Printed Circuit Design & Fab - November 2007 - (Page 27)

PLATING The Fluid Mechanic Modeling of PCB PLATING SOLUTIONS Aspect ratio is important in defining the flow rate through a hole, but hole diameter and the agitation speed are equally significant. by J. LEE PARKER It has been the conventional wisdom of the industry that the predominant board parameter associated with through-hole plating is the aspect ratio. While this is intuitively understandable, very little has been done to analytically verify the assertion. This paper will explore this hypothesis by developing a first principle flow model using the Navier-Stokes analog for viscous fluids. The first concern is to define the proper flow regime – laminar or turbulent – based on the Reynolds Number associated with the process. Once this is established, a proper mathematical model can then be identified. At that point, the governing equations are parameterized and the crucial parameters identified. Faraday’s Law will then be folded into the model to define an algebraic model for electrolytic plating. Finally, an order of magnitude analysis is presented to determine the relative importance of the critical parameters. it is well accepted that the aspect ratio of the through hole plays an important role in the process, but it is not understood if the impact is linear, sub-linear or super linear. This analysis will provide that insight. First, the flow regime – turbulent or laminar – will be determined followed by development of the governing equations describing the fluid mechanics of the plating process. This will then be coupled with the governing laws of electroplating (Faraday’s second law) to complete the analog. Flow Regime The flow regime is determined by the dimensionless Reynolds Number. For the case at hand, a good and well-developed analogy is the flow in a linear pipe. This type of flow is referred to as Hagen-Poiseuille Flow, and the Reynolds Number is given by: R= u0 υ Introduction The theory of through-hole plating has evolved primarily from anecdotal and empirical evidence as well as hearsay. Very little has been forthcoming to present a defendable mathematical analysis of the process. Doing so will require combining the physics of fluid mechanics and electrochemistry. The importance of such an analog is to both identify the parameters that govern the process, as well as the degree to which a particular variable impacts the process. For instance, Y X P- ΔP l PTH u V0 Io C o P d (Eq. 1) Where and for our purposes: u0 is the mean velocity of the fluid in the hole (we will use 10 ft./min. to maximize the Reynolds Number) d is the diameter (we will use 30 mils to again maximize the Reynolds Number) v is the kinematic viscosity (for most acids 0.00016 ft.2/sec.) A = 10 Hole diameter = 18 mils c 0 = 140 g/ft 3 V0 = • 8 ft/min w )s = 0 .0001 g/sec χ = 0.0367 ft 3 /g FIGURE 1. When plating fluid passes through a through hole, it is governed by the Navier-Stokes equations. NOVEMBER 2007 TABLE 1. Based line parameters. PRINTED CIRCUIT DESIGN & FAB 27

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Printed Circuit Design & Fab - November 2007

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