臺灣博碩士論文加值系統

近年來MOFET元件不斷的微型化過程中，由二氧化矽所構成的介電層將因過薄而導致嚴重的漏電流，導致元件操作上的不穩定性。然而，為了使元件在微型化過程中能夠維持同樣的性能及正常運作，目前解決方案是以較高介電常數(high-κ)的材料來取代傳統的二氧化矽。由於高介電常數材料可形成較厚的介電層，因電流穿隧所造成的漏電情況可因此獲得緩解。在眾多高介電常數材料中，二氧化鉿(HfO2)與其矽酸鹽(Hf1-xSixO2)已被認為最有希望取代二氧化矽(SiO2)做為MOS元件閘極介電層材料。儘管近年來在這方面研究已有不錯的進展，採用高介電常數材料當作MOSFET元件介電層的效能仍遠不及傳統的二氧化矽，其主要原因為高介電常數材料卻比二氧化矽更容易結晶；針對此一問題，目前的解決方法是在二氧化鉿的結構中加入矽，鋁，氮，或其它元素來提高介電材料的再結晶溫度。但是，值得注意的是加入二氧化矽雖然提高了二氧化鉿的再結晶溫度，其同時也降低了介電層的介電常數，所以如何在其中取得一個平衡也是一個考量的重點。儘管仍有上述諸多問題與缺點存在，二氧化鉿及其矽酸鹽仍是目前作為MOSFET元件中介電層的最佳候選材料。如欲解決這些問題，我們實必須對介電材料本身的結構以及其缺陷的行為有更深入的瞭解。
本研究的主要目的是嘗試運用第一原理計算與分子動態模擬來建構合理的非晶相二氧化鉿及其矽酸鹽的原子級結構模型。根據我們所建構的模型，我們將探討材料本身的組成、微結構、以及氧空缺等各種基本性質，並進一步分析其與材料之電子和介電性質的關連性，從而增進我們對此一材料系統的瞭解。
本研究經由嚴謹的升溫以及降溫程序建構出合理的非晶相二氧化鉿的原子結構模型，並將所得結果進行各種基本性質與結構的分析。根據我們所產生的模型，我們所預測非晶相二氧化鉿的密度為8.63 ± 0.11g/cm3，約只有單斜晶相結構的83%。在非晶相結構中氧空位的平均生成能高於在立方晶相，但略低於在單斜晶相結構中的氧空位生成能，且顯示不論在任何結構中二氧化鉿的氧空位生成能均高於在二氧化矽中的氧空位生成能。在電性計算方面，我們的結果發現非晶相二氧化鉿的能隙值僅略低於其在單斜晶相結構之能隙，顯示結構的轉變並未對二氧化鉿的能隙值產生顯著的影響。關於介電性質分析方面，我們所預測之二氧化鉿非晶相結構之靜介電常數值為22.7，與最近實驗量測到的結果相符。
本研究藉由”置換−冷卻”以及”置換−回火”不同組成的非晶質Hf1-xSixO2結構模型。我們的結果顯示這兩種方式所產生的矽酸鉿模型其結構特徵以及結構特徵隨組成而變化的趨勢大致相符。在配位數分析方面，我們可以看到隨著矽濃度的增加，各種原子的平均配位數都有隨之下降的趨勢。此外，我們也觀察到雖然矽酸鉿的密度會隨著矽濃度的增加而持續下降，其超晶胞的體積卻有隨著矽原子數目的增加而有先降後升的趨勢，而這樣的結果也具體反應了原子結構隨矽濃度增加而變化的過程。在電性計算方面，我們發現晶體結構的矽酸鉿其能隙值比非晶質結構高，顯示結構的轉變會對矽酸鉿的電性產生顯著的影響。另外，我們也觀察到矽酸鉿的能隙值並未因結構中矽濃度的變化而產生明顯的改變。介但是電性質分析方面，我們的結果顯示結構中矽濃度的增加會導致矽酸鉿的靜介電常數值急速下降，而整個過程是呈現非線性的變化關係。在氧空位分析方面，我們計算的結果顯示在矽酸鉿結構中如果氧原子只與鉿原子產生鍵結，其平均氧空位生成能與在非晶質 HfO2 中的氧空位生成能近乎相同，若如果氧原子只與矽原子產生鍵結，其平均氧空位生成能則與在非晶相二氧化矽中的氧原子近似。就整體而言，矽酸鉿的平均氧空位生成能比在晶相以及非晶相 HfO2 中都來的低，特別是有與矽原子形成鍵結的氧原子，其氧空位生成能已與二氧化矽中的氧空位生成能相當接近。

Due to the continuous down-scaling of the CMOS transistors, the conventional gate dielectric layers, SiO2, has become so thin that it may lead to large leakage current and thus degrade the reliability of devices. To solve this problem, the current trend is to replace SiO2 with a high dielectric constant material so that it can keep the same capacitance while decreasing the tunneling currents. To date, HfO2 and Hf1-xSixO2 are considered as the replacements for SiO2 as the gate dielectric materials. However, there remain several critical problems unresolved such as the low re-crystallization temperatures and high defect density at the HfO2/Si interface. Although many theoretical calculations have been done for high-k materials, most of them are focused on the electronic and dielectric properties of their crystalline phases. Little is known about the structures and properties of their amorphous counterpart, particularly for hafnium silicates.
