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January 2016 • The PCB Design Magazine 57 the lower thermal and electrical resistance of the via-in-pad copper. Additionally, most con- ductive materials have higher thermal expan- sion coefficients than copper, which can cause via walls to rupture. For these reasons non-con- ductive fill is typically used in high-volume pro- duction, but as the state of the industry contin- ues to evolve, conductive materials may begin to dramatically outperform non-conductive fill materials without the risk of yield losses. According to first-order heat flow and ther- mal conduction, the primary influencing fac- tors of heat flow from a source to a volume are the distance between source, the cross-section (copper in connection) and the temperature dif- ference between the source and the volume 1 . Equation 1 In which H (Heat) = Q (heat flow)/∆t (seconds), k (Watts/(meter*Kelvin)) = thermal conductivity of the material, A (Area (m 2 ) = area of the cross-section perpendicular to the heat path, ∆T (˚K) = difference in temperature from the IC to the adjoining copper surface, and L(m) = length of the heat flow path While this simple approximation may not appear to solve the current problem, it indicates that in order to transfer more heat, area should be maximized and the length of the path the heat flows through should be minimized. The important relationship for maximizing heat flow is the ratio of cross-section to length of the connecting copper to a surface, such as a copper plane. In Figure 2, the vertical heat transfer is im- pacted by three parallel thermal resistances. Q 1 is the copper that is the wall of the via and it is the most effective at thermal transfer. Q 2 is article ENHANCINg THERMAL PERFoRMANCE oF CSP INTEgRATED CIRCuITS Figure 2: Heat flow paths from CSP device pins to PCB & via-in-pad fill materials.