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Review: 3-\(\omega\) Technique for Thermal Conductivity Measurement—Contemporary and Advancement in Its Methodology

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Abstract

As the size of electronic devices is reducing the heat generation is increasing tremendously within the devices. Thermal management is an effective way to control the heat generation in the devices. One of the governing factors of the thermal management is thermal conductivity of the materials. Thermal conductivity varies abruptly as the material dimension shrinks and becomes concern when material dimension equals to an order of mean free path of thermal energy carriers. The state-of-art devices contains thin films and nanostructures having dimension varying from 100 µm to 10 nm, which is expected to decrease to a size of few layers of atoms in the near future. Thermal conductivity of the thin films and nanostructures measured using steady state and transient techniques. Among them, the 3-\(\omega\) technique is a versatile method to find thermal conductivity of thin films, fluids, and gases quickly and efficiently. This article provides an elaborate review on the state-of-art 3-\(\omega\) characterization technique and methodology, device morphology, advantages, and mathematical model for various device configurations along with its advancement for accurate thermal management in microelectronics, nanoelectronics and nanofluidics industry. Detailed description on effectiveness and limitations of various 3-\(\omega\) device design is understood, and critical comments are presented. Importantly, this review will aid new graduate students and researchers in the field of thermal conductivity measurement.

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References

  1. S. Lee, F. Yang, J. Suh, S. Yang, Y. Lee, G. Li, H.S. Choe, A. Suslu, Y. Chen, C. Ko, Nat. Commun. 6, 1 (2015)

    ADS  Google Scholar 

  2. S.S. Ghai, W.T. Kim, P.S. Chung, C.H. Amon, M.S. Jhon, Anisotropic thermal conductivity of nanoscale confined thin films via lattice Boltzmann method. In The 2006 Annual Meeting

  3. M. Asheghi, M. Touzelbaev, K. Goodson, Y. Leung, S. Wong, J. Heat Transfer 120, 1 (1998)

    Article  Google Scholar 

  4. J. Zhong, D. Liu, Z. Li, X. Sun, High thermal conductivity materials and their application on the electronic products. In 2012 IEEE Asia-Pacific Conference on Antennas and Propagation. IEEE

  5. M.S. Al-Homoud, Build. Environ. 40, 3 (2005)

    Article  Google Scholar 

  6. Y. Yang, S.M. Sadeghipour, W. Liu, M. Asheghi, M. Touzelbaev, in S. L. Shindé, J. S. ed. by H.T.C. Materials (Goela Springer, New York, 2006), pp. 69–118

    Google Scholar 

  7. T.L. Bergman, F.P. Incropera, D.P. DeWitt, A.S. Lavine, Fundamentals of Heat and Mass Transfer, 7th edn. (Wiley, Chichester, 2011)

    Google Scholar 

  8. L. Qiu, Y. Ouyang, Y. Feng, X. Zhang, X. Wang, J. Wu, Int. J. Therm. Sci. 162, 106781 (2021)

    Article  Google Scholar 

  9. D.G. Cahill, H.E. Fischer, T. Klitsner, E. Swartz, R. Pohl, J. Vac. Sci. Technol. A 7, 1259 (1989)

    Article  ADS  Google Scholar 

  10. J. Lee, Y. Kim, S.R. Joshi, M.S. Kwon, G.-H. Kim, Polym. Chem. 12, 7 (2021)

    Google Scholar 

  11. S. Sandell, E. Chávez-Ángel, A. El Sachat, J. He, C.M. SotomayorTorres, J. Maire, J. Appl. Phys. 128, 131101 (2020)

    Article  ADS  Google Scholar 

  12. K. Mylvaganam, Y. Chen, W. Liu, M. Liu, L. Zhang, in M. ed. by A.-A. Nanocoatings (Publishing, Aliofkhazraei Woodhead, 2015), pp. 543–567

    Google Scholar 

  13. D.T. Morelli, G.A. Slack, in S. L. Shindé, J. S. ed. by H.T.C. Materials (Goela Springer, New York, 2006), pp. 37–68

    Google Scholar 

  14. S. Deng, C. Xiao, J. Yuan, D. Ma, J. Li, N. Yang, H. He, Appl. Phys. Lett. 115, 10 (2019)

    Google Scholar 

  15. K. Termentzidis, J. Parasuraman, C.A. Da Cruz, S. Merabia, D. Angelescu, F. Marty, T. Bourouina, X. Kleber, P. Chantrenne, P. Basset, Nanoscale Res. Lett. 6, 1 (2011)

    Article  Google Scholar 

  16. E.A. Scott, J.T. Gaskins, S.W. King, P.E. Hopkins, APL Mater. 6, 5 (2018)

    Article  Google Scholar 

  17. A. Shahidian, M. Ghassemi, J. Mohammadi, M. Hashemi, Bio-Engineering Approaches to Cancer Diagnosis and Treatment (Academic Press, 2020).

