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.

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.

scholarly journals Body-centered-cubic structure and weak anharmonic phonon scattering in tungsten

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Yani Chen ◽  
Jinlong Ma ◽  
Shihao Wen ◽  
Wu Li
Keyword(s):  
Phonon Scattering ◽  
Phonon Transport ◽  
High Symmetry ◽  
Body Centered Cubic ◽  
Phonon Branch ◽  
High Frequencies ◽  
Transverse Acoustic ◽  
Two Factors ◽  
Electron Phonon Scattering ◽  
Isotropy Condition

Abstract It was recently found that the anharmonic phonon–phonon scattering in tungsten is extremely weak at high frequencies, leading to a predominance of electron–phonon scattering and consequently anomalous phonon transport behaviors. In this work, we calculate the phonon linewidths of W along high-symmetry directions from first principles. We find that the weak phonon–phonon scattering can be traced back to two factors. The first is the triple degeneracy of the phonon branches at the P and H points, a universal property of elemental body-centered-cubic (bcc) structures. The second is a relatively isotropic character of the phonon dispersions. When both are met, phonon–phonon scattering rates must vanish at the P and H points. The weak phonon–phonon scattering feature is also applicable to Mo and Cr. However, in other elemental bcc substances like Na, the isotropy condition is violated due to the unusually soft character of the lower transverse acoustic phonon branch along the Γ-N direction, opening emission channels and leading to much stronger phonon–phonon scattering. We also look into the distributions of electron mean-free paths (MFPs) at room temperature in tungsten, which can help engineer the resistivity of nanostructured W for applications such as interconnects.

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.

The effect of nickel doping on electron and phonon transport in the n-type nanostructured thermoelectric material CoSbS

2015 ◽  
Vol 3 (40) ◽  
pp. 10442-10450 ◽  
Author(s):  
Zihang Liu ◽  
Huiyuan Geng ◽  
Jing Shuai ◽  
Zhengyun Wang ◽  
Jun Mao ◽  
...  
Keyword(s):  
Effective Mass ◽  
Carrier Concentration ◽  
Thermoelectric Material ◽  
Phonon Scattering ◽  
Phonon Transport ◽  
Strong Electron ◽  
Nickel Doping ◽  
Electron Phonon Scattering

The optimized carrier concentration, high effective mass and strong electron–phonon scattering for Ni doped CoSbS contribute to the enhanced ZT value.

Coupled Non-Equilibrium Green’s Function (NEGF) Electron-Phonon Interaction in Thermoelectric Materials

2011 ◽  
Author(s):  
T. D. Musho ◽  
D. G. Walker
Keyword(s):  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Computational Method ◽  
Direct Result ◽  
Inelastic Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering ◽  
Non Equilibrium

Over the last decade, nano-structured materials have shown a promising avenue for enhancement of the thermoelectric figure of merit. These performance enhancements in most cases have been a direct result of selectively modifying certain geometric attributes that alter the thermal or electrical transport in a desirable fashion. More often, models used to study the electrical and/or thermal transport are calculated independent of each other. However, studies have suggested electrical and thermal transport are intimately linked at the nanoscale. This provides an argument for a more rigorous treatment of the physics in an effort to capture the response of both electrons and phonons simultaneously. A simulation method has been formulated to capture the electron-phonon interaction of nanoscale electronics through a coupled non-equilibrium Greens function (NEGF) method. This approach is unique because the NEGF electron solution and NEGF phonon solution have only been solved independently and have never been coupled to capture a self-consistent inelastic electron-phonon scattering. One key aspect of this formalism is that the electron and phonon description is derived from a quantum point of view and no correction terms are necessary to account for the probabilistic nature of the transport. Additionally, because the complete phonon description is solved, scattering rates of individual phonon frequencies can be investigated to determine how electron-phonon scattering of particular frequencies influences the transport. This computational method is applied to the study of Si/Ge nanostructured superlattice thermoelectric materials.

