methods for this type of problem (the iterative method described in references 3,4,8). The voltage value U а has little effect on the computation time.…”

Section: Resultssupporting

confidence: 67%

“…To test the effectiveness of the developed algorithm, the same example was calculated by the method of simple iterations using the upper relaxation method with sweeping along the line. 3,4,8 Calculation time for an example Figure 3: the relaxation method: 10.04 minutes; our proposed method: 1.11 minutes. Calculation time for an example Figure 4: the relaxation method: 48.51 minutes; our proposed method: 5.34 minutes.…”

Section: The Results Of the Calculationsmentioning

confidence: 99%

“…Laplace's equation with nonlinear boundary conditions described in references 3,4 is used for mathematical modeling of the distribution of metal deposited on the cathode surface, taking into account polarization, due to which additional resistance arises. For overcome this resistance, it is required to increase the voltage supplied to the electroplating bath (overvoltage).…”

Section: Introductionmentioning

confidence: 99%

“…The finite difference method, 5 the finite element method, 6 the Green's functions method, 7 and others can be used to solve the model equations. For satisfy the desired functions of nonlinear boundary conditions, the authors 3,4 used a combination of the upper relaxation method with sweep along a row and an additional iterative procedure that provides the fulfillment of the boundary conditions with a given accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of metal distribution when coating flat metal plates in electroplating baths

Pchelintseva

Pchelintsev

Litovka

2020

Int J Numerical Modelling

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Electrolytic metal coating processes are used to protect products from corrosion, decorative surface finish and other purposes. Electroplated coating has an important quantitative characteristic, which is coating thickness. Since the electric field in the electrolyte is not uniform, the coating thickness at different points on the surface of detail is different. An important task here is to apply a more uniform coating. To solve this problem, it is necessary to calculate the distribution of potentials in a galvanic bath from Laplace's equation. The study aims to increase the convergence rate of the numerical procedure in order to solve Laplace's equation with nonlinear boundary conditions by developing a numerical scheme based on Newton's method. Based on a numerical solution of Laplace's equation with nonlinear boundary conditions describing the potential distribution in a galvanic bath, the thickness of the nickel deposition layer on the surface of a flat metal cathode plate was calculated for different sizes of galvanic baths and anode voltages. A feature of the numerical calculation scheme is the use of Newton's method for the approximate solution of the resulting system of nonlinear algebraic equations with a given accuracy. The obtained results show the effectiveness of the applied numerical method: the quadratic convergence rate of Newton's method gives a time gain of 10 times in comparison with one of the best numerical methods for this type of problem.

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Section: Resultssupporting

confidence: 67%

Section: The Results Of the Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling of metal distribution when coating flat metal plates in electroplating baths

Pchelintseva

Pchelintsev

Litovka

2020

Int J Numerical Modelling

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“…There are several methods to simulate the electroplating process: numerical [4] , analytical [5] and finite element method [6] . Finite element method has its verified unique advantages in electric field simulation for different geometries.…”

Section: Introductionmentioning

confidence: 99%

Study on non-uniformity of Through-Mask electroplated Ni thin-film

Wang

Liu

Mao

et al. 2008

2008 International Conference on Electronic Packaging Technology &Amp; High Density Packaging

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Through-Mask Electroplating has been widely used in the fabrication of chips, BGA substrates and PCBs etc. The uniformity of plating thin-film is the major factor contributed to the reliability of the products. Currently, it is usually by setting optimum plating parameters and adopting electrochemical method to achieve the uniformity of plating. However, the problem of non-uniform distribution of electric field, which is the major cause of the non-uniformity of the plating thin-film, has not been solved. In this paper, Finite Element Method (FEM) was developed to analyze the nonuniform distribution of electric field under different conditions in the process of electroplating. The results show that different thickness of photo-resist and size of electroplating cell are two major factors contribute to the uniformity of plating thin-film. The uniform of electroplating cell can be improved by adding in-chip auxiliary electrode. Also better uniformity of the plating film in radial direction can achieved by setting a shield in the proper position of the plating solution and annular out-chip auxiliary electrode (Cu) around the wafer. The simulation results were consistent with experimental results, which proved that Finite Element Method is an effect way to simulate the electroplating process.

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Asymmetric bipolar electrochemistry: Detailed empirical description and determination of output characteristics of a galvanic system with multiple short-circuited cells in one electrolyte

Lacina

Kazda

Syrový

et al. 2019

Electrochimica Acta

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Numerical calculation of the electric field in an electroplating bath with bipolar electrodes

Cited by 9 publications

References 1 publication

Modeling of metal distribution when coating flat metal plates in electroplating baths

Modeling of metal distribution when coating flat metal plates in electroplating baths

Study on non-uniformity of Through-Mask electroplated Ni thin-film

Asymmetric bipolar electrochemistry: Detailed empirical description and determination of output characteristics of a galvanic system with multiple short-circuited cells in one electrolyte

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