Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-18T04:42:00.432Z Has data issue: false hasContentIssue false
  • English
  • Français

Electronic States in Amorphous Solids, Liquids, and Alloys

Published online by Cambridge University Press:  26 February 2011

Y. Bar-Yam ,
D. Adler  and
J. D. Joannopoulos
Y. Bar-Yam
Affiliation:
IBM T. J. Watson Research Center, Yorktown Heights NY 10598 MIT Dept. of Physics Cambridge MA 02139
J. D. Joannopoulos
Affiliation:
MIT Dept. of Physics Cambridge MA 02139
Get access

Abstract

We describe elements of a thermodynamical ensemble theory of electronic states in a variety of disordered systems. Equilibrium energies and kinetics of phase space exploration combine to determiine the ensembles describing disordered systems. Electronic properties are then related to structural energies. This relationship serves to determine the distribution of electronic states present in real materials. Thus we obtain directly electronic properties without a need for detailed microscopic information about the diverse systems. Applications range from the Urbach edge to defect properties providing a unified understanding.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 95: Symposium E – Amorphous Silicon Semiconductors--Pure and Hydrogenated , 1987 , 3
Copyright
Copyright © Materials Research Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

l. Anderson, P. W., Phy. Rev. 109, 1492 (1958); N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd ed. (Clarendon, Oxford, 1979)Google Scholar
2. For some recent developments see a) Pantelides, S. T., this volume; andb) A. Ourmazd, J. C. Bean, and J. C. Phillips, Phys. Rev. Lett. 55, 1599 (1985).Google Scholar
3. Bar-Yam, Y., Adler, D., and Joannopoulos, J. D., Phys. Rev. Lett. 57, 467 (1986); and unpublished; also Ref. 32.Google Scholar
4. see the discussion of work on random and correlated distributions of impurities in Electronic Properties of Doped Semiconductors by A. L. Efros and B. I. Shklovskii (Springer-Verlag, 1984), Chap. 11–13 We also do not use the terms “annealed” or “quenched” ensembles because in this context we emphasise the non-random nature of the ensemble whether “annealed” or “quenched” (ie. whether structure is in active equilibration or frozen).Google Scholar
5. Chemical potentials may be introduced to impose system constraints (eg. stoichiometry, boundary conditions, flatness of space). A second type of “pixing” transition can be introduced which occurs when system constraints (boundary conditions, flatness of space) result in the inaccessibility of all states of lower energy than those accessible at a temperature Tx. For such systems freezing may occur even when barriers may still be overcome. For example, dislocations at interfaces. This picture is closely related to structural constraint models which are equivalent to redefining the ground state.Google Scholar
6. Equilibration of the electronic density of states corresponds to equilibration of structural degrees of freedom. Generally, but not always, equilibration of electronic occupations occurs under such circumstances.Google Scholar
7. Urbach, F., Phys. Rev. 92, 1324 (1953); see also H. Mahr Phys. Rev. 125, 1510 (1962)Google Scholar
8. Some of theoretical approaches which have attracted the most attention are: Toyozawa, Y., Prog. of Theor. Phys. 20, 53 (1958) J. D. Dow and D. Redfield, Phys. Rev. Lett. 26, 762 (1971); Phys. Rev. B 5, 594 (1972) S. Abe and Y. Toyozawa, J. Phys. Soc. Jpn. 50, 2185 (1981) C. M. Soukoulis, M. H. Cohen, and E. N. Economou, Phys. Rev. Lett. 53,616 (1984) S. John, C. Soukoulis, M. H. Cohen and E. N. Economou, Phys. Rev. Lett. 57, 1777 (1986)Google Scholar
9. Halperin, B. I. and Lax, M., Phys. Rev. 148, 722 (1966); 153, 802 (1967)Google Scholar