Cross-Plane Phonon Conduction in Polycrystalline Silicon Films

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Jungwan Cho ◽  
Daniel Francis ◽  
Pane C. Chao ◽  
Mehdi Asheghi ◽  
Kenneth E. Goodson
Keyword(s):  
Thermal Conductivity ◽  
Polycrystalline Silicon ◽  
Transport Theory ◽  
Phonon Scattering ◽  
Transport Model ◽  
Phonon Transport ◽  
Silicon Films ◽  
Theoretical Predictions ◽  
Crystalline Films ◽  
Polycrystalline Silicon Films

Silicon films of submicrometer thickness play a central role in many advanced technologies for computation and energy conversion. Numerous thermal conductivity data for silicon films are available in the literature, but they are mainly for the lateral, or in-plane, direction for both polycrystalline and single crystalline films. Here, we use time-domain thermoreflectance (TDTR), transmission electron microscopy, and semiclassical phonon transport theory to investigate thermal conduction normal to polycrystalline silicon (polysilicon) films of thickness 79, 176, and 630 nm on a diamond substrate. The data agree with theoretical predictions accounting for the coupled effects of phonon scattering on film boundaries and defects related to grain boundaries. Using the data and the phonon transport model, we extract the normal, or cross-plane thermal conductivity of the polysilicon (11.3 ± 3.5, 14.2 ± 3.5, and 25.6 ± 5.8 W m−1 K−1 for the 79, 176, and 630 nm films, respectively), as well as the thermal boundary resistance between polysilicon and diamond (6.5–8 m2 K GW−1) at room temperature. The nonuniformity in the extracted thermal conductivities is due to spatially varying distributions of imperfections in the direction normal to the film associated with nucleation and coalescence of grains and their subsequent columnar growth.

Validation of a Physics Based Three Phonon Scattering Algorithm Implemented in the Statistical Phonon Transport Model

2020 ◽  
Author(s):  
Michael P. Medlar ◽  
Edward C. Hensel
Keyword(s):  
Relaxation Time ◽  
Momentum Space ◽  
Phonon Scattering ◽  
Transport Model ◽  
Phonon Transport ◽  
High Fidelity ◽  
Type I ◽  
Computational Domain ◽  
Simulated Event ◽  
Scattering Rates

Abstract Three phonon scattering is the primary mechanism by which phonon transport is impeded in insulating and semiconducting bulk materials. Accurate computational modeling of this scattering mechanism is required for high fidelity simulations of thermal transport across the ballistic (quantum mechanics) to Fourier (continuum mechanics) range of behavior. Traditional Monte Carlo simulations of phonon transport use a scaling factor such that each scattering event is considered representative of a large number of phonons, often on the order of 104 physical phonons per simulated event. The ability to account for every phonon scattering event is desirable to enhance model fidelity. A physics-based model using time dependent perturbation theory (Fermi’s Golden Rule) is implemented to compute three phonon scattering rates for each permissible phonon interaction subject to selection rules. The strength of the interaction is based on use of a Gruneisen-like parameter. Both Type I and Type II scattering rates are computed for the allowable interactions that conserve energy and momentum (up to the addition of a reciprocal lattice vector) on a given discretization of momentum space. All of the phonons in the computational domain are represented and phonon populations are updated in momentum space and real space based on the computed number of phonons involved in given scattering events. The computational algorithm is tested in an adiabatic single cell of silicon of dimension 100 × 100 × 100 nm at a nominal temperature of 500 Kelvin containing approximately 108 fully anisotropic phonons. The results indicate that phonon populations return to equilibrium if artificially displaced from that condition. Two approaches are introduced to model the relaxation time of phonon states: the single mode relaxation time (SMRT) which is consistent with the underlying assumptions for previously reported theoretical estimates, and the multi model relaxation time (MMRT) which is more consistent with in-situ conditions. The trends meet physical expectations and are comparable to other literature results. In addition, an estimate of error associated with the relaxation times is presented using the statistical nature of the model. The three phonon scattering model presented provides a high fidelity representation of this physical process that improves the computational prediction of anisotropic phonon transport in the statistical phonon transport model.

scholarly journals A Wignerfunction Approach to Phonon Scattering

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 339-350 ◽  
Author(s):  
Florian Frommlet ◽  
Peter A. Markowich ◽  
Christian Ringhofer
Keyword(s):  
Phonon Scattering ◽  
Transport Model ◽  
Scaling Limits ◽  
Wigner Equation ◽  
Phonon Interaction ◽  
Second Quantization ◽  
Electron Phonon Interaction ◽  
Wigner Transformation ◽  
Quantization Formalism ◽  
Electron Phonon Scattering

We consider the motion of a single electron under phonon scattering caused by a crystal lattice. Starting from the Fröhlich Hamiltonian in the second quantization formalism we derive a kinetic transport model by using the Wigner transformation. Under the assumption of small electron-phonon interaction we derive asymptotically the operator representing electron-phonon scattering in the Wigner equation. We then consider some scaling limits and finally we give the connection of our result to the well known Barker-Ferry equation.

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