J. Semicond. > 2013, Volume 34 > Issue 9 > 092002
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SEMICONDUCTOR PHYSICS

Comparison of band-to-band tunneling models in Si and Si-Ge junctions

Yipeng Jiao1, Kangliang Wei2, Taihuan Wang1, Gang Du2 and Xiaoyan Liu2,

+ Author Affiliations

 Corresponding author: Liu Xiaoyan, Email:xyliu@ime.pku.edu.cn

DOI: 10.1088/1674-4926/34/9/092002

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Abstract: We compared several different band-to-band tunneling (BTBT) models with both Sentaurus and the two-dimensional full-band Monte Carlo simulator in Si homo-junctions and Si-Ge hetero-junctions. It was shown that in Si homo-junctions, different models could achieve similar results. However, in the Si-Ge hetero-junctions, there were significant differences among these models at high reverse biases (over 2 V). Compared to the nonlocal model, the local models in Sentaurus underrated the BTBT rate distinctly, and the Monte Carlo method was shown to give a better approximation. Additionally, it was found that in the Si region near the interface of the Si-Ge hetero-junctions, the direct tunneling rates increased largely due to the interaction of the band structures of Si and Ge.

Key words: hetero-structure, Monte Carlo device simulation, carrier transport, band-to-band tunneling



[1]
Vandenberghe W, Sorée B, Magnus W, et al. Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields:a rigorous approach. J Appl Phys, 2011, 109(12):124503 doi: 10.1063/1.3595672
[2]
Kim S H, Kam H, Hu C, et al. Germanium-source tunnel field effect transistors with record high ION/IOFF. IEEE Symposium on VLSI Technology (VLSIT), 2009:178 http://ieeexplore.ieee.org/document/5200679/
[3]
Luisier M, Klimeck G. Performance comparisons of tunneling field effect transistors made of InSb, Carbon, and GaSb-InAs broken gap hetero-structures. IEEE International Electron Devices Meeting (IEDM), 2009:1 doi: 10.1007%2Fs00339-016-0151-3.pdf
[4]
Avci U E, Rios R, Kuhn K, et al. Comparison of performance, switching energy and process variations for the TFET and MOSFET in logic. IEEE Symposium on VLSI Technology (VLSIT), 2011:124 doi: 10.1007/978-3-319-31653-6_4/fulltext.html
[5]
Krishnamohan T, Kim D, Raghunathan S, et al. Double-gate strained-Ge hetero-structure tunneling FET (TFET) with record high drive currents and <<ll 60 mV/dec sub threshold slope. IEEE International Electron Devices Meeting (IEDM), 2008:1
[6]
Chynoweth A G, Feldmann W L, Lee C A, et al. Internal field emission at narrow silicon and germanium pn junctions. Phys Rev, 1960, 118(2):425 doi: 10.1103/PhysRev.118.425
[7]
Ionescu A M, Riel H. Tunnel field-effect transistors as energy-efficient electronic switches. Nature, 2011, 479(7373):329 doi: 10.1038/nature10679
[8]
Wei K L, Zeng L, Wang J C, et al. Simulation of band-to-band tunneling in Si/Ge and Si/Si1-xGex hetero-junctions by using Monte Carlo method. IEEE International Conference on Solid-State and Integrated Circuit Technology (ICSICT), 2012:1
[9]
Xia Z L, Du G, Song Y C, et al. Monte Carlo simulation of band-to-band tunneling in silicon devices. Jpn J Appl Phys, 2007, 46:2023 doi: 10.1143/JJAP.46.2023
[10]
Hurkx G A M, Klaassen D B M, Knuvers M P G. A new recombination model for device simulation including tunneling. IEEE Trans Electron Devices, 1992, 39(2):331 doi: 10.1109/16.121690
[11]
Liou J J. Modeling the tunneling current in reverse-biased p/n junctions. Solid-State Electron, 1990, 33(7):971 doi: 10.1016/0038-1101(90)90081-O
[12]
Schenk A. Rigorous theory and simplified model of the band-to-band tunneling in silicon. Solid-State Electron, 1993, 36(1):19 doi: 10.1016/0038-1101(93)90065-X
[13]
Fischetti M V, O'Regan T P, Narayanan S, et al. Theoretical study of some physical aspects of electronic transport in nMOSFETs at the 10-nm gate-length. IEEE Trans Electron Devices, 2007, 54(9):2116 doi: 10.1109/TED.2007.902722
[14]
Kao K H, Verhulst A S, Vandenberghe W G, et al. Direct and indirect band-to-band tunneling in germanium-based TFETs. IEEE Trans Electron Devices, 2012, 59(2):292 doi: 10.1109/TED.2011.2175228
[15]
Kane E O. Theory of tunneling. J Appl Phys, 1961, 32(1):83 doi: 10.1063/1.1735965
[16]
Sentaurus Device, Synopsys, Version D-2010. 03: 362
[17]
Wernersson L E, Kabeer S, Zela V, et al. SiGe Esaki tunnel diodes fabricated by UHV-CVD growth and proximity rapid thermal diffusion. Electron Lett, 2004, 40(1):83 doi: 10.1049/el:20040048
[18]
Wei K L, Liu X Y, Du G, et al. Simulation of carrier transport in hetero-structures using the 2D self-consistent full-band ensemble Monte Carlo method. Journal of Semiconductors, 2010, 31(8):084004 doi: 10.1088/1674-4926/31/8/084004
[19]
Du G, Liu X Y, Xia Z L, et al. Monte Carlo simulation of p-and n-channel GOI MOSFETs by solving the quantum Boltzmann equation. IEEE Trans Electron Devices, 2005, 52(10):2258 doi: 10.1109/TED.2005.856806
Fig. 1.  Simulated BTBT current density of an Si linearly graded junction compared with the experimental data.

