American Institute of Mathematical Sciences

Advanced
2013, 2013(special): 737-746. doi: 10.3934/proc.2013.2013.737

Modeling the thermal conductance of phononic crystal plates

Stefanie Thiem 1, and  Jörg Lässig 2,

1. 

Rudolf Peierls Center for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
2. 

Department of Electrical Engineering and Computer Science, University of Applied Sciences Zittau/Görlitz, D-02826 Görlitz, Germany

Received  September 2012 Published  November 2013

The paper presents a model to compute the phonon thermal conductance of phononic crystal plates. The goal is the optimization of the figure of merit for these materials, which is the primary criterion for the efficiency of a thermoelectric device. Values of about three or higher allow for the construction of thermoelectric generators based on the Seebeck effect, which are more efficient than conventional electrical generators. The paper introduces a numerical method to optimize the phonon thermal conductance of a given phononic material by varying the geometrical structure with respect to the width and thickness of a sample as well as pore size, shape, and mass density.
Keywords: figure of merit, Landauer-Büttiker thermal conductance, Phononic crystal plates, thermoelectric material, supercell Plane-Wave-Expansion approach..
Mathematics Subject Classification: 35Q7.
Citation: Stefanie Thiem, Jörg Lässig. Modeling the thermal conductance of phononic crystal plates. Conference Publications, 2013, 2013 (special) : 737-746. doi: 10.3934/proc.2013.2013.737
References:
[1]

D. Y. Chung, T. Hogan, J. Schindler, L. Iordarridis, P. Brazis, C. R. Kannewurf, B. Chen, C. Uher, and M.G. Kanatzidis, Complex bismuth chalcogenides as thermoelectrics, 16th International Conference on Thermoelectrics, 1 (1997), 459-462. Google Scholar

[2]

A. Grigorevskii, V. Grigorevskii, and S. Nikitov, Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes, Acoustical Physics, 54 (2008), 289-293. Google Scholar

[3]

T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, Quantum dot superlattice thermoelectric materials and devices, Science, 297 (2002), 2229-2232. Google Scholar

[4]

A. I. Hochbaum, C. Renkun, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature, 451 (2008), 163-167. Google Scholar

[5]

J.-C. Hsu and T.-T. Wu, Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates, Physical Review B, 74 (2006), 144303. Google Scholar

[6]

W. Kuang, Z. Hou and Y. Liu, The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals, Physics Letters A, 332 (2004), 481-490. Google Scholar

[7]

M. S. Kushwaha, P. Halevi, G. Martínez, I. Dobrzynski, and B. Djafari Rouhani, Theory of acoustic band structure of periodic elastic composites, Physical Review B, 49 (1994), 2313-2322. Google Scholar

[8]

N. Mingo, Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations, Physical Review B, 68 (2003), 113308. Google Scholar

[9]

G. G. Samsonidze., R. Saito, A. Jorio, M. A. Pimenta, A. G. Souza Filho, A. Grüneis, G. Dresselhaus, and M. S. Dresselhaus, The concept of cutting lines in carbon nanotube science, Journal of Nanoscience and Nanotechnology, 3 (2003), 431-458. Google Scholar

[10]

G. A. Slack, New materials and performance limits for thermoelectric cooling, in ''CRC Handbook of Thermoelectrics'' (ed. D. M. Rowe), CRC Press, (1995), 407-440. Google Scholar

[11]

Y. Tanaka, Y. Tomoyasu, and S. Tamura, Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch, Physical Review B, 62 (2000), 7387-7392. Google Scholar

[12]

J. Tang, H.-T. Wang, D. H. Lee, M. Fardy, Z. Huo, T. P. Russell, and P. Yang, Holey silicon as an efficient thermoelectric material, Nano Letters, 10 (2010), 4279-4283. Google Scholar

[13]

J. O. Vasseur, P. A. Deymier, B. Djafari Rouhani, Y. Pennec, and A.-C. Hladky Hennion, Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates, Physical Review B, 77 (2008), 085415. Google Scholar

[14]

R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature, 413 (2001), 597-602. Google Scholar

show all references

References:
[1]

D. Y. Chung, T. Hogan, J. Schindler, L. Iordarridis, P. Brazis, C. R. Kannewurf, B. Chen, C. Uher, and M.G. Kanatzidis, Complex bismuth chalcogenides as thermoelectrics, 16th International Conference on Thermoelectrics, 1 (1997), 459-462. Google Scholar

[2]

A. Grigorevskii, V. Grigorevskii, and S. Nikitov, Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes, Acoustical Physics, 54 (2008), 289-293. Google Scholar

[3]

T. C. Harman, P. J. Taylor, M. P. Walsh, and B. E. LaForge, Quantum dot superlattice thermoelectric materials and devices, Science, 297 (2002), 2229-2232. Google Scholar

[4]

A. I. Hochbaum, C. Renkun, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature, 451 (2008), 163-167. Google Scholar

[5]

J.-C. Hsu and T.-T. Wu, Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates, Physical Review B, 74 (2006), 144303. Google Scholar

[6]

W. Kuang, Z. Hou and Y. Liu, The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals, Physics Letters A, 332 (2004), 481-490. Google Scholar

[7]

M. S. Kushwaha, P. Halevi, G. Martínez, I. Dobrzynski, and B. Djafari Rouhani, Theory of acoustic band structure of periodic elastic composites, Physical Review B, 49 (1994), 2313-2322. Google Scholar

[8]

N. Mingo, Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations, Physical Review B, 68 (2003), 113308. Google Scholar

[9]

G. G. Samsonidze., R. Saito, A. Jorio, M. A. Pimenta, A. G. Souza Filho, A. Grüneis, G. Dresselhaus, and M. S. Dresselhaus, The concept of cutting lines in carbon nanotube science, Journal of Nanoscience and Nanotechnology, 3 (2003), 431-458. Google Scholar

[10]

G. A. Slack, New materials and performance limits for thermoelectric cooling, in ''CRC Handbook of Thermoelectrics'' (ed. D. M. Rowe), CRC Press, (1995), 407-440. Google Scholar

[11]

Y. Tanaka, Y. Tomoyasu, and S. Tamura, Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch, Physical Review B, 62 (2000), 7387-7392. Google Scholar

[12]

J. Tang, H.-T. Wang, D. H. Lee, M. Fardy, Z. Huo, T. P. Russell, and P. Yang, Holey silicon as an efficient thermoelectric material, Nano Letters, 10 (2010), 4279-4283. Google Scholar

[13]

J. O. Vasseur, P. A. Deymier, B. Djafari Rouhani, Y. Pennec, and A.-C. Hladky Hennion, Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates, Physical Review B, 77 (2008), 085415. Google Scholar

[14]

R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature, 413 (2001), 597-602. Google Scholar

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