10. Tiedje, T., in Semiconductors and Semimetals, Vol.21C, 207 (1984)Google Scholar
11. Kastner, M. A., J. Non-Cryst. Solids 78, 1173 (1985)Google Scholar
12. see also Tauc, J., Mat. Res. Bull. 5,721 (1970) for the related idea of “frozen phonons”.Google Scholar
13. similar ideas are suggested independently in Phillips, J. C., Chan, C. T., S. G. Louie (preprint); A. Ksendzov, F. H. Possak, G. P. Espinosa, and J. C. Phillips (preprint)Google Scholar
14. Cody, G. D. Semiconductors and Semimetals 21B, 11 (1984) impling, that zero temperature disorder in a-Si:H is positional not alloy disorder. Band edges shift due to entropy terms.Google Scholar
15. Anderson, P. W., Phys. Rev. Lett. 34, 953 (1975)Google Scholar
16. LeComber, P. G. and Spear, W. E. in Amorphous Semiconductors, Brodsky, M. H., ed., Springer (1979) p. 251.Google Scholar
17. Adler, David, Phys. Rev. Lett. 41, 1755 (1978)Google Scholar
18. Phillips, J. C., Phys. Rev. Lett. 42, 1151 (1979)Google Scholar
19. Street, R. A., Phys. Rev. Lett. 49, 1187 (1982); J. Mon-Cryst. Solids 77, 1 (1985)Google Scholar
20. Abkowitz, M., J. Non-Cryst. Solids 78, 1191 (1985)Google Scholar
21. Lang, D. V., Cohen, J. D., and Harbison, J. P., Phys. Rev. Lett. 48, 421 (1982)Google Scholar
22. Smith, Z E. and Wagner, S., Phys. Rev. B 32, 5510 (1985); Z E. Smith, S. Aljishi, D. Slobodin, V. Chu, S. Wagner, P. M. Lenahan, R. R. Arya and M. S. Bennett, Phys. Rev. Lett. 57,2450 (1986)Google Scholar
23. Street, R. A., Kakalios, J., and Hayes, T. M., Phys. Rev. B 34, 3030 (1986)Google Scholar
24. We note that available experimental results may, in principle, be explained entirely in terms of local rearangement. Long range diffusion more commonly observed in crystals is still to be demonstrated for amorphous materials or glasses.Google Scholar
25. A possible realization may have been found in Han, H.-X. and Feldman, B. J. (this volume)Google Scholar
26. Mosseri, R., DiVincenzo, D. P., Sadoc, J. F., and Brodsky, M. H., Phys. Rev. B 32, 3974 (1985); D. R. Nelson and M. Widom, Nucl. Phys. B240 [FS12], 113 (1984)Google Scholar
27. see Guha, S., J. Non-Cryst. Solids 77&78 8745 (1982)Google Scholar
28. Adler, David, Solar Cells 9, 133 (1983); A.I.P. Proc. 120, 70 (1984)Google Scholar
29. see Street, R. A. and Biegelsen, D. K. in The Physics of Hydrogenated Amorphous Silicon, Joannopoulos, J. D. and Lucovsky, G., eds., Springer Verlag (1984), p. 195; Z. Vardeny and J. Tauc, Phys. Rev. Lett. 54, 1844 (1985);Google Scholar
30. Photovoltaics for Solar Energy Applications II, Adler, D. ed., SPIE Proc. 407 (1983) Amorphous Semiconductors for Microelectronics, D. Adler ed., SPIE Proc. 617 (1983); A.I.P. Int. Conf. on Stability of Amorphous Silicon Alloy Materials and Devices (1987)Google Scholar
31. Staebler, D. L. and Wronski, C. R., J. Appl. Phys. 51, 3262 (1980)Google Scholar
32. Bar-Yam, Y., Adler, D., and Joannopoulos, J. D., A.I.P. Int. Conf. on Stability of Amorphous Silicon Alloy Materials and Devices (in press, 1987); J. D. Joannopoulos, D. Adler and Y. Bar-Yam, in Disordered Semiconductors, M. Kastner, G. A. Thomas, and S. R. Ovshinsky eds. Plenum (1987) Y. Bar-Yam, D. Adler, and J. D. Joannopoulos (unpublished)Google Scholar
33. Daxing Han and Fritzsche, H., J. Non-Cryst. Solids, 59&60, 397(1983)Google Scholar
34. Guha, S., Huang, C.-Y., Hudgens, S. J. and Payson, J. S., J. Non-Cryst. Solids 66, 65 (1984)Google Scholar
35. Stutzmann, M., Jackson, W. B., and Tsai, C. C., Phys. Rev. B 32, 23 (1985)Google Scholar
36. Lee, Charles, Ohlsen, W. D., Taylor, P. C., Ullal, H. S. and Ceasar, G. P., Phys. Rev. B 31, 100 (1985)Google Scholar
37. Krühler, W., Pfleiderer, H., Plättner, R. and Stetter, W., A.I.P. Proc. 120, 311 (1984)Google Scholar
38. Kolodzey, J., Aljishi, S. Smith, Z E., Chu, V., Schwarz, R. and Wagner, S., Materials Research Society Vol.70 (1986) p. 371 Google Scholar