摘要
量子穿隧場效電晶體理論上能克服傳統金氧半場效電晶體在常溫下所面臨的次臨界斜率的限制。在理想的電路中，量子穿隧場效電晶體操作電壓較小、因而能降低次臨界電壓及功率消耗。實際上該元件目前面臨最主要的挑戰之一為相較金氧半場效電晶體還要小的操作電流，其主要原因來自於在間接能隙半導體材料中（如：矽）需要聲子協助電子以量子穿隧傳遞。為了得到更好的穿隧機率，在此討論以四族為主的穿隧場效電晶體及利用半古典Kane模型了解直接與間接能隙對元件特性的影響.
儘管純鍺與矽鍺有較小的能隙與較輕的等效質量在理論與實驗結果操作電流仍然不足夠，為了增進穿隧場效電晶體探索直接帶與帶穿隧的四族元素半導體以成為研究，鍺錫具有可調變直接能隙的四族材料，藉由增加錫的比例，從間接能隙轉為直接能隙，此外鍺錫有比矽鍺與純鍺更小的能隙及更輕的等效質量，在本論文中將探討以鍺錫為材料的場效電晶體.
我們利用8-k.p模型計算出鍺錫材料中能隙及等效質量,並且探討非拋物、多個能帶及量子尺寸效應對鍺錫元件的影響，最後使用TCAD模擬以鍺錫為材料的數個元件分別是,傳統型量子穿隧場效電晶體、PNIN穿隧場效電晶體、金氧半場效電晶體進行特性比較.
*作者 **指導教授
關鍵字: 金氧半場效電晶體、互補式金氧半場效、電晶體、穿隧場效電晶體、次臨界斜率、鍺錫

Modeling and Simulation of GeSn-based Field Effect Transistors

Jen-Hong Liao*　　　 Kuo-Hsing Kao**

MS Degree program on Nano-Integrated Circuit Engineering,
National Cheng Kung University
Abstract
Tunnel field-effect transistors have the potential to overcome the subthreshold slope limit of the conventional metal-oxide-semiconductor field effect transistors at room temperature. They allow to further scale down the supply voltage, threshold voltage and power consumption of the integrated circuits. The one of the main challenges of group-IV-based TFETs is the unsatisfactory on-current due to the phonon-assisted tunneling through the large indirect bandgaps. This article is devoted to discuss the direct and indirect band-to-band tunneling in group-IV semiconductors.
Although Ge and SiGe possess smaller bandgaps and lighter carrier effective masses, theoretical and experimental result still unsatisfactory improvement. To further enhance the TFET performance, exploitation of direct BTBT in group-IV semiconductors is a promising approach. GeSn has emerged as a promising alternative alloy to achieve tunable direct bandgap among group IV materials. By increasing the Sn concentration, the bandgaps of relaxed GeSn alloys exhibit a transition from indirect to direct. In addition, GeSn possess smaller bandgaps and lighter carrier effective masses than Ge. In this dissertation, I will discuss GeSn-based Field Effect TransistorsIn this study we utilize 8-k·p model to calculate GeSn energy bandgap and effective mass. In addition we also explore GeSn physical property which consider nonparabolicity, multi-valley and quantum size confinement. At last, by using TCAD to simulate and compare GeSn-based property which include TFETs, PNIN TFETs and MOSFET devices.

*Author **Advisor
Keywords: MOSFET、CMOS、Tunnel FET、subthreshold slope SS、Germanium tin

References
References in Chapter 1
1. International Technology Roadmap for Semiconductors, 2012
2. A. M. Ionesscu, et al., Nature, 479,329, 2011.
3. B. Meyerson, in IBM Semico Conf., 2004.
4. S. M. Sze, et al., Physics of Semiconductor devices, 3rd edition, New York: John Wiley & sons, 2007.
5. J. Appenzeller, et al., IEEE Trans. Electron Devices, 55, 2827, 2008.
6. K. Tomioka, et al., VLSI Tech. Dig., 47, 2012.
7. H. Kam, et al., IEDM Tech. Dig., 463, 2005.
8. R. Nathanael, et al., IEDM Tech. Dig., 1, 2009.
9. C. W. Yeung, et al., VLSI Tech. Dig., 176, 2009.
10. S. Salahuddin, et al., Nanolett., 8, 405, 2008.
11. A. I. Khan, et al., IEDM Tech. Dig., 255, 2011.
12. E. Gnani, et al., IEDM Tech. Dig., 91, 2011.
13. K. Gopalakrishnan, et al., IEEE Trans. Electron Devices, 52, 69, 2005.
14. C. W. Yeung, et al., SISPAD, 257, 2012.
15. K. Boucart, et al., IEEE Trans. Electron Devices, 54, 1725, 2007.
16. W. Y. Choi, et al., IEEE Electron Device Lett., 28, 743, 2007.
17. S. H. Kim, et al., VLSI Tech. Dig., 178, 2009.
18. F. Mayer, et al., IEDM Tech. Dig., 1, 2008.
19. T. Krishnamohan, et al., IEDM Tech. Dig., 947, 2008.

