Urbach Edge, Disorder, and Absorption On-set in a-Si:H


This paper presents a brief review of the research that began in the early ‘80s, continued through the ‘90s, and produced a “standard model” for the optical absorption edge of amorphous silicon. The research began as a response to the invention of a-Si:H solar cells by Carlson and Wronski at RCA laboratories in 1976, and the subsequent worldwide interest in the optical characterization of a-Si:H thin films. The immediate need was soon met, but the research continued as an effort to understand the physics of the optical absorption edge in a-Si:H, as well as to understand the differences between, and similarities to, the indirect optical absorption edge of c-Si. In this paper, we highlight the successes of this standard model, and briefly cover its experimental and theoretical development over the last 25 years. We summarize its current status, and suggest some experimental and theoretical opportunities for, and challenges to, what may now be called a standard model for the optical absorption edge of both a-Si:H and a-Ge:H.

This is a preview of subscription content, access via your institution.


  1. 1

    C. R. Wronski, D. E. Carlson, R. E. Daniel, Appl. Phys. Lett. 29, 602 (1976).

    CAS  Article  Google Scholar 

  2. 2

    J. Tauc, in Optical Properties of Solids F. Abeles, Ed. (North-Holland, Amsterdam, 1972) pp. 279.

  3. 3

    J. Tauc, in Amorphous and Liquid Semiconductors J. Tauc, Ed. (Plenum, New York, 1974).

  4. 4

    G. D. Cody, in Hydrogenated Amorphous Silicon, Volume 21B: Optical Properties J. I. Pankove, Ed. (Academic Press, Orlando, 1984) pp. 11–82.

    Article  Google Scholar 

  5. 5

    G. D. Cody, Journal of Non-Crystalline Solids 141, 3–15 (1992).

    CAS  Article  Google Scholar 

  6. 6

    M. V. Kurik, Phys. Stat. Sol. (a) 8, 9, 9–45 (1971).

    CAS  Article  Google Scholar 

  7. 7

    T. Skettrup, Phys. Rev. B. 18, 2622–2631 (1978).

    CAS  Article  Google Scholar 

  8. 8

    J. D. Wiley, D. Thomas, E. Schonherr, A. Breitschwerdt, J. Phys. Chem. Solids 41, 801–807 (1979).

    Article  Google Scholar 

  9. 9

    B. Abeles, C. R. Wronski, T. Tiedje, G. D. Cody, Solid State Communications 36, 537–540 (1980).

    CAS  Article  Google Scholar 

  10. 10

    J. Tauc, R. Gigorovici, A. Vancu, Phys. Status Solidi 15, 627–637 (1966).

    CAS  Article  Google Scholar 

  11. 11

    K. C. Hass, H. Ehrenreich, Annals of Physics 164, 77–102 (1985).

    CAS  Article  Google Scholar 

  12. 12

    G. D. Cody, B. G. Brooks, B. Abeles, Solar Energy Materials 8, 231–240 (1982).

    CAS  Article  Google Scholar 

  13. 13

    S. Abe, Y. Toyazawa, J. Physical Society of Japan 50, 2185–2194 (1981).

    CAS  Article  Google Scholar 

  14. 14

    G. D. Cody, in Physics and Applications of Amorphous Semiconductors F. Demichelis, Ed. (World Scientific, Singapore, 1988) pp. 28–62.

  15. 15

    A. Frova, A. Selloni, in Tetrahedrally-Bonded Amorphous Semiconductors D. Adler, H. Fritzsche, Eds. (Plenum, New York, NY, 1985) pp. 271–285.

  16. 16

    W. B. Jackson, S. M. Kelso, C. C. Tsai, J. W. Allen, S.-J. Oh, Phys. Rev. B 31, 5187–5198 (1985).

    Article  Google Scholar 

  17. 17

    B. G. Bagley, D. E. Aspnes, G. K. Celler, A. C. Adams, in Laser and Electron Beam Interactions with solids B. R. Appleton, G. K. Cellar, Eds. (Elsevier, Amsterdam, 1982) pp. 483.

  18. 18

    C. M. Fortman, Physical Review Letters 81, 3683–6 (1998).

    Article  Google Scholar 

  19. 19

    S. K. O'Leary, Applied Physics Letters 72, 1332–34 (1998).

    CAS  Article  Google Scholar 

  20. 20

    S. M. Malik, S. K. O'Leary, Appl. Phs. Lett. 80, 790 (2002).

    CAS  Article  Google Scholar 

  21. 21

    S. K. O'Leary, S. M. Malik, J. Appl. Phys. 92, 4276 (2002).

    CAS  Article  Google Scholar 

  22. 22

    N. F. Mott, E. A. Davis, Electronic Processes in Non-Crystalline Materials (Oxford University Press (Clarendon), London and New York, ed. 2nd, 1979).

