Modeling Asymmetric Shift in the Threshold Voltage of MOS Structures under Thermal Field Treatment
https://doi.org/10.32603/1993-8985-2025-28-2-69-79
Abstract
Introduction. Thermal field treatment (TFT) of MOS structures causes instability of the threshold voltage associated with the transport of mobile ions of alkaline earth metal impurities (mainly Na+) in the electric field of the gate dielectric. Experimental kinetics of accumulation and restoration of the mobile charge during TFT deviate from the known descriptions by Snow’s diffusion and Hofstein’s boundary capture models.
Aim. Development of a quantitative model for the behavior of MOS structures during thermal field treatment in the modes of accumulation and restoration of the mobile charge of an ionic impurity.
Materials and methods. The model is based on the analysis of the capture kinetics of mobile impurity ions on polyenergetic traps in the volume of an amorphous gate dielectric. Following the analysis of physical processes, a system of differential equations is compiled and solved by the finite difference method using explicit and implicit difference schemes.
Results. The conducted comparison of the data calculated by the developed model and the experimental data reported in literature for the time dependencies of the threshold voltage shift of MOS structures with positive and subsequent negative gate bias determined the range of binding energies, the characteristic dispersion energy, the concentrations of impurity ions and traps near the gate and the silicon substrate, and the width of the region of their localization. A decrease in the range of binding energies in the vicinity of the SiO2–Si interface compared to the SiO2–metal gate interface was found, which may indicate the presence of an ordered thin SiO2 layer in the vicinity of silicon.
Conclusion. It was shown that the charge recovery process occurs at a higher rate than the accumulation process due to the difference in the distribution of traps in the vicinity of the interphase boundaries of SiO2 with the silicon substrate and with the gate. The proposed model can be used to describe the experimental asymmetric behavior of MOS structures contaminated with alkaline earth metal ions during TFT.
About the Authors
O. V. AleksandrovRussian Federation
Oleg V. Aleksandrov, Dr Sci. (Phys.-Math.) (2003), Professor (2008) of the Department of Electronic Instrumentation
5 F, Professor Popov St., St Petersburg 197022
N. N. Morozov
Russian Federation
Nikita N. Morozov, Master's degree in Electronics and Nanoelectronics (2022), Postgraduate student and assistant of the Department of Electronic Instrumentation
5 F, Professor Popov St., St Petersburg 197022
References
1. Bias Temperature Instability for Devices and Circuits. Ed. by T. Grasser. New York, Springer, 2013, 810 p. doi: 10.1007/978-1-4614-7909-3
2. Zhang J. F., Gao R., Duan M., Ji Z., Zhang W., Marsland J. Bias Temperature Instability of MOSFETs: Physical Processes, Models and Prediction. Electronics. 2022, vol. 11, iss. 9, art. no. 1420. doi: 10.3390/electronics11091420
3. Snow E. H., Grove A. S., Deal B. E., Sah C. T. Ion Transport Phenomena in Insulating Films. J. of Applied Physics. 1965, vol. 36, no. 5, pp. 1664–1673. doi: 10.1063/1.1703105
4. Hofstein S. R. An Investigation of Instability and Charge Motion in Metal-Silicon Oxide-Silicon Structures. IEEE Transactions on Electron Devices. 1966, vol. ED-13, iss. 2, pp. 222–237. doi: 10.1109/T-ED.1966.15674
5. Aleksandrov O. V., Morozov N. N. Influence of Traps on Mobile Charge Accumulation in MOS Structures in Thermal Field Treatments. LETI Transactions on Electrical Engineering & Computer Science. 2023, vol. 16, no. 6, pp. 20–28. doi: 10.32603/2071-8985-2023-16-6-20-28
6. Krasnikov G. Ya., Zaitsev N. A. Sistema kremnii-dioksid kremniya submikronnykh SBIS [Silicon-Silicon Dioxide System of Submicron VLSI]. Moscow, Tekhnosfera, 2003, 383 p. (In Russ.)
7. Scher H., Montroll E. W. Anomalous Transit-Time Dispersion in Amorphous Solids. Physical Review B. 1975, vol. 12, no. 6, art. no. 2455. doi: 10.1103/PhysRevB.12.2455
8. Curtis Jr O. L., Srour J. R. The Multiple Trapping Model and Hole Transport in SiO2. J. of Applied Physics. 1977, vol. 48, no. 9, pp. 3819–3828. doi: 10.1063/1.324248
9. Schmidlin F. W. Theory of Multiple Trapping. Solid State Communications. 1977, vol. 22, iss. 7, pp. 451–453. doi: 10.1016/0038-1098(77)90123-5
10. Noolandi J. Equivalence of Multiple-Trapping Model and Time-Dependent Random Walk. Physical Review B. 1977, vol. 16, no. 10, art. no. 4474. doi: 10.1103/PhysRevB.16.4474
11. Arkhipov V. I., Nikitenko V. R. Dispersion Transport in Materials with Non-Monotonic Energy Distribution of Localized States. Physics and Technology of Semiconductors. 1989, vol. 23, no. 6, pp. 978–984. (In Russ.)
