Solution of Time Dependent Joule Heat Equation for a Graphene Sheet Under Thomson Effect
19 Aug 2013-IEEE Transactions on Electron Devices (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC)-Vol. 60, Iss: 10, pp 3548-3554
TL;DR: In this article, a physics-based solution of the joule heating phenomenon in a single-layer graphene (SLG) sheet under the presence of Thomson effect is presented. And the authors demonstrate that the temperature in an isotopically pure (containing only C12) SLG sheet attains its saturation level quicker than when doped with its isotopes (C13), and further develop an analytical model of the SLG specific heat using the quadratic (out of plane) phonon band structure over the room temperature.
Abstract: We address a physics-based solution of joule heating phenomenon in a single-layer graphene (SLG) sheet under the presence of Thomson effect. We demonstrate that the temperature in an isotopically pure (containing only C12) SLG sheet attains its saturation level quicker than when doped with its isotopes (C13). From the solution of the joule heating equation, we find that the thermal time constant of the SLG sheet is in the order of tenths of a nanosecond for SLG dimensions of a few micrometers. These results have been formulated using the electron interactions with the inplane and flexural phonons to demonstrate a field-dependent Landauer transmission coefficient. We further develop an analytical model of the SLG specific heat using the quadratic (out of plane) phonon band structure over the room temperature. Additionally, we show that a cooling effect in the SLG sheet can be substantially enhanced with the addition of C13. The methodologies as discussed in this paper can be put forward to analyze the graphene heat spreader theory.
Citations
More filters
TL;DR: In this article, a multiphysics coupling model of a single-chip 3.3-kV/50-A PP-IGBT device is presented to analyze the fretting wear failure, and the weak layer and the fatigue effect are obtained by power cycling simulation.
Abstract: Press-pack insulated-gate bipolar transistor (PP-IGBT) device is used in high-power modular multilevel converter high-voltage direct current (MMC-HVDC) system due to the advantages of high reliability and short-circuit failure. Considering safeties and stable operations, it is necessary to model and analyze the fatigue failure evolution of PP-IGBT device that improves the reliability of MMC-HVDC system. This paper proposes a method to analyze from fretting wear failure to short-circuit failure in PP-IGBT device. First, a multiphysics coupling model of a single-chip 3.3-kV/50-A PP-IGBT device is presented to analyze the fretting wear failure, and the weak layer and the fatigue effect are obtained by power cycling simulation. Second, considering the Al-Si diffusion reaction mechanism on the interface of IGBT chip, the short-circuit failure is investigated by the finite-element method model of PP-IGBT device with Al-Si osmotic hole, and the changing trend of characteristic parameters is estimated during short-circuit failure process. Finally, the steady state, power cycling, and short-circuit tests are used to verify the multiphysics coupling model, fretting wear failure, and short-circuit failure. The experiment indicates that the fatigue failure evolution of PP-IGBT device occurs from fretting wear failure to short-circuit failure, and it suggests that the proposed method can be applied to optimize design and condition monitoring of PP-IGBT device.
38 citations
Cites methods from "Solution of Time Dependent Joule He..."
...The average power loss of IGBT chip is estimated by the following formula [13]:...
[...]
03 Mar 2012
TL;DR: In this paper, the authors investigated the thermal transport in suspended graphene and graphene supported on copper substrate using equilibrium molecular dynamics simulations, Green-Kubo method and relaxation time approximation (RTA) approach.
Abstract: The present study investigates the thermal transport in suspended graphene and graphene supported on copper substrate using equilibrium molecular dynamics simulations, Green-Kubo method and relaxation time approximation (RTA) approach. The thermal coupling between graphene and copper substrate was investigated by varying the interaction strength between the carbon atoms and Cu atoms at the interface. The contribution of different phonon modes to the thermal conductivity of suspended and supported graphene was analyzed in order to elucidate the graphene-substrate thermal interactions. The thermal conductivity of graphene decreases with the increasing strength of the interfacial interaction. The analysis shows that the interactions with copper substrate can reduce the thermal conductivity by up to 44%. The decrease of thermal conductivity is primarily due to the suppression of contribution from out-of-plane acoustic (ZA) phonons in the large wave vector region.Copyright © 2012 by ASME
20 citations
TL;DR: In this paper, the effect of topological and lattice vacancy defects on the electro-thermal transport properties of the metallic zigzag graphene nano ribbons at their ballistic limit was investigated.