In this study, we performed first principles molecular dynamics simulations to generate atomistic structure models for amorphous HfO2 and Hf1-xSixO2. According to our structure models, the density of amorphous HfO2 is predicted to be 8.63 ± 0.11g/cm3, which is about 83% of the monoclinic phase. The average formation energy of a neutral oxygen vacancy in the amorphous structure is found to be slightly higher than that in the cubic one, but still lower than that in the monoclinic phase by ~0.3 eV. Our calculations also show that the formation energy of a neutral oxygen vacancy in amorphous HfO2 is always higher than that in SiO2. Regarding the band gap calculations, our results show that the band gap of a-HfO2 is simply lower than that of the monoclinic phase by ~0.3eV, indicating that structural transformation may not have significant effect on the electronic properties of HfO2. Furthermore, our calculations show that the dielectric constant of amorphous HfO2 is found to be 22.7, which is in good agreement with a recent experimental measurement.
For hafnium silicates, we applied two different procedures, melt-and-quench and substitution-annealing, respectively, to generate the atomistic models of Hf1-xSixO2 with different compositions. We find that the structural models generated using these two approaches show pretty similar structural characteristics and structural evolution with compositions. The average coordination numbers of each kind of atoms are found to decrease with increasing the concentration of silicon (x), but the distributions of the bond lengths or the nearest neighbor distances remain unchanged. In addition, our results show that the densities of Hf1-xSixO2 decrease continuously with the Si concentration, but interestingly, their volumes shrink at the beginning but later expand as the concentration of silicon increases. Regarding the electronic properties of silicates, our calculations show that the band gaps of Hf1-xSixO2 do not change significantly as the concentration of Si increase from 0 to 0.5. For the analysis of the dielectric properties, their static dielectric constants are found to decrease nonlinearly with the Si content. Regarding the vacancy formation energy calculations, our results show that as an oxygen atom is just bonded with Hf atoms, the average formation energy of an oxygen vacancy is nearly the same as that in amorphous HfO2. Similarly, as an oxygen atom is only bonded with Si atoms, the average oxygen vacancy formation energy is nearly the same as that in amorphous SiO2. In general, the average formation energy of an oxygen vacancy in hafnium silicates is lower than that in hafnia, particularly as the oxygen atom is bonded to silicon atoms.

