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management solutions. The present direct liquid immersion interface significantly reduces thermal resistance, allows for extremely compact packaging, alleviates thermo-mechanical stresses, and is easily scalable. Fig. 1. Immersion cooling of 3D stack in FC-77 using sandwiched solid spreaders arranged in truncated pyramid shape An important aspect of the integration of a 3-D chip stack to the heat sink is the thermal interface between the stack and the heat spreader. This interface is complicated not only by the need to implement a low-resistance thermal interface in a 3-D configuration that includes significant internal and external connections, but also by the need to minimize thermally- and assembly-induced mechanical stresses. 7-9 October 2009, Leuven, Belgium convection is laminar with Gr based on the height of the enclosure (which is the largest value compared to individual heights of the spreaders from the enclosure top surface) was 3x10 6 and Gr based on the lateral extension of each spreader was found to be ~1x10 4 , both of which are
7-9 October 2009, Leuven, Belgium for some cases. Therefore, to save computational time and memory, grids consisting of element count around 18,161 were used for all the simulations. Sudden spikes in the numerical solution (in both velocity and temperature fields), especially at the solid-fluid of the tiers that are closely spaced, resulting in a very narrow gap for the fluid to circulate in the vertical direction. Hence, the only mode of heat transfer is natural convection to the sides in the narrow vertical region between the ends of the tiers and the enclosure, which is weak and results in interface, were dampened by introducing numerical unacceptably high temperatures. It must be noted that for diffusion in the equation system. This was done by this simulation, the geometry setup was assumed to have no manually adding a diffusion coefficient to the electrical connections between two successive tiers as a flow/thermophysical property/diffusivity of the dielectric simplification. fluid. This technique enabled stability and convergence of the solution. Reducing the numerical diffusion coefficient below 0.5 was found to not alter the solution field significantly but allowed substantially large mesh sizes. Therefore, a value of 0.5 was used for numerical diffusion for all the simulations. IV. RESULTS AND DISCUSSION The developed numerical model was used to study the effect of key enabling features on the functionality of the proposed thermal management solution. A. Importance of solid spreaders The effectiveness of sandwiched solid spreaders between the tiers was first studied. Table I gives the material and thermophysical property data used for all the simulations in this paper. Thermophysical properties of the dielectric fluid were considered as functions of temperature [14]. Part TABLE I MATERIAL AND THERMOPHYSICAL PROPERTY DATA Material Thermal Conductivity (W/m.K) Density (kg/m 3 ) Specific Heat (J/kg.K) Substrate FR-4 0.3 1900 1369 IC Si 163 2330 703 Heat Spreader Dielectric Fluid Dielectric Box Heat Sink Base Cu 400 8700 385 FC-77 [14] Dynamic Viscosity (Pa.s) 0.065-8x10 -5 T * 1838-2.45T 1014+1.554T 56.25x10 -5 Cu 400 8700 385 Cu 400 8700 385 Heat Sink Cu 400 8700 385 Solder Bumps Epoxy (to join IC to the Spreader) Pb-Sn 50 Pyroduct ®597A [15] 9 * T is the temperature in 0 C Fig. 4 shows the geometry of the stack enclosure. A maximum allowable chip temperature, T max , of 350 K (77 0 C) was assumed. The maximum chip temperature can be observed as 358 K (at the end of first 300 s) for the dielectric fluid in natural convection. The steady state value was found to be over 400 K. Therefore, natural convection alone was found to be inadequate for effectively removing heat from the tiers. This is because of the horizontal orientation Fig. 4. Natural convection cooling of the 3D stack – geometry and results Following this, the heat transfer in stack integrated with solid spreaders sandwiched between the circuit tiers (Fig. 5) was investigated for comparison. Fig. 5. Immersion cooling of 3D pyramid-structures stack submerged in a dielectric liquid. In Fig. 1, the assumed values are, A=42.5, E=15, F=7.48, G=0.5, H=0.87 and I=1, all in mm. The remaining values are chosen from case V as described in the next subsection. The induced natural convection velocity field between the edges of the stack and the cavity surfaces is shown in Fig. 6. It is remarkable that even though the height of the stack enclosure is only 8 mm, strong natural convection of the FC- 77 is prevalent over the entire fluid domain. This effect is due to the truncated pyramidal arrangement. This is not possible if no spreaders are used, or if all the spreaders have the same size. Fig. 6. The 3D velocity field associated with natural convection of the dielectric fluid Of particular note is a vortical structure that forms near the corner of the cavity. It appears that the appearance of the secondary flow is enabled by the stepwise edge of the pyramid. The recirculating flow results in effective ©<strong>EDA</strong> <strong>Publishing</strong>/THERMINIC 2009 188 ISBN: 978-2-35500-010-2
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International Workshop on THERMal I
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of 75 o C for fair comparison. Only
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