研究生: |
盧俊源 Chun-Yuan Lu |
---|---|
論文名稱: |
先進金氧半電晶體缺陷分佈偵測技術研究 A Study on Trap-Profiling Techniques for Advanced MOSFET Devices |
指導教授: |
張廖貴術
Kuei-Shu Chang-Liao |
口試委員: | |
學位類別: |
博士 Doctor |
系所名稱: |
原子科學院 - 工程與系統科學系 Department of Engineering and System Science |
論文出版年: | 2007 |
畢業學年度: | 96 |
語文別: | 英文 |
論文頁數: | 111 |
中文關鍵詞: | 電荷汲引 、高介電係數介電材料 、邊緣缺陷 、界面陷阱 、縱深輪廓偵測 、能量分布 、汲引電荷量 、上升/下降緣 |
外文關鍵詞: | charge-pumping, high-k, border trap, interface trap, depth profiling, energy distribution, charge pumped per cycle, rise/fall times |
相關次數: | 點閱:1 下載:0 |
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摘要
高介電係數介電材料(high-k)與矽基底鍵結不完全以及材料本身的差異,一般認為是造成high-k閘電晶體電特性退化的主因之一,因此如何準確且快速地量測界面陷阱和本體缺陷的數量及分佈,顯然是一個相當有價值的研究工作。本文中簡介了數個以CP量測 (charge-pumping, CP , measurement) 為基礎所發展出來的量測技術,並針對實際量測到的現象提供原理說明。傳統調變脈衝上升/下降緣 (rise/fall times of gate pulse) 的CP量測技術,已成功地應用在探測high-k閘電晶體內部界面陷阱密度及其能量分佈。並且為了有效偵測邊緣缺陷 (border trap),本文提出一套以變化頻率牽動汲引電荷Qcp (即Icp/f) 產生變化為基礎的數學計算模式,用以估算在high-k介電層內邊緣缺陷縱深分佈。另外,就邊緣缺陷對CP量測的影響以及邊緣缺陷本身特有的行為也將逐一被介紹。並且從實際的邊緣缺陷縱深分佈結果可以清楚發現,在high-k堆疊閘介電層內部的本體缺陷分佈是相當不均勻的。脈衝振幅 (amplitude of gate pulse) 增加以及電應力施加後介電層內部因熱載子所衍生的缺陷對整体CP量測的影響,也將在本文中被討論。從實驗結果來看,high-k介電層內部固有的弱鍵 (weak bonds) 似乎容易因為電應力施加而捕陷電荷形成氧化層缺陷電荷,並造成一定程度的臨界電壓漂移。此外,電應力所衍生的邊緣缺陷可能不是傳統所認知固定位置的缺陷捕陷中心 (fixed trapping center),而是一可移動的缺陷其反映出電性的行為類似電洞。在考慮了變化頻率以及變化脈衝振幅兩種不同的CP量測方式,變頻的方式顯示較為合適探究邊緣缺陷以及延展穿遂縱深。在導入有關邊緣缺陷載子穿遂的影響之後,本文也提出一套新穎的CP量測技術用以觀測high-k閘電極元件內部淺界面缺陷空間及能量分佈。從量測結果顯示有相當低的邊緣缺陷密度存在於HfOxNy/SiO2界面中間的過渡層,而這可能的原因是這層過渡層具有較好的材料鍵結所致。
Abstract
High-k dielectric constant (high-k) material has been proposed to replace the conventional silicon dioxide as gate dielectrics of metal-oxide-semiconductor (MOS) devices in the near future. However, the characteristic and extent of charge trapping in the interfacial layer between high-k dielectric and silicon have been reported to affect strongly the electrical characteristics of high-k gated MOS devices. Hence, providing an accurate and quick measurement for density and distribution of interface and bulk traps is believed to be a valuable research topic. This work proposes several measurement techniques based on the principle of charge pumping (CP) and provides some discussion in depth for measurement results. A CP technique with varying fall and rise times has been successfully applied to determine the mean capture cross-section and the energy distribution of the interface-trap density Dit(E) in high-k gated MOS devices. Also, in order to further study the border traps near the high-k/Si interface, a calculation model based on the variation of the charge pumped per cycle (Qcp) with frequency has been proposed to estimate the depth profile of border trap in the high-k dielectric. Besides, the influence of border traps on CP measurement and its unique behavior are also investigated. It is found that there is a non-uniform distribution of bulk trap density existing in high-k gate stack dielectric. Moreover, the effects of amplitude of gate pulse and electrical stress-induced traps by a CP measurement are studied. Measurement results indicate that the weak bonds in high-k gate dielectric are easily trapped by charges after stressing; thus, stress results in a large threshold voltage (Vth) shift. It is also observed that the stress-induced border trap is probably not a fixed trapping center but a mobile defect like hole. By taking into account on the effect of carrier tunneling in slow oxide traps, a promising CP technique has been proposed to obtain a clear observation on the spatial and energy distribution of the near-interface traps in the gate dielectric of high-k gated MOSFETs. The CP method with varying-frequency has been shown to be more effective for probing border traps than that with varying-amplitude. Border-trap density is relatively lower in the HfSiON layer due to its better bonding.