中文摘要 I
Abstract III
目錄 VI
表目錄 VIII
圖目錄 IX
第一章 緒論 1
1.1 研究背景 1
1.2 研究目的及方向 2
第二章 文獻回顧與理論基礎 6
2.1 金-氧-半場效電晶體（MOSFET） 6
2.1.1 高介電常數材料取代二氧化矽成為閘極介電層材料之原因 7
2.1.2 高介電常數材料之選擇 11
2.1.3 二氧化鉿作為閘極介電層材料之所面臨之問題 13
2.2 第一原理計算 14
2.2.1 密度泛函理論 （Density Functional Theory, DFT） 15
2.2.2 Kohn-Sham方程式 18
2.2.2 虛位勢法(pseudopotential method) 19
2.2.3 分子動態模擬（Molecular Dynamics Simulations） 20
第三章 研究方法 21
3.1 研究使用之軟體、參數與流程 21
3.1.1 非晶相二氧化鉿結構的產生 21
3.1.2 非晶相二氧化鉿矽酸鹽結構的產生 22
3.2 計算條件選定之測試 24
第四章 結果與討論 30
4.1 液體二氧化鉿結構產生 30
4.2 非晶相二氧化鉿結構之產生與分析 38
4.3二氧化鉿之電性與缺陷性質分析 44
4.3.1能隙（band gap）分析 44
4.3.2 介電性質（dielectric properties）之分析 51
4.3.3 二氧化鉿氧空缺之生成能（oxygen vacancy formation energy） 53
4.4 二氧化鉿矽酸鹽之分析 56
4.4.1 非晶相矽酸鉿結構之產生 56
4.4.2 非晶相矽酸鉿結構之分析 57
4.5 矽酸鉿之電性與缺陷性質分析 79
4.5.1 能隙之分析 79
4.5.2 介電常數之分析 81
4.5.3 矽酸鉿中氧空缺之生成能 83
第五章 結論 88
參考文獻 91

1.Gordon E. Moore, Electronics, Volume 38, Number 8, April 19, 1965
2.M. Houssa, L. Pantisano, L.-Å. Pagnarsson, R. Degraeve, T. Schram, G. Pourtois, S. De Gendt, G. Groeseneken, M.M. Heyns, Materials Science and Engineering R51, 37-85 (2006)
3.John Robertson, P.W. Peacock, in : M. Houssa (Ed.), High-κ /gate Dielectrics, IOP, London, 2003, p. 372
4.J. Kwo, M. Hong, A. R. Kortan, K. T. Queeney, Y. J. Chabal, J. P. Mannaerts, T. Boone, J.J. Krajewski, A. M. Sergent and J. M. Rosamilia, High ε gate dielectrics Gd2O3 and Y2O3 for silicon, Appl. Phys. Lett. 77, 130 (2000)
5.John Robertson, Eur. Phys. J. Appl. Phys. 28, 265 (2004)
6.John Robertson, Rep. Prog. Phys. 69 (2006) 327-396
7.A. I. Kingon, J. P. Maria, and S. K. Streiffer, Nature (London) 406, 1032 (2000). first citation in article
8.S. V. Ushakov et al., Mater. Res. Soc. Symp. Proc. 745, N1.4 (2002). first citation in article
9.Xinyuan Zhao, and David Vanderbilt, Phys. Rev B 65, 233106
10.Xinyuan Zhao, Davide Ceresoli, and David Vanderbilt, Phys. Rev B 71, 085107 (2005)
11.David Vanderbilt, Xinyuan Zhao, and Davide Ceresoli, Thin Solid Films 486, 125-128 (2005)
12.Wanderlã L. Scopel, Antônio J. R. da Silva, and A. Fazzio, Phys. Rev B 77, 172101 (2008)
13.S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981)
14.R. H. Dennard, F. H. Gaensslen, H. Yu, V. L. Rideout, E. Bassous and A. R. LeBlanc, Design of ion-implanted MOSFET’s with very small physical dimensions, IEEE J. Solid-State Circuits 9, 256 (1974)
15.D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. Evans-Lutterodt and G. Timp, The electronic structure at the atomic scale of ultrathin gate oxides, Nature 399, 758 (1999)
16.D. A. Muller, T. Sorsch, S. Moccio, F. H. Baumann, K. Evans-Lutterodt and G. Timp, The electronic structure at the atomic scale of ultrathin gate oxides, Nature 399, 758 (1999)
17.G. Timp, A. Agarwal, F. H. Baumann, T. Boone, M. Buonanno, R. Cirelli, V. Donnelly, M. Foad, D. Grant, M. Green et al., Low leakage, ultra-thin gate oxides for extremely high performance sub-100 nm nMOSFETs, Tech. Dig. Int. Electron Devices Meet. 7-10 Dec, 930 (1997)
