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Modeling semiconductor nanostructures thermal properties: The dispersion role
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10.1063/1.3086409
/content/aip/journal/jap/105/7/10.1063/1.3086409
http://aip.metastore.ingenta.com/content/aip/journal/jap/105/7/10.1063/1.3086409

Figures

Image of FIG. 1.
FIG. 1.

Geometry representation.

Image of FIG. 2.
FIG. 2.

quadrature (first octant).

Image of FIG. 3.
FIG. 3.

Four principle cardinal directions surrounding point with a given propagation direction . and are the known values. Their positions are fixed in opposition to the propagation direction.

Image of FIG. 4.
FIG. 4.

Silicon dispersion relation in direction (100) given by Pop et al. (Ref. 31).

Image of FIG. 5.
FIG. 5.

Germanium dispersion relation in direction (100) given by Nilsson and Nelin (Ref. 32).

Image of FIG. 6.
FIG. 6.

This study is done in a silicon structure, where the dimension parameters equal to 7.16 mm. The solid line is the conductivity obtain with Holland’s method, relaxation times, and phonon dispersion. The dot line is the conductivity obtained with Holland’s method and relaxation times but with the phonon dispersion of Pop et al. Dots (●) and (○) are the conductivity obtain with BTE resolution but with our relaxation times and the phonon dispersion of Pop et al. The wire corresponds to represented by (●) and the film to drawn with (○) [Eq. (4)]. Cross dots are Glassbrenner and co-workers’ experimental conductivities.

Image of FIG. 7.
FIG. 7.

This study is done in a germanium structure whose geometrical dimensions are and . The solid line is the conductivity obtained with Holland’s method (relaxation times and phonon dispersion). The hyphen line is the conductivity resulting from Holland’s method with Nilsson and Nelin’s phonon dispersion. The dash dot line is the conductivity obtained with Holland’s method but with Asen relaxation time parameters and its dispersion. The dotted line is the conductivity calculated with Asen parameters on Holland relaxation time forms with Nilsson and Nelin’s dispersion. Dots (●) and (○) are conductivities obtained with BTE resolution but with our relaxation times and Nilsson and Nelin’s phonon dispersion. The cylinder (wire) corresponds to represented with (●) and the film to drawn with (○) [Eq. (4)]. Cross dots are Glassbrenner and co-workers’ experimental data on a sample of and .

Image of FIG. 8.
FIG. 8.

Film surface unit conductance vs thickness at different temperatures.

Image of FIG. 9.
FIG. 9.

Axis temperature field in a silicon film.

Image of FIG. 10.
FIG. 10.

Surface unit conductance comparison between a simple model (Yang et al.) and our model (Terris), of films set at 300 K.

Image of FIG. 11.
FIG. 11.

Nanowire thermal conductivity calculated with . Comparison with experimental results of Chen (Ref. 16), analytical data of Chantrenne et al. (Ref. 40), and Monte Carlo simulations of Lacroix et al. (Ref. 41).

Image of FIG. 12.
FIG. 12.

Nanowire thermal conductivity calculated with of Table IV. Comparison with experimental results of Chen (Ref. 16), analytical data of Chantrenne et al. (Ref. 40), and Monte Carlo simulations of Lacroix et al. (Ref. 41).

Tables

Generic image for table
Table I.

Relaxation time forms. [ is the wave vector, with corresponding to the maximum wave vector in the first Brillouin zone and is Boltzmann’s constant. , where the lattice parameter for silicon (Refs. 44 and 45) and for germanium (Ref. 45).]

Generic image for table
Table II.

Parameters for silicon relaxation times.

Generic image for table
Table III.

Parameters for germanium relaxation times.

Generic image for table
Table IV.

Ratio of diffuse to total reflection used in Fig. 12 for silicon nanowires.

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/content/aip/journal/jap/105/7/10.1063/1.3086409
2009-04-07
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Modeling semiconductor nanostructures thermal properties: The dispersion role
http://aip.metastore.ingenta.com/content/aip/journal/jap/105/7/10.1063/1.3086409
10.1063/1.3086409
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