S. Kanuparthi

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

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 authors (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.

Random network percolation models for particulate thermal interface materials

Thermal interface materials (TIMs) are widely used in the microelectronics industry to adequately expel the waste heat generated in the chips, by reducing the contact resistance between the chip and the heat sink. A critical need in developing these TIMs is apriori modeling using fundamental physical principles to predict the effect of particle volume fraction and arrangements on effective behavior. Such models enables one to optimize the structure and arrangement of the material. The existing analytical descriptions of thermal transport in particulate systems under predict (as compared to the experimentally observed values) the effective thermal conductivity since these models do not accurately account for the effect of inter-particle interactions, especially when particle volume fractions approach the percolation limits of approximately 50% - 60%. Another crucial drawback in the existing analytical as well as the network models is the inability to model random size distributions of the filler material particles, which is what one obtains when particulates are produced. While mil-field simulations (using the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop efficient network models that capture the inter-particle interactions and also allow random size distributions. Fifteen microstructural arrangements of alumina as well as aluminum particles in silicone matrix were first experimentally characterized. Microstructures that are representative of the experimentally tested systems were simulated using a drop-fall-shake algorithm implemented in Java. Thirty such microstructural arrangements were evaluated through both full field simulations as well as the network models. In all cases, it is shown that the full-field simulations of effective behavior are accurate to within 10% of the experimentally measured values and the random network models are accurate to within 10% of the full field simulations. The random network models were efficient since they required a few minutes to run, while the full field simulations required 4-5 hours on an average to complete

Full-Field Simulations of Particulate Thermal Interface Materials: Separating the Effects of Random Distribution from Interfacial Resistance

The effective behavior of particulate thermal interface materials depend, in addition to particle/matrix conductivities and volume loading of the particles, on the randomness of distribution, on the randomness of the size as well as on the interfacial thermal resistance between the particles and matrix. However, the relative contributions of these effects have not been identified in the literature with sufficient clarity owing to a lack of realistic simulations of these systems. In this paper we present a computationally efficient analysis procedure to simulate realistic three-dimensional microstructures of thermal interface materials. The computational procedure is based on constructing complex behavioral fields through Boolean operations (compositions) on primitive fields. It is demonstrated that the Boolean operations and an associated meshless implementation efficiently model topological changes caused by the modification/rearrangement of the second phases in the heterogeneous material microstructure. The developed method was applied to evaluate the effective thermal conductivity of the thermal interface material. Thirty three-dimensional simulations of random arrangements of the heterogeneous microstructure at a fixed 58% volume fraction were carried out. The microstructures were systematically characterized using void nearest surface exclusion probability functions. The results of the simulation range within 10% of the fifteen experimentally measured values of an identically constituted system. We demonstrate that in the absence of simulations of realistic microstructures, non-physical thermal interface resistance values may have to be assumed to describe the effect of random distributions of particles

The Effect of Polydispersivity on the Thermal Conductivity of Particulate Thermal Interface Materials

A critical need in developing thermal interface materials (TIMs) is an understanding of the effect of particle/matrix conductivities, volume loading of the particles, the size distribution, and the random arrangement of the particles in the matrix on the homogenized thermal conductivity. Commonly, TIM systems contain random spatial distributions of particles of a polydisperse (usually bimodal) nature. A detailed analysis of the microstructural characteristics that influence the effective thermal conductivity of TIMs is the goal of this paper. Random microstructural arrangements consisting of lognormal size-distributions of alumina particles in silicone matrix were generated using a drop-fall-shake algorithm. The generated microstructures were statistically characterized using the matrix-exclusion probability function. The filler particle volume loading was varied over a range of 40%-55%. For a given filler volume loading, the effect of polydispersivity in the microstructures was captured by varying the standard deviation(s) of the filler particle size distribution function. For each particle arrangement, the effective thermal conductivity of the microstructures was evaluated through numerical simulations using a network model previously developed by the authors. Counter to expectation, increased polydispersivity was observed to increase the effective conductivity up to a volume loading of 50%. However, at a volume loading of 55%, beyond a limiting standard deviation of 0.9, the effective thermal conductivity decreased with increased standard deviation suggesting that the observed effects are a tradeoff between resistance to transport through the particles versus transport through the interparticle matrix gap in a percolation chain.

