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Numerical Modeling of the Electroplating Process for Microvia Fabrication Nadia Strusevich1, Chris Bailey1, Suzanne Costello2, Mayur Patel1, Marc Desmulliez2 1

School of Computing and Mathematical Sciences, University of Greenwich Old Royal Naval College, Park Row, SE10 9LS, London, UK 2 MIcroSystems Engineering Cenre (MISEC), School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK Emails: {N.Stroussevitch,C.Bailey}@greenwich.ac.uk Figure 1. A principal scheme of ED into a blind via in a plating cell

Abstract For numerical simulation of electrodeposition in small features, we have developed a novel method that allows an explicit tracking of the interface between the electrolyte and the deposited metal. The method is implemented in the CFD package PHYSICA and validated by comparing the delivered simulation results with those achieved by real-life measurements and/or obtained by another piece of software, COMSOL Multiphysics using a standard electrodeposition module. 1. Introduction One of the recognized trends of modern microelectronics is multi-layer (or 3D) packaging of the components placed on several printed circuit boards (PCBs). The research and development in the area of interconnection and packaging is motivated by increasing requirements on performance and reliability of electronic devices and systems, as well as on their miniaturization. The connection between different layers of a package is provided by the so-called vertical interconnect access (via) or feature, which is a hole or cavity in the PCB filled with metal to facilitate conductivity. In this paper, we focus on the blind vias (known as trenches) exposed on one side of the board only. The size of such a via is at the micrometer scale, and it may have a high aspect ratio (AR), i.e., the ratio of the height of the feature to its diameter. The most widely used technique for filling microvias is electrodeposition (ED) of metal (e.g., copper) into a microvia from an electrolyte solution.

Without going into technical details, a typical ED process used in microelectronics can be roughly described as follows. PCBs with predrilled microvias, are immersed into a plating cell, which is a bath filled with an electrolyte solution that contains ions of copper. In the presence of direct electric current, the metal ions are attracted to the panel and are deposited on the sides and bottom of the microvias. Schematically this process is shown in Figure 1. The figure also zooms into a small part of the PCB showing a blind via. We study ED under the basic conditions, assuming that the electrolyte is a still solution with no additives. Although basic ED does not normally guarantee a good filling of high AR microvias, the study of this core process is of considerable importance, since it forms the basis for more advanced and enhanced forms of ED. A microvia can be seen as electroplated successfully if it is completely full, with no internal voids. The pinching of the mouth due to crowding effects closes the via and prevents the replenishing of electrolyte solution. The resulting lack of fluid circulation in the via is further compounded by the depletion in metal ions at the bottom of the blind via, resulting in the formation of voids.

Figure 2. Key dimensions in a trench

Figure 2 illustrates a microvia of radius d and height H. Using this figure we define two metrics that allow us to judge the quality of filling; see [1, 2]. Relative Deposition Thickness (RDT): This parameter represents the ratio of the deposition at the bottom of the via (h3) to the deposition level on the PCB surface (h1) and is defined as RDT=h3/h1. Higher

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values of RDT are an indication of a better quality of filling. Via Fill (VF): is a quantitative measure of via filling that describes the effectiveness of the deposition process. It is a proportion of the filled part of the trench 2 2 and is defined as VF= 1–(d–h2) (H–h3)/d /H. The values of VF closer to 1 correspond to a better quality of filling. Additionally, in our study we use the following characteristic of ED in features: Filling Time (FT): is defined as the time elapsed either till a complete filling of the via or till depletion. Smaller values of FT are preferable. 2. Mathematical and Numerical Modeling of Basic Electrodeposition In our study of basic ED, we consider the process that satisfies the following assumptions: (i) at the cathode, only cupric ions are deposited; (ii) the anode does not change shape during ED; (iii) the physical properties of the electrolyte remain constant; (iv) the activation overpotential η at the cathode is constant; (v) no use of additives or other forms of enhancement is assumed. Two processes are mainly responsible for ion ransport during basic ED: diffusion which is caused by the difference in concentration of cupric ions, and migration which is caused by the electric field, i.e., positively charged cupric ions move towards the negatively charged cathode. Let C denote the concentration of the Cu²⁺ ions and z be their charge. An equation that describes the rate of change of copper concentration in the electrolyte can be derived from the Nerst-Planck equation, and in our case can be written as

