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随着CMOS工艺的发展, 热载流子效应对沟道热噪声的影响随着器件尺寸的降低而增大, 传统热噪声模型未能准确表征沟道的热噪声. 本文通过解能量平衡方程, 得到电子温度表达式, 并结合沟道漏电流表达式, 建立了沟道热噪声模型. 利用建立的电子温度表达式, 该热噪声模型考虑了热载流子效应的影响, 并且在计算热噪声的过程中考虑了电子温度对迁移率降低的影响以及温度梯度对热噪声的影响. 通过分析与计算, 结果显示, 随着器件尺寸的减小, 温度梯度对电子温度产生显著影响, 使得热载流子效应的影响增大, 热载流子效应对热噪声的增长作用超过了迁移率降低对热噪声的减小作用, 最终导致热噪声增大. 本文建立的沟道热噪声模型可应用于纳米尺寸金属-氧化物半导体场效应晶体管器件的噪声性能分析及建模.
With the development of the integrated circuit manufacturing process, the device dimensions have been on a nanoscale, while the device performance, such as the mobility and thermal noise, is significantly affected by the hot-carrier effect, which further affects the channel thermal noise of the device. However, the thermal noise model based on the existing electron temperature expression does not take into account the influence of the temperature gradient on the electron temperature when it deals with the influence of the hot carrier effect. As the size of the device decreases, the thermal noise model based on the existing electron temperature expression underestimates the influence of the hot carrier effect and the channel thermal noise cannot be accurately predicted with this expression. In this paper, the expression of the channel transverse electric field is derived based on the channel potential equation and the boundary condition of the channel electric field. By combining the distribution of the temperature gradient and the expression of the transverse electric field, the energy balance equation is solved with considering the influence of the temperature gradient, and then the electron temperature expression is obtained. The electron temperature expression shows the distribution of the electron temperature along the channel. By utilizing the derived electron temperature expression and combining with the drain current expression, a channel thermal noise model is established. The hot carrier effect is taken into account in the thermal noise model by utilizing the proposed electron temperature expression. Meanwhile in calculating the thermal noise, the influence of the electron temperature on mobility degradation and the temperature gradient on thermal noise are also involved. The results show that the temperature gradient has a significant influence on the electron temperature with the reduction of the device size, which further increases the influence of the hot carrier effect, resulting in the increase of the thermal noise caused by the hot carrier effect exceeding the decrease of the thermal noise caused by the mobility degradation, thus leading the thermal noise to increase. The influence of the hot carrier effect on the channel thermal noise also increases significantly with the bias increasing. The channel thermal noise model proposed in this paper can be applied to analyzing the noise performance and modeling the nano-sized MOSFET devices. -
Keywords:
- electron temperature /
- mobility degradation /
- hot carrier effect /
- temperature gradient /
- channel thermal noise
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图 2 沟道坐标y = y1处有一虚拟直流源的晶体管结构图
Fig. 2. Schematic of the transistor with a fictitious dc source placed at point y = y1 in the channel.
图 3 不同栅源偏置下的沟道热噪声与仅考虑沟道长度调制效应模型的对比(a); 以及与采用现有温度模型的对比(b)
Fig. 3. The channel thermal noise at different gate-source bias: (a) Comparison with the model only considering the channel length modulation effect; (b) comparison with the model using the existing temperature model.
图 4 不同栅源偏置下的沟道热噪声(Leff = 0.13 μm)
Fig. 4. The channel thermal noise at different gate-source bias (Leff = 0.13 μm).
表 1 NMOS的器件参数
Table 1. Parameters of NMOS.
