DOI QR코드

DOI QR Code

실리콘 박막 트랜지스터 내 포논 평균자유행로 스펙트럼 비등방성 열전도 특성에 대한 수치적 연구

A Numerical Study on the Anisotropic Thermal Conduction by Phonon Mean Free Path Spectrum of Silicon in Silicon-on-Insulator Transistor

  • 강형선 (조선이공대학교 기계설계과) ;
  • 고영하 (조선이공대학교 기계설계과) ;
  • 진재식 (조선이공대학교 기계설계과)
  • Kang, Hyung-sun (Dept. of Mechanical Design, Chosun College of Science & Technology) ;
  • Koh, Young Ha (Dept. of Mechanical Design, Chosun College of Science & Technology) ;
  • Jin, Jae Sik (Dept. of Mechanical Design, Chosun College of Science & Technology)
  • 투고 : 2015.10.26
  • 심사 : 2015.12.20
  • 발행 : 2016.02.01

초록

본 연구의 목적은 실리콘 열전달 조절을 위한 포논의 평균자유행로(Mean free path, MFP) 스펙트럼 열전달 기여도 예측이다. 열전달의 크기 효과는 포논의 MFP 와 재료의 특성길이가 비슷할 때 나타나는데, 나노시스템 응용을 위한 재료의 열전달 증감을 위해 포논 MFP 스펙트럼에 대한 열전달 기여도 예측이 중요하다. 이를 위해 포논의 주파수 의존성이 고려된 볼츠만 수송방정식(Boltzmann transport equation) 근간의 full phonon dispersion 모델을 통해 실리콘 박막(Silicon-on-Insulator) 트랜지스터의 실리콘 박막 두께 변화(41-177 nm)에 따른 포논 MFP 스펙트럼 열전달 특성 및 비등방성을 해석함으로써, 본 연구 결과는 향후 박막 트랜지스터에 대한 고효율 열소산(heat dissipation) 설계전략에 활용될 수 있다.

The primary concern of this research is to examine the phonon mean free path (MFP) spectrum contribution to heat conduction. The size effect of materials is determined by phonon MFP, and the size effect appears when the phonon MFP is similar to or less than the characteristic length of materials. Therefore, knowledge of the phonon MFP is essential to increase or decrease the heat conduction of a material for engineering applications, such as micro/nanosystems. In this study, frequency dependence of the phonon transport is considered using the Boltzmann transport equation based on a full phonon dispersion model. Additionally, the phonon MFP spectrums of in-plane and out-of-plane heat transport are investigated by varying the film thickness of the silicon layer from 41 nm to 177 nm. This will increase the understanding of anisotropic heat conduction in a SOI (Silicon-on-Insulator) transistor.

