JSTS:Journal of Semiconductor Technology and Science

  • 제10권3호
  • /
  • Pages.203-212
  • /
  • 2010
  • /
  • 1598-1657(pISSN)
  • /
  • 2233-4866(eISSN)
대한전자공학회 (The Institute of Electronics and Information Engineers)
권호 표지
DOI QR코드

DOI QR Code

An Analytical Model of the First Eigen Energy Level for MOSFETs Having Ultrathin Gate Oxides

  • Yadav, B. Pavan Kumar (Department of Electrical Engineering Indian Institute of Technology) ;
  • Dutta, Aloke K. (Department of Electrical Engineering Indian Institute of Technology)
  • 투고 : 2009.09.19
  • 심사 : 2010.07.09
  • 발행 : 2010.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we present an analytical model for the first eigen energy level ($E_0$) of the carriers in the inversion layer in present generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. Commonly used approaches to evaluate $E_0$ make either or both of the following two assumptions: one is that the barrier height at the oxide-semiconductor interface is infinite (with the consequence that the wave function at this interface is forced to zero), while the other is the triangular potential well approximation within the semiconductor (resulting in a constant electric field throughout the semiconductor, equal to the surface electric field). Obviously, both these assumptions are wrong, however, in order to correctly account for these two effects, one needs to solve Schrodinger and Poisson equations simultaneously, with the approach turning numerical and computationally intensive. In this work, we have derived a closed-form analytical expression for $E_0$, with due considerations for both the assumptions mentioned above. In order to account for the finite barrier height at the oxide-semiconductor interface, we have used the asymptotic approximations of the Airy function integrals to find the wave functions at the oxide and the semiconductor. Then, by applying the boundary condition at the oxide-semiconductor interface, we developed the model for $E_0$. With regard to the second assumption, we proposed the inclusion of a fitting parameter in the wellknown effective electric field model. The results matched very well with those obtained from Li's model. Another unique contribution of this work is to explicitly account for the finite oxide-semiconductor barrier height, which none of the reported works considered.

키워드

참고문헌

  1. A. Ghatak and S. Lokanathan, “Quantum Mechanics:Theory and Applications,” 5th Ed., McMillan,2004.
  2. L.D. Landau and E.M. Lifshitz, “Quantum Mechanics:Non-Relativistic Theory,” Translated fromRussian by J.B. Sykes and J.S. Bell, Course ofTheoretical Physics, Vol.3, pp.491-492, 1956.
  3. Julian Schwinger, “Quantum Mechanics: Symbolismof Atomic Measurements,” Edited by Berthold-Georg Englert, Springer, 2001.
  4. T. Janik and B. Majkusiak, “Analysis of the MOStransistor based on the self-consistent solution tothe Schrödinger and Poisson equations and on thelocal mobility model,” IEEE Transactions on ElectronDevices, Vol.45, No.6, pp.1263-1271, 1998. https://doi.org/10.1109/16.678531
  5. F. Stern, “Self-consistent results for n-type Si inversionlayers,” Physical Review B, Vol.5, No.12,pp.4891-4899, 1972. https://doi.org/10.1103/PhysRevB.5.4891
  6. S. Mudanai, L.F. Register, A.F. Tasch, and S.K.Banerjee, “Understanding the effects of wave functionpenetration on the inversion layer capacitanceof NMOSFETs,” IEEE Electron Device Letters,Vol.22, No.3, pp.145-147, 2001. https://doi.org/10.1109/55.910624
  7. H.H. Mueller and M.J. Schulz, “Simplified methodto calculate the band bending and the subband energiesin MOS capacitors,” IEEE Transactions onElectron Devices, Vol.44, No.9, pp.1539-1543,1997. https://doi.org/10.1109/16.622612
  8. Y. Ma, L. Liu, Z. Yu, and Z. Li, “Thorough analysisof quantum mechanical effects on MOS structurecharacteristics in threshold region,” MicroelectronicsJournal, Vol.31, No.11-12, pp.913-921, 2000. https://doi.org/10.1016/S0026-2692(00)00097-5
  9. X. Liu, J. Kang, X. Guan, R. Han, and Y. Wang,“The influence of tunneling effect and inversionlayer quantization effect on threshold voltage ofdeep submicron MOSFETs,” Solid State Electronics,Vol.44, No.8, pp.1435-1439, 2000. https://doi.org/10.1016/S0038-1101(00)00065-4
  10. F. Li, S. Mudanai, L.F. Register, and S.K. Banerjee,“A physically based compact gate C-V model forultrathin (EOT 1 nm and below) gate dielectricMOS devices,” IEEE Transactions on Electron Devices,Vol.52, No.6, pp.1148-1158, 2005. https://doi.org/10.1109/TED.2005.848079
  11. I.B. Shams, K.M.M. Habib, Q.D.M. Khosru,A.N.M. Zainuddin, and A. Haque, “On the physicallybased compact gate C-V model for ultrathingate dielectric MOS devices using the modifiedAiry function approximation,” IEEE Transactionson Electron Devices, Vol.54, No.9, pp.2566-2569,2007. https://doi.org/10.1109/TED.2007.902987
  12. F. Rana, S. Tiwari, and D.A. Buchanan, “Selfconsistentmodeling of accumulation layers andtunneling currents through very thin oxides,” AppliedPhysics Letters, Vol.69, No.8, pp.1104-1106,1996. https://doi.org/10.1063/1.117072
  13. J.C. Ranuarez, M.J. Deen, and C.H. Chen, “A reviewof gate tunneling current in MOS devices,”Microelectronics Reliability, Vol.46, No.12, pp.1939-1956, 2006. https://doi.org/10.1016/j.microrel.2005.12.006
  14. H. Wu, Y. Zhao, and M.H. White, “Quantum mechanicalmodeling of MOSFET gate leakage forhigh-k gate dielectrics,” Solid State Electronics, Vol.50. No. 6, pp. 1164-1169, 2006. https://doi.org/10.1016/j.sse.2006.04.036
  15. R.H. Fowler and L. Nordheim, “Electron emissionin intense electric fields,” Proceedings of the RoyalSociety of London, Series A, Vol. 119, No. 781, pp.173-181, 1928. https://doi.org/10.1098/rspa.1928.0091
  16. X. Liu, J. Kang, and R. Han, “Direct tunneling currentmodel for MOS devices with ultrathin gate oxideincluding quantization effect and polysilicondepletion effect,” Solid State Communications, Vol.125, No.3, pp.219-223, 2003. https://doi.org/10.1016/S0038-1098(02)00719-6
  17. Y.P. Tsividis, “Operation and Modeling of the MOSTransistor,” 2nd Ed., Oxford University Press, 1999.
  18. M. Shur, “Physics of Semiconductor Devices,”Prentice Hall, 1995.
  19. A.K. Dutta, “Semiconductor Devices and Circuits,”Oxford University Press, 2008.
  20. D. Basu and A.K. Dutta, “An explicit surfacepotential-based MOSFET model incorporating thequantum mechanical effects,” Solid State Electronics,Vol.50, No.7-8, pp.1299-1309, 2006. https://doi.org/10.1016/j.sse.2006.05.022

피인용 문헌

  1. Insights on the Body Charging and Noise Generation by Impact Ionization in Fully Depleted SOI MOSFETs vol.64, pp.12, 2017, https://doi.org/10.1109/TED.2017.2762733
  2. Application of the generalized logistic functions in modeling inversion charge density of MOSFET vol.17, pp.2, 2018, https://doi.org/10.1007/s10825-018-1137-5
  3. Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations vol.0, pp.0, 2019, https://doi.org/10.1515/zna-2018-0495