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Fig. 2.  Simulation results for the Si step homo-junction by Sentaurus and the MC simulators at forward bias. The valence and conduction band at 0.5 V is shown in the inset.

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Fig. 3.  Simulated BTBT current density of an Si homo-junction with three BTBT models in Sentaurus and the MC simulator. The solid line plots the results in Ref. [10].

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Fig. 4.  Simulated BTBT rate of an Si homo-junction with two models at different biases.

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Fig. 5.  The $D$ factor (right vertical axis) and BTBT (left vertical axis) rates calculated by Hurkx's model at 1 V (reverse bias). The curves with square symbols are the results from Sentaurus, and the curves with triangular symbols are from the MC simulator. The inset shows the electrostatic fields from the two simulators.

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Fig. 6.  Comparison of the current density of Si and Si–Ge diodes with two different BTBT models.

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Fig. 7.  Simulation results using different methods and BTBT models.

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Fig. 8.  The BTBT rates of the Si–Ge hetero-junction calculated under reverse biases of 1 V and 4 V.

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Fig. 9.  Simulated BTBT rates of three different hetero-structure diodes. The donor concentration of the n-region for each diode is 10$^{20}$ cm$^{-3}$. The inset shows the $I$–$V$ curves from 1 to 4 V (reverse bias).

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Table 1.   The values of parameters $A$, $B$ and $P$ with tunneling directions along [100] in Eq. (1). The "Direct BTBT" and "Indirect BTBT" columns list the results calculated in Ref. [14], and the "Sentaurus" columns list the default values in Sentaurus[16].
[1]
Vandenberghe W, Sorée B, Magnus W, et al. Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields:a rigorous approach. J Appl Phys, 2011, 109(12):124503 doi: 10.1063/1.3595672
[2]
Kim S H, Kam H, Hu C, et al. Germanium-source tunnel field effect transistors with record high ION/IOFF. IEEE Symposium on VLSI Technology (VLSIT), 2009:178 http://ieeexplore.ieee.org/document/5200679/
[3]
Luisier M, Klimeck G. Performance comparisons of tunneling field effect transistors made of InSb, Carbon, and GaSb-InAs broken gap hetero-structures. IEEE International Electron Devices Meeting (IEDM), 2009:1 doi: 10.1007%2Fs00339-016-0151-3.pdf
[4]
Avci U E, Rios R, Kuhn K, et al. Comparison of performance, switching energy and process variations for the TFET and MOSFET in logic. IEEE Symposium on VLSI Technology (VLSIT), 2011:124 doi: 10.1007/978-3-319-31653-6_4/fulltext.html
[5]
Krishnamohan T, Kim D, Raghunathan S, et al. Double-gate strained-Ge hetero-structure tunneling FET (TFET) with record high drive currents and <<ll 60 mV/dec sub threshold slope. IEEE International Electron Devices Meeting (IEDM), 2008:1
[6]
Chynoweth A G, Feldmann W L, Lee C A, et al. Internal field emission at narrow silicon and germanium pn junctions. Phys Rev, 1960, 118(2):425 doi: 10.1103/PhysRev.118.425
[7]
Ionescu A M, Riel H. Tunnel field-effect transistors as energy-efficient electronic switches. Nature, 2011, 479(7373):329 doi: 10.1038/nature10679
[8]
Wei K L, Zeng L, Wang J C, et al. Simulation of band-to-band tunneling in Si/Ge and Si/Si1-xGex hetero-junctions by using Monte Carlo method. IEEE International Conference on Solid-State and Integrated Circuit Technology (ICSICT), 2012:1
