Fully Coupled Nonequilibrium Electron–Phonon Transport in Nanometer-Scale Silicon FETs

Rowlette, Jeremy; Goodson, Kenneth E.

doi:10.1109/ted.2007.911043

Cited by 81 publications

(64 citation statements)

References 48 publications

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“…The term, lumped, used in the title of this sub-section represents these assumptions. Spatial average electron temperature in the device area, T ea , is estimated from the energy conservation between the energy supplied by the applied electric field and the energy relaxation to the lattice [3]. It results in the following expression…”

Section: Modelingmentioning

confidence: 99%

“…Rowlette and Goodson [2] have discussed the coupling electron and phonon transport model for the heat conduction in nanoscale silicon-based devices. Phonon transport models for hotspot predictions have been reviewed by Narumanchi et al [3]. These papers have exhibited the importance of applying Boltzmann Transport Equation (BTE)-based analysis for silicon MOSFETs with typical length smaller than 100 nm.…”

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confidence: 99%

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Scaling consideration on local hotspot for Si MOSFETs - for device length scale typically larger than 100 nm

Fushinobu

Yamamoto

Hatakeyama

2010

2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems

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Non-equilibrium thermal characteristics in Si MOSFETs are considered. Both lumped and rigorous electro-thermal model are deployed to examine the device lattice and electron temperatures. Non-equilibrium nature of electrons and phonons becomes important for devices with gate length typically shorter than 10 -6 m. Lumped model cannot capture the local heat generation distribution at the device level. Further discussion on the heat generation characteristics revealed that the hotspot predictions of devices typically shorter than 200 nm needs different strategy from larger devices. KEY WORDS: Si MOSFET, Length scale, NOMENCLATURE J current density, A/m 2 L gate length, m N, n, p number density, electron, hole number density, m -3 P heat dissipation rate, W q unit charge, C T temperature, K t ox oxide thickness, m V voltage, V v velocity, m/s W gate width, m x, y spatial coordinate, m Greek symbols ε 0 permeability of vacuum, F/m ε ox dielectric constant of gate oxide ε Si dielectric constant of gate oxide κ thermal conductivity ∝ mobility, m 2 /(V-s) φ potential, V Subscripts A acceptor a average in the device area D drain, donor e electron h hole G gate L lattice S source INTRODUCTIONFeature size of the current silicon MOSFETs are entering the sub-40 nm length scale, and the CMOS devices are expected to play a continuing key role in the semiconductor industries. Energy and thermal management for the CMOS devices are becoming more and more important due to the increasing demand for the energy savings of the ICT equipment. It must be pointed out that the energy and thermal management has to be considered at different length scales due to their governing physics. System level energy and thermal management including high performance cooling technology play a crucial role to control the system level temperature profile to govern the equipment design. Sub-micron scale device level energy and thermal management, on the other hand, determine two important features in operating devices: the heat dissipation and the intensity of the local hotspot (device-level temperature rise due to the self-heating.) The intensity is mainly governed by the heat generation and by the local heat conduction. It gives additional temperature rise of the devices that cannot be controlled by the system level energy and thermal management. In order to discuss the local hotspot, it is important to review the nature of heat generation, the local self-heating characteristics. Pop et al.[1] has reviewed the trend in the heat generation and transport in nanoscale transistors. Rowlette and Goodson [2] have discussed the coupling electron and phonon transport model for the heat conduction in nanoscale silicon-based devices. Phonon transport models for hotspot predictions have been reviewed by Narumanchi et al. [3]. These papers have exhibited the importance of applying Boltzmann Transport Equation (BTE)-based analysis for silicon MOSFETs with typical length smaller than 100 nm. It is shown that the hydrodynamic-based model under-predicts the local hotspot...

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Section: Modelingmentioning

confidence: 99%

mentioning

confidence: 99%

Scaling consideration on local hotspot for Si MOSFETs - for device length scale typically larger than 100 nm

Fushinobu

Yamamoto

Hatakeyama

2010

2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems

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show abstract

“…Rowlette and Goodson [23] coupled the electron Monte Carlo (e-MC) model of Refs. [8][9][10] with the split-flux model for phonon transport to perform a self-consistent simulation of non-equilibrium transport in MOSFETs.…”

Section: Introductionmentioning

confidence: 99%

Coupled electro-thermal simulation of MOSFETs

Akšamija

Murthy

2012

J Comput Electron

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Thermal transport in metal-oxide-semiconductor field effect transistors (MOSFETs) due to electron-phonon scattering is simulated using phonon generation rates obtained from an electron Monte Carlo device simulation. The device simulation accounts for a full band description of both electrons and phonons considering 22 types of electron-phonon scattering events. Detailed profiles of phonon emission/absorption rates in the physical and momentum spaces are generated and are used in a MOS-FET thermal transport simulation with a recently-developed anisotropic relaxation time model based on the Boltzmann transport equation (BTE). Comparisons with a Fourier conduction model reveal that the anisotropic heat conduction model predicts higher maximum temperatures because it accounts for the bottlenecks in phonon scattering pathways. Heat fluxes leaving the boundaries associated with different phonon polarizations and frequencies are also examined to reveal the main modes responsible for transport. It is found that though the majority of the heat generation is in the optical modes, the heat generated in the acoustic modes is not negligible. The modes primarily responsible for the transport of heat are found to be medium-to-high frequency acoustic phonon modes.

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“…They showed further decreased of the membrane thickness in the two-dimensional limit led to increase radiated power. The fully coupled nonequilibrium electron-phonon transport in nanometer-scale silicon field effect transistors was investigated by Rowlette and Goodson (2008). They illustrated that the nanoscale-transport phenomena was critically important for low-dimensional silicon-based devices.…”

Section: Introductionmentioning

confidence: 99%

Laser short-pulse heating of silicon-aluminum thin films

Mansoor

Yilbaş

2011

Opt Quant Electron

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Energy transport in silicon-aluminum thin films is examined during the laser short-pulse irradiation subjected to the silicon film. The silicon film is considered to be at the top of the aluminum film. Thermal boundary resistance at the interface of the films is incorporated in the analysis. The absorption of laser radiation in the silicon and aluminum films is modeled using the transfer matrix method. Since the silicon film is dielectric, the phonon radiative transport basing the Boltzmann transport equation is incorporated to determine equivalent equilibrium temperature in the film while modified two-equation model is used to account for the non-equilibrium energy transport due to thermal separation of electron and phonon sub-systems in the aluminum film during the laser short-pulse heating process.

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Fully Coupled Nonequilibrium Electron–Phonon Transport in Nanometer-Scale Silicon FETs

Cited by 81 publications

References 48 publications

Scaling consideration on local hotspot for Si MOSFETs - for device length scale typically larger than 100 nm

Scaling consideration on local hotspot for Si MOSFETs - for device length scale typically larger than 100 nm

Coupled electro-thermal simulation of MOSFETs

Laser short-pulse heating of silicon-aluminum thin films

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