  18. D.G. Cahill, Rev. Sci. Instrum. 61, 2 (1990)

    Article  Google Scholar 

  19. R.E. Bernhardsgrütter, C.J. Hepp, K. Schmitt, M. Jaegle, H.-F. Pernau, J. Wöllenstein, Sens. Actuators A 321, 112 (2021)

    Article  Google Scholar 

  20. S.R. Choi, J. Kim, D. Kim, Rev. Sci. Instrum. 78, 8 (2007)

    Google Scholar 

  21. S.N. Schiffres, J.A. Malen, A modified 3-omega technique to measure thermal conductivity in liquids, gases, and powders. in ASME/JSME Thermal Engineering Joint Conference

  22. S.N. Schiffres, J.A. Malen, Rev. Sci. Instrum. 82, 6 (2011)

    Article  Google Scholar 

  23. A. Jacquot, F. Vollmer, B. Bayer, M. Jaegle, D. Ebling, H. Böttner, J. Electron. Mater. 39, 9 (2010)

    Google Scholar 

  24. L. Tian, Y. Li, R.C. Webb, S. Krishnan, Z. Bian, J. Song, X. Ning, K. Crawford, J. Kurniawan, A. Bonifas, Adv. Funct. Mater. 27, 26 (2017)

    Google Scholar 

  25. A. Palacios, L. Cong, M. Navarro, Y. Ding, C. Barreneche, Renew. Sustain. Energy Rev. 108, 32 (2019)

    Article  Google Scholar 

  26. D.G. Cahill, R.O. Pohl, Phys. Rev. B 35, 8 (1987)

    Article  Google Scholar 

  27. D.A. Chernodoubov, A.V. Inyushkin, Rev. Sci. Instrum. 90, 2 (2019)

    Article  Google Scholar 

  28. D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, J. Electron. Packag. 138, 4 (2016)

    Article  Google Scholar 

  29. Y. Ju, K. Kurabayashi, K. Goodson, Thin Solid Films 339, 1–2 (1999)

    Article  Google Scholar 

  30. P.E. Hopkins, L.M. Phinney, J. Heat Transfer 131, 4 (2009)

    Google Scholar 

  31. S.Y. Lee, G.S. Kim, M.R. Lee, H. Lim, W.D. Kim, S.K. Lee, Nanotechnology 24, 18 (2013)

    Google Scholar 

  32. T.Y. Choi, D. Poulikakos, J. Tharian, U. Sennhauser, Appl. Phys. Lett. 87, 1 (2005)

    Google Scholar 

  33. B.W. Olson, S. Graham, K. Chen, Rev. Sci. Instrum. 76, 5 (2005)

    Article  Google Scholar 

  34. I. Moon, Y.H. Jeong, S. Kwun, Rev. Sci. Instrum. 67, 1 (1996)

    Article  Google Scholar 

  35. J. Hong, D. Kim, J. Heat Transfer 134, 9 (2012)

    Google Scholar 

  36. R. Karthik, R.H. Nagarajan, B. Raja, P. Damodharan, Exp. Therm Fluid Sci. 40, 1 (2012)

    Article  Google Scholar 

  37. S. Gauthier, P. Combette, A. Giani, Gas thermal conductivity measurement based on the three-omega method. in SENSORS, 2012 IEEE. IEEE

  38. S. Kommandur, A. Mahdavifar, P.J. Hesketh, S. Yee, Sens. Actuators A 233, 231 (2015)

    Article  Google Scholar 

  39. J. Kimling, S. Martens, K. Nielsch, Rev. Sci. Instrum. 82, 7 (2011)

    Article  Google Scholar 

  40. F. Warkusz, J. Phys. D: Appl. Phys. 11, 5 (1978)

    Article  Google Scholar 

  41. J.H. Kim, A. Feldman, D. Novotny, J. Appl. Phys. 86, 7 (1999)

    Google Scholar 

  42. C. Grosse, M. A. Ras, A. Varpula, K. Grigoras, D. May, M. Prunnila, B. Wunderle, S. Gomès, Development, design and fabrication of a measurement chip for thermal material characterization based on the 3-omega method. in 2017 23rd international workshop on thermal investigations of ICs and systems (THERMINIC). IEEE.