[9]
Xia Z L, Du G, Song Y C, et al. Monte Carlo simulation of band-to-band tunneling in silicon devices. Jpn J Appl Phys, 2007, 46:2023 doi: 10.1143/JJAP.46.2023
[10]
Hurkx G A M, Klaassen D B M, Knuvers M P G. A new recombination model for device simulation including tunneling. IEEE Trans Electron Devices, 1992, 39(2):331 doi: 10.1109/16.121690
[11]
Liou J J. Modeling the tunneling current in reverse-biased p/n junctions. Solid-State Electron, 1990, 33(7):971 doi: 10.1016/0038-1101(90)90081-O
[12]
Schenk A. Rigorous theory and simplified model of the band-to-band tunneling in silicon. Solid-State Electron, 1993, 36(1):19 doi: 10.1016/0038-1101(93)90065-X
[13]
Fischetti M V, O'Regan T P, Narayanan S, et al. Theoretical study of some physical aspects of electronic transport in nMOSFETs at the 10-nm gate-length. IEEE Trans Electron Devices, 2007, 54(9):2116 doi: 10.1109/TED.2007.902722
[14]
Kao K H, Verhulst A S, Vandenberghe W G, et al. Direct and indirect band-to-band tunneling in germanium-based TFETs. IEEE Trans Electron Devices, 2012, 59(2):292 doi: 10.1109/TED.2011.2175228
[15]
Kane E O. Theory of tunneling. J Appl Phys, 1961, 32(1):83 doi: 10.1063/1.1735965
[16]
Sentaurus Device, Synopsys, Version D-2010. 03: 362
[17]
Wernersson L E, Kabeer S, Zela V, et al. SiGe Esaki tunnel diodes fabricated by UHV-CVD growth and proximity rapid thermal diffusion. Electron Lett, 2004, 40(1):83 doi: 10.1049/el:20040048
[18]
Wei K L, Liu X Y, Du G, et al. Simulation of carrier transport in hetero-structures using the 2D self-consistent full-band ensemble Monte Carlo method. Journal of Semiconductors, 2010, 31(8):084004 doi: 10.1088/1674-4926/31/8/084004
[19]
Du G, Liu X Y, Xia Z L, et al. Monte Carlo simulation of p-and n-channel GOI MOSFETs by solving the quantum Boltzmann equation. IEEE Trans Electron Devices, 2005, 52(10):2258 doi: 10.1109/TED.2005.856806

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    Received: 21 February 2013 Revised: 02 April 2013 Online: Published: 01 September 2013

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      Article Navigation >  Journal of Semiconductors  > 2013  >  34(9): 092002
      Yipeng Jiao, Kangliang Wei, Taihuan Wang, Gang Du, Xiaoyan Liu. Comparison of band-to-band tunneling models in Si and Si-Ge junctions[J]. Journal of Semiconductors, 2013, 34(9): 092002. doi: 10.1088/1674-4926/34/9/092002 ****Y P Jiao, K L Wei, T H Wang, G Du, X Y Liu. Comparison of band-to-band tunneling models in Si and Si-Ge junctions[J]. J. Semicond., 2013, 34(9): 092002. doi: 10.1088/1674-4926/34/9/092002.
      Citation:
      Yipeng Jiao, Kangliang Wei, Taihuan Wang, Gang Du, Xiaoyan Liu. Comparison of band-to-band tunneling models in Si and Si-Ge junctions[J]. Journal of Semiconductors, 2013, 34(9): 092002. doi: 10.1088/1674-4926/34/9/092002 ****
      Y P Jiao, K L Wei, T H Wang, G Du, X Y Liu. Comparison of band-to-band tunneling models in Si and Si-Ge junctions[J]. J. Semicond., 2013, 34(9): 092002. doi: 10.1088/1674-4926/34/9/092002.
      shu

      Comparison of band-to-band tunneling models in Si and Si-Ge junctions

      DOI: 10.1088/1674-4926/34/9/092002
      • 1.

        Shenzhen Graduate School, Peking University, Shenzhen 518055, China

      • 2.

        Institute of Microelectronics, Peking University, Beijing 100871, China

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      • Corresponding author: Liu Xiaoyan, Email:xyliu@ime.pku.edu.cn
      • Received Date: 2013-02-21
      • Revised Date: 2013-04-02
      • Published Date: 2013-09-01

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