Nanoscale Effects: Inversion Layer Quantization

  • Amit Chaudhry


In this chapter, inversion layer quantization effects on carrier distribution in poly-Si gate, p-type, and n-type substrate are studied. The two approaches viz. triangular well and variation approach for inversion layer quantization are discussed. The capacitance and drain current are also modeled under the inversion layer quantization conditions.


Surface Potential Gate Voltage Inversion Layer Gate Capacitance Transverse Electric Field 
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  1. 1.
    Kahng D (1976) A historical perspective on the development of MOS transistors and related devices. IEEE T Electron Dev ED-23:655–660CrossRefGoogle Scholar
  2. 2.
    Snow EH, Grove AS, Deal BE, Sah CT (1965) Ion transport phenomena in insulating films. J Appl Phys 36(5):1664–1674CrossRefGoogle Scholar
  3. 15.
    Pregaldiny F, Lallement C, Grabinski W, Kammerer JB, Mathiot D (2003) An analytical quantum model for the surface potential of deep sub micron MOSFETs, 10th international conference on Mixed Design Integrated Circuits and Systems (MIXDES’03), June 2003Google Scholar
  4. 62.
    Ip BK, Brews JR (1998) Quantum effects upon drain current in a biased MOSFET. IEEE T Electron Dev 45(10):2213–2221CrossRefGoogle Scholar
  5. 63.
    Stern F, Howard WE (1967) Properties of semiconductor surface inversion layers in the electric quantum limit. Phys Rev 163:816–835CrossRefGoogle Scholar
  6. 64.
    Stern F (1972) Self-consistent results for n-type Si inversion layers. Phys Rev B 5:4891–4899CrossRefGoogle Scholar
  7. 65.
    Moglestue C (1986) Self-consistent calculation of electron and hole inversion charges at Si-Si dioxide interfaces. J Appl Phys 59:3175–3183CrossRefGoogle Scholar
  8. 66.
    Yu Z, Dutton RW, Kiehl RA (2000) Circuit/Device modeling at the quantum level. IEEE T Electron Dev 47(10):1819–1825CrossRefGoogle Scholar
  9. 67.
    Yuhua Cheng, Kai Chen, Kiyotaka Imai, Chenming Hu, (1997) ICM- An analytical inversion charge model for accurate modeling of thin gate oxide MOSFETs, IEEE international conference on Simulation of Semiconductor Processes and Devices – SISPAD, pp 109–112Google Scholar
  10. 68.
    Ma Y, Liu L, Yu Z, Li Z (2000) Validity and applicability of triangular potential well approximation in modeling of MOS structure inversion and accumulation layer. IEEE T Electron Dev 47(9):1764–1767CrossRefGoogle Scholar
  11. 69.
    Powel J, Crasemann B Quantum mechanics, New Delhi: Oxford and IBH PublishingGoogle Scholar
  12. 70.
    Chaudhry A, Roy JN (2012) Analytical modeling of energy quantization effects in nanoscale MOSFETs. Int J Nanoelectronics Mater 5(1):1–9Google Scholar
  13. 71.
    Hareland S et al (1998) A physically-based model for quantization effects in hole inversion layers. IEEE T Electron Dev 45(1):179–186CrossRefGoogle Scholar
  14. 72.
    Hou T et al (2001) A simple and efficient model for quantization effects of hole inversion layers in MOS devices. IEEE T Electron Dev 48(12):2893–2898CrossRefGoogle Scholar
  15. 73.
    Hou T, Li M (2001) Hole quantization and hole direct tunneling in deep sub micron p-MOSFETs, IEEE, pp 895–900Google Scholar
  16. 74.
    Hou T, Li M (2001) Hole quantization effects and threshold voltage shift in pMOSFET—assessed by improved one-band effective mass approximation. IEEE T Electron Dev 48(6):1188–1193CrossRefGoogle Scholar
  17. 75.
    Hu C et al (1996) Quantization effects in inversion layers of p channel MOSFET’s on Si (100) substrates. IEEE Electron Devic Lett 17(6):276–278CrossRefGoogle Scholar
  18. 76.
    Takagi S et al (1999) Characterization of inversion-layer capacitance of holes in Si MOSFET’s. IEEE T Electron Dev 46(7):1446–1450CrossRefGoogle Scholar
  19. 77.
    Chaudhry A, Roy JN (2010) A comparative study of hole and electron inversion layer quantization in MOS structures. Serb J Elec Eng 7(2):185–193CrossRefGoogle Scholar
  20. 78.
    Rodriguez N, Gamiz F, Roldan JB (2007) Modeling of inversion layer centroid and polysilicon depletion effects on ultrathin gate oxide MOSFET behavior: the influence of crystalline orientation. IEEE T Electron Dev 54(4):723–732CrossRefGoogle Scholar
  21. 79.
    Chaudhry A, Roy JN (2010) Inversion layer quantization in arbitrarily oriented substrates: an analytical study. Elektrica-UTM J Elec Eng 12(1):1–6Google Scholar
  22. 80.
    Amit Chaudhry, JN Roy (2010) Impact of quantum inversion charge centroid on the various parameters of a nano-MOSFET, Proceedings of international conference on Microelectronic Devices, Rome, Apr 2010Google Scholar
  23. 81.
    Yang K, Ya-Chin K, Chenming.H (1999) Quantum effect in oxide thickness determination from capacitance measurement, VLSI Technol, pp 77–78Google Scholar
  24. 82.
    Pacelli A et al (1999) Carrier quantization at flat bands in MOS devices. IEEE T Electron Dev 46(2):383–387CrossRefGoogle Scholar
  25. 83.
    Chaudhry A, Roy JN (2011) Analytical modeling of gate capacitance of an ultra thin oxide MOS capacitor: a quantum mechanical study. J Electron Dev 10:456–463Google Scholar
  26. 84.
    Richter CA, Hefner AR, Vogel EM (2001) A comparison of quantum mechanical capacitance–voltage simulators. IEEE T Electron Devic Lett 22(1):35–37CrossRefGoogle Scholar
  27. 85.
    Spinelli AS, Pacelli A, Lacaita AL (2002) Simulation of poly silicon quantization and its effect on n- and p-MOSFET performance. Solid State Electron 46(3):423–428CrossRefGoogle Scholar
  28. 86.
    Chaudhry A, Roy JN (2010) Mathematical modeling of MOS capacitance in the presence of depletion and energy quantization in poly silicon gate. J Semiconduct 31(11):400-1–400-4Google Scholar
  29. 87.
    Janik T, Majkusaik B (1994) Influence of carrier energy quantization on threshold voltage of metal oxide semiconductor transistor. J Appl Phys 75(10):5186–5190CrossRefGoogle Scholar
  30. 88.
    Garverick S, Sodini C (1987) A simple model for scaled MOS transistors that includes field dependent mobility. IEEE J Solid St Circ SC-22:111–114CrossRefGoogle Scholar
  31. 89.
    Graff H, Klassen F (1990) Compact transistor modeling for circuit design. Springer, New YorkCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Amit Chaudhry
    • 1
  1. 1.University Institute of Engineering and Technology Punjab UniversityChandigarhIndia

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