Reference
[1] G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-k gate dielectrics: current status and materials properties considerations,” J. Appl. Phys., vol. 89, pp. 5243-5275, 2001.
[2] K. Yamamoto, S. Hayashi, M. Kubota, and M. Niwa, “Effect of Hf metal predeposition on the properties of sputtered HfO2/Hf stacked gate dielectrics,” Appl. Phys. Lett., vol. 81, pp. 2053-2055, 2002.
[3] M. R. Visokay, J. J. Chambers, A. L. P. Rotondaro, A. Shanware, and L. Colombo, “Application of HfSiON as a gate dielectric material,” Appl. Phys. Lett., vol. 80, pp. 3183-3185, 2002.
[4] C. S. Kang, H.-J. Cho, R. Choi, Y. H. Kim, C. Y. Kang, S. J. Rhee, C. Choi, M. S. Akbar, and J. C. Lee, “The electrical and material characterization of Hafnium oxynitride gate dielectric with TaN-gate electrode,” IEEE Trans. Electron Devices, vol. 51, pp. 220-227, 2004.
[5] X. Wang, J. Liu, F. Zhu, N. Yamada, and D. L. Kwong, “A simple approach to fabrication of high-quality HfSiON gate dielectric with improved nMOSFET performances,” IEEE Trans. Electron Devices, vol. 51, pp. 1798-1804, 2004.
[6] X. Yu, C. Zhu, M. F. Li, A. Chin, M. B. Yu, A. Y. Du, and D. L. Kwong, “Mobility enhancement in TaN metal-gate MOSFETs using tantalum incorporated HfO2 gate dielectric,” IEEE Electron Device Lett., vol. 25, pp. 501-503, 2004.
[7] C. S. Park, B. J. Cho, and D. L. Kwong, “MOS characteristics of synthesized HfAlON-HfO2 stack uaing AlN-HfO2,” IEEE Electron Device Lett., vol. 25, pp. 619-621, 2004.
[8] A. Paskaleva, A. J. Bauer, M. Lemberger, and S. Zurcher, “Different current conduction mechanisms through thin high-k HfxTiySizO films due to the varying Hf to Ti ratio,” J. Appl. Phys., vol. 95, pp. 5583-5590, 2004.
[9] W. Zhu, T. P. Ma, T. Tamagawa, Y. Di, J. Kim, R. Carruthers, M. Gibson, T. Furukawa, “HfO2 and HfAlO for CMOS: thermal stability and current transport,” in IEDM Tech. Dig., pp. 463–466, 2001.
[10] C. C. Hobbs, L. R. C. Fonseca, A. Knizhnik, V. Dhandapani, S. B. Samavedam, W. J. Taylor, J. M. Grant, L. G. Dip, D. H. Triyoso, R. I. Hegde, D. C. Gilmer, R. Garcia, D. Roan, M. L. Lovejoy, R. S. Rai, E. A. Hebert, H.-H. Tseng, S. G. H. Anderson, B. E. White, and P. J. Tobin, “Fermi-level pinning at the polysilicon/metal oxide interface-Part I,” IEEE Trans. Electron Devices, vol. 51, no. 6, pp. 971–977, Jun. 2004.
[11] -------, “Fermi-level pinning at the polysilicon/metal oxide interface-Part II,” IEEE Trans. Electron Devices, vol. 51, no. 6, pp. 978–984, Jun. 2004.
