Skip to main content
Log in

Surface roughness modulated resistivity in copper thin films

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

The surfaces of metallic thin films are never flat. The resistivity in thin films is very different from that in bulk because of the unavoidable rough surfaces. In this study, we apply a quantum-mechanical method to study the resistivity in metallic thin films. The resulting resistivity formula for metallic thin films merely involves two parameters: bulk relaxation time and surface roughness. We use the formula to fit a large number of experimental data sets for copper thin films obtained using different growing methods. With an additional tuning parameter for calibrating the film thickness, the quantum formula can provide a universal fitting to most data with a satisfactory precision, regardless of their growing methods or data source.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. C. Andricacos, C. Uzoh, J. O. Dukovic, J. Horkans, and H. Deligianni, IBM J. Res. Dev. 42, 567 (1998).

    Article  Google Scholar 

  2. W. L. Prater, E. L. Allen, W. Y. Lee, M. F. Toney, A. Kellock, J. S. Daniels, J. A. Hedstrom, and T. Harrell, J. Appl. Phys. 97, 093301 (2005).

    Article  ADS  Google Scholar 

  3. S. K. Mukherjee, L. Joshi, and P. K. Barhai, Surf. Coatings Tech. 205, 4582 (2011).

    Article  Google Scholar 

  4. J. J. Diaz Leon, D. M. Fryauf, R. D. Cormia, M. X. M. Zhang, K. Samuels, R. S. Williams, and N. P. Kobayashi, ACS Appl. Mater. Interfaces 8, 022337 (2016).

    Article  Google Scholar 

  5. A. Ghosh, A. Maity, R. Banerjee, and S. B. Majumder, J. Alloys Compd. 692, 108 (2016).

    Article  Google Scholar 

  6. B. Giroire, M. Ali Ahmad, G. Aubert, L. Teule-Gay, D. Michau, J. J. Watkins, C. Aymonier, and A. Poulon-Quintin, Thin Solid Films 643, 53 (2017).

    Article  ADS  Google Scholar 

  7. X. Zhang, J. Han, J. J. Plombon, A. P. Sutton, D. J. Srolovitz, and J. J. Boland, Science 357, 397 (2017).

    Article  ADS  Google Scholar 

  8. K. Fuchs, and N. F. Mott, Math. Proc. Camb. Phil. Soc. 34, 100 (2008).

    Article  ADS  Google Scholar 

  9. E. H. Sondheimer, Adv. Phys. 50, 499 (1952).

    Article  ADS  Google Scholar 

  10. A. F. Mayadas, and M. Shatzkes, Phys. Rev. B 1, 1382 (1970).

    Article  ADS  Google Scholar 

  11. A. F. Mayadas, R. Feder, and R. Rosenberg, J. Vacuum Sci. Tech. 6, 690 (1969).

    Article  ADS  Google Scholar 

  12. Y. Namba, J. Appl. Phys. 39, 6117 (1968).

    Article  ADS  Google Scholar 

  13. Y. Namba, Jpn. J. Appl. Phys. 9, 1326 (1970).

    Article  ADS  Google Scholar 

  14. Z. Tešanović, M. V. Jarić, and S. Maekawa, Phys. Rev. Lett. 57, 2760 (1986).

    Article  ADS  Google Scholar 

  15. N. Trivedi, and N. W. Ashcroft, Phys. Rev. B 38, 12298 (1988).

    Article  ADS  Google Scholar 

  16. J. W. Lim, K. Mimura, and M. Isshiki, Appl. Surf. Sci. 217, 95 (2003).

    Article  ADS  Google Scholar 

  17. L. Zhou, V. L. Grigoryan, S. Maekawa, X. Wang, and J. Xiao, Phys. Rev. B 91, 045407 (2015), arXiv: 1407.8310.

    Article  ADS  Google Scholar 

  18. V. L. Grigoryan, J. Xiao, X. Wang, and K. Xia, Phys. Rev. B 96, 144426 (2017).

    Article  ADS  Google Scholar 

  19. M. Jalochowski, and E. Bauer, Phys. Rev. B 38, 5272 (1988).

    Article  ADS  Google Scholar 

  20. O. Pfennigstorf, A. Petkova, Z. Kallassy, and M. Henzler, Eur. Phys. J. B 30, 111 (2002).

    Article  ADS  Google Scholar 

  21. M. Jałochowski, R. Zdyb, and M. C. Tringides, Phys. Rev. Lett. 116, 086101 (2016).

    Article  ADS  Google Scholar 

  22. M. C. Tringides, M. Jałochowski, and E. Bauer, Phys. Today 60, 50 (2007).

    Article  Google Scholar 

  23. Y. Ke, F. Zahid, V. Timoshevskii, K. Xia, D. Gall, and H. Guo, Phys. Rev. B 79, 155406 (2009).

    Article  ADS  Google Scholar 

  24. Y. N. Zhao, S. X. Qu, and K. Xia, J. Appl. Phys. 110, 075414R (2011).

    Google Scholar 

  25. A. A. Solovyev, V. A. Semenov, V. O. Oskirko, K. V. Oskomov, A. N. Zakharov, and S. V. Rabotkin, Thin Solid Films 631, 72 (2017).

