DOI: 10.1063/1.1870106. Monte Carlo simulation of Joule heating in bulk and strained silicon

Monte Carlo simulation of Joule heating in bulk and strained silicon

10.1063/1.1870106

Crossref journal-article

AIP Publishing

Applied Physics Letters (317)

Abstract

This work examines the details of Joule heating in silicon with a Monte Carlo method including efficient, analytic models for the electron bands, acoustic and optical phonon dispersion. We find that a significant portion of the initially generated phonons have low group velocity, and therefore low contribution to heat transport, e.g., optical phonons or acoustic modes near the Brillouin zone edge. The generated phonon spectrum in strained silicon is different from bulk silicon at low electric fields due to band splitting and scattering selection rules which favor g-type and reduce f-type phonon emission. However, heat generation is essentially the same in strained and bulk silicon at high fields, when electrons have enough energy to emit across the entire phonon spectrum despite the strain-induced band splitting. The results of this study are important for electro-thermal analysis of future silicon nanoscale devices.

Bibliography

Pop, E., Dutton, R. W., & Goodson, K. E. (2005). Monte Carlo simulation of Joule heating in bulk and strained silicon. Applied Physics Letters, 86(8).

Authors 3

Eric Pop (first)
Robert W. Dutton (additional)
Kenneth E. Goodson (additional)

References 17 Referenced 62

{'key': '2023070301403893400_c1', 'first-page': '1141', 'volume': '9', 'year': '1990', 'journal-title': 'IEEE Trans. Electron Devices'} / IEEE Trans. Electron Devices (1990)
10.1063/1.356450 / J. Appl. Phys. (1994)
10.1115/1.1337651 / J. Heat Transfer (2001)
10.1063/1.361424 / J. Appl. Phys. (1996)
10.1063/1.123994 / Appl. Phys. Lett. (1999)
10.1115/1.1377018 / J. Heat Transfer (2001)
10.1063/1.343027 / J. Appl. Phys. (1989)
10.1103/PhysRevLett.59.716 / Phys. Rev. Lett. (1987)
10.1063/1.1788838 / J. Appl. Phys. (2004)
10.1103/RevModPhys.55.645 / Rev. Mod. Phys. (1983)
10.1103/PhysRevB.38.9721 / Phys. Rev. B (1988)
10.1103/PhysRevB.48.1512 / Phys. Rev. B (1993)
{'volume-title': 'Basic Semiconductor Physics', 'year': '2001', 'key': '2023070301403893400_c13'} / Basic Semiconductor Physics (2001)
10.1109/16.766884 / IEEE Trans. Electron Devices (1999)
10.1109/16.310101 / IEEE Trans. Electron Devices (1994)
10.1063/1.109949 / Appl. Phys. Lett. (1993)
{'first-page': '37', 'article-title': 'Symposium on Inelastic Scattering of Neutrons in Solids and Liquids', 'year': '1963', 'key': '2023070301403893400_c17'} / Symposium on Inelastic Scattering of Neutrons in Solids and Liquids (1963)

Dates

Type	When
Created	20 years, 6 months ago (Feb. 15, 2005, 6:02 p.m.)
Deposited	2 years, 1 month ago (July 2, 2023, 9:40 p.m.)
Indexed	2 weeks, 1 day ago (Aug. 6, 2025, 9:45 a.m.)
Issued	20 years, 6 months ago (Feb. 16, 2005)
Published	20 years, 6 months ago (Feb. 16, 2005)
Published Online	20 years, 6 months ago (Feb. 16, 2005)
Published Print	20 years, 6 months ago (Feb. 21, 2005)

Funders 0

None

BibTeX

@article{Pop_2005, title={Monte Carlo simulation of Joule heating in bulk and strained silicon}, volume={86}, ISSN={1077-3118}, url={http://dx.doi.org/10.1063/1.1870106}, DOI={10.1063/1.1870106}, number={8}, journal={Applied Physics Letters}, publisher={AIP Publishing}, author={Pop, Eric and Dutton, Robert W. and Goodson, Kenneth E.}, year={2005}, month=feb }

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