Analytical modeling of the direct tunneling current through high-<i>k</i> gate stacks for long-channel cylindrical surrounding-gate MOSFETs

Lina Shi; Yiqi Zhuang; Cong Li; Dechang Li

doi:10.1088/1674-4926/35/3/034009

J. Semicond. > 2014, Volume 35 > Issue 3 > 034009, doi: 10.1088/1674-4926/35/3/034009

SEMICONDUCTOR DEVICES

Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs

Lina Shi, Yiqi Zhuang, Cong Li and Dechang Li

+ Author Affiliations

Corresponding author: Shi Lina, Email:shilinaa85819021@163.com

Abstract: An analytical direct tunneling gate current model for cylindrical surrounding gate (CSG) MOSFETs with high-k gate stacks is developed. It is found that the direct tunneling gate current is a strong function of the gate's oxide thickness, but that it is less affected by the change in channel radius. It is also revealed that when the thickness of the equivalent oxide is constant, the thinner the first layer, the smaller the direct tunneling gate current. Moreover, it can be seen that the dielectric with a higher dielectric constant shows a lower tunneling current than expected. The accuracy of the analytical model is verified by the good agreement of its results with those obtained by the three-dimensional numerical device simulator ISE.

Key words: direct tunneling, gate current, high dielectric, gate stacks, cylindrical surrounding gate MOSFETs

References

[1]	Han R, Li C. Analytical model for direct tunneling gate current in long-channel undoped cylindrical surrounding gate metal-oxide-semiconductor field effect transistors. Jpn J Appl Phys, 2013, 52(2):024302 doi: 10.7567/JJAP.52.024302/meta;jsessionid=9D75E5C220A9027B9385D280AD3A9214.c3.iopscience.cld.iop.org
[2]	Li C, Zhuang Y, Han R. Cylindrical surrounding-gate MOSFETs with electrically induced source/drain extension. Microelectron J, 2011, 42(2):341 doi: 10.1016/j.mejo.2010.11.010
[3]	Ghosh P, Haldar S, Gupta R S, et al. An analytical drain current model for dual material engineered cylindrical/surrounded gate MOSFET. Microelectron J, 2012, 43(1):17 doi: 10.1016/j.mejo.2011.10.001
[4]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of the gate tunneling leakage for the determination of adequate high-k dielectrics in double-gate SOI MOSFETs at the 22 nm node. Solid-State Electron, 2010, 54(10):1083 doi: 10.1016/j.sse.2010.06.015
[5]	Zhong Xinghua, Wu Junfeng, Yang Jianjun, et al. Electrical properties of ultra thin nitride/oxynitride stack dielectrics pMOS capacitor with refractory metal gate. Chinese Journal of Semiconductors, 2005, 26(4):651 http://www.oalib.com/paper/1519803#.WcSsf_lJLy8
[6]	Zhao Y, White M H. Modeling of direct tunneling current through interfacial oxide and high-k gate stacks. Solid-State Electron, 2004, 48(10/11):1801 https://www.researchgate.net/publication/243274930_Modeling_of_direct_tunneling_current_through_interfacial_oxide_and_high-_K_gate_stacks
[7]	Yang N, Henson W K, Hauser J R, et al. Modeling study of ultrathin gate oxides using direct tunneling current and capacitance-voltage measurements in MOS devices. IEEE Trans Electron Devices, 1999, 46(7):1464 doi: 10.1109/16.772492
[8]	Zheng Changyong, Zhang Wei, Xu Tailong, et al. A compact model for single material double work function gate MOSFET. Journal of Semiconductors, 2013, 34(9):094006 doi: 10.1088/1674-4926/34/9/094006
[9]	Lee J C, Cho H J, Kang C S, et al. High-k dielectrics and MOSFET characteristics. IEDM Tech Dig, Washington, DC, USA, 2003 http://ieeexplore.ieee.org/document/1269174/
[10]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 doi: 10.1002/pssc.v6:12
[11]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 https://experts.umich.edu/en/publications/gate-current-modeling-of-high-k-stack-nanoscale-mosfets
[12]	Chaujar R, Kaur R, Saxena M, et al. Investigation of multi-layered-gate electrode workfunction engineered recessed channel (MLGEW E-RC) sub-50 nm MOSFET:a novel design. International Journal of Numerical Modelling:Electronic Networks, Devices and Fields, 2009, 22(3):259 doi: 10.1002/jnm.v22:3
[13]	Kauerauf T, Govoreanu B, Degraeve R, et al. Finding the gate stack with the lowest leakage current. Solid-State Electron, 2005, 49(5):695 doi: 10.1016/j.sse.2005.01.018
[14]	Darbandy G, Lime F, Cerdeira A, et al. Study of potential high-k dielectric for UTB SOI MOSFETs using analytical modeling of the gate tunneling leakage. Semicond Sci Technol, 2011, 26(11):115002 doi: 10.1088/0268-1242/26/11/115002
[15]	Cerdeira A, Moldovan O, Iniguez B, et al. Modeling of potentials and threshold voltage for symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(5):830 doi: 10.1016/j.sse.2007.10.046
[16]	Cerdeira A, Iniguez B, Estrada M. Compact model for short channel symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(7):1064 doi: 10.1016/j.sse.2008.03.009
[17]	Li C, Zhuang Y, Han R. Analytical threshold model for nanoscale cylindrical surrounding-gate metal-oxide-semiconductor field effect transistor with high-k gate dielectric and tri-material gate stack. Jpn J Appl Phys, 2010, 49(12):124202 doi: 10.1143/JJAP.49.124202
[18]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of direct tunneling current through gate stacks for the determination of suitable high-k dielectrics for nanoscale double-gate MOSFETs. Semicond Sci Technol, 2011, 26(4):045002 doi: 10.1088/0268-1242/26/4/045002
[19]	Houssa M, Tuominen M, Naili M, et al. Trap-assisted tunneling in high permittivity gate dielectric stacks. J Appl Phys, 2000, 87(12):8615 doi: 10.1063/1.373587
[20]	Garduño S I, Cerdeira A, Estrada M. Inclusion of direct tunneling gate current in the symmetric doped double gate MOSFETs model. 6th International Conference on Electrical Engineering, Computing Science and Automation Control, University of Autonoma Estado Mexico, FacIngenieria, Toluca, Mexico, 2009 http://ieeexplore.ieee.org/document/5393382/
[21]	Lee W C, Hu C. Modeling CMOS tunneling currents through ultrathin gate oxide due to conduction-and valence-band electron and hole tunneling. IEEE Trans Electron Devices, 2001, 48(7):1366 doi: 10.1109/16.930653

