A Split-Flux Model for Phonon Transport Near Hotspots

2004 ◽  
Author(s):  
S. Sinha ◽  
E. Pop ◽  
K. E. Goodson
Keyword(s):  
Electric Fields ◽  
Phonon Scattering ◽  
Semiconductor Device ◽  
Longitudinal Optical ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Relaxation Time Approximation ◽  
Occupation Numbers ◽  
The Impact

Intense electron-phonon scattering near the peak electric field in a semiconductor device results in nanometer-scale phonon hotspots with power densities on the order of 1 W/μm3. To study the impact of the hotspot on phonon transport, we solve the phonon Boltzmann transport equation under the relaxation time approximation to yield the departure from equilibrium amongst phonon modes. The departure function is split into two contributions: one arising from the far-from-equilibrium emitted phonons and the other from the near-equilibrium thermal phonons. The model predictions are compared with existing data on ballistic phonon transport in silicon. Computations of transient and steady state phonon occupation numbers for a device geometry show the predominance of longitudinal optical phonons for electric fields on the order of 1 MV/m. Due to the low group velocity of these modes, there is an energy stagnation at the hotspot which results in an excess temperature rise of about 13% for a 90 nm bulk silicon device. During device switching, emitted phonons have sufficient time to relax completely when the duty cycle is 30% on a period of 100 ps.

Thermal Transport in Novel Silicon Transistors

2004 ◽  
Author(s):  
Keivan Etessam-Yazdani ◽  
Wenjun Liu ◽  
Yizhang Yang ◽  
Mehdi Asheghi
Keyword(s):  
Thermal Conductivity ◽  
Semiconductor Device ◽  
Silicon Layer ◽  
Phonon Transport ◽  
Interface Roughness ◽  
Strained Silicon ◽  
Boltzmann Transport ◽  
Strained Si ◽  
Thin Silicon ◽  
The Impact

This manuscript investigates the relevance and impact of nanoscale thermal phenomena in the state-of-the-art semiconductor device technologies such as: silicon-on-insulator (SOI), strained silicon, and tri-gate CMOS transistors. The experimental data and predictions for thin silicon layer thermal conductivity and the solutions of the Boltzmann transport equations (BTE) for phonon transport in strained-Si/Ge bi-layer configuration are used to estimate the thermal resistance of the SOI, tri-gate, and strained-silicon-on-SiGe-on-insulator (SGOI) transistors, respectively. In particular, the impact of SiGe underlayer and interface roughness on the lateral thermal conductivity of the silicon layer at room temperature is investigated. In order to avoid the complexity of the BTE for predictions of the temperature distribution, Lumped Analytical (LA) models are introduced that are simple to implement and also adequate enough to capture the sub-continuum effects. It is concluded that the SOI, SGOI and tri-gate transistors are all susceptible to self-heating for very thin silicon device layers.

Non-Equilibrium Phonon Distributions in Sub-100nm Silicon Transistors

2005 ◽  
Vol 128 (7) ◽  
pp. 638-647 ◽  
Author(s):  
S. Sinha ◽  
E. Pop ◽  
R. W. Dutton ◽  
K. E. Goodson
Keyword(s):  
Phonon Scattering ◽  
Semiconductor Device ◽  
Transport Model ◽  
Ballistic Transport ◽  
Longitudinal Optical ◽  
Phonon Transport ◽  
Silicon Transistors ◽  
Zero Group ◽  
Electron Phonon Scattering ◽  
Non Equilibrium

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 90nm 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 50W∕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.

Study on Phonon Drag Effect and Phonon Transport in Thin Si-on-Insulator Layers

2015 ◽  
Vol 1117 ◽  
pp. 86-89 ◽  
Author(s):  
Hiroya Ikeda ◽  
Takuro Oda ◽  
Yuhei Suzuki ◽  
Yoshinari Kamakura ◽  
Faiz Salleh
Keyword(s):  
Seebeck Coefficient ◽  
Carrier Concentration ◽  
Phonon Scattering ◽  
Phonon Transport ◽  
Infrared Photodetector ◽  
Phonon Drag ◽  
Drag Effect ◽  
Phonon Modes ◽  
Highly Sensitive ◽  
Insulator Layers

