분수계 수학을 사용한 박막트랜지스터의 문턱전압 이동 모델 확장

Expansion of Thin-Film Transistors' Threshold Voltage Shift Model using Fractional Calculus

  • 정태호 (서울과학기술대학교 전자공학과)
  • Taeho Jung (Department of Electronic Engineering, Seoul National University of Science and Technology)
  • 투고 : 2024.05.28
  • 심사 : 2024.06.21
  • 발행 : 2024.06.30

초록

The threshold voltage shift in thin-film transistors (TFTs) is modeled using stretched-exponential (SE) and stretched-hyperbola (SH) functions. These models are derived by introducing empirical parameters into reaction rate equations that describe defect generation or charge trapping caused by hydrogen diffusion in the dielectric or interface. Separately, the dielectric relaxation phenomena are also described by the same reaction rate equations based on defect diffusion. Dielectric relaxation was initially modeled using the SE model, and various models have been proposed using fractional calculus. In this study, the characteristics of the threshold voltage shift and the dielectric relaxation phenomena are compared and analyzed to explore the applicability of analytical models used in the field of dielectric relaxation, in addition to the conventional SE and SH models.

키워드

참고문헌

  1. A. J. Snell, K. D. Mackenzie, W. E. Spear, P. G. LeComber and A. J. Hughes, "Application of amorphous silicon field effect transistors in addressable liquid crystal display panels," Appl. Phys. A, Vol. 24, pp. 357-362, 1981. 
  2. W. B. Jackson, "Role of band-tail carriers in metastable defect formation and annealing in hydrogenated amorphous silicon," Phys. Rev. B, Vol. 41, pp. 1059-1075, 1990. 
  3. T. Jung, "Modeling of stretched-exponential and stretched-hyperbola time dependence of threshold voltage shift in thin-film transistors," J. Appl. Phys., Vol. 117, pp. 144501, 2015. 
  4. R. Metzler and J. Klafter, "From stretched exponential to inverse power-law: fractional dynamics, Cole-Cole relaxation processes, and beyond," J. Non-Cryst. Solids, Vol. 305, pp. 81-87, 2002. 
  5. W. Jackson, C. C. Tsai and R. Thompson, "Estimates of the diffusion rate of the dominant paramagnetic defect in hydrogenated amorphous silicon," J. Non-Cryst. Solids, Vol. 114, pp. 396-398, 1989. 
  6. R. B. Wehrspohn, M. J. Powell and S. C. Deane, "Kinetics of defect creation in amorphous silicon thin film transistors," J. Appl. Phys., Vol. 93, pp. 5780-5788, 2003. 
  7. J. Kakalios, R. A. Street and W. B. Jackson, "Stretched-exponential relaxation arising from dispersive diffusion of hydrogen in amorphous silicon," Phys. Rev. Lett., Vol. 59, pp. 1037-1040, 1987. 
  8. M. N. Berberan-Santos, E. N. Bodunov and B. Valeur, "Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)," Chem. Phys., Vol. 315, pp. 171-182, 2005. 
  9. Y. F. Chen and S. F. Huang, "Connection between the Meyer-Neldel rule and stretched-exponential relaxation," Phys. Rev. B, Cond. Matt., Vol. 44, pp. 13775-13778, 1991. 
  10. H. L. Gomes, P. Stallinga, F. Dinelli, M. Murgia, F. Biscarini, D. M. de Leeuw, T. Muck, J. Geurts, L. W. Molenkamp and V. Wagner, "Bias-induced threshold voltages shifts in thin-film organic transistors," Appl. Phys. Lett., Vol. 84, pp. 3184-3186, 2004. 
  11. S. C. Deane, R. B. Wehrspohn and M. J. Powell, "Unification of the time and temperature dependence of dangling-bond-defect creation and removal in amorphous-silicon thin-film transistors," Phys. Rev. B, Vol. 58, pp. 12625-12628, 1998. 
  12. H. J. Haubold and A. M. Mathai, "The Fractional Kinetic Equation and Thermonuclear Functions," Astrophys. Space Sci., Vol 273, pp. 53-63, 2000. 
  13. T. R. Prabhakar, "A Singular Integral Equation with A Generalized Mittag Leffler Function in The Kernel," Yokohama Math. J., Vol. 19, pp. 7-15, 1971. 
  14. R. Garrappa, F. Mainardi and G. Maione, "Models of Dielectric Relaxation Based on Completely Monotone Functions," Fcaa, Vol. 19, pp. 1105-1160, 2016. 
  15. K. S. Cole and R. H. Cole, "Dispersion and Absorption in Dielectrics II. Direct Current Characteristics," J. Chem. Phys., Vol. 10, pp. 98-105, 1942. 
  16. U. Saglam and D. Deger, "A Phenomenological Approach to Anomalous Transport in Complex or Disordered Media," Can. J. Phys., Vol. 100, pp. 180-184, 2022. 
  17. A. Allagui, H. Benaoum, A. S. Elwakil and M. Alshabi, "Extended RC Impedance and Relaxation Models for Dissipative Electrochemical Capacitors," Ted, Vol. 69, pp. 5792-5799, 2022. 
  18. A. A. Khamzin, R. R. Nigmatullin and I. I. Popov, "Justification of the empirical laws of the anomalous dielectric relaxation in the framework of the memory function formalism," Fcaa, Vol. 17, pp. 247-258, 2014. 
  19. V. V. Novikov and V. P. Privalko, "Temporal fractal model for the anomalous dielectric relaxation of inhomogeneous media with chaotic structure," Phys. Rev. E, Vol. 64, 2001.