Fig. 1. (a) Schematic representation of the long-channel cylindrical surrounding-gate MOSFETs structure with gate stack. (b) Potential profile analyzed.

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Fig. 2. Analytical model calculation and ISE simulation of channel central potential at different channel radii as a function of gate voltage.

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Fig. 3. Analytical model calculation and ISE simulation of the channel central potential at different oxide thicknesses as a function of the gate voltage.

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Fig. 4. Analytical model calculation and ISE simulation of channel surface potential at different channel radii as a function of the gate voltage.

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Fig. 5. Analytical model calculation and ISE simulation of channel surface potential at different oxide thicknesses as a function of gate voltage.

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Fig. 6. Analytical model calculation and ISE simulation of direct tunneling current for long-channel cylindrical surrounding-gate MOSFETs versus the gate voltage at different channel radii.

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Fig. 7. Analytical model calculation and ISE simulation of the direct tunneling current for long-channel cylindrical surrounding-gate MOSFETs versus gate voltage at different oxide thicknesses.

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Fig. 8. Analytical model calculation and ISE simulation of direct tunneling current for long-channel cylindrical surrounding-gate MOSFETs versus gate voltage with 2.25 nm EOT of oxide layer.

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Fig. 9. Analytical model calculation and ISE simulation of the direct tunneling current for long-channel cylindrical surrounding-gate MOSFETs versus the gate voltage with different high-$k$ materials.