  43. C. Grosse, M.A. Ras, A. Varpula, K. Grigoras, D. May, B. Wunderle, P.-O. Chapuis, S. Gomès, M. Prunnila, Sens. Actuators A 278, 33 (2018)

    Article  Google Scholar 

  44. S. Ahmed, R. Liske, T. Wunderer, M. Leonhardt, R. Ziervogel, C. Fansler, T. Grotjohn, J. Asmussen, T. Schuelke, Diamond Relat. Mater. 15, 2–3 (2006)

    Article  Google Scholar 

  45. J. Alvarez-Quintana, J. Rodriguez-Viejo, Sens. Actuators A 142, 232 (2008)

    Article  Google Scholar 

  46. S.-M. Lee, D.G. Cahill, Microscale Thermophys. Eng. 1, 1 (1997)

    Article  Google Scholar 

  47. X. Zheng, L. Qiu, G. Su, D. Tang, Y. Liao, Y. Chen, J. Nanopart. Res. 13, 12 (2011)

    Google Scholar 

  48. M.G. McDowell, I.G. Hill, Rev. Sci. Instrum. 84, 5 (2013)

    Article  Google Scholar 

  49. Z. Li, H. Wang, H. Zhao, H. Gu, J. Wang, X. Wei, Rev. Sci. Instrum. 91, 8 (2020)

    Google Scholar 

  50. A. Jain, K.E. Goodson, J. Heat Transfer 130, 10 (2008)

    Article  Google Scholar 

  51. M. Bogner, A. Hofer, G. Benstetter, H. Gruber, R.Y. Fu, Thin Solid Films 591, 267 (2015)

    Article  ADS  Google Scholar 

  52. X. Zheng, P. Yue, S. Li, L. Wang, X. Yang, H. Chen, Rev. Sci. Instrum. 89, 8 (2018)

    Google Scholar 

  53. G. Boussatour, P.-Y. Cresson, B. Genestie, N. Joly, J.-F. Brun, T. Lasri, Polym. Test. 70, 503 (2018)

    Article  Google Scholar 

  54. D. Kim, D. Kim, S. Cho, S. Kim, S. Lee, J. Kim, Int. J. Thermophys. 25, 1 (2004)

    Article  Google Scholar 

  55. T. Pan, Y. Zhang, J. Huang, B. Zeng, D. Hong, S. Wang, H. Zeng, M. Gao, W. Huang, Y. Lin, J. Appl. Phys. 112, 4 (2012)

