Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach

2010 ◽  
Author(s):  
Aydin Nabovati ◽  
Daniel P. Sellan ◽  
Cristina H. Amon
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Fourier Law ◽  
Transport Models ◽  
Size Dependent ◽  
Semiconductor Electronic ◽  
Ballistic Heat Transfer ◽  
The Mean ◽  
Boltzmann Method

It is well known that continuum-based thermal transport models, such as the Fourier law, fail when the characteristic size of a system becomes comparable to the mean free path of carriers that transport thermal energy. The current work uses the lattice Boltzmann method to develop two modifications to the Fourier heat equation so that it can capture sub-continuum effects. The two modifications are: (i) a size-dependent thermal conductivity and (ii) a size-dependent temperature jump at the system boundaries.

Design and Optimization of Conductive Heat Trees at Micro and Nanoscales for Cooling Electronics

2012 ◽  
Author(s):  
Masoud Daneshi ◽  
Ebrahim Shirani
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Small Scale ◽  
Conductive Heat ◽  
Structural Dimension ◽  
Cooling Systems ◽  
Nano Technology ◽  
Conductive Material ◽  
Design And Optimization ◽  
The Mean

In this research, we consider the generation of conductive heat trees at micro and nano scales for cooling electronics which are considered as heat-generating disc-shaped solids. Due to the development of nano technology and its role in the production of small scale electronics in recent decades, the necessity of designing cooling systems for them will be revealed more than any other time. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loop are generated for cooling such electronic devices. Furthermore, Constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree-shaped architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. When the smallest features of the internal structure are so small, the conventional description of conduction breaks down. Hence, the effective thermal conductivity exhibits the “size effect”, and is governed by the smallest structural dimension which is comparable with the mean free path of the energy carriers. Therefore, we consider a model which was proposed for small-scale bodies in order to evaluate conductivity of heat trees.

Thermal Transport in Hotspots Using the Lattice Boltzmann Method with Application to Silicon-on-Insulator Transistors

2014 ◽  
Vol 960-961 ◽  
pp. 337-340
Author(s):  
Yu Dong Mao ◽  
Ming Tian Xu
Keyword(s):  
Energy Density ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Thermal Wave ◽  
Electronic Devices ◽  
Silicon On Insulator ◽  
Thermal Waves ◽  
Fourier Law ◽  
Wave Effect ◽  
Boltzmann Method

Silicon-on-insulator (SOI) transistors have been widely used in the micro-electronic devices. The Lattice Boltzmann method (LBM) is employed to simulate the heat conductions of hotspots appeared in a SOI transistor. The results show that a thermal wave effect is appeared in micro-region, and it can not be found in Fourier prediction. Comparing the results obtained by the Fourier law and LBM, we find that the LBM solution shows approximately 22% higher energy density than the Fourier prediction. When two thermal waves form different hotspots meet together, a significant energy enhancement will be appeared.

scholarly journals Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011 ◽  
Vol 468 (2141) ◽  
pp. 1217-1229 ◽  
Author(s):  
A. Sellitto ◽  
D. Jou ◽  
J. Bafaluy
Keyword(s):  
Heat Transport ◽  
Local Equilibrium ◽  
Mean Free Path ◽  
Thin Layers ◽  
Graphene Sheets ◽  
Fourier Law ◽  
Local Effects ◽  
Radial Heat ◽  
Non Local ◽  
The Mean

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

Lattice Boltzmann Modeling of Phonon Heat Conduction in Superlattice Structures

2010 ◽  
Author(s):  
Cristian J. San Marti´n ◽  
Amador M. Guzma´n ◽  
Rodrigo A. Escobar
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Lattice Boltzmann ◽  
Phonon Dispersion ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
One Dimension ◽  
The Mean ◽  
Superlattice Structures ◽  
Boltzmann Method

The results of temperature prediction and determination of effective thermal conductivity in periodic Si-Ge superlattice in one dimension, at length scale comparable to the mean free path are presented. Classical heat transfer models such as Fourier’s law do not represent what actually happens within electronic devices at these length scales. Phonon-border and phonon-interface scattering effects provide discontinuous jumps in temperature distribution when the mean free path is comparable with the device’s characteristic length, a relation given by the Knudsen number (Kn). For predicting the temperature within the periodic Si-Ge superlattice use is made of the lattice Boltzmann method in one dimension, using Debye’s model in the phonon dispersion relation. The predictions show that as Kn increases, so do the jumps at the borders, the same as at the interfaces. The prediction also shows that the effective conductivity of the Si-Ge superlattice decreases as Kn and the number of layers of material increase, and that keff decreases as the magnitude of p increases, a factor that allows heat flow between one layer and another. Use of gray LBM leads to good approximations of the actual temperature field and thermal conductivity values for the superlattice materials model when the physics of phonons established by Debye’s model is used.