DownLoad: Full-Size Img PowerPoint

[1]	Han R, Li C. Analytical model for direct tunneling gate current in long-channel undoped cylindrical surrounding gate metal-oxide-semiconductor field effect transistors. Jpn J Appl Phys, 2013, 52(2):024302 doi: 10.7567/JJAP.52.024302/meta;jsessionid=9D75E5C220A9027B9385D280AD3A9214.c3.iopscience.cld.iop.org
[2]	Li C, Zhuang Y, Han R. Cylindrical surrounding-gate MOSFETs with electrically induced source/drain extension. Microelectron J, 2011, 42(2):341 doi: 10.1016/j.mejo.2010.11.010
[3]	Ghosh P, Haldar S, Gupta R S, et al. An analytical drain current model for dual material engineered cylindrical/surrounded gate MOSFET. Microelectron J, 2012, 43(1):17 doi: 10.1016/j.mejo.2011.10.001
[4]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of the gate tunneling leakage for the determination of adequate high-k dielectrics in double-gate SOI MOSFETs at the 22 nm node. Solid-State Electron, 2010, 54(10):1083 doi: 10.1016/j.sse.2010.06.015
[5]	Zhong Xinghua, Wu Junfeng, Yang Jianjun, et al. Electrical properties of ultra thin nitride/oxynitride stack dielectrics pMOS capacitor with refractory metal gate. Chinese Journal of Semiconductors, 2005, 26(4):651 http://www.oalib.com/paper/1519803#.WcSsf_lJLy8
[6]	Zhao Y, White M H. Modeling of direct tunneling current through interfacial oxide and high-k gate stacks. Solid-State Electron, 2004, 48(10/11):1801 https://www.researchgate.net/publication/243274930_Modeling_of_direct_tunneling_current_through_interfacial_oxide_and_high-_K_gate_stacks
[7]	Yang N, Henson W K, Hauser J R, et al. Modeling study of ultrathin gate oxides using direct tunneling current and capacitance-voltage measurements in MOS devices. IEEE Trans Electron Devices, 1999, 46(7):1464 doi: 10.1109/16.772492
[8]	Zheng Changyong, Zhang Wei, Xu Tailong, et al. A compact model for single material double work function gate MOSFET. Journal of Semiconductors, 2013, 34(9):094006 doi: 10.1088/1674-4926/34/9/094006
[9]	Lee J C, Cho H J, Kang C S, et al. High-k dielectrics and MOSFET characteristics. IEDM Tech Dig, Washington, DC, USA, 2003 http://ieeexplore.ieee.org/document/1269174/
[10]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 doi: 10.1002/pssc.v6:12
[11]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 https://experts.umich.edu/en/publications/gate-current-modeling-of-high-k-stack-nanoscale-mosfets
[12]	Chaujar R, Kaur R, Saxena M, et al. Investigation of multi-layered-gate electrode workfunction engineered recessed channel (MLGEW E-RC) sub-50 nm MOSFET:a novel design. International Journal of Numerical Modelling:Electronic Networks, Devices and Fields, 2009, 22(3):259 doi: 10.1002/jnm.v22:3
[13]	Kauerauf T, Govoreanu B, Degraeve R, et al. Finding the gate stack with the lowest leakage current. Solid-State Electron, 2005, 49(5):695 doi: 10.1016/j.sse.2005.01.018
[14]	Darbandy G, Lime F, Cerdeira A, et al. Study of potential high-k dielectric for UTB SOI MOSFETs using analytical modeling of the gate tunneling leakage. Semicond Sci Technol, 2011, 26(11):115002 doi: 10.1088/0268-1242/26/11/115002
[15]	Cerdeira A, Moldovan O, Iniguez B, et al. Modeling of potentials and threshold voltage for symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(5):830 doi: 10.1016/j.sse.2007.10.046
[16]	Cerdeira A, Iniguez B, Estrada M. Compact model for short channel symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(7):1064 doi: 10.1016/j.sse.2008.03.009
[17]	Li C, Zhuang Y, Han R. Analytical threshold model for nanoscale cylindrical surrounding-gate metal-oxide-semiconductor field effect transistor with high-k gate dielectric and tri-material gate stack. Jpn J Appl Phys, 2010, 49(12):124202 doi: 10.1143/JJAP.49.124202
[18]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of direct tunneling current through gate stacks for the determination of suitable high-k dielectrics for nanoscale double-gate MOSFETs. Semicond Sci Technol, 2011, 26(4):045002 doi: 10.1088/0268-1242/26/4/045002
[19]	Houssa M, Tuominen M, Naili M, et al. Trap-assisted tunneling in high permittivity gate dielectric stacks. J Appl Phys, 2000, 87(12):8615 doi: 10.1063/1.373587
[20]	Garduño S I, Cerdeira A, Estrada M. Inclusion of direct tunneling gate current in the symmetric doped double gate MOSFETs model. 6th International Conference on Electrical Engineering, Computing Science and Automation Control, University of Autonoma Estado Mexico, FacIngenieria, Toluca, Mexico, 2009 http://ieeexplore.ieee.org/document/5393382/
[21]	Lee W C, Hu C. Modeling CMOS tunneling currents through ultrathin gate oxide due to conduction-and valence-band electron and hole tunneling. IEEE Trans Electron Devices, 2001, 48(7):1366 doi: 10.1109/16.930653

