Thermal conductivity and localization in glasses: Numerical study of a model of amorphous silicon

Feldman, Joseph L.; Kluge, M.; Allen, Philip B.; Wooten, F.

doi:10.1103/physrevb.48.12589

Cited by 318 publications

(328 citation statements)

References 45 publications

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“…This is in accord with Refs. 13,17,18 where the Kubo Formula has been evaluated for concrete systems and the results have been counter-checked by either experiments or other theoretical methods. This is furthermore in accord with Refs.…”

Section: Discussionmentioning

confidence: 99%

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

2006

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The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extend it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. "Modular" we call systems that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schrödinger equation.

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Section: Discussionmentioning

confidence: 99%

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

2006

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“…Experimental measurements, estimates based on experiments, and modeling predictions have demonstrated that propagating modes contribute significantly to the thermal conductivity of amorphous silicon (a-Si) [4][5][6][7][8][9][10] and amorphous silicon nitride [11], but not to that of amorphous silica (a-SiO 2 ) [5,10,[12][13][14][15][16][17][18]. Notably, using broadband frequency domain thermoreflectance, Regner et al measured how the thermal conductivity of a-SiO 2 and a-Si thin films at a temperature of 300 K change with the thermal penetration depth associated with the heating laser, which identifies the depth normal to the surface at which the temperature amplitude is 1/e of its surface amplitude [10].…”

Section: Introductionmentioning

confidence: 99%

“…* mcgaughey@cmu.edu Traditionally, empirical expressions and simple models have been the only means to estimate MFPs in amorphous materials [12][13][14]22], while the Allen-Feldman (AF) theory can be used to model the nonpropagating modes [1,4].…”

Section: Introductionmentioning

confidence: 99%

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Thermal conductivity accumulation in amorphous silica and amorphous silicon

2014

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We predict the properties of the propagating and nonpropagating vibrational modes in amorphous silica (a-SiO 2 ) and amorphous silicon (a-Si) and, from them, thermal conductivity accumulation functions. The calculations are performed using molecular dynamics simulations, lattice dynamics calculations, and theoretical models. For a-SiO 2 , the propagating modes contribute negligibly to thermal conductivity (6%), in agreement with the thermal conductivity accumulation measured by Regner et al. [Nat. Commun. 4, 1640]. For a-Si, propagating modes with mean-free paths up to 1 μm contribute 40% of the total thermal conductivity. The predicted contribution to thermal conductivity from nonpropagating modes and the total thermal conductivity for a-Si are in agreement with the measurements of Regner et al. The accumulation in the measurements, however, takes place over a narrower band of mean-free paths (100 nm-1 μm) than that predicted (10 nm-1 μm).

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“…That is, infinite continuous random networks with no defects such as under and/or overcoordinated atoms have not been found so far, 22 and such an infinite continuous random network has not been generated even by computer experiments. 23 These results suggest that random networks having no definite defects cannot exceed a certain dimension. Conversely, a defect-free amorphous structural unit, of which dimension is smaller than a certain value, could be made up of continuous random networks.…”

Section: A Model For the Glass Transition In Noncrystalline Solidsmentioning

confidence: 92%

Model for the glass transition in amorphous solids based on fragmentation

1996

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A model for the glass transition in a heating process has been proposed. In the model, noncrystalline solids are assumed to be assemblies of pseudomolecules or structural units. When the noncrystalline solid is heated, a bond breaking process becomes dominant compared with a rebinding process of broken bonds. At high temperature, successive bond breaking causes the fragmentation of the solid and the fragment size becomes smaller as the temperature further increases. Consequently, the solid begins to show some viscous behavior when the fragment size reaches a critical value. To construct mathematical expressions for the fragmentation model, we employed a simple rate equation for the bond breaking process first and then obtained the temperature dependence of dangling bond density in a noncrystalline solid. Second, the expressions for the fragment density and size as a function of temperature were obtained based on the following assumptions: ͑1͒ bond breaking takes place mainly at the boundaries between pseudomolecules, ͑2͒ once buds of microcracks are generated, successive bond breaking occurs mostly at the tip of the microcracks, and ͑3͒ the fragments are Voronoy polyhedra. Finally, the diffusion coefficient in the system was obtained by assuming the vacancy mechanism in solids and then the temperature dependence of viscosity was derived through Stokes-Einstein relation. To examine the present model, applications of the model to the phase changes of a-Si in heating processes are carried out and the results were discussed.

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Thermal conductivity and localization in glasses: Numerical study of a model of amorphous silicon

Cited by 318 publications

References 45 publications

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

Limited validity of the Kubo formula for thermal conduction in modular quantum systems

Thermal conductivity accumulation in amorphous silica and amorphous silicon

Model for the glass transition in amorphous solids based on fragmentation

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