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Modeling, Characterization, and Properties of Transparent Conducting Oxides

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Handbook of Transparent Conductors

Abstract

Other authors in this book have discussed at length the applications and synthesis of transparent conducting oxides (TCOs). Our purpose in this chapter is to discuss some elementary aspects of TCO properties, which can be explained surprisingly well using the Drude free-electron theory [1]. Although this theory explains the electrical properties and fits the optical data so well, many have questioned whether any fundamental understanding of TCOs can be gained from its use. We believe that much can be learned about the properties of the conduction electrons in some, but not all, TCOs. The conduction electrons are important because they dominate the optical properties of the materials in the visible and near-infrared (NIR) wavelengths. The functional form of the free-electron theory often accounts for measurable properties of TCOs such as transmittance and reflectance, and their relationship to extrinsically controllable properties (e.g., carrier concentration and relaxation time) and intrinsic, uncontrollable, properties (e.g., crystal lattice and effective mass,).

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Notes

  1. 1.

    This can be shown from the second of Newton’s equations of motion, \( s = 1/2a{t^2} \). We put \( \bar{a} = e\bar{E}/m ^* \) and \( t = 1/2f \), where \( f = \omega /2\pi. \) For a wavelength of 1.5µm, an effective mass of 0.35m e and an electric field strength of 1Vm−1, the amplitude, s, is about 2×10−7nm. Even though the electric field strength is assumed to be constant, this approach is sufficient to make an order of magnitude estimate. If we include scattering of the electrons, then an estimate of the amplitude may be made from (3.7). With a mobility of 50cm2V−1s−1, and the same conditions as above, the amplitude is about 4×10−8nm.

  2. 2.

    For a typical plasma wavelength of 1.5µm, an effective mass of 0.35m e, and a relaxation time of about 5×10−15s, corresponding to a mobility of about 25cm2V−1s−1, this inequality is obeyed to within about 2.5%. It is obeyed to better than 10% over the full range of frequencies shown in Fig.3.2.

  3. 3.

    The Fresnel reflection coefficient is given by \( R = \frac{{{{\left( {N - 1} \right)}^2} + {k^2}}}{{{{\left( {N + 1} \right)}^2} + {k^2}}} \). Hence, at low frequency, where both N and k are relatively large, the reflection coefficient is also large.

References

  1. P. Drude, Annalen der Physik 1, 3, 566, 369 (1900).

    Google Scholar 

  2. B. O’Neill, in Indium: Markets, Applications and Alternatives, Lisbon, Portugal (2005).

    Google Scholar 

  3. T. J. Coutts, X. Li, T. M. Barnes, B. M. Keyes, C. L. Perkins, S. E. Asher, S. B. Zhang, S. H. Wei, and S. Limpijumnong, in Zinc Oxide Bulk, Thin Films and Nanostructures: Processing, Properties and Applications, edited by C. Jagadish and S. J. Pearton (Elsevier, Amsterdam, 2006), pp. 43–84.

    Chapter  Google Scholar 

  4. S. Ghosh, A. Sarkar, S. Chaudhuri, and A. K. Pal, Thin Solid Films 205, 64–68 (1991).

    Article  Google Scholar 

  5. H. Kim, C. M. Gilmore, J. S. Horwitz, A. Pique, H. Murata, G. P. Kushto, R. Schlaf, Z. H. Kafafi, and D. B. Chrisey, Applied Physics Letters 76, 259–261 (2000).

    Article  Google Scholar 

  6. M. W. J. Prins, D.-O. Grosse-Holz, J. F. M. Cillessen, and L. F. Feiner, Journal of Applied Physics 83, 888–893 (1998).

    Article  Google Scholar 

  7. W. P. Mulligan, Ph.D. Thesis, Colorado School of Mines (1997).

    Google Scholar 

  8. T. J. Coutts, D. L. Young, X. Li, W. P. Mulligan, and X. Wu, Journal of Vacuum Science and Technology A 18, 2646–2660 (2000).

    Article  Google Scholar 

  9. V. Kaydanov, Thesis, Colorado School of Mines (1999).

    Google Scholar 

  10. D. H. Zhang and H. L. Ma, Applied Physics A 62, 487–492 (1996).

    Article  Google Scholar 

  11. J. R. Bellingham, Thesis, Emmanuel College (1989).

    Google Scholar 

  12. X. Li, T. A. Gessert, and T. J. Coutts, Applied Surface Science 223, 138–143 (2004).

    Article  Google Scholar 

  13. M. P. Taylor, Ph.D. Thesis, Colorado School of Mines (2005).

    Google Scholar 

  14. R. H. Williams, R. R. Varma, and V. V. Montgomery, Journal of Vacuum Science and Technology 16, 1418 (1979).

    Article  Google Scholar 

  15. J. Y. W. Seto, Journal of Applied Physics 46, 5247–5254 (1975).

    Article  Google Scholar 

  16. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction (Cambridge University Press, New York, NY, 1999).

    Google Scholar 

  17. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt Brace College Publishers, Fort Worth, TX, 1976).

