Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors

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.

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Intense electron-phonon scattering near the peak electric field in a semiconductor device results in nanometer-scale phonon hotspots. Past studies have argued that ballistic phonon transport near such hotspots serves to restrict heat conduction. We reexamine this assertion by developing a new phonon transport model. In a departure from previous studies, we treat isotropic dispersion in all phonon branches and include a phonon emission spectrum from independent Monte Carlo simulations of electron-phonon scattering.  We cast the model in terms of a non-equilibrium phonon distribution function and compare predictions from this model with data for ballistic transport in silicon. The solution to the steady-state transport equations for bulk silicon transistors shows that energy stagnation at the hotspot results in an excess equivalent temperature rise of about 13% in a 90 nm gate-length device. Longitudinal optical phonons with non-zero group velocities dominate transport. We find that the resistance associated with ballistic transport does not overwhelm that from the package unless the peak power density approaches 50 W/micron3. A transient calculation shows negligible phonon accumulation and retardation between successive logic states. This work highlights and reduces the knowledge gaps in the electro-thermal simulation of transistors.

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