J. Semicond. > 2014, Volume 35 > Issue 3 > 034001
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SEMICONDUCTOR DEVICES

Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects

P. Vimala and N. B. Balamurugan

+ Author Affiliations

 Corresponding author: P. Vimala, Email:vimalapalanichamy@tce.edu

DOI: 10.1088/1674-4926/35/3/034001

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Abstract: Quantum effects are predominant in tri-gate MOSFETs, so a model should be developed. For the first time, this paper presents the analytical model for quantization effects of thin film silicon tri-gate MOSFETs by using variational approach. An analytical expression of the inversion charge distribution function (ICDF) or wave function for the tri-gate MOSFETs has been obtained. This obtained ICDF is used to calculate the important device parameters, such as the inversion charge centroid and inversion charge density. The results are validated against with the simulation data.

Key words: device modeling, energy quantization, inversion charge density, Poisson-Schrodinger equation, trigate MOSFET



[1]
Frank D J, Dennard R H, Nowak E, et al. Device scaling limits of Si MOSFETs and their application dependencies. Proc IEEE, 2001, 89(3):259 doi: 10.1109/5.915374
[2]
Doyle B, Arghavani R, Barlage D, et al. Transistor elements for 30 nm physical gate lengths and beyond. Intel Technol J, 2002, 6(2):42
[3]
He J, Liu F, Bian W, et al. An approximate carrier-based compact model for fully depleted surrounding-gate MOSFETs with a finite doping body. Semicond Sci Technol, 2007, 22(6):671 doi: 10.1088/0268-1242/22/6/015
[4]
Son A, Kim J, Jeong N, et al. Improved explicit current-voltage model for long-channel undoped surrounding-gate metal oxide semiconductor field effect transistor. Jpn J Appl Phys, 2009, 48:412 doi: 10.1143/JJAP.48.04C035/meta
[5]
Lixin G, Fossum J G. Analytical modeling of quantization and volume inversion in thin Si-film DG MOSFETs. IEEE Trans Electron Devices, 2002, 49(2):287 doi: 10.1109/16.981219
[6]
Jimenez D, Inguiez B. Continuous analytic Ⅳ model for surrounding-gate MOSFETs. IEEE Electron Device Lett, 2004, 25(8):571 doi: 10.1109/LED.2004.831902
[7]
Iniguez B, Jimenez D, Roig J, et al. Explicit continuous model for long-channel undoped surrounding-gate MOSFETs. IEEE Trans Electron Devices, 2005, 52(8):1868 doi: 10.1109/TED.2005.852892
[8]
Colinge J P. FinFETs and other multi-gate MOSFETs. Springer, 2008:49
[9]
Kranti A, Armstrong G A. Performance assessment of nanoscale double-and triple-gate FinFETs. Semicond Sci Technol, 2006, 21(2):409 doi: 10.1088/0268-1242/21/4/002/meta
[10]
Jin Y W, Zeng C, Ma L, et al. Analytical threshold voltage model with TCAD simulation verification for design and evalution of tri-gate MOSFETs. Solid-State Electron, 2007, 51:347 doi: 10.1016/j.sse.2007.01.023
[11]
Tsormpatzoglou A, Dimitriadis C A, Clerc R, et al. Semi analytical modeling of short-channel effects in lightly doped silicon trigate MOSFETs. IEEE Trans Electron Devices, 2008, 55:2623 doi: 10.1109/TED.2008.2003096
[12]
Tsormpatzoglou A, Tassis D H, Dimitriadis C A, et al. Analytical threshold voltage model for lightly doped short-channel tri-gate MOSFETs. Solid-State Electron, 2011, 57:31 doi: 10.1016/j.sse.2010.10.022
[13]
Colinge J P, Alderman J C, Xiong W, et al. Quantum mechanical effects in trigate SOI MOSFET. IEEE Trans Electron Devices, 2006, 53(5):1131 doi: 10.1109/TED.2006.871872
[14]
Granzner R, Thiele S, Schippel C, et al. Quantum effects on the gate capacitance of trigate SOI MOSFETs. IEEE Trans Electron Devices, 2010, 57(12):3231 doi: 10.1109/TED.2010.2077639
[15]
Juan A, L'opez-Villanueva, Cartujo-Casinello P, et al. Effects of the Inversion layer centroid on MOSFET behaviour. IEEE Trans Electron Devices, 1997, 44(11):1915 doi: 10.1109/16.641361
[16]
Roldan J B, Godoy A, Gamiz F, et al. Modeling the centroid and the inversion charge in cylindrical surrounding gate MOSFETs, including quantum effects. IEEE Trans Electron Devices, 2008, 55(1):411 doi: 10.1109/TED.2007.911096
Fig. 1.  Cross section of the silicon tri-gate MOSFETs under study.

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Fig. 2.  Electron density along the normalized position of silicon film in $y$ direction for $V_{\rm gs}$ $=$ 2 V and $x$ $=$ 1 nm. The classical simulation is shown in the solid line and the quantum simulation is shown in the dotted line. Symbols correspond to our model.

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Fig. 3.  The plot of probability density function versus normalized position of silicon film in $y$ direction for various values of gate voltage ($V_{\rm gs}$ $=$ 0.5 V, 1 V, 1.5 V and 2 V) and $x=$ 1 nm.

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Fig. 4.  Inversion charge distribution function plot for tri-gate MOSFET along $x$-axis for different values of $y$-values at $V_{\rm gs}$ $=$ 0.5 V. Dotted lines correspond to our model and symbols correspond to simulation data.

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Fig. 5.  Inversion charge centroids versus silicon thickness in trigate MOSFETs structure for various values of inversion electron concentration with $W$ $=$ 5 nm.