[12] W. J. Zhu, T. P. Ma, S. Zafar, and T. Tamagawa, “Charge trapping in ultrathin hafnium oxide,” IEEE Electron Device Lett., vol. 23, no. 10, pp. 597–599, Oct. 2002.
[13] S. Zafar, A. Callegari, E. Gusev, and M. V. Fischetti, “Charge trapping in high-k gate dielectric stacks,” in IEDM Tech. Dig., pp. 517–520, 2002.
[14] S. Zafar, A. Kumar, E. Gusev, and E. Cartier, “Threshold voltage instabilities in high-k gate dielectric stacks,” IEEE Trans. Device Mater. Rel., vol. 5, no. 1, Mar. 2005.
[15] M. Houssa, S. D. Gendt, J. L. Autran, G. Groeseneken, and M. M. Heyns, “Detrimental impact of hydrogen on negative bias temperature instabilities in HfO2-based pMOSFETs,” in Symp. VLSI Tech. Dig., pp. 212-213, 2004.
[16] M. V. Fischetti, D. A. Neumayer, and E. A. Cartier, “Effective electron mobility in Si inversion layers in metal-oxide-semiconductor systems with a high-k insulator: The role of remote phonon scattering,” J. Appl. Phys., vol. 90, pp. 4587–4608, 2001.
[17] W. Zhu, J.-P. Han, and T. P. Ma, “Mobility measurement and degradation mechanisms of MOSFETs made with ultrathin high-k dielectrics,” IEEE Trans. Electron Devices, vol. 51, no. 1, pp. 98–105, Jan. 2004.
[18] D. K. Schroder, and J. A. Babcock, “Negative bias temperature instability: Road to cross in deep submicron silicon semiconductor manufacturing,” J. Appl. Phys., vol. 94, no. 1, pp. 1–18, 2003.
[19] P. V. Gray, and D. M. Brown, “Density of SiO2-Si interface states,” Appl. Phys. Lett., vol. 8, no. 2, pp. 31-33, 1966.
[20] S. M. Sze, “Semiconductor devices, physics and technology,” John Wiley & Sons, 1985.
[21] Y. Taur, and T. K. Ning, “Fundamentals of modern VLSI devices,” Cambridge University Press, 1998.
[22] J. S. Brugler, and P. G. A. Jespers, “Charge pumping in MOS devices,” IEEE Trans. Electron Devices, vol. ED-16, pp. 297-302, 1969.
[23] G. V. Groeseneken, H. E. Maes, N. Beltran, and R. F. De Keersmaecker, “A Reliable Approach to Charge Pumping Measurement in MOS Transistors,” IEEE Trans. Electron Devices, ED-31, pp.42-53, Jan. 1984.
[24] A. B. M. Elliot, “The use of charge pumping current to measure surface state densities in MOS Transistors,” Solid-State Electron., vol. 19, pp. 241-247, Mar. 1976.
[25] R. A. Wachnik and J. R. Lowney, “A model for the charge-pumping current based on small rectangular voltage pulses,” Solid-State Electron., vol. 29, pp. 447-460, Apr. 1986.
[26] W. L. Tseng, “A new charge pumping method of measuring Si-SiO2 interface states,” J. Appl. Phys., vol. 62, pp. 591-599, July 1987.
[27] N. S. Saks, and M. G. Ancona, “Determination of interface trap capture cross sections using three-level charge pumping,” IEEE Electron Device Lett., vol. 11, pp. 339-341, Aug. 1990.
[28] J. P. Han, E. M. Vogel, E. P. Gusev, C. D’Emic, C. A. Richter, D. W. Heh, and J. S. Suehle, “Energy Distribution of Interface Traps in High-K Gated MOSFETs,” in Symp. VLSI Tech. Dig., 2003, pp. 161-162.
[29] G. W. Lee, J. H. Lee, H. W. Lee, M. K. Park, D. G. Kang, and H. K. Toun, “Trap evaluations of metal/oxide/silicon field-effect transistors with high-k gate dielectric using charge pumping method,” Appl. Phys. Lett., vol. 81, no. 11, pp. 2050-2052, Sept. 2002.
[30] W. Chen, A. Balasinski, and T. P. Ma, “Lateral profiling of oxide charge and interface traps near MOSFET junctions,” IEEE Trans. Electron Devices, vol. 40, pp. 187-196, Jan. 1993.
