Research Papers

Modeling Thermal Microspreading Resistance in Via Arrays

[+] Author and Article Information
Michael Fish

Department of Mechanical Engineering,
Clark School of Engineering,
University of Maryland,
College Park, MD 20742
e-mail: mcfish@umd.edu

Patrick McCluskey

Department of Mechanical Engineering,
Clark School of Engineering,
University of Maryland,
College Park, MD 20742
e-mail: mcclupa@umd.edu

Avram Bar-Cohen

Department of Mechanical Engineering,
Clark School of Engineering,
University of Maryland,
College Park, MD 20742
e-mail: abc@umd.edu

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received September 25, 2015; final manuscript received December 17, 2015; published online March 11, 2016. Assoc. Editor: Xiaobing Luo.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Electron. Packag 138(1), 010909 (Mar 11, 2016) (9 pages) Paper No: EP-15-1097; doi: 10.1115/1.4032348 History: Received September 25, 2015; Revised December 17, 2015

As thermal management techniques for three-dimensional (3D) chip stacks and other high-power density electronic packages continue to evolve, interest in the thermal pathways across substrates containing a multitude of conductive vias has increased. To reduce the computational costs and time in the thermal analysis of through-layer via (TXV) structures, much research to date has focused on defining effective anisotropic thermal properties for a pseudohomogeneous medium using isothermal boundary conditions. While such an approach eliminates the need to model heat flow through individual vias, the resulting properties are found to depend on the specific boundary conditions applied to a unit TXV cell. More specifically, effective properties based on isothermal boundary conditions fail to capture the local “microspreading” resistance associated with more realistic heat flux distributions and local hot spots on the surface of these substrates. This work assesses how the thermal microspreading resistance present in arrays of vias in interposers, substrates, and other package components can be properly incorporated into the modeling of these arrays. We present the conditions under which spreading resistance plays a major role in determining the thermal characteristics of a via array and propose methods by which designers can both account for the effects of microspreading resistance and mitigate its contribution to the overall thermal behavior of such substrate–via systems. Finite element modeling (FEM) of TXV unit cells is performed using commercial simulation software (ansys).

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Fig. 1

Via unit cells. From left to right: (a) TSV cell as used in Ref. [8], showing the many features that can appear in a TXV array, (b) Cu–glass via cell used to investigate boundary conditions, and (c) Cu–glass cell for investigating the contribution of films

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Fig. 2

Heat flux vectors at a vertical cross section of a unit cell. The top and bottom faces of the cell have constant flux boundary conditions of the same magnitude. The midplane contains an isotherm, as evidenced by the parallel flux vectors there. Units are in W/m2.

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Fig. 3

Unit cell for investigating convection boundary condition. The lateral dimensions and materials are held constant, while the top boundary condition and substrate thickness are varied. Due to symmetry, a quarter-cell is modeled in practice.

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Fig. 4

Dependence of keff,z on substrate thickness and applied heat transfer coefficient

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Fig. 5

Via cell total thermal resistance, calculated from FEM. Related to keff,z data presented in Fig. 4 by Eq. (7). Cells in the “thick substrate” regime have converged to a linear asymptote unique to each h. Three high h datasets are not plotted for clarity.

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Fig. 6

Microspreading resistance of thick TXV substrates. Each point is the intercept of the linear asymptote for datasets of the type in Fig. 5 (there were three not included for clarity). The curve is the correlation given by Eq. (10).

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Fig. 7

Unit cell for investigating the effect of material contact. Lateral dimensions, via, and substrate material are held constant. Film conductivity and substrate thickness are varied. After demonstrating the limiting case of thick films, film thickness and the varying upper boundary are held constant.

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Fig. 8

Evolution of keff,z of a TXV array as an adhered film increases in thickness. Film conductivity is 40 W/m K, and substrate thickness is 200 μm.

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Fig. 9

keff,z versus contacting material thermal conductivity for different substrate/cell thicknesses

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Fig. 10

Microspreading resistance versus contacting material conductivity. Each point is obtained from FEM data in Fig. 9. The curve is the correlation given by Eq. (11).

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Fig. 11

Maximum cell spreading resistance as a function of nondimensional via diameter and conductivity

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Fig. 12

Value of the discount factor, f, for all 1200 axisymmetric cells. The points that fall farthest from the curve are those cells with the smallest via diameters. Circles correspond to the convection boundary condition, while diamonds correspond to film contact.

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Fig. 13

Detail view of data in Fig. 12, with ± 15% bounds on ζ plotted. Cells with (d/P*)< 0.18 are excluded.




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