参数 数值 vsat/m·s–1 1.0 ×105 σ 0.02 tox/nm 1 θ/V–1 1.058 εSi/F·cm–1 11.7 × (8.85 × 10–14) εox/F·cm–1 3.9 × (8.85 × 10–14) λ 5.23 
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[1] Chen X S, Chih H C, Ryan L 2018 IEEE Trans. Electron Devices 65 1502
Google Scholar
[2] McAndrew C C 2018 IEEE Trans. Electron Devices 99 12
[3] Chen X S, Chen C H, Deen M J 2017 International Conference on Noise and Fluctuations (ICNF) Vilnius, Lithuania, June 20–13, 2017 p1
[4] Wang J, Peng X M, Liu Z J, Wang L, Luo Z, Wang D D 2018 Chin. Phys. B 27 027201
Google Scholar
[5] Antonopoulos A, Bucher M, Papathanasiou K, Mavredakis N, Makris N, Sharma R K, Sakalas P, Schroter M 2013 IEEE Trans. Electron Devices 60 3726
Google Scholar
[6] Das R R, Maity S, Muchahary D, Bhunia C T 2017 Superlattices Microstruct. 103 262
Google Scholar
[7] Smit G D J, Scholten A J, Pijper R M T, Tiemeijer L F, Toorn R V D, Klaassen D B M 2013 IEEE Trans. Electron Devices 61 245
[8] Chen C H, Lee R, Tan G, Chen D C, Lei P, Yeh C S 2012 IEEE Trans. Electron Devices 59 2215
Google Scholar
[9] Ong S N, Yeo K S, Chew K W J, Chan L H K, Loo X S, Boon C C, Do M A 2012 Solid-State Electron. 72 8
Google Scholar
[10] Ong S N, Yeo K S, Chew K W J, Chan L H K, Loo X S, Boon C C, Do M A 2012 Solid-State Electron. 68 32
Google Scholar
[11] Li Z Y, Ma J G, Ye Y Z, Yu M Y 2009 IEEE Trans. Electron Devices 56 1300
Google Scholar
[12] Roy A S, Enz C C 2005 IEEE Trans. Electron Devices 52 611
Google Scholar
[13] Han K S, Shin H C, Lee K R 2004 IEEE Trans. Electron Devices 51 261
Google Scholar
[14] Chen C H, Chen D, Lee R, Lei P, Wan D 2013 Proceedings of the IEEE 2013 Custom Integrated Circuits Conference San Jose, CA, USA, September 22–25, 2013 p1
[15] Lee K Y 2017 Solid-State Electron. 130 63
Google Scholar
[16] Valdovinos S M, Gurevich Y G 2016 Phys. Lett. A 380 2021
Google Scholar
[17] Volovichev I N, Gurevich Y G 2016 Curr. Appl. Phys. 16 191
Google Scholar
[18] 刘畅, 卢继武, 吴汪然, 唐晓雨, 张睿, 俞文杰, 王曦, 赵毅 2015 物理学报 64 167305
Google Scholar
Liu C, Lu J W, Wu W R, Tang X Y, Zhang R, Yu W J, Wang X, Zhao Y 2015 Acta Phys. Sin. 64 167305
Google Scholar
[19] Qu Y M, Chen B, Liu W, Han J H, Lu J W, Zhao Y 2018 Microelectron. Reliab. 85 93
Google Scholar
[20] Qu Y M, Lin X, Li J K, Cheng R, Yu X, Zheng Z J, Lu J W, Chen B, Zhao Y 2017 Proceedings of the 2017 IEEE International Electron Devices Meeting (IEDM) San Francisco, CA, USA, December 2–6, 2017 p39.2.1
[21] Cheng R, Yu X, Chen B, Li J F, Qu Y M, Han J H, Zhang R, Zhao Y 2017 IEEE Trans. Electron Devices 64 909
Google Scholar
[22] Zhao Y, Qu Y M 2019 IEEE J. Electron Devices Soc. 7 829
Google Scholar
[23] Sho S, Odanaka S, Hiroki A 2016 J. Comput. Electron. 15 76
Google Scholar
[24] Asgaran S, Deen M J, Chen C H 2004 IEEE Trans. Electron Devices 51 2109
Google Scholar
[25] Chen C H, Deen M J 2002 IEEE Trans. Electron Devices 49 1484
Google Scholar
[26] Lundstrom M 2009 Fundamentals of carrier transport Second Edition (Cambridge: Cambridge University Press) pp230–293
[27] Lim K Y, Zhou X 2002 Microelectron. Reliab. 42 1857
Google Scholar
[28] Tsividis Y 2011 Operation and Modeling of the MOS Transistor (3rd Ed.) (New York: Oxford University Press) pp194–201
[29] Rakheja S, Lundstrom M, Antoniadis D 2014 IEEE International Electron Devices Meeting San Francisco, CA, USA, December 15–17, 2014 p35.1.1
[30] Jeon J, Lee J D, Park B G, Shin H C 2007 Solid-State Electron. 51 1034
Google Scholar
[31] Yamaguchi K, Sakurai S, Tomizawa K 2010 Jpn. J. Appl. Phys. 49 024303
Google Scholar
[32] Ong S N, Chew K W J, Yeo K S, Chan L H K, Loo X S, Boon C C, Do M A 2009 Proceedings of the 2009 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT 2009) Singapore, Singapore, December 9–11, 2009 p280
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