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Received: 19 August 2013 Revised: 18 October 2013 Online: Published: 01 March 2014

Article Navigation > Journal of Semiconductors > 2014 > 35(3): 034009

Lina Shi, Yiqi Zhuang, Cong Li, Dechang Li. Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs[J]. Journal of Semiconductors, 2014, 35(3): 034009. doi: 10.1088/1674-4926/35/3/034009 L N Shi, Y Q Zhuang, C Li, D C Li. Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs[J]. J. Semicond., 2014, 35(3): 034009. doi: 10.1088/1674-4926/35/3/034009.Export: BibTex EndNote

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L N Shi, Y Q Zhuang, C Li, D C Li. Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs[J]. J. Semicond., 2014, 35(3): 034009. doi: 10.1088/1674-4926/35/3/034009.

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Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs

doi: 10.1088/1674-4926/35/3/034009

School of Microelectronics, Xidian University, Xi'an 710071, China

Funds:

the Fundamental Research Funds for the Central Universities of China K50511250001

Project supported by the National Natural Science Foundation of China (Nos. 61076101, 61204092) and the Fundamental Research Funds for the Central Universities of China (No. K50511250001).

the National Natural Science Foundation of China 61076101

the National Natural Science Foundation of China 61204092

More Information

Corresponding author: Shi Lina, Email:shilinaa85819021@163.com
Received Date: 2013-08-19
Revised Date: 2013-10-18
Published Date: 2014-03-01

Abstract

Abstract

An analytical direct tunneling gate current model for cylindrical surrounding gate (CSG) MOSFETs with high-k gate stacks is developed. It is found that the direct tunneling gate current is a strong function of the gate's oxide thickness, but that it is less affected by the change in channel radius. It is also revealed that when the thickness of the equivalent oxide is constant, the thinner the first layer, the smaller the direct tunneling gate current. Moreover, it can be seen that the dielectric with a higher dielectric constant shows a lower tunneling current than expected. The accuracy of the analytical model is verified by the good agreement of its results with those obtained by the three-dimensional numerical device simulator ISE.
- direct tunneling,
- gate current,
- high dielectric,
- gate stacks,
- cylindrical surrounding gate MOSFETs

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References(21)

