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

Abstract

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...

Electro-Thermal Scaling Analysis of Si MOSFETs with Device Length Typically Larger than 100nm

“…shown in the present modified analysis. Also, the trend is significant at smaller feature sizes, where the lattice temperature rise is about 40 K higher than in the previous analysis [9] at 100 nm. This is mainly due to the decreasing thermal conductivity since the electrical characteristics such as mobility do not have a significant impact under the constant field assumption.…”

“…[9] Power dissipation, P, is estimated from the long-channel approximation of MOSFETs. The spatially averaged device lattice temperature rise, ∆T La , can then be calculated using the power dissipation.…”

“…[7][8] An idea of thermal scaling considerations for longer devices, for the devices with length typically longer than 100 nm, is introduced later. [9] In the thermal scaling considerations, however, the solution for the lumped model is not self-consistent, and the rigorous model does not consider the important features governing the profiles. In this paper, the heat generation and the resulting device level temperature rise in…”