Interface-induced phenomena in polarization response of ferroelectric thin films

Journal of Applied Physics

Volumn 100, Issue 5, 2006, Pages

  Tagantsev, A K ^a   Gerra, G ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CAPACITORS; DIELECTRIC PROPERTIES; ELECTRODES; POLARIZATION;

INTERFACE INDUCED EFFECTS; POLING EFFECT; THIN FILM CAPACITORS;

FERROELECTRIC THIN FILMS;

EID: 33748849243     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2337009     Document Type: Review

References (90)

1. A. K. Tagantsev, M. Landivar, E. Colla, and N. Setter, J. Appl. Phys. 78, 2623 (1995).
2. C. J. Brennan, Ferroelectrics 132, 245 (1992).
3. S. L. Miller, R. D. Nasby, J. R. Schwank, M. S. Rogers, and P. V. Dressendorfer, J. Appl. Phys. 58, 6463 (1990).
4. m. This condition can be met. An example of the data on the thickness dependence of the loop tilt, which have been acquired while checking the validity of this condition, has been reported by Tagantsev et al. (Ref. 5).
5. A. K. Tagantsev, M. Landivar, E. Colla, and N. Setter, in Science and Technology of Electroceramic Thin Films, NATO ASI, edited by O. Auciello and R. Waser (Kluwer Academic, Dordrecht, 1995), pp. 301-314.
6. c an essential part of the polarization does not vanish (cf. Ref. 1 for a discussion). In Ref. 8, the depolarizing field is wrongly taken to be parallel - instead of antiparallel - to the direction of polarization.
7. P. K. Larsen, G. J. M. Dormans, D. J. Taylor, and P. J. Vanveldhoven, J. Appl. Phys. 76, 2405 (1994).
8. M. Dawber, P. Chandra, P. B. Littlewood, and J. F. Scott, J. Phys.: Condens. Matter 15, L393 (2003).
9. J. F. M. Cillessen, M. W. J. Prins, and R. W. Wolf, J. Appl. Phys. 81, 2777 (1997).
10. A. K. Tagantsev and I. A. Stolichnov, Appl. Phys. Lett. 74, 1326 (1999).
11. f-σ, since the variation of the latter is not fully controlled by the current in the external circuit.
12. J. Zhu, X. Zhang, Y. Zhu, and S. B. Desu, J. Appl. Phys. 83, 1610 (1998).
13. S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, and R. Ramesh, Appl. Phys. Lett. 85, 2044 (2004).
14. M. W. Chu, I. Szafraniak, R. Scholz, C. Harnagea, D. Hesse, M. Alexe, and U. Gösele, Nat. Mater. 3, 87 (2004).
15. L. P. Batra and B. D. Silverman, Solid State Commun. 11, 291 (1972).
16. R. D. Tilley and B. Zeks, Ferroelectrics 134, 313 (1992).
17. J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, 1972).
18. R. Kretschmer and K. Binder, Phys. Rev. B 20, 1065 (1979).
19. Making allowance for the background permittivity becomes important when the depolarizing effect is involved, cf. Ref. 20.
20. A. K. Tagantsev, Ferroelectrics 69, 321 (1986).
21. A. K. Tagantsev, E. Courtens, and L. Arzel, Phys. Rev. B 64, 224107 (2001).
22. Y. Yamada, G. Shirane, and A. Linz, Phys. Rev. 177, 848 (1969).
23. Actually, the correlation length is anisotropic, i.e., the parameter δ-cf. Eq. (2.19) - is different for different orientations of the polarization and of its gradient. Since we are now interested in an estimate, we neglect this anisotropy in our consideration.
24. O. G. Vendik and S. P. Zubko, J. Appl. Phys. 88, 5343 (2000).
25. S. K. Streiffer, C. Basceri, C. B. Parker, S. E. Lash, and A. I. Kingon, J. Appl. Phys. 86, 4565 (1999).
26. C. Basceri, S. K. Streiffer, A. I. Kingon, and R. Waser, J. Appl. Phys. 82, 2497 (1997).
27. O. G. Vendik and S. P. Zubko, J. Appl. Phys. 82, 4475 (1997).
