Sub-micron thermal transport in ultra-scaled metal oxide semiconductor (MOS) devices

Tianjiao Wang, Purdue University

Abstract

In recent years, the aggressive scaling trends of modern microelectronic devices have resulted in increased power dissipation and thermal failures. Accordingly, there has been increasing interest in modeling sub-micron thermal transport in semi-conductors and dielectrics to better understand the mechanisms for self-heating in ultra-scaled microelectronics. The Fourier conduction model is now understood to be inadequate at the sub-micron scale. A variety of models based on the phonon Boltzmann transport equation (BTE) have been used to make thermal predictions at the sub-micron scale. However, most published studies make gray or semi-gray and relaxation time assumptions, and do not account adequately for phonon dispersion and scattering between phonon polarizations. In addition, these models are not easily extended to confined geometries in which dispersion curves are strongly modified with respect to their bulk counterparts. The central objective of the present work is to substantially improve the modeling of sub-micron heat transfer in microelectronic devices. First, a general computational procedure for computing three-phonon scattering rates is developed, fully accounting for phonon energy and momentum conservation rules. Second, the full scattering terms are incorporated into the phonon BTE and the relaxation time approximation to the BTE is discarded. The effects of dispersion curve anisotropy are considered as well. A conservative finite volume method is then developed which accounts for phonon scattering and transport as well as electron-phonon interactions. Finally, a variety of verification and validation problems are computed to demonstrate the correctness of the implementation as well as its ability to match published experimental data. The thermal conductivities of bulk silicon over a wide temperature range, as well as doped and undoped silicon thin films are predicted and validated by the experimental data. The proposed model is then applied to simulate a bulk silicon transistor in microelectronics devices. Numerical results are compared with those obtained from the Fourier diffusion equation and the gray BTE model. Significantly different temperature rise is obtained with the proposed model compared to the Fourier and gray models because of the finite rates of energy exchange and transport of the different phonon groups. Recommendations for future research, including coupling to electron Monte-Carlo simulations, improved numerical methods, inclusion of phonon confinement effects and parallel programming for solver speed-up, are summarized in the last chapter.

Degree

Ph.D.

Advisors

Murthy, Purdue University.

Subject Area

Mechanical engineering

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