臺灣博碩士論文加值系統

先進的金氧半場效電晶體(MOSFET)元件，由新穎矽基合金材料所組成，像是矽鍺合金，擁有低成本和製程簡單的優點。因此，在本論文中，我們注重MOSFET在反轉層的電洞遷移率，藉由使用新穎矽鍺合金來當作通道材料，所以在這個主題中，我們理論計算了矽鍺合金PMOSFET反轉層的電洞遷移率。
我們使用k.p微擾法計算能帶結構，以及Kubo-Greenwood的遷移率公式，矽鍺合金反轉層的電洞遷移率可以被計算，本模型在計算上所使用的參數，校準之方法由量測低電場時，矽和鍺的遷移率來進行匹配。最後，我們研究了(001)、(110)和(111)基板的鬆弛和雙軸應變矽鍺合金反轉層的合金極限遷移率、聲子極限遷移率和總遷移率。

Advanced MOSFET device formed from novel Si-based materials, such as silicon-germanium (SiGe) alloys, are simple and low cost to manufacture. In this thesis we focus on hole mobility in the inversion layer of the MOSFETs using novel silicon-germanium alloy channel materials. The primary topic of this work is the theoretical calculation of hole mobility in the SiGe alloy PMOSFET inversion layer.
Hole mobility in the SiGe alloy inversion layer is calculated using a k.p band structure method and the Kubo-Greenwood mobility formula. The model parameters used in the calculations are calibrated by matching the measured low-field mobility of Si and Ge. We study alloy-limited, phonon-limited, and total mobilities in the inversion layers of relaxed and biaxial strained SiGe on (100), (110), and (111) substrates, respectively.

誌謝辭 i
中文摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 vi
第一章 導論 1
1–1 研究動機 1
1–2 文獻回顧 2
第二章 應變矽工程的理論基礎 3
2–1 應變和應力 3
2–2 應變矽簡介 9
2–3 應變對價帶結構影響 12
2–4 應變矽PMOSFET次能帶能量分布 14
第三章 電洞k•p能帶理論 17
3–1 Bulk k•p能帶理論 18
3–2 Inversion Layer k•p能帶理論 25
3–3 座標轉換 27
第四章 電洞遷移率模型和理論 31
4–1 Quantization Effective Mass 31
4–2 Density Of States Effective Mass 33
4–3 mobility Derivation and Conductivity Effective Mass 34
4–4 聲子散射理論 37
4–5 表面粗糙散射理論 42
4–6 合金散射理論 44
4–7 Schrődinger and Poisson Self-consistent 46
第五章 Sentaurus-Sband計算矽基合金之遷移率結果 49
5–1 Sentaurus－Sband功能與模型介紹 49
5–2 Relaxed Si1-xGex之遷移率 51
5–2–1 Alloy Limited Mobility 51
5–2–2 Phonon Limited Mobility 58
5–2–3 Total Mobility 62
5–3 Strained Si1-xGex之遷移率 69
5–3–1 Alloy Limited Mobility 69
5–3–2 Phonon Limited Mobility 76
5–3–3 Total mobility 80
第六章 結論與未來展望 93
6–1 結論 93
6–2 未來展望 93
參考文獻 94