The Seebeck coefficient of P-doped ultrathin Si-on-insulator (SOI) layers is investigated for the application to a highly-sensitive thermopile infrared photodetector. It is found that the Seebeck coefficient originating from the phonon drag is significant in the lightly doped region and depends on the carrier concentration with increasing carrier concentration above ~5×1018 cm-3. On the basis of Seebeck coefficient calculations considering both electron and phonon distribution, the phonon-drag part of SOI Seebeck coefficient is mainly governed by the phonon transport, in which the phonon-phonon scattering process is dominant rather than the crystal boundary scattering even in the SOI layer with a thickness of 10 nm. This fact suggests that the phonon-drag Seebeck coefficient is influenced by the phonon modes different from the thermal conductivity.

scholarly journals Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors

Materials ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 124 ◽  
Author(s):  
Toufik Sadi ◽  
Cristina Medina-Bailon ◽  
Mihail Nedjalkov ◽  
Jaehyun Lee ◽  
Oves Badami ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Small Diameter ◽  
Golden Rule ◽  
Impurity Scattering ◽  
Boltzmann Transport ◽  
Nanowire Transistors ◽  
Scattering Mechanisms ◽  
Relaxation Time Approximation ◽  
Ionized Impurity Scattering ◽  
The Impact

Nanowire transistors (NWTs) are being considered as possible candidates for replacing FinFETs, especially for CMOS scaling beyond the 5-nm node, due to their better electrostatic integrity. Hence, there is an urgent need to develop reliable simulation methods to provide deeper insight into NWTs’ physics and operation, and unlock the devices’ technological potential. One simulation approach that delivers reliable mobility values at low-field near-equilibrium conditions is the combination of the quantum confinement effects with the semi-classical Boltzmann transport equation, solved within the relaxation time approximation adopting the Kubo–Greenwood (KG) formalism, as implemented in this work. We consider the most relevant scattering mechanisms governing intraband and multi-subband transitions in NWTs, including phonon, surface roughness and ionized impurity scattering, whose rates have been calculated directly from the Fermi’s Golden rule. In this paper, we couple multi-slice Poisson–Schrödinger solutions to the KG method to analyze the impact of various scattering mechanisms on the mobility of small diameter nanowire transistors. As demonstrated here, phonon and surface roughness scattering are strong mobility-limiting mechanisms in NWTs. However, scattering from ionized impurities has proved to be another important mobility-limiting mechanism, being mandatory for inclusion when simulating realistic and doped nanostructures, due to the short range Coulomb interaction with the carriers. We also illustrate the impact of the nanowire geometry, highlighting the advantage of using circular over square cross section shapes.

scholarly journals Direct observation of large electron–phonon interaction effect on phonon heat transport

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Jiawei Zhou ◽  
Hyun D. Shin ◽  
Ke Chen ◽  
Bai Song ◽  
Ryan A. Duncan ◽  
...  
Keyword(s):  
Heat Transport ◽  
Phonon Scattering ◽  
Crystalline Silicon ◽  
Substantial Reduction ◽  
Phonon Transport ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Exciting Electron ◽  
Energy Conversion Devices ◽  
The Impact

AbstractAs a foundational concept in many-body physics, electron–phonon interaction is essential to understanding and manipulating charge and energy flow in various electronic, photonic, and energy conversion devices. While much progress has been made in uncovering how phonons affect electron dynamics, it remains a challenge to directly observe the impact of electrons on phonon transport, especially at environmental temperatures. Here, we probe the effect of charge carriers on phonon heat transport at room temperature, using a modified transient thermal grating technique. By optically exciting electron-hole pairs in a crystalline silicon membrane, we single out the effect of the phonon–carrier interaction. The enhanced phonon scattering by photoexcited free carriers results in a substantial reduction in thermal conductivity on a nanosecond timescale. Our study provides direct experimental evidence of the elusive role of electron–phonon interaction in phonon heat transport, which is important for understanding heat conduction in doped semiconductors. We also highlight the possibility of using light to dynamically control thermal transport via electron–phonon coupling.

Electron-Phonon Scattering in GaN/AlN and GaAs/AlAs Quantum Wells

1997 ◽  
Vol 482 ◽  
Author(s):  
T. F. Forbang ◽  
C. R. McIntyre
Keyword(s):  
Quantum Wells ◽  
Optical Phonon ◽  
Phonon Spectrum ◽  
Phonon Scattering ◽  
Relaxation Times ◽  
Longitudinal Optical ◽  
Longitudinal Optical Phonon ◽  
Phonon Modes ◽  
Optical Phonon Scattering ◽  
Electron Phonon Scattering

AbstractWe have studied the effects on the phonon spectrum and on the electron-longitudinal optical phonon scattering in GaN/AlN and GaAs/AlAs quantum wells. Phonon modes and potentials have been calculated for both systems. Results for emission due to electroninterface phonons interactions are presented. We will discuss the implications for relaxation times and electron mobility due to modified LO-phonon scattering in both systems.