    Article  ADS  Google Scholar 

  26. E. V. Barnat, D. Nagakura, and T. M. Lu, Rev. Sci. Instrum. 74, 3385 (2003).

    Article  ADS  Google Scholar 

  27. P. Y. Zheng, R. P. Deng, and D. Gall, Appl. Phys. Lett. 105, 042116 (2014).

    Google Scholar 

  28. E. Shahriari, and M. Ghasemi Varnamkhasti, Superlattices Micro- Struct. 75, 523 (2014).

    Article  ADS  Google Scholar 

  29. E. V. Barnat, P. I. Wang, D. Nagakura, and T. M. Lu, MRS Proc. 721, 73 (2002).

    Article  Google Scholar 

  30. E. V. Barnat, D. Nagakura, P. I. Wang, and T. M. Lu, J. Appl. Phys. 91, 1667 (2002).

    Article  ADS  Google Scholar 

  31. H. Marom, and M. Eizenberg, J. Appl. Phys. 99, 123705 (2006).

    Article  ADS  Google Scholar 

  32. W. Zhang, S. H. Brongersma, O. Richard, B. Brijs, R. Palmans, L. Froyen, and K. Maex, Microelectron. Eng. 76, 146 (2004).

    Article  Google Scholar 

  33. K. Mech, R. Kowalik, and P. Zabinski, Archiv. Metall. Mate. 56, 903 (2011).

    Google Scholar 

  34. F. Cemin, D. Lundin, D. Cammilleri, T. Maroutian, P. Lecoeur, and T. Minea, J. Vacuum Sci. Tech. A-Vacuum Surf.s Films 34, 051506 (2016).

    Article  ADS  Google Scholar 

  35. Y. Hanaoka, K. Hinode, K. Takeda, and D. Kodama, Mater. Trans. 43, 1621 (2002).

    Article  Google Scholar 

  36. J. M. Camacho, and A. I. Oliva, Microelectron. J. 36, 555 (2005).

    Article  Google Scholar 

  37. J. Vancea, H. Hoffmann, and K. Kastner, Thin Solid Films 121, 201 (1984).

    Article  ADS  Google Scholar 

  38. U. Jacob, J. Vancea, and H. Hoffmann, Phys. Rev. B 41, 11852 (1990).

    Article  ADS  Google Scholar 

  39. H. D. Liu, Y. P. Zhao, G. Ramanath, S. P. Murarka, and G. C. Wang, Thin Solid Films 384, 151 (2001).

    Article  ADS  Google Scholar 

  40. Y. P. Timalsina, A. Horning, R. F. Spivey, K. M. Lewis, T. S. Kuan, G. C. Wang, and T. M. Lu, Nanotechnology 26, 075704 (2015).

    Article  ADS  Google Scholar 

  41. Y. P. Timalsina, X. Shen, G. Boruchowitz, Z. Fu, G. Qian, M. Yamaguchi, G. C. Wang, K. M. Lewis, and T. M. Lu, Appl. Phys. Lett. 103, 191602 (2013).

    Article  ADS  Google Scholar 

  42. I. V. Antonets, L. N. Kotov, S. V. Nekipelov, and Y. A. Golubev, Tech. Phys. 49, 306 (2004).

    Article  Google Scholar 

  43. S. M. Rossnagel, and T. S. Kuan, J. Vac. Sci. Technol. B 22, 240 (2004).

    Article  Google Scholar 

  44. J. W. Lim, and M. Isshiki, J. Appl. Phys. 99, 094909 (2006).

    Article  ADS  Google Scholar 

  45. Y. Lantasov, R. Palmans, and K. Maex, Microelectron. Eng. 50, 441 (2000).

    Article  Google Scholar 

  46. X. Cui, D. A. Hutt, and P. P. Conway, Thin Solid Films 520, 6095 (2012).

    Article  ADS  Google Scholar 

  47. T. Hara, Y. Shimura, and K. Namiki, Jpn. J. Appl. Phys. 44, L408 (2005).

    Article  ADS  Google Scholar 

  48. J. R. Shi, S. P. Lau, Z. Sun, X. Shi, B. K. Tay, and H. S. Tan, Surf. Coat. Tech. 138, 250 (2001).

    Article  Google Scholar 

  49. Z. Li, and R. Gordon, Chem. Vap. Deposition 12, 435 (2010).

    Article  Google Scholar 

  50. S. K. Pandian, Preparation and Characterization of Titanium Based Coatings by DC Magnetron Sputtering Process, Dissertation for Master Degree (Tampere University of Technology, Finland, 2016), pp. 39–61.

    Google Scholar 

  51. A. Y. Cho, and J. R. Arthur, Prog. Solid State Chem. 10, 157 (1975).

    Article  Google Scholar 

  52. G. Dehm, M. Rühle, G. Ding, and R. Raj, Philos. Mag. B 71, 1111 (1995).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Ke Xia or Jiang Xiao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, H., Xia, K. & Xiao, J. Surface roughness modulated resistivity in copper thin films. Sci. China Phys. Mech. Astron. 61, 107011 (2018). https://doi.org/10.1007/s11433-018-9199-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-018-9199-8

Keywords

PACS number(s)

Navigation