[31] M. G. Ancona, N. S. Saks, and D. McCarthy, “Lateral distribution of hot-carrier-induced interface traps in MOSFET’s,” IEEE Trans. Electron Devices, vol. 35, pp. 2221-2228, Dec. 1988.
[32] M. Tsuchiaki, H. Hara, T. Morimoto, and H. Iwai, “A new charge pumping method for determining the spatial distribution of hot-carrier-induced fixed charge in p-MOSFET’s,” IEEE Trans. Electron Devices, vol. 40, pp. 1768-1779, Oct. 1993.
[33] F. P. Heimann and G. Warfield, “The effect of oxide traps on MOS capacitance,” IEEE Trans. Electron Devices, vol. ED-12, pp.167-178, 1964.
[34] M. Declercq, and P. Jespers, “Analysis of interface properties in MOS transistors by means of charge pumping measurements,” Rev. HF, Acta. Tech. Belg., vol. 9, pp. 244-244, 1974.
[35] R. E. Paulsen and M. H. White, “Theory and Application of Charge Pumping for the Characterization of Si-SiO2 Interface and Near-Interface Oxide Traps,” IEEE Trans. Electron Devices, vol. 41, pp. 1213-1216, 1994.
[36] R. E. Paulsen, R. R. Siergiej, M. L. French, and M. H. White, “Observation of Near-Interface Oxide Traps with the Charge-Pumping Technique,” IEEE Electric Device Lett., vol. 13, pp. 627-629, Dec., 1992.
[37] Y. Maneglia and D. Bauza, “Extraction of slow trap concentration profiles in metal-oxide-semiconductor transistors using the charge pumping method,” J. Appl. Phys., vol. 79, pp. 4187–4192, 1996.
[38] P. J. McWhorter, and P. S. Winokur, “Simple technique for separating the effects of interface traps and trapped oxide charge in metal-oxide-semiconductor transistor,” Appl. Phys. Lett., vol. 48, no. 2, pp. 133-135, Jan. 1986.
[39] K. T. San, and T. P. Ma, “Determination of trapped oxide charge in flash EPROM’s and MOSFET’s with thin oxides,” IEEE Electron Device Lett., vol. 13, pp. 439-441, Aug. 1992.
[40] C. Chen, and T. P. Ma, “Direct lateral profiling of hot-carrier-induced oxide charge and interface traps in thin gate MOSFET’s,” IEEE Trans. Electron Devices, vol. 45, pp. 512-520, Feb. 1998.
[41] J. Bosch, Ph.D. thesis, Tech. Phys. Lab., Groningen State University, 1979.
[42] D. K. Schroder, “Semiconductor material and device characterization,” John wiley & Sons, 1998.
[43] D. Bauza, “Extraction of Si-SiO2 interface trap densities in MOS structures with ultrathin oxides,” IEEE Electron Device Lett., vol. 23, no. 11, pp. 658-660, 2002.
[44] S. S. Chung, S. J. Chen, C. K. Yang, S. M. Cheng, S. H. Lin, Y. C. Sheng, H. S. Lin, K.-T. Hung, D. Y. Wu, T. R. Yew, S. C. Chien, F. T. Liou, and Frank Wen, “A novel and direct determination of the interface traps in sub-100 nm CMOS devices with direct tunneling regime (12-16 Å) gate oxide,” in Symp. VLSI Tech. Dig., pp. 74-75, 2002.
[45] P. Masson, J.-L. Autran, and J. Brini, “On the tunneling component of charge pumping current in ultrathin gate oxide MOSFETs,” IEEE Electron Device Lett., vol. 20, no. 2, pp. 92-94, 1999.
[46] A. Melik-Martirosian and T. P. Ma, “Improved charge-pumping method for lateral profiling of interface traps and oxide charge in MOSFET devices,” in IEDM Tech. Dig., pp. 93-96, 1999.
[47] C. Y. Lu, and K. S. Chang-Liao, “Minimized constrains for lateral profiling of hot-carrier-induced oxide charge and interface traps in MOSFETs,” IEEE Electron Device Lett., vol. 25, no. 2, pp. 98-100, Fab. 2004.
[48] J. G. Simmons and L. S. Wei, “Theory of dynamic charge current and capacitance characteristics in MIS systems containing distributed surface traps,” Solid-State Electron., vol. 16, p. 53, 1973.