where D is diffusivity of cupric ions in the electrolyte, R is the universal gas constant, T is temperature, and F is Faraday's number. The potential difference is computed as the difference of potentials between the anode and the cathode divided by the distance L between them. The value can be taken as constant, since L changes insignificantly during the ED process. Additionally, equation (1) includes a source term RC that represents the amount of deposited moles of copper. Below, we refer to RC as the sink. To compute it, we use Faraday's Law for the deposition rate v given by where Ω is the atomic volume of copper, n is the vector normal to the deposition surface, and i is the current density, i.e., the amperage of the ED current divided by the area of the deposition surface. We follow [3, 4] and throughout this paper apply the following formula for i, which is a version of the Butler-Volmer equation

where i₀ is the initial exchange current density, Cint is the molar concentration at the metal/electrolyte interface, i.e., in the vicinity of the cathode, and C∞ is the concentration in the far field. Besides, α=1.5 is the dimensionless transfer coefficient. Equation (1) is a form of the general transport equation well-known in computational fluid dynamics (CFD). This is a well established area with multiple pieces of software developed for solving the relevant equations. To solve an equation similar to (1) numerically, the domain is split into fairly small nonoverlapping fragments (cells); this process is known as meshing. For each cell, the derivatives are replaced by their discrete analogues. This reduces the original problem described by partial differential equations to a system of algebraic equations. Such a process is known as discretization. A mesh that is used in the Finite Volume Method (FVM) creates polyhedral control volumes (CV). In this paper, we mainly use the cell-centered modification of the FVM. The center of each CV is associated with the values of independent and dependent variables computed as the average value across the whole CV. FVM is currently the most popular method in numerical modelling; see, e.g., [5, 6] The FVM is implemented in the software package PHYSICA, which is a modular suite of components for the simulation of coupled physical phenomena in 3D and time; see, e.g., [7]. A different approach to discretization is implemented in the form of the Finite Element Method (FEM), which the platform that forms a basis of COMSOL Multiphysics, a package that is capable of numerical modelling of various physics phenomena and of combining multiple physical effects. Unlike PHYSICA, the most recent version of COMSOL Multiphysics 4.2a includes the Electrodeposition module. For a purpose of its validation, we compare our results with those obtained using COMSOL, as well as with the real-life measurements, when applicable. 3. Explicit Interface Tracking Method In this section, we present the Explicit Interface Tracking Method for numerical modelling of basic ED in small features, implemented in PHYSICA. Our study of numerical modeling of basic ED is the first stage of a larger project with an ultimate goal of developing computational approaches to handling various forms of enhanced ED. Our choice for an appropriate piece of software and methodology is mainly driven by that ultimate goal. We need a technique that not only allows the user to be permanently aware of the position of the interface between the electrolyte and the deposited metal, but also makes the user able to dynamically prescribe and

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change additional parameters (such as additional flow, acoustic streaming, etc.) to various parts of the changing computational domain. This poses several challenges summarized below: 1. ED is a dynamic process, and in each time step of transient numerical simulation we have to determine concentration of cupric ions in each element of the mesh. Three types of the elements can be distinguished: (i) representing the interface between the electrolyte and solid metal, (ii) representing solid copper, and (iii) representing the electrolyte. During a transient run, the elements change their status, so that we need the corresponding monitoring mechanism. 2. In each time step, for every interface element we determine the amount of solid copper to be added, and this essentially defines the sink RC. To avoid overflow of an element, we need a mechanism for redistributing the excess metal. 3. Designing a monitoring mechanism is especially challenging for complex geometry of the domain, since the inadequate treatment of vulnerable parts of the domain, e.g., corners, will result in distorting information on some undesirable effects (void formation, overcrowding, etc.). 4. Another difficulty of electrodeposition in small trenches is related to the micro scale of the domain, which leads to very small elements of the mesh. To overcome all these difficulties, we have designed and implemented a special method that we call Explicit Interface Tracking Method (EITM) Informally, in the EITM, in each time step we distinguish between three groups of the mesh elements by the use a special variable ψ that shows a portion of a cell filled with solid copper: the interface elements with 0