Conclusions
The thermal mode analysis was adopted in this paper to opti- mize the thermal management with optimal locations and chip sizes for MCP. The average thermal resistance was defined and investigated. It was found that the thermal resistance matrix is independent of power dissipation. Thus one can evaluate the opti- mal locations and sizes of chips without considering the nonlinear effect of power dissipation. The spreading thermal resistance can be expanded into Fourier series so that the thermal modes can be established. From the function analysis, one can see that for the infinite thermal modes, only a few terms are needed to be considered due to the rapid convergence property. The optimal locations and chip sizes can be determined only using the first few modes by reducing the thermal resistance as minimal as pos- sible. The optimal locations have the cosine wave property so that the wave nodes might be the suitable sites. On the other hand, the optimal chip sizes have the cardinal sine property which decays monotonously. The dominated modes may be influenced by the locations of chips. For given optimal locations, the optimal chip sizes are determined by some specific modes. These special modes can be used to evaluate the range of optimal locations and chip sizes.