    Google Scholar 

  23. 23

    G. D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Physical Review Letters 47, 1480–1483 (1981).

    CAS  Article  Google Scholar 

  24. 24

    P. D. Persans, A. F. Ruppert, S. S. Chan, G. D. Cody, Solid State Communications 51, 203–207 (1984).

    CAS  Article  Google Scholar 

  25. 25

    P. D. Persans, A. F. Ruppert, G. D. Cody, B. G. Brooks, Solid State Communications 54, 461–464 (1985).

    CAS  Article  Google Scholar 

  26. 26

    C. M. Soukoulis, M. H. Cohen, E. N. Economou, Phs. Rev. Letters 53, 616–619 (1984).

    CAS  Article  Google Scholar 

  27. 27

    C. H. Grein, S. John, Physical Review B 36, 7457–7648 (1987).

    CAS  Article  Google Scholar 

  28. 28

    C. H. Grein, S. John, Physical Review B 39, 1140–1151 (1989).

    CAS  Article  Google Scholar 

  29. 29

    C. H. Grein, S. John, Solid State Communications 70, 87–91 (1989).

    CAS  Article  Google Scholar 

  30. 30

    C. H. Grein, S. John, Physical Review B 41, 7641–7647 (1990).

    CAS  Article  Google Scholar 

  31. 31

    S. John, C. H. Grein, Reviews of Solids State Sciences 4, 1–59 (1990).

    CAS  Google Scholar 

  32. 32

    G. E. MacFarlane, T. P. McLean, J. E. Quarrington, V. Roberts, Phys. Rev. 111, 1245 (1956).

    Article  Google Scholar 

  33. 33

    D. E. Aspnes, in Properties of Silicon - Inspec DataRreview Series. (INSPEC, London and New York, 1988).

    Google Scholar 

  34. 34

    W. Bludeau, A. Onton, H. J. Heinke, J. Appl. Phys. 45 1846 (1974).

    Article  Google Scholar 

  35. 35

    R. Braunstein, A. Moore, F. Herman, Phys. Rev. 109, 695 (1958).

    CAS  Article  Google Scholar 

  36. 36

    I. A. Weinstein, A. F. Zatsepin, V. S. Kortov, Physics of the Solid State 43, 246–250 (2001).

    CAS  Article  Google Scholar 

  37. 37

    M. Beaudoin, A. J. G. DeVries, S. R. Johnson, H. Laman, T. Tiedje, Applied Physics Letters 70, 3540–2 (1997).

    CAS  Article  Google Scholar 

  38. 38

    F. Orapunt, S. K. O'Leary, Applied Physics Letters 84, 523–525 (2004).

    CAS  Article  Google Scholar 

  39. 39

    G. D. Cody, C. R. Wronski, B. Abeles, R. B. Stephens, B. Brooks, Solar Cells 2, 227–242 (1980).

    CAS  Article  Google Scholar 

  40. 40

    Z. Remes, Ph. D. Thesis, Charles University, Prague, (1999).

  41. 41

    R. E. Viturro, K. Weiser, Philosophical Magazine B 53, 93–103 (1986).

    CAS  Article  Google Scholar 

  42. 42

    Q. Wang, H. Antoniadis, E. A. Schiff, S. Guha, Phys. Rev. B. 47, 9435–9448 (1993).

    CAS  Article  Google Scholar 

  43. 43

    E. A. Schiff, J. Phys: Condens. Matter 16, S5265–S5275 (2004).

    CAS  Google Scholar 

  44. 44

    E. Yablonovitch, G. D. Cody, IEEE Transactions on Electron Devices ED-29, 300–305 (1982).

    CAS  Article  Google Scholar 

  45. 45

    T. Tiedje, E. Yablonovitch, G. D. Cody, B. G. Brooks, IEEE Transactions on Electron Devices ED-31, 711–716 (1984).

    CAS  Article  Google Scholar 

  46. 46

    G. D. Cody, T. Tiedje, in Energy and the Environment B. Abeles, A. J. Jacobson, P. Sheng, Eds. (World Scientific, Singapore, 1992) pp. 147–213.

  47. 47

    C. R. Wronski, in Hydrogenated Amorphous Silicon, Volume 21C: Electronic and Transport Properties J. I. Pankove, Ed. (Academic Press, Orlando, 1984) pp. 347–374.

    Article  Google Scholar 

  48. 48

    C. R. Wronski, MRS Symp. Proc.: Amorphous and Microcrystalline Silicon Technology-1997, Vol. 467, E. Schiff, M. Hack, S. Wagner, R. Schropp, Eds., MRS Spring, 1997, San Francisco (MRS, 1997).

  49. 49

    T. Surek, Progress in U. S. Photovoltaics: Looking Back 30 Years and Looking Ahead 20, 3rd World Conference on Photovoltaic Energy Conversion, Osaka, Japan (May 11–18, 2003).

    Google Scholar 

Download references


Thanks to all of my colleagues and co-workers, listed in the references, for their contributions over the past 30 years, particularly to B. G. Brooks for the optical absorption measurements, to my friend, advisor, and experimental colleague of 50 years, Ben Abeles, and to my dear wife, friend, and co-parent/grandparent of our 20 member family, Francesca Benson.

Author information



Corresponding author

Correspondence to G. D. Cody.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cody, G.D. Urbach Edge, Disorder, and Absorption On-set in a-Si:H. MRS Online Proceedings Library 862, 13 (2004). https://doi.org/10.1557/PROC-862-A1.3

Download citation