[49] W. L. Hill, E. M. Vogel, V. Misra, P. K. McLarty, and J. J. Wortman, “Low-presure rapid thermal chemical vapor deposition of oxynitride gate dielectrics for n-channel and p-channel MOSFETs,” IEEE Trans. Electron Devices, vol. 43, no. 1, pp. 15-22, 1996.
[50] T. P. Ma, “Making silicon nitride film a viable gate dielectric,” IEEE Trans. Electron Devices, vol. 45, pp. 680-690, Mar. 1998.
[51] L. Manchanda, W. H. Lee, J. E. Bower, F. H. Baumann, W. L. Brown, C. J. Case, R. C. Keller, Y. O. Kim, E. J. Laskowski, M. D. Morris, R. L. Opila, P. J. Silverman, T. W. Sorsch, and G. R. Weber, “Gate quality doped high-k films for CMOS beyond 100 nm: 3- 10 nm Al2O3 with low leakage and low interface states,” in IEDM Tech. Dig., pp. 605-608, 1998.
[52] M. F. Luan, S. J. Lee, C.H. Lee, S. C. Song, Y. L. Mao, Y. Senzaki, D. Roberts, and D. L. Kwong, “”High quality Ta2O5 gate dielectrics with Tox,eq < 10 □ ,” in IEDM Tech. Dig., pp. 141-144, 1999.
[53] B. He, N. Hoilien, T. Ma, C. Yaylor, I. S. Omer, S. A. Campbell, W. L. Gladfelter, M. Gribelyuk, and D. Buchanan, “High permittivity gate insulators TiO2 and ZrO2,” in IEDM Tech. Dig., pp. 33-36, 1999.
[54] A. Kerber, E. Cartier, L. Pantisano, R. Degraeve, T. Kauerauf, Y. Kim, A. Hou, G. Groeseneken, H. E. Maes and U. Schwalke, “Origin of the threshold voltage instability in SiO2/HfO2 dual layer gate dielectrics,” IEEE Electron Device Lett., vol. 24, pp. 87-89, 2003.
[55] K. Torii, Y. Shimamoto, S. Saito, O. Tonomura, M. Hiratani, Y. Manabe, M. Caymax, and J. W. Maes, “The mechanism of mobility degradation in MISFETs with Al2O3 gate dielectric,” in Symp.VLSI Tech. Dig., 2002, pp. 188-189.
[56] E. H. Nicollian, “A method to extract interface states parameters from the MIS parallel conductance technique,” Solid-State Electron., vol. 16, pp. 121-130, 1972.
[57] E. H. Nicollian and J. R. Brews, “MOS (metal oxide semiconductor) physics and technology,” John wiley & Sons, 1982.
[58] C. N. Berglund, “Surface states at steam-grown silicon-silicon dioxide interfaces,” IEEE Trans. Electron Devices, vol. ED-13, pp. 701-705, Apr. 1966.
[59] K. K. Hung, P. K. Ko, C. Hu, and Y. C. Cheng, “A unified model for the flicker noise in metal-oxide-semiconductor field-effect transistors,” IEEE Trans. Electron Devices, vol. 37, pp. 654-660, Apr. 1990.
[60] F. H. Hooge, and L. K. J. Vandamme, “Lattice scattering causes 1/f noise,” Phys. Lett., vol. 66A, pp. 315-321, Apr. 1978.
[61] D. Bauza and G. Ghibaudo, “Analytical study of the contribution of fast and slow oxide traps to the charge pumping technique,” Solid-State Electron., vol. 39, no. 4, pp. 563-570, 1996.
[62] T. H. Hou, M F. Wang, K L. Mai, Y. M. Lin, M. H. Yang, L. G. Yao, Y. Jin, S.-C. Chen, and M. S. Liang, “Direct determination of interface and bulk traps in stacked HfO2 dielectrics using charge pumping method,” in 42nd Annual Proceedings of Reliability Physics, pp. 581-582, Phoenix, 2004.
[63] B. Djezzar, A. Smatti, and S. Qussalah, “A new oxide-trap based on charge-pumping (OTCP) extraction method for irradiated MOSFET device: Part II (Low Frequencies),” IEEE Trans. Nucl. Sci., vol. 51, pp. 1732-1736, Aug. 2004.
