NDLI: Pin-shape assessment for interlayer-cooled chip stacks with periodic boundary condition modeling

Content Provider	IEEE Xplore Digital Library
Author	Toral, G. Bender, R. Leblebici, Y. Brunschwiler, T.
Copyright Year	2010
Description	Author affiliation: ANSYS Germany GmbH, Staudenfeldweg 12, 83624 Otterfing, Germany (Bender, R.) \|\| Swiss Federal Institute of Technology in Lausanne (EPFL), Microelectronic Systems Laboratory, 1015 Lausanne, Switzerland (Toral, G.; Leblebici, Y.) \|\| IBM Research - Zurich, 8803 Rüschlikon, Switzerland (Brunschwiler, T.)
Abstract	Volumetric heat removal in high-performance 3D chip stacks can be performed by means of interlayer cooling. The heat is absorbed in water, which is pumped in the liquid phase into the cavities between the active layers. Individual through-silicon vias (TSV), which maintain the electrical communication between the layers, are embedded into silicon pins in the fluid cavity. Thousands of these TSVs are arranged on an equidistant grid. The mass transfer and consequently the heat removal strongly depend on the silicon pin-shape, which were assessed in this study. To predict the temperature field in a 3D chip-stack multi-scale, modeling approaches were proposed [6, 7, 8]. In a detailed subdomain model of the fluid cavity, the characteristic parameters, such as permeability and convective thermal resistance, are derived from a conjugate heat and masstransfer analysis. Thanks to the periodic arrangement of the pin fins only one unit cell with periodic hydrodynamic and thermal boundary conditions has to be modeled. Unfortunately, commercial computational fluid dynamics (CFD) solvers only provide periodic hydrodynamic boundary conditions. Therefore we demonstrate the implementation of periodic thermal boundary conditions for cases with imposed heat flux. At the fluid boundaries only convective energy transport is considered, whereas at the solid boundaries heat conduction is implemented. User Fortran routines are used to fetch and interpolate fluid temperature fields from the fluid outlet to the inlet, whereby the temperature gained within the unit cell is subtracted. The heat flux at the solid boundary is adjusted in a control loop with respect to the average fluid outlet to inlet temperature difference. These routines are called in the solver loop. Therefore the model only has to converge once. Compared with the classical approach with nonperiodic boundary conditions but multiple unit cells, a speed-up factor of 30 with a difference of at most 2 % could be obtained. Using this method, we computed the permeability and convective thermal resistance of circular, square, super-elliptic, and drop-shaped pins, with a pitch and height of 100 µm and a pressure gradient range of $1×10^{6}$ to $1×10^{7}$ Pa/m. The results are also compared with those obtained for parallel plates as well as with microchannel parameters derived from correlations. A pin-shape assessment was then performed for realistic fluid-cavity dimensions at a varying power map contrast. The “channel-walk-method” was used to define the maximum junction temperature for a given pressure drop and pin shape. For a peak-to-background heat-flux ratio of 1.5, the fluid temperature increase dominates the thermal budget. Therefore heat-transfer geometries with high permeability, such as parallel plates, perform best. At a higher heat-flux contrast of 5, the temperature increase caused by the convective thermal resistance at hotspot locations becomes significant. We could show that in this case drop-shaped pins, which offer a trade-off in terms of permeability and convective thermal resistance are superior.
Starting Page	1
Ending Page	10
File Size	1531716
Page Count	10
File Format	PDF
ISBN	9781424484539
e-ISBN	9782355000126
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-10-06
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	EDA Publishing
Subject Keyword	Fluids Thermal resistance Computational modeling Heating Solids Cavity resonators
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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