Electro-thermal simulation based on coupled Boltzmann transport equations for electrons and phonons

Nghiem, Thi Thu Trang; Saint-Martin, Jérôme; Dollfus, Philippe

doi:10.1007/s10825-015-0773-2

Cited by 19 publications

(7 citation statements)

References 55 publications

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“…Semi-classical Monte Carlo simulations are also starting to emerge in TE materials [241][242][243][244][245][246][247][248]. The advantage of MC is that the computational cost increases linearly with the system size and scattering events can be incorporated relatively easily.…”

Section: Simulation Essentialsmentioning

confidence: 99%

Hierarchically nanostructured thermoelectric materials: challenges and opportunities for improved power factors

et al. 2020

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The field of thermoelectric materials has undergone a revolutionary transformation over the last couple of decades as a result of the ability to nanostructure and synthesize myriads of materials and their alloys. The ZT figure of merit, which quantifies the performance of a thermoelectric material has more than doubled after decades of inactivity, reaching values larger than two, consistently across materials and temperatures. Central to this ZT improvement is the drastic reduction in the material thermal conductivity due to the scattering of phonons on the numerous interfaces, boundaries, dislocations, point defects, phases, etc., which are purposely included. In these new generation of nanostructured materials, phonon scattering centers of different sizes and geometrical configurations (atomic, nano- and macro-scale) are formed, which are able to scatter phonons of mean-free-paths across the spectrum. Beyond thermal conductivity reductions, ideas are beginning to emerge on how to use similar hierarchical nanostructuring to achieve power factor improvements. Ways that relax the adverse interdependence of the electrical conductivity and Seebeck coefficient are targeted, which allows power factor improvements. For this, elegant designs are required, that utilize for instance non-uniformities in the underlying nanostructured geometry, non-uniformities in the dopant distribution, or potential barriers that form at boundaries between materials. A few recent reports, both theoretical and experimental, indicate that extremely high power factor values can be achieved, even for the same geometries that also provide ultra-low thermal conductivities. Despite the experimental complications that can arise in having the required control in nanostructure realization, in this colloquium, we aim to demonstrate, mostly theoretically, that it is a very promising path worth exploring. We review the most promising recent developments for nanostructures that target power factor improvements and present a series of design ‘ingredients’ necessary to reach high power factors. Finally, we emphasize the importance of theory and transport simulations for materialoptimization, and elaborate on the insight one can obtain from computational tools routinely used in the electronic device communities. Graphical abstract

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Section: Simulation Essentialsmentioning

confidence: 99%

Hierarchically nanostructured thermoelectric materials: challenges and opportunities for improved power factors

et al. 2020

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“…In 1D systems, the BTE can be solved by a direct approach 21 , but for 3D problems, a stochastic particle Monte Carlo method 22 is much more efficient and it is able to include complex scattering terms 23 . This versatile approach can solve accurately the BTE much beyond the linear approximation, and in complex geometries.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer in rough nanofilms and nanowires using full band ab initio Monte Carlo simulation

Davier¹,

Larroque²,

Dollfus³

et al. 2018

J. Phys.: Condens. Matter

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I. AbstractThe Boltzmann transport equation is one of the most relevant framework to study the heat transport at the nanoscale, beyond the diffusive regime and up to the micrometer-scale. In the general case of three-dimensional devices, the particle Monte Carlo approach of phonon transport is particularly powerful and convenient, and requires reasonable computational resources.In this work, we propose an original and versatile particle Monte Carlo approach parametrized by using ab-initio data. Both the phonon dispersion and the phonon-phonon scattering rates have been computed by DFT calculation in the entire 3D Brillouin zone. To treat the phonon transport at rough interfaces, a combination of specular and diffuse reflections has been implemented in phase space.Thermal transport has been investigated in nanowires and thin films made of cubic and hexagonal Silicon, including edge roughness, in terms of effective thermal conductivity, phonon band contributions and heat flux orientation. It is shown that the effective thermal conductivity in quasi-ballistic regime obtained from our Monte Carlo simulation cannot be accurately fitted by simple semi-analytical Matthiessen-like models and that spectral approaches are mandatory to get good results. Our Full Band approach shows that some phonon branches exhibiting a negative group velocity in some parts of the Brillouin zone may contribute negatively to the total thermal flux. Besides, the thermal flux clearly appears to be oriented along directions of high density of states. The resulting anisotropy of the heat flux is discussed together with the influence of rough interfaces.

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“…Previous works [2,19,20] have highlighted the doping dependence of κ(T) of a material, in addition to its temperature dependence, and modeled the same through the temperature coefficients, κ a , κ b and κ c . In this work, while extracting R THm from the experimental data using the methodology detailed in [18], we also extract the parameters α and β of an alternate thermal conductivity model, κ(T) = βT −α [21]. From these alternate model parameters, we find κ a , κ b and κ c parameters by optimization.…”

Section: Model Extension For Structures With Beol and Parameter Extractionmentioning

confidence: 99%

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part II-Experimental Validation

et al. 2020

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In this paper, we extend the model developed in part-I of this work to include the effects of the back-end-of-line (BEOL) metal layers and test its validity against on-wafer measurement results of SiGe heterojunction bipolar transistors (HBTs). First we modify the position dependent substrate temperature model of part-I by introducing a parameter to account for the upward heat flow through BEOL. Accordingly the coupling coefficient models for bipolar transistors with and without trench isolations are updated. The resulting modeling approach takes as inputs the dimensions of emitter fingers, shallow and deep trench isolation, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are first validated against 3D TCAD simulations including the effect of BEOL followed by validation against measured data obtained from state-of-art multifinger SiGe HBTs of different emitter geometries.

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Electro-thermal simulation based on coupled Boltzmann transport equations for electrons and phonons

Cited by 19 publications

References 55 publications

Hierarchically nanostructured thermoelectric materials: challenges and opportunities for improved power factors

Hierarchically nanostructured thermoelectric materials: challenges and opportunities for improved power factors

Heat transfer in rough nanofilms and nanowires using full band ab initio Monte Carlo simulation

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part II-Experimental Validation

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