    Google Scholar 

  18. L. Scheff, M. Dressel, M. Jourdan, and H. Adrian, Nature 438, 1135 (2005).

    Article  Google Scholar 

  19. A. K. Azad, Applied Physics Letters 88, 021103-1–021103-3 (2006).

    Article  Google Scholar 

  20. ?

    Google Scholar 

  21. J. I. Pankove, Optical Processes in Semiconductors (Dover Publications, New York, NY, 1971).

    Google Scholar 

  22. P. A. Iles and S. I. Soclof, in Design Factors for Transparent Conducting Layers in Solar Cells, Baton Rouge, LA, (1976) (IEEE), pp. 978–987.

    Google Scholar 

  23. M. P. Taylor, D. W. Readey, C. W. Teplin, M. F. A. M. van Hest, J. L. Alleman, M. S. Dabney, L. M. Gedvilas, B. M. Keyes, J. D. Perkins, and D. S. Ginley, Measurement Science and Technology 16, 90–94 (2005).

    Article  Google Scholar 

  24. V. I. Kaidanov and I. A. Chernik, Soviet Physics – Semiconductors 1, 1159–1163 (1967).

    Google Scholar 

  25. K. J. Button, C. G. Fonstad, and W. Dreybrodt, Physical Review B 4, 4539–4542 (1971).

    Article  Google Scholar 

  26. T. Wang, J. Bai, and S. Sakai, Applied Physics Letters 76, 2737–2739 (2000).

    Article  Google Scholar 

  27. J. A. Marley and R. C. Dockerty, Physical Review 140, A304–A310 (1965).

    Article  Google Scholar 

  28. P. Wagner and R. Helbig, The Journal of Physics and Chemistry of Solids 35, 327–335 (1972).

    Article  Google Scholar 

  29. E. H. Hall, American Journal of Mathematics 2, 287 (1879).

    Article  MathSciNet  Google Scholar 

  30. L. L. Campbell, Galvanomagnetic and Thermomagnetic Effects the Hall and Allied Phenomena (Longmans, Green and Co, New York, NY, 1923).

    Google Scholar 

  31. A. V. Ettingshausen, Anzeiger der Akademie der Wissenshaften in Wien 16 (1887).

    Google Scholar 

  32. L. Boltzmann, Anzeiger der Akademie der Wissenshaften in Wien 24, 217 (1886).

    Google Scholar 

  33. A. V. Ettingshausen and W. Nernst, Anzeiger der Akademie der Wissenshaften in Wien 23, 114 (1886).

    Google Scholar 

  34. E. Putley, The Hall Effect and Related Phenomena (Butterworths, London, 1960).

    Google Scholar 

  35. W. Gerlach, Handbuch der Physik, Vol. 13 (Springer, Berlin, 1928).

    Google Scholar 

  36. F. Seitz, Physical Review 73, 549–564 (1948).

    Article  Google Scholar 

  37. R. Barrie, Proceedings of the Physical Society B 69, 553–561 (1956).

    Article  MATH  Google Scholar 

  38. E. O. Kane, The Journal of Physics and Chemistry of Solids 1, 249–261 (1957).

    Article  Google Scholar 

  39. W. Zawadzki and J. Kolodziejczak, Physica Status Solidi 6, 419–428 (1964).

    Article  Google Scholar 

  40. N. V. Kolomoets, Soviet Physics – Solid State 8, 799–803 (1966).

    Google Scholar 

  41. W. F. Leonard and J. T. L. Martin, Electronic Structure and Transport Properties of Crystals, First ed. (Robert E. Krieger Publishing Company, Malabar, FL, 1987).

    Google Scholar 

  42. S. S. Li, Semiconductor Physical Electronics (Plenum, New York, NY, 1993).

    Book  Google Scholar 

  43. B. M. Askerov, Electron Transport Phenomena in Semiconductors (World Scientific, Singapore, 1994).

    Book  Google Scholar 

  44. R. H. Bube, Electrons in Solids, an Introductory Survey, 3 ed. (Academic Press, San Diego, CA, 1992).

    Google Scholar 

  45. J. Kolodziejczak and S. Zukotynski, Physica Status Solidi 5, 145–158 (1964).

    Article  Google Scholar 

  46. S. Zukotynski and J. Kolodziejczak, Physica Status Solidi 3, 990–1000 (1963).

    Article  Google Scholar 

  47. L. Onsager, Physical Review 37, 405–426 (1931).

    Article  Google Scholar 

  48. L. Onsager, Physical Review 38, 2265–2279 (1931).

    Article  MATH  Google Scholar 

  49. J. Kolodziejczak, Acta Physica Polonica XX, 289–302 (1961).

    Google Scholar 

  50. J. Kolodziejczak and L. Sosnowski, Acta Physica Polonica 21, 399 (1962).

    MATH  Google Scholar 

  51. S. Zukotynski and J. Kolodziejczak, Physica Status Solidi 19, k51–k54 (1967).

    Article  Google Scholar 

  52. I. N. Dubrovskaya and Y. I. Ravich, Soviet Physics – Solid State 8, 1160–1164 (1966).

    Google Scholar 

  53. M. K. Zhitinskaya, V. I. Kaidanov, and I. A. Chernik, Soviet Physics – Solid State 8, 295–297 (1966).

    Google Scholar 

  54. I. A. Chernik, V. I. Kaidanov, N. V. Kolomoets, and M. I. Vinogradova, Soviet Physics – Semiconductors 2, 645–651 (1968).