Abstract: We report the effect of topological as well as lattice vacancy defects on the electro-thermal transport properties of the metallic zigzag graphene nano ribbons at their ballistic limit. We employ the density function theory---Non equilibrium green's function combination to calculate the transmission details. We then present an elaborated study considering the variation in the electrical current and the heat current transport with the change in temperature as well as the voltage gradient across the nano ribbons. The comparative analysis shows, that in the case of topological defects, such as the Stone-Wales defect, the electrical current transport is minimum. Besides, for the voltage gradient of 0.5 Volt and the temperature gradient of 300 K, the heat current transport reduces by $${\sim }62\,\%$$ ~ 62 % and $${\sim }50\,\%$$ ~ 50 % for the cases of Stones-Wales defect and lattice vacancy defect respectively, compared to that of the perfect one.
4 citations
Cites methods from "Solution of Time Dependent Joule He..."
...Lastly, the value of the thermal conductance, has been obtained as [43,44],...
[...]
...The Seebeck co-efficient, which interprets the induced thermoelectric voltage in response to a temperature difference, can be calculated using the formula [42,43],...
[...]
03 Jun 2019
TL;DR: In this article, the reliability difference of different package IGBT, the electro-thermal stress of full pressure and silver sintered package Press Pack IGBT (PP IGBT) are compared by using Finite Element Method (FEM).
Abstract: In order to analyze the reliability difference of different package IGBT, the electro-thermal stress of full pressure and silver sintered package Press Pack IGBT (PP IGBT) are compared by using Finite Element Method (FEM) in this paper. Based on the actual structure and material physical properties of a 3300V/50A Press pack IGBT, a machine-thermal-electrical multi-coupling field finite element model is eatablished and verified by the power cycling test platform. The simulation results show that, the silver sintered package could improves the heat dissipation capability of IGBT, while reduces the junction temperature and the saturation voltage of the device. However, the silver sintered package increases the von mises stress of PP IGBT.
2 citations
References
More filters
TL;DR: The thermal properties of carbon materials are reviewed, focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder, with special attention given to the unusual size dependence of heat conduction in two-dimensional crystals.
Abstract: Recent years have seen a rapid growth of interest by the scientific and engineering communities in the thermal properties of materials. Heat removal has become a crucial issue for continuing progress in the electronic industry, and thermal conduction in low-dimensional structures has revealed truly intriguing features. Carbon allotropes and their derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range--of over five orders of magnitude--from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. Here, I review the thermal properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. Special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe the prospects of applications of graphene and carbon materials for thermal management of electronics.
5,189 citations
"Solution of Time Dependent Joule He..." refers background in this paper
...As the thermal conductance in SLG is mainly dominated by phonons [1], [14]–[17], [21]–[25], [26], one can fairly take Kph Ke....
[...]
...Lately, there have been some remarkable experimental analyses (in both suspended and on-substrate SLG) on carrier mobility [8], electrical [9]–[13], and thermal [1], [14]–[17] (effects of C13 isotopes have been reported in [18]) resistances...
[...]
...This leads to about 0.16 ns at 300 K considering κph = 2500 Wm−1K−1 in the absence of any isotopes for the given dimensions [Fig....
[...]
...[1], [31]–[34] predicted a large κph because of the high mean free path of the long wavelength phonons....
[...]
...I. INTRODUCTION THE electrothermal analyses of metallic graphene fornext generation heat spreaders have gained momentum because of three reportedly vital reasons: 1) singlelayer graphene (SLG) can withstand a very high room temperature (RT) breakdown current density of the order of 108−109 Acm−2 [1]–[3]; 2) it has an exceptionally high RT carrier mobility of the order of 20 000–20 0000 cm2V−1s−1 [4]; and 3) it possesses a phonon-dominated high RT thermal conductivity (κ) 600–7000 Wm−1K−1 [1]....
