Non-equilibrium phonon distributions in sub-100 nm silicon transistors

Sanjiv Sinha, E. Pop, R. W. Dutton, K. E. Goodson

Research output: Contribution to journalArticlepeer-review


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/μm3. 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.

Original languageEnglish (US)
Pages (from-to)638-647
Number of pages10
JournalJournal of Heat Transfer
Issue number7
StatePublished - Jul 2006
Externally publishedYes


  • Devices
  • Heat transfer
  • Modeling
  • Nanoscale
  • Thermophysical

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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