Impact of heatsink attach loading on FCBGA package thermal performance

Flip-Chip Ball Grid Array (FCBGA) packages are prevalent in wide range of electronics applications including gaming consoles, mobile gadgets, telecommunications etc. The microelectronics industry is actively shifting towards smaller node sizes (32 nm, 28 nm etc.) and integrating multiple functionalities onto the die. This in turn increases the die power levels and more importantly drastically increases the die heat-flux densities. External heatsinks are typically needed in order to support high thermal power dissipation. The focus of this paper is to understand and quantify the impact of heatsink tilt on board-level thermal performance. her This in turn impacts the overall thermal performance as higher TIM-II bond line thickness results in greater thermal resistance. For high power applications (>;50W) wherein the desired system thermal resistances are very low (θja <; 1 C/W), controlling the TIM-II thermal resistance is critical to achieve an overall low system thermal resistance. Experimental measurements were performed using a high power FCBGA thermal test vehicle (TTV). The scope of this study includes performing thermal measurements to -level thermal understand the impact of the following on board performance: 1. Package type: Bare Die FCBGA, Molded FCBGA & Lidded FCBGA 2. Impact of uneven heat-sink loading A novel method for characterizing TIM-II thickness variation is presented in this work. Upon characterizing the TIM-II BLT thickness variation, experimental measurements were performed to quantify the impact on the board-level thermal performance. Finally, merit analysis of the various package types in achieving low overall package thermal resistance will be presented.

Hierarchical Modeling and Trade-Off Studies in Design of Thermal Interface Materials

Particle laden polymer composites are widely used as thermal interface materials in the electronics cooling industry. The projected small chip-sizes and high power applications in the near future demand higher values of effective thermal conductivity of the thermal interface materials (TIMs) used between the chip and the heat-spreader and the heat-spreader and heat-sink. However, over two decades of research has not yielded materials with significantly improved effective thermal conductivities. A critical need in developing these TIMs is apriori modeling using fundamental physical principles to predict the effect of particle volume fraction and arrangements on effective behavior. Such a model will enable one to optimize the structure and arrangement of the material. The existing analytical descriptions of thermal transport in particulate systems under predict (as compared to the experimentally observed values) the effective thermal conductivity since these models do not accurately account for the effect of inter-particle interactions, especially when particle volume fractions approach the percolation limits of approximately 60%. Most existing theories are observed to be accurate when filler material volume fractions are less than 30–35%. In this paper, we present a hierarchical, meshless, computational procedure for creating complex microstructures, explicitly analyzing their effective thermal behavior, and mathematically optimizing particle sizes and arrangements. A newly developed object-oriented symbolic, java language framework termed jNURBS implementing the developed procedure is used to generate and analyze representative random microstructures of the TIMs.Copyright

BLT control and its impact on FCBGA thermal performance

The performance of high power packages is limited in part by the interfacial resistance between the die and lid or heat sinks. The thermal resistance depends on the shape of mating surfaces, bondline thickness (BLT) of the thermal interface material (TIM), bulk thermal conductivity and contact resistance. This paper focuses on warpage modeling methods to predict the local variation of TIMs and its impact on thermal resistance as a function of assembly processes. Experimental data and simulations show that when packages are soldered to the motherboard, they tend to have less warpage than unmounted packages. A 17% reduction in thermal resistance was predicted for a bare die package once soldered to the mother board. Close agreement between warpage simulations and experimental measurements is observed.

The Study of the Polydispersivity Effect on the Thermal Conductivity of Particulate Thermal Interface Materials by Finite Element Method

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.

Thermal performance of FC M BGA: Exposed molded die compared to lidded package

Thermal resistance data were collected using two different style flip chip ball grid array (FCBGA) packages; one with an exposed molded die and a second with a lid. Eleven different heat sink designs and two different thermal interface materials (TIM) were tested to quantify the thermal interaction between heat sink size, base material and TIM resistance as a function of package style. Package style and TIM material did not appreciably change the total thermal resistance (less than 10%) for small heat sinks 50mm × 50mm smaller. The exposed molded die package thermal resistance was 14% smaller than the lidded package when tested with a heat pipe heat sink. An understanding of the long term performance impact of TIM II degradation was investigated using conduction based models. Lidded style packages may increase safety margin when TIM II materials experience pump-out, dry-out or voiding.

Microstructural characteristics influencing the effective thermal conductivity of particulate thermal interface materials

Particle laden polymer composites are widely used as thermal interface materials (TIMs) in the electronics cooling industry. A critical need in developing TIMs is apriori modeling from first principles to predict the effect of particle volume fraction and arrangements. This in turn will help optimize the material. In general, TIM systems contain random distributions of particles of a polydisperse (usually bimodal) nature. In addition to particle/matrix conductivities and volume loading of the particles in the matrix, the size distribution and the random arrangement of the particles in the matrix play an important role in determining the effective thermal conductivity of TIMs. A detailed analysis of the microstructural characteristics that influence the effective thermal conductivity of TIMs is presented in this paper. Random microstructural arrangements consisting of lognormal size-distributions of alumina particles in silicone matrix were generated using an algorithm implemented using a Java language code. The generated microstructures were statistically characterized using matrix-exclusion probability function. The filler particle volume loading was varied over a range of 40-55 %. For a given filler volume loading, the effect of polydispersivity in the microstructures was captured by varying the standard deviation(s) parameter in the lognormal filler particle size distribution function. The effective thermal conductivity of the microstructures was evaluated through simulations using a network model (previously developed by the authors). The influence of polydispersivity on the effective thermal conductivity of the microstructures is discussed.