28. J. Junquera and P. Ghosez, Nature (London) 422, 506 (2003).
29. N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998).
30. A. Kopal, P. Mokry, J. Fousek, and T. Bahnik, Ferroelectrics 223, 127 (1999).
31. A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. 80, 3177 (2000).
32. A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. B 63, 132103 (2001).
33. P. Mokry, A. K. Tagantsev, and N. Setter, Phys. Rev. B 70, 172107 (2004).
34. P. Mokry and A. K. Tagantsev (unpublished).
35. A. K. Tagantsev, I. Stolichnov, N. Setter, and J. S. Cross, J. Appl. Phys. 96, 6616 (2004).
36. M. Grossmann, O. Lohse, D. Bolten, U. Boettger, T. Schneller, and R. Waser, J. Appl. Phys. 92, 2680 (2002).
37. M. Grossmann, O. Lohse, D. Bolten, U. Boettger, and R. Waser, J. Appl. Phys. 92, 2688 (2002).
38. J. J. OODwyer, The Theory of Electrical Conduction and Breakdown in Solid Dielectrics (Clarendon, Oxford, 1973).
39. d. This obviously does not affect the results of our analysis.
40. I. L. Baginskii and E. G. Kostsov, Phys. Status Solidi A 91, 705 (1985).
41. off can be determined from simple electrostatic arguments.
42. C. J. Brennan, Integr. Ferroelectr. 7, 93 (1995).
43. J. G. Simmons, J. Phys. Chem. Solids 32, 2581 (1971).
44. f(T) at the electrochemical equilibrium temperature.
45. A. K. Tagantsev, C. Pawiaczyk, K. Brooks, and N. Setter, Integr. Ferro electr. 4, 1 (1994).
46. The model discussed here is oversimplified - e.g., the electrodes and nearby-electrode regions of the ferroelectric are considered as electrochemically identical, and electrochemical equilibrium may not be reached at the deposition or top-electrode annealing temperature. However, these factors should not influence the validity of the qualitative picture of the phenomenon described by the model.
47. J. F. Scott, C. A. P. de Araujo, B. M. Melnick, L. D. McMillan, and R. Zuleeg, J. Appl. Phys. 70, 382 (1991).
48. R. Waser and M. Klee, Integr. Ferroelectr. 2, 23 (1992).
49. C. J. Brennan, Integr. Ferroelectr. 2, 73 (1992).
50. A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. B 61, 15042 (2000).
51. A. K. Tagantsev, V. O. Sherman, K. F. Astafiev, J. Venkatesh, and N. Setter, J. Electroceram. 11, 5 (2003).
52. The dislocation population can be controlled during processing - cf., e.g., T. Yamada, K. F. Astafiev, V. O. Sherman, A. K. Tagantsev, P. Muralt, and N. Setter, Appl. Phys. Lett. 86, 142904 (2005).
53. A. K. Tagantsev, Phys. Rev. B 34, 5883 (1986).
54. A. K. Tagantsev, Phase Transitions 35, 119 (1991).
55. S. M. Kogan, Sov. Phys. Solid State 5, 2069 (1964).
56. W. Ma and L. E. Cross, Appl. Phys. Lett. 79, 4420 (2001).
57. M/ a, which does not affect the essential features of the argument.
58. K. Abe, S. Komatsu, N. Yanase, K. Sano, and T. Kawakubo, Jpn. J. Appl. Phys., Part 1 36, 5846 (1997).
59. K. Abe, N. Yanase, T. Yasumoto, and T. Kawakubo, J. Appl. Phys. 91, 323 (2002).
60. K. Abe, N. Yanase, T. Yasumoto, and T. Kawakubo, Jpn. J. Appl. Phys., Part 1 41, 6065 (2002).
61. W. J. Merz, Phys. Rev. 95, 690 (1956).
62. R. Landauer, J. Appl. Phys. 28, 227 (1957).
63. A. K. Tagantsev, Ferroelectrics 184, 79 (1996).
64. M. Molotskii, R. Kris, and G. Rosenman, J. Appl. Phys. 88, 5318 (2000).
65. G. Gerra, A. K. Tagantsev, and N. Setter, Phys. Rev. Lett. 94, 107602 (2005).