    Google Scholar 

  55. D. L. Young, T. J. Coutts, V. I. Kaydanov, A. S. Gilmore, and W. P. Mulligan, Journal of Vacuum Science and Technology A 18, 2978–2985 (2000).

    Article  Google Scholar 

  56. D. L. Young, T. J. Coutts, and V. I. Kaydanov, Review of Scientific Instruments 71, 462–466 (2000).

    Article  Google Scholar 

  57. W. Jiang, S. N. Mao, X. X. Xi, X. Jiang, J. L. Peng, T. Venkatesan, C. J. Lobb, and R. L. Greene, Physical Review Letters 73, 1291–1294 (1994).

    Article  Google Scholar 

  58. ASTM, in Annual Book of ASTM Standards (American Society of Testing and Materials, West Conshohocken, 1996).

    Google Scholar 

  59. V. I. Kaidanov and I. S. Lisker, Zavodskaya Laboratoriya 32, 1091–1095 (1966).

    Google Scholar 

  60. S. Brehme, F. Fenske, W. Fuhs, E. Nebauer, M. Poschenrieder, B. Selle, and I. Sieber, Thin Solid Films 342, 167–173 (1999).

    Article  Google Scholar 

  61. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology: Semiconductors; Vol. 17, edited by K. H. Hellwege (Springer, Berlin, 1982)

    Google Scholar 

  62. S. Bloom and I. Ortenburger, Physica Status Solidi (b) 58, 561–566 (1973).

    Article  Google Scholar 

  63. X. Yang, C. Xu, and N. Giles, in Role of Neutral Impurity Scattering in the Analysis of Hall Data from ZnO, Denver, CO (2007).

    Google Scholar 

  64. S. Lany and A. Zunger, Physical Review Letters 98, 045501-1–045501-4 (2007).

    Article  Google Scholar 

  65. H. Ohta, M. Orita, and M. Hirano, Journal of Applied Physics 91, 3547 (2002).

    Article  Google Scholar 

  66. Y. Yoshida, D. M. Wood, T. A. Gessert, and T. J. Coutts, Applied Physics Letters 84, 2097–2099 (2004).

    Article  Google Scholar 

  67. X. Wu, T. J. Coutts, and W. P. Mulligan, Journal of Vacuum Science and Technology A 15, 1057–1062 (1997).

    Article  Google Scholar 

  68. T. J. Coutts, D. L. Young, and X. Li, MRS Bulletin 25, 58–65 (2000).

    Article  Google Scholar 

  69. Y. Yoshida, T. A. Gessert, C. L. Perkins, and T. J. Coutts, Journal of Vacuum Science and Technology A 21, 1092–1097 (2003).

    Article  Google Scholar 

  70. T. A. Gessert, Y. Yoshida, and T. J. Coutts (USA, 2004).

    Google Scholar 

  71. J. Zhou, X. Wu, T. A. Gessert, Y. Yan, G. Teeter, and H. R. Moutinho, Materials Research Society Proceedings 865, 387–392 (2005).

    Article  Google Scholar 

  72. T.-H. Chen, Y. Liou, T. J. Wu, and J. Y. Chen, Applied Physics Letters 85, 2092–2094 (2004).

    Article  Google Scholar 

  73. Y.-J. Lin, C.-W. Hsu, Y.-M. Chen, and Y.-C. Wang, Journal of Electronic Materials 34, L9–L11 (2005).

    Article  Google Scholar 

  74. H. Kim, J. S. Horwitz, W. H. Kim, S. B. Qadri, and Z. H. Kafafi, Applied Physics Letters 83, 3809–3811 (2003).

    Article  Google Scholar 

  75. G. D. Wilk, R. M. Wallace, and J. M. Anthony, Applied Physics Letters 89, 5243–5275 (2001).

    Google Scholar 

  76. G. Lucovsky and G. B. Rayner, Applied Physics Letters 77, 2912–2914 (2000).

    Article  Google Scholar 

  77. R. Groth, Physica Status Solidi 14, 69–75 (1966).

    Article  Google Scholar 

  78. T. Koida and M. Mondo, Applied Physics Letters, 082104-1–082104-3 (2006).

    Google Scholar 

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Acknowledgements

This work was performed under U.S. Department of Energy contract number DE-AC36-GO9910337. The authors would like to express their thanks for the input given by Yuki Yoshida (now of Sanyo) and Viktor Kaydanov (formerly of the Colorado School of Mines).

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    Timothy J. Coutts

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    David S. Ginley

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Coutts, T.J., Young, D.L., Gessert, T.A. (2011). Modeling, Characterization, and Properties of Transparent Conducting Oxides. In: Ginley, D. (eds) Handbook of Transparent Conductors. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1638-9_3

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