12. Stagg J. P. Drift Mobilities of Na+ and K+ Ions in SiO2 Films. Applied Physics Let. 1977, vol. 31, no. 8, pp. 532–533. doi: 10.1063/1.89766
13. Kriegler R. J., Devenyi T. F. Temperature-Bias Aging of (HCl) MOS Structures. 11th Reliability Physics Symp. Las Vegas, USA, 03–05 Apr. 1973. IEEE, 1973, pp. 153–158. doi: 10.1109/IRPS.1973.362587
14. Sugano T., Hoh K., Kudo K., Hishinuma N. Ordered Structure And Ion Migration In Silicon Dioxide Films. Japan. J. Appl. Phys. 1968, vol. 7, no. 7, pp. 715–730. doi: 10.1143/JJAP.7.715
15. Boudry M. R., Stagg J. P. The Kinetic Behavior of Mobile Ions in the Al–SiO2–Si System. J. of Applied Physics. 1979, vol. 50, no. 2, pp. 942–950. doi: 10.1063/1.326016
16. Hickmott T. W. Thermally Stimulated Ionic Conductivity of Sodium in Thermal SiO2. J. of Applied Physics. 1975, vol. 46, no. 6, pp. 2583–2598. doi: 10.1063/1.321935
17. Goldman E. I., Zhdan A. G., Chucheva G. V. Transport of Free Ions in a Dielectric Layer and Effects of Electron-Ion Exchange at the Dielectric-Semiconductor Interface during Thermally Stimulated Ion Depolarization of Silicon MOS Structures. Physics and Technology of Semiconductors. 1999, vol. 33, no. 8, pp. 962–968. (In Russ.)
18. Oh J. H., Yeom H. W., Hagimoto Y., Ono K., Oshima M., Hirashita N., Nywa M., Toriumi A., Kakizaki A. Chemical Structure of the Ultrathin SiO2/Si(100) Interface: An Angle-Resolved Si 2p Photoemission Study. Physical Review B. 2001, vol. 63, no. 20, art. no. 205310. doi: 10.1103/PhysRevB.63.205310
19. Sugita Y., Watanabe S., Awaji N., Komiya S. Structural Fluctuation of SiO2 Network at the Interface with Si. Applied Surface Science. 1996, vol. 100–101, pp. 268–271. doi: 10.1016/0169-4332(96)00302-9
20. Monakhov V. V., Romanov O. V., Kirillov S. N., Uritskii V. Ya., Smirnov V. A. Stages of Formation of the Interface between Silicon and Thermal Oxide. Physics and Technology of Semiconductors. 1986, vol. 20, no. 3, pp. 477–480. (In Russ.)
21. Ono H., Ikarashi T., Ando K., Kitano T. Infrared Studies of Transition Layers at SiO2/Si Interface. J. of Applied Physics. 1998, vol. 84, no. 11, pp. 6064–6069. doi: 10.1063/1.368917
22. Kimura K., Nakajima K. Compositional Transition Layer in SiO2/Si Interface Observed by High-Resolution RBS. Applied Surface Science. 2003, vol. 216, no. 1–4, pp. 283–286. doi: 10.1016/S0169-4332(03)00386-6
23. Bongiorno A., Pasquarello A., Hybertsen M. S., Feldman L. C. Transition Structure at the Si (100)–SiO2 Interface. Physical Review Let. 2003, vol. 90, no. 18, art. no. 186101. doi: 10.1103/PhysRevLett.90.186101
24. Smith F. W., Ghidini G. Reaction of Oxygen with Si (111) and (100): Critical Conditions for the Growth of SiO2. J. of the Electrochemical Society. 1982, vol. 129, no. 6, art. no. 1300. doi: 10.1149/1.2124122
25. Fuoss P. H., Fuoss Paul H., Norton L. J., Brennan S., Fischer-Colbrie A. X-ray Scattering Studies of the Si–SiO2 Interface. Physical Review Let. 1988, vol. 60, no. 7, pp. 600–603. doi: 10.1103/PhysRevLett.60.600
26. Ourmazd A., Taylor D. W., Rentschler J. A. Si→SiO2 Transformation: Interfacial Structure and Mechanism. Physical Review Let. 1987, vol. 59, no. 2, art. no. 213. doi: 10.1103/PhysRevLett.59.213
27. Munkholm A., Brennan S., Comin F., Ortega L. Observation of a Distributed Epitaxial Oxide in Thermally Grown SiO2 on Si (001). Physical Review Let. 1995, vol. 75, no. 23, art. no. 4254. doi: 10.1103/PhysRevLett.75.4254
28. Shimura T., Misaki H., Umeno M., Takahashi I., Harada J. X-ray Diffraction Evidence for the Existence of Epitaxial Microcrystallites in Thermally Oxidized SiO2 Thin Films on Si (111) Surfaces. J. of Crystal Growth. 1996, vol. 166, no. 1–4, pp. 786–791. doi: 10.1016/0022-0248(95)00496-3
29. Awaji N., Sugita Y., Horii Y., Takahashi I. In Situ Observation of Epitaxial Microcrystals in Thermally Grown SiO2 on Si (100). Applied Physics Let. 1999, vol. 74, no. 18, pp. 2669–2671. doi: 10.1063/1.123953
30. Ikarashi N., Watanabe K., Miyamoto Y. High-Resolution Transmission Electron Microscopy of an Atomic Structure at a Si (001) Oxidation Front. Physical Review B. 2000, vol. 62, no. 23, art. no. 15989. doi: 10.1103/PhysRevB.62.15989
31. Tu Y., Tersoff J. Structure and Energetics of the Si–SiO2 Interface. Physical Review Let. 2000, vol. 84, no. 19, art. no. 4393. doi: 10.1103/PhysRevLett.84.4393
32. Dreiner S., Schürmann M., Westphal C. Structural Analysis of the SiO2/Si (100) Interface by Means of Photoelectron Diffraction. Physical Review Let. 2004, vol. 93, no. 12, art. no. 126101. doi: 10.1103/PhysRevLett.93.126101
Review
For citations:
Aleksandrov O.V., Morozov N.N. Modeling Asymmetric Shift in the Threshold Voltage of MOS Structures under Thermal Field Treatment. Journal of the Russian Universities. Radioelectronics. 2025;28(2):69-79. (In Russ.) https://doi.org/10.32603/1993-8985-2025-28-2-69-79