66. The following expression for c is valid when the argument of the logarithmic function is much greater than unity, which is typically the case for ferroelectrics.
67. A. P. Levanyuk and A. S. Sigov, Defects and Structural Phase Transitions (Gordon and Breach, New York, 1988).
68. The thermodynamic coercive field introduced in this way is the field at which the antiparallel orientation of polarization relative to the applied field becomes absolutely unstable with respect to an infinitesimal increment of the polarization in the longitudinal direction. One should note that such quantity may not be the real thermodynamic coercive field of the system if more than two antiparallel domain states are involved in the switching - cf. Ref. 69.
69. M. Iwata and Y. Ishibashi, Jpn. J. Appl. Phys., Part 1 38, 5670 (1999).
70. T. Yamamoto, Jpn. J. Appl. Phys., Part 1 35, 5104 (1996).
71. A. K. Tagantsev, I. Stolichnov, N. Setter, J. S. Cross, and M. Tsukada, Phys. Rev. B 66, 214109 (2002).
72. Y. Imry and S. Ma, Phys. Rev. Lett. 35, 1399 (1975).
73. A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. 94, 107601 (2005).
74. A similar result was previously found by Glinchuk and Morozovska (Ref. 75), who considered the poling effect of the lattice mismatch between ferroelectric and substrate. In this case, the smearing of the phase transition is less pronounced, as the effect is proportional to the square of the misfit strain (typically less than 1%). Moreover, the relation between misfit strain and surface polarization in Eqs. (5) and (7) of Ref. 75 is incorrect: it is the latter quantity that is induced by the former via the piezoelectric effect, and not the other way around, so that strain should be multiplied -and not divided - by the piezoelectric coefficient to get the induced polarization!
75. M. D. Glinchuk and A. N. Morozovska, J. Phys.: Condens. Matter 16, 3517 (2004).
76. R. Takayama and Y. Tomita, J. Appl. Phys. 65, 1666 (1989).
77. D. Dimos, W. L. Warren, M. B. Sinclair, B. A. Tuttle, and R. W. Schwartz, J. Appl. Phys. 76, 4305 (1994).
78. A. L. Kholkin, K. G. Brooks, D. V. Taylor, S. Hiboux, and N. Setter, Integr. Ferroelectr. 22, 1045 (1998).
79. M. Alexe, C. Harnagea, D. Hesse, and U. Gösele, Appl. Phys. Lett. 79, 242 (2001).
80. S. Traynor, T. Hadnagy, and L. Kammerdiner, Integr. Ferroelectr. 16, 63 (1997).
81. K. Abe, N. Yanase, and T. Kawakubo, Jpn. J. Appl. Phys., Part 1 39, 4059 (2000).
82. off. This relation, Eq. (1), is valid only in the absence of charges on the electrodes. The formula taking into account these charges, Eq. (2.54) in the present paper, does not predict such dependence.
83. K. Carl and K. H. Hardtl, Ferroelectrics 17, 473 (1978).
84. E. G. Lee, D. J. Wouters, G. Willems, and H. E. Maes, Appl. Phys. Lett. 70, 2404 (1997).
85. S. Hiboux and P. Murait, Integr. Ferroelectr. 36, 83 (2001).
86. S. Hiboux, Ph. D. thesis, Swiss Federal Institute of Technology (EPFL), 2001.
87. J. Lee, R. Ramesh, V. G. Keramidas, W. L. Warren, G. E. Pike, and J. T. Evans, Appl. Phys. Lett. 66, 1337 (1995).
88. G. E. Pike, W. L. Warren, D. Dimos, B. A. Tuttle, R. Ramesh, J. Lee, V. G. Keramidas, and J. T. Evans, Appl. Phys. Lett. 66, 484 (1995).
89. W. L. Warren, D. Dimos, G. E. Pike, B. A. Tuttle, M. V. Raymond, R. Ramesh, and J. T. Evans, Appl. Phys. Lett. 67, 866 (1995).
90. P. Schorn, U. Ellerkmann, D. Bolten, U. Boettger, and R. Waser, Integr. Ferroelectr. 53, 361 (2003).