Spectral Detail of Phonon Conduction and Scattering in Graphene

2011 ◽  
Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Conductivity ◽  
Phonon Scattering ◽  
Interatomic Potential ◽  
Phonon Dispersion ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Phonon Transport ◽  
Temperature Perturbation ◽  
Boltzmann Transport ◽  
Wide Range

This paper examines the thermodynamic and thermal transport properties of the 2D graphene lattice. The interatomic interactions are modeled using the Tersoff interatomic potential and are used to evaluate phonon dispersion curves, density of states and thermodynamic properties of graphene as functions of temperature. Perturbation theory is applied to calculate the transition probabilities for three-phonon scattering. The matrix elements of the perturbing Hamiltonian are calculated using the anharmonic interatomic force constants obtained from the interatomic potential as well. An algorithm to accurately quantify the contours of energy balance for three-phonon scattering events is presented and applied to calculate the net transition probability from a given phonon mode. Under the linear approximation, the Boltzmann transport equation (BTE) is applied to compute the thermal conductivity of graphene, giving spectral and polarization-resolved information. Predictions of thermal conductivity for a wide range of parameters elucidate the behavior of diffusive phonon transport. The complete spectral detail of selection rules, important phonon scattering pathways, and phonon relaxation times in graphene are provided, contrasting graphene with other materials, along with implications for graphene electronics. We also highlight the specific scattering processes that are important in Raman spectroscopy based measurements of graphene thermal conductivity, and provide a plausible explanation for the observed dependence on laser spot size.

DSMC Scheme for Phonon Transport in Solid Thin Films

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Mitsuhiro Matsumoto ◽  
Masaya Okano ◽  
Yusuke Masao
Keyword(s):  
Thin Films ◽  
Input Parameter ◽  
Direct Simulation Monte Carlo ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Phonon Dynamics ◽  
Solid Thin Films ◽  
Simulation Monte Carlo ◽  
Phonon Model

Analysis of phonon dynamics based on a linearized Boltzmann transport equation is widely used for thermal analysis of solid thin films, but couplings among various phonon modes appear in some situations. We propose a direct simulation Monte Carlo (DSMC) scheme to simulate the phonon gas starting without the conventional linearization approximation. This requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes. A prototype code based on a simple phonon model was developed, and energy flux was evaluated for thin films of various thickness as a test calculation.

scholarly journals PREDICTION OF ELECTRON DRIFT VELOCITY IN HELICALLY COILED CARBON NANOTUBES

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Zoran P. Popović ◽  
Tatjana Vuković ◽  
Božidar Nikolić ◽  
Milan Damnjanović ◽  
Ivanka Milošević
Keyword(s):  
Carbon Nanotubes ◽  
Electric Fields ◽  
Drift Velocity ◽  
Phonon Scattering ◽  
Single Wall Carbon Nanotubes ◽  
Strong Impact ◽  
Electron Drift ◽  
Boltzmann Transport ◽  
Single Wall Carbon ◽  
Scattering Rate

We studied electron transport in single wall carbon nanotubes placed in stationary homogeneous electric fields, oriented along tubes. Electron distributions for various electric fields are determined by solving stationary multi bands Boltzmann transport equation in presence of electron phonon scattering mechanisms. Contributions of all possible scattering channels, allowed by selection rules and energy conservation, are taken into account for finding scattering rate and collision integrals. As it is previously predicted, large electron drift velocities in straight single wall carbon nanotubes are obtained. Frequent electron scattering as well as low group velocity have strong impact on reduction of drift velocity in helically coiled carbon nanotubes.

Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

2003 ◽  
Vol 125 (5) ◽  
pp. 896-903 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Relaxation Time ◽  
Heat Source ◽  
Time Scales ◽  
Electric Fields ◽  
Hot Spot ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Phonon Relaxation Time

In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller than the phonon mean free path in the medium. In this paper, we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the relaxation time approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localization effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.

Sign in / Sign up

Export Citation Format

Share Document