키워드

참고문헌

  1. Tien, C. L., Majumdar, A. and Gerner, F. M., 1998, MICROSCALE ENERGY TRANSPORT, Taylor & Francis, Washington D. C., pp. 3-94.
  2. Kim, S. I., Lee, K. H., Mun, H. A, Kim, H. S., Hwang, S. W., Roh, J. W., Yang, D. J., Shin, W. H., Li, X. S., Lee, Y. H., Snyder, G. J. and Kim, S. W., 2015, "Dense Dislocation Arrays Embedded in Grain Boundaries for Highperformance Bulk Thermoselect-rics," Science, Vol. 348, No. 6230, pp. 109-114. https://doi.org/10.1126/science.aaa4166
  3. Kim, W., Zide, J., Gossard, A., Klenov, D., Stemmer, S., Shakouri, A. and Majumdar, A, 2006, "Thermal Conductivity Reduction and Thermoelectric Figure of Merit Increase by Embedding Nanoparticles in Crystalline Semiconductors," Physical Review Letters, Vol. 96, No. 4, Paper Number 045901.
  4. Maldovan, M., 2001, "Sound and Heat Revolutions in Phononics," Nature, Vol. 503, No. 7475, pp. 209-217. https://doi.org/10.1038/nature12608
  5. Zhang, Z. M., 2007, Nano/Microscale Heat Transfer, Mc Graw Hill, New York, pp. 101-192.
  6. Maldovan, M., 2013, "Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals," Physical Review Letters, Vol. 110, No. 2, Paper Number 025902.
  7. Estreicher, S. K., Gibbons, T. M., and Bebek, M. B., 2015, "Thermal Phonons and Defects in Semiconductors; The Physical Reason Why Defects Reduce Heat Flow, and How to Control It," Journal of Applied Physics, Vol. 117, No. 11, Paper Number 112801.
  8. Minnich, A. J., Johnson, J. A., Schmidt, A. J., Esfarjani, K., Dresselhaus, M. S., Nelson, K. A., and Chen, G., 2011, "Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths," Physical Review Letters, Vol. 107, No. 9, Paper Number 095901.
  9. Hu, Y., Zeng, L., Minnich, A. J., Dresselhaus, M. S., and Chen, G., 2015, "Spectral Mapping of Thermal Conductivity Through Nanoscale Ballistic Transport," Nature Nanotechnology, Vol. 10, No. 8, pp. 701-706. https://doi.org/10.1038/nnano.2015.109
  10. Minnich, A. J., 2012, "Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport," Physical Review Letters, Vol. 109, No. 20, Paper Number 205901.
  11. Regner, K. T., Sellan, D. P., Su, Z., Amon, C. H., McGaughey, A. J. H. and Malen, J. A., 2013, "Broadband Phonon Mean Free Path Contributions to Thermal Conductivity Measured Using Frequency Domain Thermoreflectance," Nature Communications, Vol. 4, Paper Number 1640.
  12. Yang, F. and Dames, C., 2013, "Mean Free Path Spectra as a Tool to Understand Thermal Conductivity in Bulk and Nanostructures," Physical Review B, Vol. 87, No. 3, Paper Number 035437.
  13. Xie, G., Guo, Y., Wei, X., Zhang, K., Sun, L., Zhong, J., Zhang, G. and Zhang, Y.-W., 2014, "Phonon Mean Free Path Spectrum and Thermal Conductivity for Si1−xGex Nanowires," Applied Physics Letters, Vol. 104, No. 23, Paper Number 233901.
  14. Ramu, A. T. and Ma, Y., 2014, "An Enhanced Fourier Law Derivable from the Boltzmann Transport Equation and a Sample Application in Determining the Mean-free Path of Nondiffusive Phonon Modes," Journal of Applied Physics, Vol. 116, No. 9, Paper Number 093501.
  15. Wang, X. and Huang, B., 2014, "Computational Study of In-Plane Phonon Transport in Si Thin Films," Scientific Reports, Vol. 4, Paper Number 6399.
  16. Cuffe, J., Eliason, J. K., Maznev, A. A., Collins, K. C., Johnson, J. A., Shchepetov, A., Prunnila, M., Ahopelto, J., Torres, C. M. S., Chen, G. and Nelson, K. A., 2015, "Reconstructing Phonon Mean-free-path Contributions to Thermal Conductivity Using Nanoscale Membranes," Physical Review B, Vol. 91, No. 24, Paper Number 245423.
  17. Narumanchi, S. V. J., Murthy, J. Y. and Amon, C. H., 2004, "Submicron Heat Transfer Model in Silicon Accounting for Phonon Dispersion and Polarization," ASME Journal of Heat Transfer, Vol. 126, No. 6, pp. 946-955. https://doi.org/10.1115/1.1833367
  18. Narumanchi, S. V. J., Murthy, J. Y. and Amon, C. H., 2005, "Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-insulator Transistors," ASME Journal of Heat Transfer, Vol. 127, No. 7, pp. 713-723. https://doi.org/10.1115/1.1924571
  19. Brockhouse, B. N., 1959, "Lattice Vibrations in Silicon and Germanium," Physical Review Letters, Vol. 2, No. 6, pp. 256-258. https://doi.org/10.1103/PhysRevLett.2.256
  20. Goodson, K. E., Flik, M. I., Su, L. T. and Antoniadis, D. A., 1995, "Prediction and Measurement of Temperature Fields in Silicon-on-Insulator Electronic Circuits," Journal of Nanoscience and Nanotechnology, Vol. 117, No. 3, pp. 574-581.
  21. Jin, J. S. and Lee, J. S., 2007, "Electron-Phonon Interaction Model and Prediction of Thermal Energy Transport in SOI Transistor," Journal of Nanoscience and Nanotechnology, Vol. 7, No. 11, pp. 4094-4100. https://doi.org/10.1166/jnn.2007.010
  22. Jin, J. S. and Lee, J. S., 2009, "Electron-Phonon Interaction Model and Its Application to Thermal Transport Simulation during ESD Event in NMOS Transistor," ASME Journal of Heat Transfer, Vol. 131, No. 9, Paper Number 092401.
  23. Jin, J. S. and Lee, J. S., 2009, "Effect of Joule Heating Variation on Phonon Heat Flow in Thin Film Transistor," Trans. Korean Soc. Mech. Eng. B, Vol. 33, No. 10, pp. 820-826. https://doi.org/10.3795/KSME-B.2009.33.10.820
  24. Swartz, E. T. and Pohl, R. O., 1989, "Thermal Boundary Resistance," Reviews of Modern Physics, Vol. 61, No. 3, pp. 605-668. https://doi.org/10.1103/RevModPhys.61.605
  25. Mazumder, S. and Majumdar, A., 2001, "Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization," ASME Journal of Heat Transfer, Vol. 123, No. 4, pp. 749-759. https://doi.org/10.1115/1.1377018
  26. Jin, J. S., 2014, "Prediction of Phonon and Electron Contributions to Thermal Conduction in doped Silicon Films," Journal of Mechanical Science and Technology, Vol. 28, No. 6, pp. 2287-2292. https://doi.org/10.1007/s12206-014-0518-3
  27. Cahill, D. G., Goodson, K. E. and Majumdar, A, 2002, "Thermometry and Thermal Transport in Micro_Nanoscale Solid-State Devices and Structures," ASME Journal of Heat Transfer, Vol. 124, No. 2, pp. 223-241. https://doi.org/10.1115/1.1454111

피인용 문헌

  1. Direct Determination of Spectral Phonon-Surface Scattering Rate from Experimental Data on Spectral Phonon Mean Free Path Distribution vol.40, pp.9, 2016, https://doi.org/10.3795/KSME-B.2016.40.9.621