[1] S. M. Sze "Physics of semiconductor devices,2nd ed."
[2] Y. Zhang et al. , J. Appl. Phys. 106, 083704 (2009)
[3] T. Ghani et al., “A 90nm High Volume Manufacturing Logic Technology Featuring Novel 45nm Gate Length Strained Silicon CMOS Transistors,” IEDM Tech. Dig., 978 (2003).
[4] J.-S. Lim et al., “Comparison of Threshold-Voltage Shifts for Uniaxial and Biaxial Tensile-Stressed n-MOSFETs,” IEEE Electron Device Lett., vol. 25, 731 (2004).
[5] Ming-Fu Li, “Modern semiconductor quantum physics”
[6] C. Kittel, "Introduction to Solid State Physics, Eighth Edition"
[7] 奈米通訊第十二卷第一期局部與全面形變矽通道(strained Si channel)互補式金氧半(CMOS) 之材料、製程與元件特性分析(I)
[8] Shun Lien Chuang, “Physics of optoelectronic devices”
[9] W. Tom Wenckebach, “Essentials of semiconductor physics”
[10] J. M. Hinckley and J. Singh, J. Appl. Phys. 76, 4192 (1994)
[11] Yong-Hua Li and X. G. Gong, Phys. Rev. B 73, 245206 (2006)
[12] D. Rideau et al. , Phys. Rev. B 74, 195208 (2006)
[13] Jasprit Singh, “Electronic and Optoelectronic Properties of Semiconductor Structures”
[14] T. Ando, A. B. Fowler, and F. Stern, “Electronic properties of two-dimensional systems,” Rev. Mod. Phys., vol. 54, pp. 437–672, Apr. 1982.
[15] Agostino Pirovano, Andrea L. Lacaita, Günther Zandler, and Ralph Oberhuber, “Explaining the Dependences of the Hole and Electron Mobilities in Si Inversion Layers,” IEEE Trans. Electron Devices, vol. 47, no.4, pp. 718-724, April 2000.
[16] Tony Low, Yong-Tian Hou, and Ming-Fu Li, “Improved One-Band Self-Consistent Effective Mass Methods for Hole Quantization in p-MOSFET,” IEEE Trans. Electron Devices, vol. 50, no.5, pp. 1284-1289, May 2003.
[17] Shinya Yamakawa, Hiroaki Ueno, Kenji Taniguchi and Chihiro Hamaguchi,“Study of interface roughness dependence of electron mobility in Si inversionlayers using the Monte Carlo method,” J. Appl. Phys., vol. 79, no. 2, pp. 911-916,Jan. 1996.
[18]樊君偉 "應變矽碳合金應用於二維PMOS反轉層與塊材之價帶結構" 碩士論文
[19]樊君偉 "應變矽鍺合金通道金屬-氧化物-半導體場效電晶體的次能帶結構和傳輸特性" 博士論文
[20]周謙 "應變矽MOSFET載流子遷移率增強機理研究與建模"
[21] Jasprit Singh, “PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES” chapter 11, printed in 1990
[22] J.W. Harrsion and J. R. Hauser, Phys. Rev. B , vol3 , pp.5347, 1976
[23] K. Yeom, J. M. Hinckley and J. Singh, J. Appl. Phys. 80(12) 1996
[24] M. V. Fischetti and S. E. Laux, J. Appl. Phys. 80(4) 1996
[25] F. M. Bufler and B. Meinerzhagen J. Appl. Phys. 84(10) 1998
[26] Paul Harrison, “Quantum Wells, Wires and Dots,” Eq.(9.92), 2005
[27] Synopsys Sentaurus201206 PDF Manual.
[28] H. Brooks and C. Herring, “Electron scattering by ionized impurities in semiconductors,” Phys. Rev., vol. 83, pp879, 1951.
[29] G. Abstreiter, H. Brugger, T. Wolf, H. Jorke, and H. J. Herzog, "Strain-induced two-dimensional electron gas in selectively doped Si/SixGe1-x superlattices", Phys. Rev. Lett. 54, 2441, 1985.
[30] G. Schuberth, F. Schaffler, M. Besson, G. Abstreiter, “High electron mobility in modulation-doped Si/SiGe quantum well structures,” and E. Gornik, Appl. Phys. Lett. 59, 3318, 1991.
[31] Shin-ichi Takagi, Judy L. Hoyt, Jeffrey J.Welser, and James F. Gibbons, “Comparative study of phonon-limited mobility of two-dimensional electrons in strained and unstrained Si metal-oxide-semiconductor field-effect transistors”, J. Appl. Phys. 80, 1567, August 1996.
[32] F. M. Bufler, Yoshinori Asahi, Hisao Yoshimura, Christoph Zechner, A. Schenk, and Wolfgang Fichtner, “Monte Carlo Simulation and Measurement of Nanoscale n-MOSFETs,” IEEE, Vol.50, No.2, Feb 2003.

[33] Santhosh Krishnan, Dragica Vasileska, “Self-Consistent Subband Structure and Mobility of Two Dimensional Holes in Strained SiGe MOSFETs,” Journal of Computational Electronics 2: 449–454, 2003.
[34] P. W. Liu, J. W. Pan, T. Y. Chang, T. L. Tsai, T. F. Chen, Y. C. Liu, C. H. Tsai, B. C. Lan, Y. H. Lin, W. T. Chiang, and C. T. Tsai, “Superior current enhancement in SiGe channel p-MOSFETs fabricated on (110) surface,” VLSI Symp. Tech. Dig., pp. 148–149, 2006.
[35] S. Joshi, S. Dey, S. Lee, C. Krug, H. J. Na, P. Sivasubramani, P. D. Kirsch, P. Majhi, W. Wang, A. Campion, and S. K. Banerjee, “3X hole mobility enhancement in epitaxially grown SiGe pMOSFETs on (110) Si substrates with high K/metal gate for hybrid orientation technology,” Proc. Device Res. Conf., pp. 53–54, 2007.
[36] Ghassem Ansaripour, “Mobility of holes in a Si/Si0.8Ge0.2/Si metal oxide semiconductor field effect transistor,” Thin Solid Films 518 (2010) 5599–5603.