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Fig. 6.  Inversion charge centroid versus electron density for trigate MOSFETs at room temperature with $H$ $=$ 5, 7 and 9 nm and $W$ $=$ 5 nm.

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Fig. 7.  Inversion charge density of tri-gate MOSFET with $W=$ 3 nm and $H=$ 6 nm at room temperature. The classical and quantum simulation results are plotted in dotted and solid line respectively.

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Fig. 8.  Inversion charge density in trigate MOS structures as a function of the gate voltage. Three sets of trigate SOI MOSFETs are considered with $W$ $=$ 3 nm.

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[1]
Frank D J, Dennard R H, Nowak E, et al. Device scaling limits of Si MOSFETs and their application dependencies. Proc IEEE, 2001, 89(3):259 doi: 10.1109/5.915374
[2]
Doyle B, Arghavani R, Barlage D, et al. Transistor elements for 30 nm physical gate lengths and beyond. Intel Technol J, 2002, 6(2):42
[3]
He J, Liu F, Bian W, et al. An approximate carrier-based compact model for fully depleted surrounding-gate MOSFETs with a finite doping body. Semicond Sci Technol, 2007, 22(6):671 doi: 10.1088/0268-1242/22/6/015
[4]
Son A, Kim J, Jeong N, et al. Improved explicit current-voltage model for long-channel undoped surrounding-gate metal oxide semiconductor field effect transistor. Jpn J Appl Phys, 2009, 48:412 doi: 10.1143/JJAP.48.04C035/meta
[5]
Lixin G, Fossum J G. Analytical modeling of quantization and volume inversion in thin Si-film DG MOSFETs. IEEE Trans Electron Devices, 2002, 49(2):287 doi: 10.1109/16.981219
[6]
Jimenez D, Inguiez B. Continuous analytic Ⅳ model for surrounding-gate MOSFETs. IEEE Electron Device Lett, 2004, 25(8):571 doi: 10.1109/LED.2004.831902
[7]
Iniguez B, Jimenez D, Roig J, et al. Explicit continuous model for long-channel undoped surrounding-gate MOSFETs. IEEE Trans Electron Devices, 2005, 52(8):1868 doi: 10.1109/TED.2005.852892
[8]
Colinge J P. FinFETs and other multi-gate MOSFETs. Springer, 2008:49
[9]
Kranti A, Armstrong G A. Performance assessment of nanoscale double-and triple-gate FinFETs. Semicond Sci Technol, 2006, 21(2):409 doi: 10.1088/0268-1242/21/4/002/meta
[10]
Jin Y W, Zeng C, Ma L, et al. Analytical threshold voltage model with TCAD simulation verification for design and evalution of tri-gate MOSFETs. Solid-State Electron, 2007, 51:347 doi: 10.1016/j.sse.2007.01.023
[11]
Tsormpatzoglou A, Dimitriadis C A, Clerc R, et al. Semi analytical modeling of short-channel effects in lightly doped silicon trigate MOSFETs. IEEE Trans Electron Devices, 2008, 55:2623 doi: 10.1109/TED.2008.2003096
[12]
Tsormpatzoglou A, Tassis D H, Dimitriadis C A, et al. Analytical threshold voltage model for lightly doped short-channel tri-gate MOSFETs. Solid-State Electron, 2011, 57:31 doi: 10.1016/j.sse.2010.10.022
[13]
Colinge J P, Alderman J C, Xiong W, et al. Quantum mechanical effects in trigate SOI MOSFET. IEEE Trans Electron Devices, 2006, 53(5):1131 doi: 10.1109/TED.2006.871872
[14]
Granzner R, Thiele S, Schippel C, et al. Quantum effects on the gate capacitance of trigate SOI MOSFETs. IEEE Trans Electron Devices, 2010, 57(12):3231 doi: 10.1109/TED.2010.2077639
[15]
Juan A, L'opez-Villanueva, Cartujo-Casinello P, et al. Effects of the Inversion layer centroid on MOSFET behaviour. IEEE Trans Electron Devices, 1997, 44(11):1915 doi: 10.1109/16.641361
[16]
Roldan J B, Godoy A, Gamiz F, et al. Modeling the centroid and the inversion charge in cylindrical surrounding gate MOSFETs, including quantum effects. IEEE Trans Electron Devices, 2008, 55(1):411 doi: 10.1109/TED.2007.911096

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    Received: 22 August 2013 Revised: 29 September 2013 Online: Published: 01 March 2014

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      Article Navigation >  Journal of Semiconductors  > 2014  >  35(3): 034001
      P. Vimala, N. B. Balamurugan. Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects[J]. Journal of Semiconductors, 2014, 35(3): 034001. doi: 10.1088/1674-4926/35/3/034001 ****P. Vimala, N. B. Balamurugan. Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects[J]. J. Semicond., 2014, 35(3): 034001. doi: 10.1088/1674-4926/35/3/034001.
      Citation:
      P. Vimala, N. B. Balamurugan. Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects[J]. Journal of Semiconductors, 2014, 35(3): 034001. doi: 10.1088/1674-4926/35/3/034001 ****
      P. Vimala, N. B. Balamurugan. Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects[J]. J. Semicond., 2014, 35(3): 034001. doi: 10.1088/1674-4926/35/3/034001.
      shu

      Modeling and simulation of nanoscale tri-gate MOSFETs including quantum effects

      DOI: 10.1088/1674-4926/35/3/034001

      • Department of Electronics and Communication Engineering, Thiagarajar College of Engineering, Madurai-625015, Tamilnadu, India

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      • Corresponding author: P. Vimala, Email:vimalapalanichamy@tce.edu
      • Received Date: 2013-08-22
      • Revised Date: 2013-09-29
      • Published Date: 2014-03-01

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