Influence of anharmonic phonon decay on self-heating in Si nanowire transistors

Rhyner, Reto; Luisier, Mathieu

doi:10.1063/1.4893378

Cited by 11 publications

(19 citation statements)

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“…However, the modeling of non-equilibrium phonons is a difficult task for small nanowires. Recent calculations of self-heating using atomistic phonons show a decrease in the current [36].…”

Section: Power Dissipation In Silicon Nanowire Transistorsmentioning

confidence: 99%

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Impact of phonon scattering in Si/GaAs/InGaAs nanowires and FinFets: a NEGF perspective

et al. 2016

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This paper reviews our previous theoretical studies and gives further insight into phonon scattering in 3D small nanotransistors using non-equilibrium Green function methodology. The focus is on very small gate-all-around nanowires with Si, GaAs or InGaAs cores. We have calculated phonon-limited mobility and transfer characteristics for a variety of cross-sections at low and high drain bias. The nanowire cross-sectional area is shown to have a significant impact on the phonon-limited mobility and on the current reduction. In a study of narrow Si nanowires we have examined the spatially resolved power dissipation and the validity of Joule's law. Our results show that only a fraction of the power is dissipated inside the drain region even for a relatively large simulated length extension (approximately 30 nm). When considering large source regions in the simulation domain, at low gate bias, a slight cooling of the source is observed. We have also studied the impact of College of Science and Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, UK the real part of phonon scattering self-energy on a narrow nanowire transistor. This real part is usually neglected in nanotransistor simulation, whereas we compute its impact on current-voltage characteristic and mobility. At low gate bias, the imaginary part strongly underestimated the current and the mobility by 50 %. At high gate bias, the two mobilities are similar and the effect on the current is negligible.Keywords Silicon and III-V nanowire field effect transistors · Non-equilibrium Green's functions · Electronphonon scattering self-energies · Phonon-limited mobility · Local power dissipation

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“…However, the modeling of non-equilibrium phonons is a difficult task for small nanowires. Recent calculations of self-heating using atomistic phonons show a decrease in the current [36].…”

Section: Power Dissipation In Silicon Nanowire Transistorsmentioning

confidence: 99%

“…Using the dispersion relation we may compute Figure 22 shows the real and imaginary parts of the selfenergy computed according to (34) and (35) for a relatively large coupling constant C 3 . (35) and (36) Note that the real part extends across the whole spectrum and is by no means negligible. In Fig.…”

Section: A Simple Einstein Model For the Self-energymentioning

confidence: 99%

Impact of phonon scattering in Si/GaAs/InGaAs nanowires and FinFets: a NEGF perspective

et al. 2016

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“…With few exceptions [15], most of EPC with both the BTE and within NEGF assumes that the phonons can be described within the harmonic approximation, since addition of anharmonic effects significantly increases the computational burden. However, at room temperatures and above there * troels.markussen@quantumwise.com will be anharmonic contributions to the phonons for many materials.…”

Section: Introductionmentioning

confidence: 99%

Electron-phonon scattering from Green's function transport combined with molecular dynamics: Applications to mobility predictions

et al. 2017

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We present a conceptually simple method for treating electron-phonon scattering and phonon limited mobilities. By combining Green's function based transport calculations and molecular dynamics (MD), we obtain a temperature dependent transmission from which we evaluate the mobility. We validate our approach by comparing to mobilities and conductivies obtained by the Boltzmann transport equation (BTE) for different bulk and one-dimensional systems. For bulk silicon and gold we successfully compare against experimental values. We discuss limitations and advantages of each of the computational approaches.

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“…This feature was pointed out using a super-resolvent non-linear time-dependent quantum kinetic equation based on the density matrix formalism [45][46][47], and confirmed in later studies by the NEGF formalism [41]. Electro-thermal simulations have been carried out using a variety of methodologies ranging from semiclassical [48], a blend of quantum transport with classical heat equation to a pure quantum mechanical [49] and atomistic methodologies [50]. All these methodologies have their weaknesses and strengths.…”

Section: Review Of Modelling Approachesmentioning

confidence: 92%

“…(iii) If the lattice is considered to be held at constant ambient temperature, there is no further issue; if not, the heat equation(s) driven by the heat dissipation into the phonon system must be considered self-consistently. In the most advanced modelling, this latter step has been replaced by coupling the above equations self-consistently to the phonon Green functions [50,75]. A few groups use local atomic or molecular orbitals as the basis for tight binding style Hamiltonian models, but these techniques are restricted to a few hundred atoms [76].…”

Section: Numerical Solution Of Negf Equationsmentioning

confidence: 99%

Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation

Martı́nez

Barker

2020

Materials

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A review and perspective is presented of the classical, semiclassical and fully quantum routes to the simulation of electrothermal phenomena in ultrascaled silicon nanowire fieldeffect transistors. It is shown that the physics of ultrascaled devices requires at least a coupled electron quantum transport semiclassical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires selfconsistency with the Poisson equation and that the electronic LDOS must be determined within at least the selfconsistent Born approximation. To bring in this description and to provide the energy resolved local carrier distributions it is necessary to adopt the nonequilibrium Green function (NEGF) formalism, briefly surveyed here. The NEGF approach describes quantum coherent and dissipative transport, Pauli exclusion and nonequilibrium conditions inside the device. There are two extremes of NEGF used in the community. The most fundamental is based on coupled equations for the Green functions electrons and phonons that are computed at the atomically resolved level within the nanowire channel and into the surrounding device structure using a tight binding Hamiltonian. It has the advantage of treating both the nonequilibrium heat flow within the electron and phonon systems even when the phonon energy distributions are not described by a temperature model. The disadvantage is the grand challenge level of computational complexity. The second approach, that we focus on here, is more useful for fast multiple simulations of devices important for TCAD (Technology Computer Aided Design). It retains the fundamental quantum transport model for the electrons but subsumes the description of the energy distribution of the local phonon subsystem statistics into a semiclassical Fourier heat equation that is sourced by the local heat dissipation from the electron system. It is shown that this selfconsistent approach retains the salient features of the fullscale approach. For focus, we outline our electrothermal simulations for a typical narrow Si nanowire gate allaround fieldeffect transistor. The selfconsistent Born approximation is used to describe electronphonon scattering as the source of heat dissipation to the lattice. We calculated the effect of the device selfheating on the current voltage characteristics. Our fast and simpler methodology closely reproduces the results of a more fundamental computeintensive calculations in which the phonon system is treated on the same footing as the electron system. We computed the local power dissipation and “local lattice temperature” profiles. We compared the selfheating using hot electron heating and the Joule heating, i.e., assuming the electron system was in local equilibrium with the potential. Our simulations show that at low bias the source region of the device has a tendency to cool down for the case of the hot electron heating but not for the case of Joule heating. Our methodology opens the possibility of studying thermoelectricity at nanoscales in an accurate and computationally efficient way. At nanoscales, coherence and hot electrons play a major role. It was found that the overall behaviour of the electron system is dominated by the local density of states and the scattering rate. Electrons leaving the simulated drain region were found to be far from equilibrium.

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Influence of anharmonic phonon decay on self-heating in Si nanowire transistors

Abstract: Articles you may be interested inModeling of phonon scattering in n-type nanowire transistors using one-shot analytic continuation technique

Cited by 11 publications

References 21 publications

Impact of phonon scattering in Si/GaAs/InGaAs nanowires and FinFets: a NEGF perspective

Impact of phonon scattering in Si/GaAs/InGaAs nanowires and FinFets: a NEGF perspective

Electron-phonon scattering from Green's function transport combined with molecular dynamics: Applications to mobility predictions

Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation

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