Thermal transport of small systems

2017 ◽  
Author(s):  
Takahiro Yamamoto ◽  
Kazuyuki Watanabe ◽  
Satoshi Watanabe
Keyword(s):  
Thermal Transport ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Fourier Law ◽  
Small Systems ◽  
One Dimensional ◽  
Sample Dimension ◽  
The Mean

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

Accuracy of the Lattice-Boltzmann Method

1997 ◽  
Vol 08 (04) ◽  
pp. 747-752 ◽  
Author(s):  
Robert S. Maier ◽  
Robert S. Bernard
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Free Path ◽  
Lattice Boltzmann ◽  
Mean Free Path ◽  
Duct Flow ◽  
Reynolds Number Flow ◽  
The Mean ◽  
Boltzmann Method

The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.

scholarly journals Diffusion Mechanism of Radiation of a Charged Particle on the Randomly Spaced Dust Grains in the X-Rays

1999 ◽  
Vol 194 ◽  
pp. 319-320
Author(s):  
Zh. S. Gevorkian ◽  
V. V. Hambaryan ◽  
A. A. Akopian
Keyword(s):  
Dielectric Constant ◽  
Charged Particle ◽  
Diffusion Mechanism ◽  
Wavelength Region ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Dust Particles ◽  
X Rays ◽  
The Mean ◽  
A Charge

The theory of diffusion radiation of a charged particle on the fluctuations of the dielectric constant developed by Gevorkian can be explained as follows:A charge moving in a medium creates an electromagnetic field (pseudophoton) which is scattered on the fluctuations of the dielectric constant (here, dust particles) and converted into radiation. In the wavelength region (l « λ « L) (l is the mean free path of the photon in the medium, L is the characteristic size of the system) the main mechanism of the radiation is the diffusion of the pseudophoton (Gevorkian & Atayan 1990, Gevorkian 1992, Gevorkian 1993).

Anisotropic Nature of Thermal Transport in Nanoscale Materials

2005 ◽  
Author(s):  
Xinwei Wang
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Axial Direction ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Appreciable Effect ◽  
Temperature Differential ◽  
Energy Carriers ◽  
Different Shapes ◽  
The Mean

In this work, an equilibrium technique is developed to study the thermal transport in nanomaterials. By directly tracking the relaxation behavior of energy carriers, the developed technique is able to determine the effect of boundary scattering on thermal transport. Since no temperature differential across the material is required to determine its thermal conductivity, the developed technique is applicable to nanomaterials of different shapes and capable of capturing the anisotropic nature of the thermal transport inside. Applying this technique, the thermal transport in several typical nanomaterials—nanofilms, square and round nanowires, and spherical and cubic nanoparticles are studied in detail. A strong anisotropic nature of thermal transport in nanomaterials is observed. For nanofilms and nanowires, the thermal conductivity in the restricted directions (thickness and radial) is smaller than that in the unrestricted direction. This anisotropic nature is more obvious and important when the characteristic size of nanomaterials becomes comparable to or smaller than the mean free path of energy carriers. Our results comparison shows that with the same characteristic size, the shape of the cross section of nanowires has appreciable effect on the thermal transport in the axial direction. For spherical and cubic nanoparticles, little difference is observed between their thermal conductivities.

Ballistic Effect and Application in Circuit Design of Wide Band-Gap Semiconductor

2014 ◽  
Vol 644-650 ◽  
pp. 3597-3600
Author(s):  
Xin Xiang Liang ◽  
Zhi Qun Cheng ◽  
Min Shi Jia
Keyword(s):  
Semiconductor Devices ◽  
Electronic Devices ◽  
Ballistic Transport ◽  
Wide Band ◽  
Mean Free Path ◽  
Molecular Devices ◽  
Wide Band Gap ◽  
Transport Distance ◽  
The Mean ◽  
Crystal Interfaces

With manufacturing technology innovation and progress of electronic devices of semiconductors, dimensions of electronic devices get smaller nowadays. There has been processing of 90nm and 20nm in production. With in-depth research, scientists are more and more interested in molecular devices. Since the size of molecular devices is small, electrons transfer by ballistic transport. In semiconductor devices, when the transport distance is at micrometer or smaller sizes, the ballistic transport phenomena of electrons and holes of carriers occur. This transfer form is not affected by lattice defects, doping, and interaction of crystal interfaces. Since there is no interference of these interactions, carrier’s velocity can be faster several times than common electronic devices, resulting in the doubled operating speed of these devices. Although it is difficult to achieve pure ballistic transport, when the size of semiconductor devices is close to the mean free path of carriers, the speed of carriers will still be greatly improved.

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