Department of Mechanical Engineering

Stanford University

Principal Investigator

Kenneth E. Goodson

Many of the heat transfer and energy conversion phenomena in our research are governed by thermal conduction, and in many cases the dominant mechanism is phonon transport. In order to account for nanoscale scattering mechanisms and sub-continuum aspects, it can be useful to use phonon transport theory involving either Monte Carlo methods or solution of th Peierls-Boltzmann transport equation. This approach can be more detailed and rigorous than solutions to the energy equation based on Fourier's heat conduction law, in fact the Fourier law is derived through a variety of simplifications to the transport equation. However, phonon transport theory is arguably to as rigorous as modern molecular dynamics methods, which are just now becoming suitable for very simple heat conduction studies in nano structures. Phonon transport theory herefor occupies a critical place in the hierarchy of heat conduction simulation tools and strikes a compromise between the comprehensive (but sometimes prohibitive) detail of molecular dynamics and the simple (and sometimes inaccurate) application of Fourier's law at the nanoscale.

Our work in this area started with interpretation of thin film thermal conductivity data in several high cited papers from the mid 1990's, with a focus on crystalline, polycrystalline, doped, and intrinsic silicon. This work made progress in defining the spectral variation of the phonon mean free path by means of the conductivity reduction at small scales. More recently we have used phonon transit theory to simulate heat generation and conduction in nano transistors considering sub continuum scattering phenomena and nonequilibrium populations among he various phonon modes. This work culminated in the first simultaneously ballistic simulations of electon and phonon transport in silicon field effect transistors using the phonon transit equation and electron Monte Carlo. Our most recent progress in this area is interpreting experimental data for heat conduction along laterally periodic porous silicon nano structures with applications to photonic and thermoelectric energy conversion.

**Pop, E.**, Dutton, R.W., and Goodson, K.E., 2005, "Monte Carlo simulation of Joule Heating in Bulk and Strained Silicon," *Applied Physics Letters*, Vol. 86, pp. 082101-082103.

**Asheghi, M.**, Leung, Y.K., Wong, S.S., and Goodson, K.E., 1997, "Phonon-Boundary Scattering in Thin Silicon Layers," *Applied Physics Letters*, Vol. 71, pp. 1798-1800.

**Ju, Y.S.**, and Goodson, K.E., 1999, "Phonon Scattering in Silicon Films of Thickness Below 100 nm," *Applied Physics Letters*, Vol. 74, pp. 3005-3007.

**Asheghi, M.**, **Kurabayashi, K.**, Kasnavi, K., and Goodson, K.E., 2002, "Thermal Conduction in Doped Single-Crystal Silicon Films," *Journal of Applied Physics*, Vol. 91, pp. 5079-5088.

**Sinha S**., and Goodson, K.E., 2005, "Review: Multiscale Thermal Modeling in Nanoelectronics," *International Journal for Multiscale Computational Engineering*, Vol. 3, pp. 107-133.

**Sinha, S., Pop, E**., Dutton R.W., and Goodson, K.E., 2006, "Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors," *ASME Journal of Heat Transfer*, Vol. 128, pp. 638-647.

**Pop, E., Sinha, S.**, and Goodson, K.E., 2006, "Heat Generation and Transport in Nanometer Scale Transistors," *Proceedings of the IEEE*, Vol. 94, pp. 1587-1601.

**Rowlette, J.A.**, and Goodson, K.E., 2008, "Fully-Coupled, Nonequilibrium, Electron-Phonon Transport in Nanometer-Scale Silicon FETs," *IEEE Transactions on Electronic Devices*, Vol. 55, pp. 220-232.

**Sinha, S**., Shelling, P.K., Phillpot, S.R., Goodson, K.E., 2005, "Scattering of g-Process Longitudinal Phonons at Hotspots in Silicon," *Journal of Applied Physic*s, Vol. 97, no.2, pp. 023702-1-023702-9.

**Sverdrup, P.G., Ju, Y.S.,**and Goodson, K.E., 2001, "Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors," *ASME Journal of Heat Transfer*, Vol. 123, pp. 30-37.

**Pop, E.**, Dutton, R.W., and Goodson, K.E., 2005, "Monte Carlo simulation of Joule Heating in Bulk and Strained Silicon," *Applied Physics Letters*, Vol. 86, pp. 082101-082103.