Printed Circuit Design & Fab - November 2007 - (Page 28)

PLATING Volume Flow Rate (cubic in/min) 0.0040 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 Flow Rate Hole Diameter=14 mils AR=5 AR=10 AR=15 Figure 4 u • w Control Volume 1 dx 0 5 10 Agitation Velocity (ft/min) 15 FIGURE 4. Plating fluid is shown moving through the PTH. FIGURE 2. Agitation velocity impacts flow rate more significantly than aspect ratio. Flow Rate for V=10 Ft/Min 0.0040 0.0035 AR=5 AR=10 AR=15 dP dx = ΔP l = 1 / 2 ρ V2 l (Eq. 4) Flow rate (cubic in/min) 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0 5 V is the speed of the plating fluid relative to the surface being plated and the density. The numerator is often referred to as the dynamic pressure and is the pressure component associated with a moving fluid. The volume flow rate is: Q= or Q= π π r 4 u0 µ (− dP dx ) (Eq. 5) D3 V 2 Aυ 16 (Eq. 6) 10 15 20 Hole Diameter (mils) FIGURE 3. Hole diameter impacts flow rate more significantly than aspect ratio. The numerical value of the Reynolds Number in this case is: R=2.6 It is generally accepted that the flow will be laminar, as opposed to turbulent, for a Reynolds Number less than 2300. Keep in mind that the Reynolds Number is a point function, and the flow can vary between laminar and turbulent over a very small distance. where A is the aspect ratio of the hole. It is desirable to maximize the volume flow rate. Conventional wisdom has been that the volume flow rate is inversely proportional to the aspect ratio, which is in agreement with the analysis. Even more important is the hole diameter, which has a super linear impact on the volume flow rate and explains why small holes are difficult to plate even at relatively low aspect ratios. It is also seen that the relative velocity or agitation speed also plays a super linear role. These effects are shown in FIGURES 2 and 3. In summary, while the aspect ratio is a very important parameter in defining the flow rate in a hole, both the hole diameter and the agitation speed are even more significant. Electroplating Issues The Governing Equations of Fluid Mechanics In this case, as depicted in FIGURE 1, plating fluid passes through a through hole and is governed by equations known as the Navier-Stokes equations. When adapted to the case at hand, the result1 is expressed as seen in the following equation: u=− 1 4µ dp dx (r 2 − y 2 ) The next step in this analysis is to combine the laws of electrochemistry into the above analysis. The physics of electroplating were first developed by Faraday. According to Effect of Aspect Ratio 1 Plating Ratio (Barrel/Surface) 0 0.1 0.05 0.1 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 (Eq. 2) r is the radius of the hole and y the radial distance from the center of the hole to some position in the flow. The mean velocity (u0), which will become of great importance in the next section on electroplating, is u0 = r2 8µ (− dP dx ) (Eq. 3) 0.01 AR=14 0.001 AR=10 AR=6 0.0001 Position in Barrel, x/l (%) where µ is the viscosity and FIGURE 5. Effect of aspect ratio and hole diameter on plating thickness. NOVEMBER 2007 28 PRINTED CIRCUIT DESIGN & FAB

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Printed Circuit Design & Fab - November 2007

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