References in Chapter 2
1. J. H. Davies, The physics of low-dimensional semiconductors, Cambridge, U.K.: Cambridge Univ. Press, 1998.
2. E. O. Kane, J. Phys. Chem. Solids, 12, 181, 1959.
3. E. O. Kane, J. Appl. Phys., 32, 83, 1961.
4. Sze, SM. Physics of Semiconductor Devices , 3rd ed., Wiley: New York, 2007.
5. W. G. Vandenberghe, et al., J. Appl. Phys., 107, 054520, 2010.
6. S. C. Jain, et al., Solid-State Electron., 34, 453, 1991.
7. J. M. Lopez-Gonzalez, et al., IEEE Trans. on Electron Devices, 44, 1046, 1997.
8. J. Poortmans, et al., Solid-State Electron., 36, 1763, 1993.
9. R.C. Aguilera, et al., Appl. Phys. Lett., 102, 152106, 2013.
10. P. Y. Yu, et al., Fundamentals of SEMICONDUCTORS, Springer, New York, 1999.
11. T. Manku, et al., Phys. Rev. B, 43, 12634, 1991.
12. S. K. Chun, et al., IEEE Trans. on Electron Devices, 39, 2153, 1992.
13. M. V. Fischetti, et al., J. Appl. Phys., 80, 2234, 1996.
14. T. Manku, et al., J. Appl. Phys., 62, 8414, 1991.
15. Y. Fu, et al., J. Appl. Phys., 74, 402, 1993.
16. D. Rideau, et al., Phys. Rev. B, 74, 195208, 2006.
17. M. M. Rieger, et al., Phys. Rev. B, 48, 14276, 1993.
18. Available at: http://www.ioffe.ru/SVA/NSM/Semicond/index.html.
19. G. Hellings, et al., IEEE Trans. on Electron Devices, 57, 2539, 2010.

References in Chapter 3
1. K. H. Kao, A. Verhulst, W. Vandenberghe, B. Soree, G. Groeseneken, and K. De Meyer, “Direct and indirect band-to-band tunneling in germanium-based TFETs,” IEEE Trans. Electron Devices, vol. 59, no. 2,pp. 292–301, Feb. 2012.
2. Sze, SM. Physics of Semiconductor Devices , 3rd ed., Wiley: New York, 2007.
3. G. Chynoweth, W. L. Feldmann, C. A. Lee, R. A. Logan, G. L. Pearson, and P. Aigrain, “Internal field emission at narrow silicon and germanium p-n junctions,” Phys. Rev., vol. 118, no. 2, pp. 425–434, Apr. 1960.
4. M. S. Tyagi, “Determination of effective mass and the pair production energy for electrons in germanium from Zener diode characteristics,” Jpn. J. Appl. Phys., vol. 12, no. 1, pp. 106–108, Jan. 1973.
5. S. Gupta et al., IEDM Tech. Dig., 2011, pp. 398.
6. K. L. Low, Y. Yang, G. Han, W.-J. Fan, and Y.-C. Yeo, “Electronic band structure and effective mass parameters of Ge1−xSnx alloys,” J. Appl.Phys., vol. 112, pp. 103715-1–103715-9, Nov. 2012.
7. C. R. Pidgeon and R. N. Brown, Phys. Rev. 146, 575 (1966).
8. T. E. Ostromek, Phys. Rev. B 54, 14467 (1996).
9. Conwell, E.M., and M. O. Vassel, 1968, Phys. Rev. 166, 797.
10. Ruch, J. G., and W. Fawcett, 1970, J. Appl. Phys. 41, 384.
11. Price, P. J., and R. L. Hartman, 1964, J. Phys. Chem. Solids 25,219.
12. Vishal P. Trivedi, and Jerry G. Fossum, “Quantum-Mechanical Effects on the Threshold Voltage of Undoped Double-Gate MOSFETs, “IEEE Electron Device Letters (Volume:26 , Issue: 8 ),pp.579.

References in Chapter 4
1. Krishnamohan, T, Donghyun, K, Raghunathan, S, Saraswat, K. Double-gate strained-Ge heterostructure tunneling FET (TFET) with record high drive currents and < 60 mV/dec subthreshold slope. In IEEE Conference Proceedings of International Electron Devices Meeting , December 15 – 17, 2008, San Francisco, CA, USA, pp. 1 – 3.
2. Verhulst AS, Vandenberghe WG, Maex K, Groeseneken G. Tunnel field-effect transistor without gate-drain overlap. Appl. Phys. Lett. 2007, 91, 053102.
3. Boucart K, Ionescu AM. Length scaling of the double gate tunnel FET with a high-K gate dielectric. Solid State Electron. 2007, 51, 1500 – 1507.
4. Bhuwalka KK, Born M, Schindler M, Schmidt M, Sulima T, Eisele I. P-Channel tunnel field-effect transistors down to sub-50 nm channel lengths. Jpn. J. Appl. Phys. 2006, 45, 3106.
5. A. M. Ionescu and H. Riel, “Tunnel field-effect transistors as energy-efficient electronic switches,” Nature, vol. 479, pp. 329–337, Nov. 2011.
6. V. Nagavarapu, R. Jhaveri, and J. Woo, “The tunnel source (PNPN) n-MOSFET: A novel high performance transistor,” IEEE Trans. Electron Devices, vol. 55, no. 4, pp. 1013–1019, Apr. 2008.
7. D. Verreck et al., “Quantum mechanical performance predictions of p-n-i-n versus pocketed line tunnel field-effect transistors,” IEEE Trans. Electron Devices, vol. 60, no. 7, pp. 2128–2134, Jul. 2013.
8. R. Jhaveri, V. Nagavarapu, and J. Woo, “Effect of pocket doping and annealing schemes on the source-pocket tunnel field-effect transistor,” IEEE Trans. Electron Devices, vol. 58, no. 1, pp. 80–86, Jan. 2011.