[...]
TL;DR: In this paper, the authors review thermal and thermoelectric properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder.
Abstract: Recent years witnessed a rapid growth of interest of scientific and engineering communities to thermal properties of materials. Carbon allotropes and derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range – of over five orders of magnitude – from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. I review thermal and thermoelectric properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. A special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe prospects of applications of graphene and carbon materials for thermal management of electronics.
3,609 citations
TL;DR: Measurements show that mobilities higher than 200 000 cm2/V s are achievable, if extrinsic disorder is eliminated and a sharp (thresholdlike) increase in resistivity observed above approximately 200 K is unexpected but can qualitatively be understood within a model of a rippled graphene sheet in which scattering occurs on intraripple flexural phonons.
Abstract: We have studied temperature dependences of electron transport in graphene and its bilayer and found extremely low electron-phonon scattering rates that set the fundamental limit on possible charge carrier mobilities at room temperature. Our measurements show that mobilities higher than 200 000 cm2/V s are achievable, if extrinsic disorder is eliminated. A sharp (thresholdlike) increase in resistivity observed above approximately 200 K is unexpected but can qualitatively be understood within a model of a rippled graphene sheet in which scattering occurs on intraripple flexural phonons.
3,100 citations
"Solution of Time Dependent Joule He..." refers background in this paper
...THE electrothermal analyses of metallic graphene for next generation heat spreaders have gained momentum because of three reportedly vital reasons: 1) singlelayer graphene (SLG) can withstand a very high room temperature (RT) breakdown current density of the order of 108−109 Acm−2 [1]–[3]; 2) it has an exceptionally high RT carrier mobility of the order of 20 000–20 0000 cm2V−1s−1 [4]; and 3) it possesses a phonon-dominated high RT thermal conductivity (κ) 600–7000 Wm−1K−1 [1]....
[...]
TL;DR: The resistivity of ultraclean suspended graphene is strongly temperature (T) dependent for 5
Abstract: The resistivity of ultraclean suspended graphene is strongly temperature ($T$) dependent for $5lTl240\text{ }\text{ }\mathrm{K}$ At $T\ensuremath{\sim}5\text{ }\text{ }\mathrm{K}$ transport is near-ballistic in a device of $\ensuremath{\sim}2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ dimension and a mobility $\ensuremath{\sim}170\text{ }000\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{V}\text{ }\mathrm{s}$ At large carrier density, $ng05\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$, the resistivity increases with increasing $T$ and is linear above 50 K, suggesting carrier scattering from acoustic phonons At $T=240\text{ }\text{ }\mathrm{K}$ the mobility is $\ensuremath{\sim}120\text{ }000\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{V}\text{ }\mathrm{s}$, higher than in any known semiconductor At the charge neutral point we observe a nonuniversal conductivity that decreases with decreasing $T$, consistent with a density inhomogeneity $l{10}^{8}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$
1,090 citations
"Solution of Time Dependent Joule He..." refers background in this paper
...Lately, there have been some remarkable experimental analyses (in both suspended and on-substrate SLG) on carrier mobility [8], electrical [9]–[13], and thermal [1], [14]–[17] (effects of C13 isotopes have been reported in [18]) resistances...
[...]
TL;DR: In this article, the authors investigated theoretically the phonon thermal conductivity of single-layer graphene lattice using the valence-force field method, and they obtained the results in good agreement with the recent measurements of the thermal conductivities of suspended graphene.
Abstract: We investigated theoretically the phonon thermal conductivity of single-layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phonon Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accounting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has also been included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single-layer graphene, calculated with a realistic Gruneisen parameter, is in the range $\ensuremath{\sim}2000--5000\text{ }\text{W}/\text{mK}$ depending on the flake width, defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.
897 citations