Model Identification for Adsorption Dynamics and Suppression Effect of Polyethylene Glycol Using Inverse Analysis Approach
Authors: Ishii Tsubasa , Amaya Kenji , Onishi Yuki 
Published: February 2020

Cu electroplating is important in LSI manufacturing. In the manufacturing process, some additives are added to a copper sulfate solution. The additive that reduces a deposition rate is called suppressor. Polyethylene Glycol (PEG) has been actively studied as a typical suppressor. PEG adsorbs to the electrode in the presence of a chloride ion and suppresses the deposition rate. The dynamics of adsorption and the mechanism of the suppression effect have been studied, and various mathematical models have been proposed from these results. However, the phenomena have not been perfectly understood and the conventional mathematical models cannot fully reproduce these phenomena.[1]
Voltammetry is often performed to observe the behavior of the additives. The rotating disc electrode(RDE) is used in order to control the concentration on the electrode surface. The RDE can control and evaluate the concentration on the electrode surface under the assumption for uniform distribution of concentration and current density on the electrode surface. However, it is observed that the adsorption of PEG occurs non-uniformly on the electrode surface.[2] The voltammogram show dynamics of the current density averaged on the working electrode. It is important to know the local current density and its distribution on the working electrode in order to understand the adsorption dynamics of PEG and the suppression of copper deposition.
On the other hand, “Inverse Problems” have attracted attention due to the development of numerical simulation. Inverse Problems is a research area dealing with finding out unknown information from external or indirect observation through a system model. In the fields of electrochemical engineering, there are many problems which can have a benefit from the inverse analysis approach.
Using an approach of the Inverse Problems, we identify the current density distribution on the electrode surface. Currents are measured by changing potential and PEG concentration with an electrochemical flow cell. Observation data such as potential, bulk concentration, average flow velocity, and current are used for the inverse analysis. From these observation data, we identify the current density distribution with estimating the models that represent the adsorption
dynamics of PEG and the suppression effect of the copper deposition. The figure shows a procedure of the inverse analysis method. The method consists of an experiment and a numerical simulation as shown.
In the experiment, observation data are obtained with the electrochemical flow cell. The experimental system consists of two solution supply devices and the electrochemical flow cell.The solution supply device can arbitrarily control a flow rate of the solution supplied to the flow cell. Copper sulfate solutions with different concentrations of PEG are prepared for the solution supply devices. The experimental system can continuously change PEG concentration supplied to the flow cell by changing a mixing ratio of the two solutions. Currents are measured with a linear sweep of potential under constant PEG concentration and a linear sweep of PEG concentration under constant potential. Potential, concentration, average flow velocity, and current are obtained as observation data.
In the numerical simulation, the adsorption dynamics of PEG and the suppression of copper deposition are treated in order to express the phenomena related to PEG. Surface coverage of PEG is introduced to express the adsorption dynamics. In this study, the dynamics of the surface coverage is represented by a piecewise linear function with current density, PEG concentration, and surface coverage. The suppression of copper deposition is expressed by the piecewise linear function with surface coverage, copper ion concentration, potential.
A velocity field is modeled by the Navier-Stokes equation, and concentration fields of copper ion and PEG are modeled by the advection-diffusion equation. Boundary conditions of the advection-diffusion equation at the electrode are given by the models representing the adsorption dynamics of PEG and the suppression effect of copper deposition. The current density distribution on the electrode surface is evaluated with solving the advection-diffusion equation.
The numerical simulation described above can be performed by assuming the parameters of these models. Currents are calculated with solving the advection-diffusion equation under the same potential, concentration, and average flow velocity as the experiment. The parameters of the models can be obtained by minimizing the residual between measured and calculated currents with a nonlinear least squares method. After the model is identified, the current
density distribution on the electrodes is easily calculated by the direct analysis.
[1]Liu Yang, Aleksandar Radisic, Johan Deconinck, and Philippe M. Vereeckena; J. Electrochem. Soc., 161(5) D269-D276(2014)
[2]D. Josell and T. P. Moffat; J. Electrochem. Soc., 163(7) D322-D331(2016)

Figure 1