Hierarchical modeling of heat transfer in silicon-based electronic devices

Heat transfer modeling in electronic devices has gained importance over the last decade in the design of better performing devices. The trend towards miniaturization of these devices has led to components that operate in the micro and nano-meter and in the micro and pico-second ranges. When the characteristic dimensions of the electronic components are comparable to or smaller than the mean free path of the energy carriers (in this case phonons), the thermal conductivity, which affects their performance and reliability, reduces due to the scattering of the energy carriers with the boundaries. Several modeling approaches have been proposed in the literature to describe sub-continuum heat transport; however, the hierarchical modeling of heat transfer in electronic devices has been limited. This has precluded, at the industry level, the analysis of how changes at sub-continuum level impact the overall performance and reliability of these devices. There are numerous devices and applications whose design, performance and reliability are suitable for optimization if a hierarchical model was available. In this work, we present a hierarchical model capable of integrating the scales involved in the thermal analysis of electronic components. The integration of participating scales is achieved in three steps. First, we use molecular dynamics simulations to estimate the thermal properties (i.e. phonon relaxation times, dispersion relations and group velocities, among others), required to solve the Boltzmann transport equation (BTE). Then we apply quantum corrections (QCs) to the MD results to make them suitable for BTE, and lastly, we solve the BTE on various domains, subject to different boundary and initial conditions. Our hierarchical model is applied to silicon-based devices.