References

[1]	Han R, Li C. Analytical model for direct tunneling gate current in long-channel undoped cylindrical surrounding gate metal-oxide-semiconductor field effect transistors. Jpn J Appl Phys, 2013, 52(2):024302 doi: 10.7567/JJAP.52.024302/meta;jsessionid=9D75E5C220A9027B9385D280AD3A9214.c3.iopscience.cld.iop.org
[2]	Li C, Zhuang Y, Han R. Cylindrical surrounding-gate MOSFETs with electrically induced source/drain extension. Microelectron J, 2011, 42(2):341 doi: 10.1016/j.mejo.2010.11.010
[3]	Ghosh P, Haldar S, Gupta R S, et al. An analytical drain current model for dual material engineered cylindrical/surrounded gate MOSFET. Microelectron J, 2012, 43(1):17 doi: 10.1016/j.mejo.2011.10.001
[4]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of the gate tunneling leakage for the determination of adequate high-k dielectrics in double-gate SOI MOSFETs at the 22 nm node. Solid-State Electron, 2010, 54(10):1083 doi: 10.1016/j.sse.2010.06.015
[5]	Zhong Xinghua, Wu Junfeng, Yang Jianjun, et al. Electrical properties of ultra thin nitride/oxynitride stack dielectrics pMOS capacitor with refractory metal gate. Chinese Journal of Semiconductors, 2005, 26(4):651 http://www.oalib.com/paper/1519803#.WcSsf_lJLy8
[6]	Zhao Y, White M H. Modeling of direct tunneling current through interfacial oxide and high-k gate stacks. Solid-State Electron, 2004, 48(10/11):1801 https://www.researchgate.net/publication/243274930_Modeling_of_direct_tunneling_current_through_interfacial_oxide_and_high-_K_gate_stacks
[7]	Yang N, Henson W K, Hauser J R, et al. Modeling study of ultrathin gate oxides using direct tunneling current and capacitance-voltage measurements in MOS devices. IEEE Trans Electron Devices, 1999, 46(7):1464 doi: 10.1109/16.772492
[8]	Zheng Changyong, Zhang Wei, Xu Tailong, et al. A compact model for single material double work function gate MOSFET. Journal of Semiconductors, 2013, 34(9):094006 doi: 10.1088/1674-4926/34/9/094006
[9]	Lee J C, Cho H J, Kang C S, et al. High-k dielectrics and MOSFET characteristics. IEDM Tech Dig, Washington, DC, USA, 2003 http://ieeexplore.ieee.org/document/1269174/
[10]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 doi: 10.1002/pssc.v6:12
[11]	Wang W, Gu N, Sun J P, et al. Gate current modeling of high-k stack nanoscale MOSFETs. Solid-State Electron, 2006, 50(9/10):1489 https://experts.umich.edu/en/publications/gate-current-modeling-of-high-k-stack-nanoscale-mosfets
[12]	Chaujar R, Kaur R, Saxena M, et al. Investigation of multi-layered-gate electrode workfunction engineered recessed channel (MLGEW E-RC) sub-50 nm MOSFET:a novel design. International Journal of Numerical Modelling:Electronic Networks, Devices and Fields, 2009, 22(3):259 doi: 10.1002/jnm.v22:3
[13]	Kauerauf T, Govoreanu B, Degraeve R, et al. Finding the gate stack with the lowest leakage current. Solid-State Electron, 2005, 49(5):695 doi: 10.1016/j.sse.2005.01.018
[14]	Darbandy G, Lime F, Cerdeira A, et al. Study of potential high-k dielectric for UTB SOI MOSFETs using analytical modeling of the gate tunneling leakage. Semicond Sci Technol, 2011, 26(11):115002 doi: 10.1088/0268-1242/26/11/115002
[15]	Cerdeira A, Moldovan O, Iniguez B, et al. Modeling of potentials and threshold voltage for symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(5):830 doi: 10.1016/j.sse.2007.10.046
[16]	Cerdeira A, Iniguez B, Estrada M. Compact model for short channel symmetric doped double-gate MOSFETs. Solid-State Electron, 2008, 52(7):1064 doi: 10.1016/j.sse.2008.03.009
[17]	Li C, Zhuang Y, Han R. Analytical threshold model for nanoscale cylindrical surrounding-gate metal-oxide-semiconductor field effect transistor with high-k gate dielectric and tri-material gate stack. Jpn J Appl Phys, 2010, 49(12):124202 doi: 10.1143/JJAP.49.124202
[18]	Darbandy G, Ritzenthaler R, Lime F, et al. Analytical modeling of direct tunneling current through gate stacks for the determination of suitable high-k dielectrics for nanoscale double-gate MOSFETs. Semicond Sci Technol, 2011, 26(4):045002 doi: 10.1088/0268-1242/26/4/045002
[19]	Houssa M, Tuominen M, Naili M, et al. Trap-assisted tunneling in high permittivity gate dielectric stacks. J Appl Phys, 2000, 87(12):8615 doi: 10.1063/1.373587
[20]	Garduño S I, Cerdeira A, Estrada M. Inclusion of direct tunneling gate current in the symmetric doped double gate MOSFETs model. 6th International Conference on Electrical Engineering, Computing Science and Automation Control, University of Autonoma Estado Mexico, FacIngenieria, Toluca, Mexico, 2009 http://ieeexplore.ieee.org/document/5393382/
[21]	Lee W C, Hu C. Modeling CMOS tunneling currents through ultrathin gate oxide due to conduction-and valence-band electron and hole tunneling. IEEE Trans Electron Devices, 2001, 48(7):1366 doi: 10.1109/16.930653

Analytical modeling of the direct tunneling current through high-k gate stacks for long-channel cylindrical surrounding-gate MOSFETs

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