An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials

Sch. of Mech. Eng., Purdue Univ., West Lafayette, IN
IEEE Transactions on Components and Packaging Technologies (Impact Factor: 0.94). 10/2008; DOI: 10.1109/TCAPT.2008.2001839
Source: IEEE Xplore

ABSTRACT Particulate composites are commonly used in microelectronics applications. One example of such materials is thermal interface materials (TIMs) that are used to reduce the contact resistance between the chip and the heat sink. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30%-80%. Another crucial drawback in the existing analytical as well as the network models is the inability to model size distributions (typically bimodal) of the filler material particles that are obtained as a result of the material manufacturing process. While full-field simulations (using, for instance, the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop an efficient network model that captures the physics of interparticle interactions and allows for random size distributions. Twenty random microstructural arrangements each of Alumina as well as Silver particles in Silicone and Epoxy matrices were generated using an algorithm implemented using a Java language code. The microstructures were evaluated through both full-field simulations as well as the network model. The full-field simulations were carried out using a novel meshless analysis technique developed in the author's (GS) research [26]. In all cases, it is shown that the random network models are accurate to within 5% of the full field simulations. The random network model simulations were efficient since they required two orders of magnitude smaller computation time to complete in comparison to the full field simulation.

1 Bookmark
  • [Show abstract] [Hide abstract]
    ABSTRACT: An innovative approach for electrical chip to substrate and chip to chip interconnects is proposed. The coexistence of solder balls and rails on a chip is discussed, supporting power delivery and heat removal for high-performance flip-chip-onboard and 3D stack applications. The concept enables further bandwidth and current density scaling at a high count of interconnects for signaling, but also at a high solder area fill factor for power delivery and heat removal. The rail-shaped solder joints are also compatible with the current floorplans of microprocessors with voltages arranged in lines. After reflow, solder rails compared to balls can result in a much larger maximal solder width relative to their pads. Therefore, a staggered array arrangement was proposed to minimize shorting risk. In addition, a solder height engineering strategy utilizing modulated pad shapes is discussed to yield equal solder heights for balls and rails present on the same device. However, improper rail design was found to lead to two instability types: 1) Balling and 2) Asymmetric Solder Accumulation. The first is the result of a solder height to width ratio of larger than approximately 0.6 considering long rail lines. The second occurs due to fabrication imperfections. The initial non-symmetric pad/solder shape can cause the accumulation of solder at one rail end (typically the end with the larger area) after reflow. The stability of Bow Tie Rails against Asymmetric Solder Accumulation was investigated to provide design rules for a robust rail design. Accordingly, a solder shape phase diagram indicating the parameters of the three identified phases is compiled. Experimental investigations of reflown solder shapes were complemented with numerical results using a surface energy minimization tool called Surface Evolver. A prediction quality of better than 9% was identified indicating the applicability of the tool to perform solder shape designs. The solver was also capable to predict the men- ioned instabilities, rendering the tool even more valuable. Finally, a thermal interface resistance benchmark of ball and rail-like interconnects is performed in a bulk thermal tester. The rail interface with a solder fill factor of 57% yielded a 7 times reduced interface resistance.
    Electronic Components and Technology Conference (ECTC), 2013 IEEE 63rd; 01/2013
  • [Show abstract] [Hide abstract]
    ABSTRACT: This work presents a methodology implementing random packing of spheres combined with commercial finite element method (FEM) software to optimize the material properties, such as Young’s modulus, Poisson’s ratio, and coefficient of thermal expansion (CTE) of two-phase materials used in electronic packaging. The methodology includes an implementation of a numerical algorithm of random packing of spheres and a technique for creating conformal FEM mesh of a large aggregate of particles embedded in a medium. We explored the random packing of spheres with different diameters using particle generation algorithms coded in MATLAB. The FEM meshes were generated using software MATLAB and TETGEN. After importing the databases of the nodes and elements into commercial FEM software ANSYS, the composite materials with spherical fillers and the polymer matrix were modeled using ANSYS. The effective Young’s modulus, Poisson’s ratio, and CTE along different axes were calculated using ANSYS by applying proper loading and boundary conditions. It was found that the composite material was virtually isotropic. The Young’s modulus and Poisson’s ratio calculated by FEM models were compared to a number of analytical solutions in the literature. For low volume fraction of filler content, the FEM results and analytical solutions agree well. However, for high volume fraction of filler content, there is some discrepancy between FEM and analytical models and also among the analytical models themselves. The discrepancy is attributed to the multi-body interaction effect of the filler particles when they are getting close.
    Journal of Materials Science 01/2011; 46(1):101-107. · 2.31 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Thermal interface materials (TIMs) are particulate composite materials widely used in the microelectronics industry to reduce the thermal resistance between the device and the heat sink. Predictive modeling using fundamental physical principles is critical to developing new TIMs, since it can be used to quantify the effect of polydispersivity, volume fraction and arrangements on the effective thermal conductivity. A random network model that can efficiently capture the near-percolation transport in these particle-filled systems was developed by the authors, which can take into account the interparticle interactions and random size distributions. In this paper, a Java-based code is used to generate the microstructures at different volume fraction and different particle-size distribution (PSD). COMSOL was used to investigate the impact of polydispersivity on the effective thermal conductivity of particulate TIMs. The log-normal distribution was used to capture the filler PSD. From the simulation results, there exists an optimum value of the polydispersivity which has the largest thermal conductivity for a given volume fraction.
    IEEE Transactions on Components, Packaging, and Manufacturing Technology 01/2013; 3(12):2068-2074. · 1.26 Impact Factor