Robert Tenno

A Method for Microvia-Fill Process Modeling in a Cu Plating System with Additives

A microvia-fill model is formulated for control-design purposes of the via-fill process in 100 m scale. The formulas required to model a Cu–Cu-electrode electroplating system with generic additive-type chemicals in both single-directional and bidirectional processes are given in detail. The model relies on principles familiar from a submicrometer-scale via-filling model known as the curvature-enhanced accelerator accumulation model. Additive coverage is modeled based on a simplified method based on local surface-area computation and an analytical formula for surfactant coverage is given. A galvanostatic control law that does not require computing cell voltage is derived. The model also considers the CuII-ion activity vs CuII-ion concentration. A finite element method-based implementation, applying the arbitrary Lagrange–Eulerian method to compute geometry changes, is tested and compared to via-fill experiment results.

Charge–discharge behaviour of VRLA batteries: model calibration and application for state estimation and failure detection

Abstract The dynamic behaviour of batteries can be predicted using theoretical cell model for basic processes. In this paper, this model is calibrated for two types of valve regulated lead acid (VRLA) batteries, and is applied for viewing unobservable processes in battery by observable processes. It is shown that unobservable parameters like overpotential, reaction rate, porosity, acid concentration, and other parameters of electrode can be evaluated by total current, terminal voltage and temperature of surrounding atmosphere of battery. The calibrated model is applied to distinguish between outwardly equal batteries with different backup time and cut-off time. It is shown that difference in morphology of electrodes, thickness of electrodes and quantity of electrolyte in separator are the main distinguishing parameters between batteries. These parameters can be tested online by current–voltage measurements using fast calculation method proposed in this paper.

An ALE Model for Prediction and Control of the Microvia Fill Process with Two Additives

A computational model for examining the microvia fill process as encountered in the multilayered printed circuit board industry is presented. The model includes mass transfer of both copper and the additive species present. The additives’ mass balance is considered between both the solution and the surface-adsorbed layer of additives, as well as on the shape-changing cathode surface where the mass balance of adsorbed additives is affected by the surface shape change and diffusive mass transfer along the surface. The model is implemented as a finite element model applying the arbitrary Lagrange–Eulerian ALE method for boundary tracking, and a weak formulation of the mass-balance equations is given to aid numerical solution of the model. Model stability and fitting against experimental data is examined over a range of relevant parameters.

Evaluation of VRLA battery under overcharging: model for battery testing

Abstract Theoretical cell model is applied for evaluation of valve-regulated lead–acid batteries under discharge, recharge and overcharge conditions. The previously presented models are improved by introducing a new formula for electrode morphology, applying charging factor to state-of-charge, electrode porosity and acid concentration as well as considering the recombination of oxygen as mass-transport limited evolution process. Also, a new model is proposed for the ohmic resistance of a battery. The modified cell model is calibrated using experimental data. Results show that high prediction accuracy can be obtained for the full discharge–recharge cycle including deep discharge and overcharge. The modified cell model is applied for evaluation of the gas formation processes using externally measured current, voltage and temperature of a battery.

Battery impedance and its relationship to battery characteristics

Impedance of valve-regulated lead-acid batteries is analysed in this paper, using a model-based method. Both double-layer impedance and electrochemical reaction impedance are evaluated, using current, voltage and temperature data measured in experiments. It is shown that the electrochemical impedance is a sensitive indicator that can be utilised to detect small inequalities between batteries while the double-layer impedance is less sensitive.

ELECTROLESS NICKEL PLATING: BATH CONTROL

Abstract In this paper, bath control is proposed for the electroless nickel plating through holes board process. The main parameters of the product (board) – thickness of the plating film and phosphorous content – are stabilized at constant levels using optimal tracking control. The set point for control is calculated from the model in dependence on the current state of the process. The pH-index and nickel percentage are stabilised at time-variable set points using simple feed-forward PI-control that is robust to the loading perturbation.

A Method for Battery Impedance Analysis

A model-based method is proposed for the impedance-spectra analysis of valve-regulated lead-acid batteries. The electrochemical and double-layer processes are analyzed in a wide range of frequencies based on current, voltage, and temperature measurements. Both slow and fast dynamics of the positive and negative electrodes are evaluated. The method is shown to be accurate, enabling the detection of differences in capacity or other parameters even in slightly differing batteries. An exact relation between battery impedance and the electrochemical cell model is established giving useful information on the contribution of different elements and processes on the impedance. The proposed method is computationally effective due to the special analytical formulation developed for impedance analysis. In addition to the basic processes, the method also allows analysis of the fast-rate discharge and overcharge processes.

State and parameter estimation for wastewater treatment processes using a stochastic model

Abstract A stochastic model of the process is introduced on the basis of an IAWPRC-model and the outlet gas formation description. The original nonlinear model is approximated with a bilinear one as a system of stochastic differential equations separated into two parts for observable and unobservable processes. The state estimation problem is formulated and solved using the normal approximation method. The estimation algorithm is obtained in finite-dimensional form. It is tested on simulated and real data. Unknown parameters of the model are evaluated using a two-stage identification procedure for rough and fine estimation. It is demonstrated that the state of biological growth and oxidation processes can be satisfactorily estimated on the basis of indirect measurements.

Microvia fill process model and control

This paper presents an overview of the modeling and model based control of the microvia fill process. A detailed, general-purpose microvia fill model that utilizes the arbitrary Lagrange–Eulerian method for shape change modeling is presented first. Modeling results are presented and compared with the measured data. Then a simplified model of the process is presented followed by a model based control algorithm being developed based on the simplified stochastic model with typical uncertainties induced by unmodelled phenomena and measurement error. The developed control algorithm is analyzed in terms of possible control errors and applied to control the firstly presented microvia fill process model.

A stochastic model for electrodeposition process with applications in filtering and boundary control

Electrodeposition is a complex partially observed mass-transfer process driven by several surface reactions without exact model. In this article, the process uncertainties are described by a finite number of Wiener processes in a stochastic model applied in the filtering and control problems. These problems are solved as a boundary observation-control problem based on a finite diffusion model with uncertainties in the domain interior and on the boundaries. A mixed boundary problem is considered on an interval with the Dirichlet data on one end (bulk solution) and Neumann data on the other end (cathode surface). The concentration of oxidising species in the domain interior is unattainable for observations but the flux on the boundary (electric current) can be measured with a limited accuracy (sensor error). The total flux for the main and side reactions is controlled by the current density on the cathode surface. The disturbing effect of the side reactions is modelled as a noise. The concentration of species is stabilised at the desired level near to the cathode surface with a relatively simple feedback control. The concentration on the boundary and in the domain is estimated as a conditionally Gaussian process in the course of filtering. The estimated conditional mean of concentration is solved from a stochastic partial differential equation in dependence on the covariance kernel. A relatively good quality of estimation and control is demonstrated in the process of simulation in the realistic conditions for a copper deposition process.