[64] C. E. Weintraub, E. Vogel, J. R. Hauser, N. Yang, V. Misra, J. J. Wortman, J. Ganem, and P. Masson, “Study of low-frequency charge pumping on thin stacked dielectrics,” IEEE Trans. Electron Devices, vol. 48, pp.2754-2762, Dec. 2001.
[65] W. Chen and T. P. Ma, “Channel-hot-carrier induced oxide charge trapping in NMOSFET’s,” in IEDM Tech. Dig., 1991, pp. 731-734.
[66] W. Chen, A. Balasinski, and T. P. Ma, “Lateral distribution of radiation-induced damage in MOSFET’s,” IEEE Trans. Nucl. Sci., vol. 38, pp. 1124-1129, Dec. 1991.
[67] C. Y. Lu, K. S. Chang-Liao, P. H. Tsai, and T. K. Wamg, “Depth profiling of border traps in MOSFET with high-k gate dielectric by charge-pumping technique,” IEEE Electron Device Lett., vol. 27, no. 10, pp. 859-862, 2007.
[68] S. Jakschik, A. Avellan, U. Schroeder, and J. W. Bartha, “Influence of Al2O3 dielectrics on the trap-depth profiles in MOS devices investigated by the charge-pumping method,” IEEE Trans. Electron Devices, vol. 51, pp.2252-2255, Dec. 2004.
[69] G. V. den Bosch, G. Groeseneken, P. Heremans, and H. Maes, “Spectroscopic charge pumping: A new procedure for measuring interface trap distributions in MOS transistors,” IEEE Trans. Electron Devices, vol. 38, pp.1820-1831, Aug. 1991.
[70] E. Simoen, A. Mercha, L. Pantisano, C. Claeys, and E. Young, “Low-frequency noise behavior of SiO2-HfO2 dual-layer gate dielectric nMOSFETs with different interfacial oxide thickness,” IEEE Trans. Electron Devices, vol. 51, No. 5, pp.780-784, May 2004.
[71] A. Kerber, E. Cartier, R. Degraeve, P. J. Roussel, L. Pantisano, T. Kauerauf, G. Groeseneken, H. E. Maes, and U. Schwalke, “Charge trapping and dielectric realibility of SiO2-Al2O3 gate stacks with TiN electrodes,” IEEE Trans. Electron Devices, vol. 50, No. 5, pp.1261-1269, May 2003.
[72] J. P. Han, E. M. Vogel, E. P. Gusev, C. D’Emic, C. A. Richter, D. W. Heh, and J. S. Suehle, “Asymmetric energy distribution of interface traps in n- and p-MOSFETs with HfO2 gate dielectric on ultrathin SiON buffer layer,” IEEE Electric Device Lett., vol. 25, pp. 126-128, Mar. 2004.
[73] M. Giannini, A. Pacelli, A. L. Lacaita, and L. M. Perron, “Effect of oxide tunneling on the measurement of MOS interface states,” IEEE Electric Device Lett., vol. 21, pp. 405-407, Aug., 2000.
[74] D. Heh, C. D. Young, G. A. Brown, P. Y. Hung, A. Diebold, G. Bersuker, E. M. Vogel, and J. B. Bernstein, “Spatial distribution of trapping centers in HfO2/SiO2 gate stacks, ” Appl. Phys. Lett., vol. 88, 152907: 1-3, 2006.
[75] A. S. Foster, F. L. Gejo, A. L. Shluger, and R. M. Nieminen, “Vacancy and interstitial defects in hafnia,” Phys. Rev. B, 65, 174117: 1-13, 2002.
[76] J. Robertson, “Interfaces and defects of high-k oxides on silicon,” Solid-State Electron., vol. 49, pp. 283-293, 2005.
[77] N. A. Chowdhury, P. Srinivasan, and D. Misra, “Trapping in Deep Defects under Substrate Hot Electron Stress in TiN/Hf-silicate Based Gate Stacks,” in Inter. Semi. Dev. Res. Symp., 2005, pp. 213 – 214.
[78] E. Cartier, B. P. Linder, V. Narayanan, and V. K. Paruchuri, “Fundamental understanding and optimization of PBTI in nFETs with SiO2/HfO2 gate stack,” published in IEDM Tech. Dig. 2006.