    Google Scholar 

  56. Z. Su, J.P. Freedman, J.H. Leach, E.A. Preble, R.F. Davis, J.A. Malen, J. Appl. Phys. 113, 21 (2013)

    Google Scholar 

  57. A. Moridi, L. Zhang, W. Liu, S. Duvall, A. Brawley, Z. Jiang, S. Yang, C. Li, Surf. Coat. Technol. 334, 233 (2018)

    Article  Google Scholar 

  58. T. Tian, K.D. Cole, Int. J. Heat Mass Transfer 55, 23–24 (2012)

    Google Scholar 

  59. G.-P. Su, L. Qiu, X.-H. Zheng, Z.-H. Xiao, D.-W. Tang, Int. J. Thermophys. 35, 2 (2014)

    Article  Google Scholar 

  60. V. Mishra, C.L. Hardin, J.E. Garay, C. Dames, Rev. Sci. Instrum. 86, 5 (2015)

    Google Scholar 

  61. L.N. Acquaroli, P. Newby, C. Santato, Y.-A. Peter, AIP Adv. 6, 10 (2016)

    Article  Google Scholar 

  62. J.H. Kwak, J.G. Kang, H.-S. Yang, E.D. Jeong, H.G. Kim, K.-S. Hong, Thin Solid Films 641, 34 (2017)

    Article  ADS  Google Scholar 

  63. A.A. Guermoudi, P.Y. Cresson, A. Ouldabbes, G. Boussatour, T. Lasri, J. Therm. Anal. Calorim. 145, 1 (2021)

    Article  Google Scholar 

  64. C. Mion, J. Muth, E.A. Preble, D. Hanser, Superlattices Microstruct. 40, 4–6 (2006)

    Article  Google Scholar 

  65. K. Valalaki, A. Nassiopoulou, J. Phys. D: Appl. Phys. 50, 19 (2017)

    Article  Google Scholar 

  66. B. Shen, Z. Zeng, C. Lin, Z. Hu, Int. J. Therm. Sci. 66, 19 (2013)

    Article  Google Scholar 

  67. F. Reisdorffer, B. Garnier, N. Horny, C. Renaud, M. Chirtoc, T.-P. Nguyen, Thermal conductivity of organic semi-conducting materials using 3omega and photothermal radiometry techniques. in EPJ Web of Conferences. EDP Sciences.

  68. A. Zhou, W. Wang, B. Yang, J. Li, Q. Zhao, Appl. Therm. Eng. 98, 683 (2016)

    Article  Google Scholar 

  69. S. Kommandur, S. Yee, Rev. Sci. Instrum. 89, 11 (2018)

    Article  Google Scholar 

  70. J.-C. Hsiao, Y.-H. Chen, C.-N. Liao, Thin Solid Films 645, 93 (2018)

    Article  ADS  Google Scholar 

  71. D. Singhal, J. Paterson, D. Tainoff, J. Richard, M. Ben-Khedim, P. Gentile, L. Cagnon, D. Bourgault, D. Buttard, O. Bourgeois, Rev. Sci. Instrum. 89, 8 (2018)

    Article  Google Scholar 

  72. N. Blumenschein, M. Slomski, P.P. Paskov, F. Kaess, M. Breckenridge, J. Muth, T. Paskova, Thermal conductivity of bulk and thin film [beta]-Ga2O3 measured by the 3 [omega] technique. in Oxide-based materials and devices IX. International Society for Optics and Photonics

  73. D. Song, C. Caylor, W. Liu, T. Zeng, T. Borca-Tasciuc, T. Sands, G. Chen, Thermal conductivity characterization of skutterudite thin films. in Eighteenth International Conference on Thermoelectrics. Proceedings, ICT'99 (Cat. No. 99TH8407). IEEE.

  74. L. Lu, W. Yi, D. Zhang, Rev. Sci. Instrum. 72, 7 (2001)

    Google Scholar 

  75. C. Dames, G. Chen, Rev. Sci. Instrum. 76, 12 (2005)

    Article  Google Scholar 

  76. L. Qiu, X. Wang, G. Su, D. Tang, X. Zheng, J. Zhu, Z. Wang, P.M. Norris, P.D. Bradford, Y. Zhu, Sci. Rep. 6, 1 (2016)

    Article  Google Scholar 

  77. X.J. Hu, A.A. Padilla, J. Xu, T.S. Fisher, K.E. Goodson, J. Heat Transfer 128, 11 (2006)

    Article  Google Scholar 

  78. Q. Kong, L. Qiu, Y.D. Lim, C.W. Tan, K. Liang, C. Lu, B.K. Tay, Surf. Coat. Technol. 345, 105 (2018)

    Article  Google Scholar 

  79. P.B. Kaul, K.A. Day, A.R. Abramson, J. Appl. Phys. 101, 8 (2007)

    Article  Google Scholar 

  80. J. Jin, M.P. Manoharan, Q. Wang, M. Haque, Appl. Phys. Lett. 95, 3 (2009)

    Google Scholar 

  81. E. Dechaumphai, J.L. Barton, J.R. Tesmer, J. Moon, Y. Wang, G.R. Tynan, R.P. Doerner, R. Chen, J. Nucl. Mater. 455, 1–3 (2014)

    Article  ADS  Google Scholar 

  82. S. Cui, M. Simmonds, W. Qin, F. Ren, G.R. Tynan, R.P. Doerner, R. Chen, J. Nucl. Mater. 486, 267 (2017)

    Article  ADS  Google Scholar 

  83. M.T. Barako, S. Roy-Panzer, T.S. English, T. Kodama, M. Asheghi, T.W. Kenny, K.E. Goodson, A.C.S. Appl, ACS Appl. Mater. Interfaces 7, 34 (2015)

