Percolation theory applied to the analysis of thermal interface materials in flip-chip technology

A very important aspect in chip design in the flip chip technology is the heat dissipation. As the surfaces of the heat sink, the heat spreader and the chip are rough there are imperfect contacts leading to higher thermal resistance due to the contact resistance. A method to decrease this contact resistance is by the use of thermal interface material. These thermal interface materials can be of various types, but most of them are polymers. Percolation theory holds a key to understanding the behavior of these polymers. Percolation, used widely in electrical engineering, is a phenomenon in which the highly conducting particles distributed randomly in the matrix form at least one continuous chain connecting the opposite faces of the matrix. This phenomenon was simulated and analytical results drawn from the program, to study the effect of considering 2-d and 3-d cases, matrix thickness, volume percentage of particles, and base material and particles of different conductivity. The simulation program was based on the matrix method, which not only simplifies the method of calculation but also increases the accuracy of the result thus obtained as compared to the calculations based on Kirchoff's Law or systematic node elimination, to obtain resultant thermal conductivity of the mixture. The analysis showed a sudden increase in thermal conductivity as soon as the percentage of particles reached the percolation threshold, which varied with all the parameters listed above. Comparison with the existing experimental results and the other existing models showed that the results from the percolation model were more accurate than other models, especially at high finer concentration.