    Article  Google Scholar 

  84. H. Zhang, F. Ye, Y. Hu, J. Liu, Y. Zhang, Y. Wu, Z. Hu, Superlattices Microstruct. 89, 312 (2016)

    Article  ADS  Google Scholar 

  85. N.W. Park, W.Y. Lee, J.A. Kim, K. Song, H. Lim, W.D. Kim, S.G. Yoon, S.K. Lee, Nanoscale Res. Lett. 9, 1 (2014)

    Article  Google Scholar 

  86. G. Athanasopoulos, E. Svoukis, M. Pervolaraki, R. Saint-Martin, A. Revcolevschi, J. Giapintzakis, Thin Solid Films 518, 16 (2010)

    Article  Google Scholar 

  87. B.K. Park, J. Park, D. Kim, Rev. Sci. Instrum. 81, 6 (2010)

    Google Scholar 

  88. L. Zhao, Y. Luo, X. Huang, X. Zhou, R. Hebibul, J. Ding, Z. Li, Z. Jiang, Rev. Sci. Instrum. 90, 1 (2019)

    Google Scholar 

  89. D.-W. Oh, A. Jain, J.K. Eaton, K.E. Goodson, J.S. Lee, Int. J. Heat Fluid Flow 29, 5 (2008)

    Article  Google Scholar 

  90. S. Mirmira, L. Fletcher, J. Thermophys Heat Transfer 12, 2 (1998)

    Google Scholar 

  91. ISO, SSEN Stockholm: Swedish Standards Institute (2015)

  92. A. Jacquot, B. Lenoir, A. Dauscher, M. Stölzer, J. Meusel, J. Appl. Phys. 91, 7 (2002)

    Article  Google Scholar 

  93. T. Borca-Tasciuc, A. Kumar, G. Chen, Rev. Sci. Instrum. 72, 4 (2001)

    Article  Google Scholar 

  94. C. Dames, Annu. Rev. Heat Transfer 16, 7 (2013)

    Article  Google Scholar 

  95. A. Sikora, H. Ftouni, J. Richard, C. Hébert, D. Eon, F. Omnès, O. Bourgeois, Rev. Sci. Instrum. 83, 5 (2012)

    Article  Google Scholar 

  96. Y. Liu, D. Tainoff, M. Boukhari, J. Richard, A. Barski, P. Bayle-Guillemaud, E. Hadji, O. Bourgeois, Sensitive 3-omega measurements on epitaxial thermoelectric thin films. in IOP Conference Series: Materials Science and Engineering. IOP Publishing.

  97. R. Minamisawa, R. Zimmerman, L. Holland, D. Ila, Instrum. Sci. Technol. 38, 5 (2010)

    Article  Google Scholar 

  98. H. Oikawa, R. Akiyama, K. Kanazawa, S. Kuroda, I. Harayama, K. Nagashima, D. Sekiba, Y. Ashizawa, A. Tsukamoto, K. Nakagawa, Thin Solid Films 574, 10 (2015)

    Article  Google Scholar 

  99. E. Marotta, N. Bakhru, A. Grill, V. Patel, B. Meyerson, Thin Solid Films 206, 1–2 (1991)

    Article  Google Scholar 

  100. P.C. Lou, A. Katailiha, R.G. Bhardwaj, T. Bhowmick, W. Beyermann, R.K. Lake, S. Kumar, Phys. Rev. B 101, 9 (2020)

    Google Scholar 

  101. R.G. Bhardwaj, P.C. Lou, S. Kumar, Appl. Phys. Lett. 112, 4 (2018)

    Article  Google Scholar 

  102. G.R. Jaffe, K.J. Smith, V.W. Brar, M.G. Lagally, M.A. Eriksson, Appl. Phys. Lett. 117, 073102 (2020)

    Article  ADS  Google Scholar 

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RGB acknowledge IIT Delhi for providing research facilities.

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RGB: Conceptualize, Writing and Reviewing – Original draft preparation. NK: Reviewing and Supervision. All authors have given approval to the final version of the manuscript.

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Correspondence to Neeraj Khare.

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Bhardwaj, R.G., Khare, N. Review: 3-\(\omega\) Technique for Thermal Conductivity Measurement—Contemporary and Advancement in Its Methodology. Int J Thermophys 43, 139 (2022). https://doi.org/10.1007/s10765-022-03056-3

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