18.C. A. Billman, P. H. Tan, K. J. Hubbard, and D. G. Kanan, Alternate gate oxides for silicon MOSFETs using high k dielectrics, Mater. Res. Soc. Symp. Proc. 567, 409 (1999)
19.D. G. Schlom and J. H. Haeni, A thermodynamic approach to selecting alternative gate dielectrics, MRS Bulletin Mar, 198 (2002)
20.K. J. Hubbard and D. G. Schlom, Thermodynamic stability of binary oxides in contact with silicon, J. Mater. Res. 11, 2757 (1996)
21.G. D. Wilk, R. M. Wallace and J. M. Anthony, High-k gate dielectrics: Current status and materials properties considerations, J. Appl. Phys. 89, 5243 (2001)
22.Robertson J 2000 J. Vac. Sci. Technol. B 18, 1785
23.Kingon A I, Maria J P and Streiffer S K 2000 Nature 406 1032
24.Kingon A I, Maria J P and Streiffer S K 2000 Nature 406 1032 C. A. Billman, P. H. Tan, K. J. Hubbard, and D. G. Kanan, Alternate gate oxides for silicon MOSFETs using high k dielectrics, Mater. Res. Soc. Symp. Proc. 567, 409 (1999)
25.D. G. Schlom and J. H. Haeni, A thermodynamic approach to selecting alternative gate dielectrics, MRS Bulletin Mar, 198 (2002)
26.K. J. Hubbard and D. G. Schlom, Thermodynamic stability of binary oxides in contact with silicon, J. Mater. Res. 11, 2757 (1996)
27.Copel M, Gribelyuk M and Gusev E 2000 Appl. Phys. Lett. 76 436
28.G. D. Wilk, R. M. Wallace and J. M. Anthony, High-k gate dielectrics: Current status and materials properties considerations, J. Appl. Phys. 89, 5243 (2001)
29.E. P. Gusev, M. Copel, E. Cartier, I. J. R. Baumvol, C. Krug, and M. A. Gribelyuk, High-resolution depth profiling in ultrathin Al2O3 films on Si, Appl. Phys. Lett. 76, 176 (2000)
30.M. Copel, M. A. Gribelyuk and E. P. Gusev, Structure and stability of ultrathin zirconium oxide layers on Si (001), Appl. Phys. Lett. 76, 436 (2000)
31.H. Kim, P. C. Mclntyre and K. C. Saraswat, Effect of crystallization on the electrical properties of ultrathin HfO2 dielectrics grown by atomic layer deposition, Appl. Phys. Lett. 82, 106 (2003)
32.K. Eisenbeiser, J. M. Finder, Z. Yu, J. Ramdani, J. A. Curless, J. A. Hallmark, R. Droopad, W. J. Ooms, L. Salem, S. Bradshaw and C. D. Overgaard, Field effect transistors with SrTiO3 gate dielectric on Si, Appl. Phys. Lett. 76, 1324 (2000)
33.S. J. Wang, C. K. Ong, S. Y. Xu, P. Chen, W. C. Tjiu, J. W. Chai, A. C. H. Huan, W. J. Yoo, J. S. Lim, W. Feng and W. K. Choi, Crystalline zirconia oxide on silicon as alternative gate dielectrics, Appl. Phys. Lett. 78, 1604 (2001)
34.S. W. Nam, J. H. Yoo, S. Nam, H. J. Choi, Dongwon Lee, D. H. Ko, J. H. Moon, J. H. Ku, S. Choi, Influence of annealing condition on the properties of sputtered hafnium oxide, J. Non-cryst. Solids. 303, 139 (2002)
35.M. Balog, M. Schieber, S. Patai, and M. Michman, Thin films of metal oxides on silicon by chemical vapor depositoin with organometallic compounds, J. Cryst. Growth 17, 298 (1972)
36.M. Balog, M. Schieber, M. Michman, and S. Patai, Chemical vapor deposition and characterization of HfO films from organo-hafnium compounds, Thin Solid Films 41, 247 (1977)
37.M. Balog, M. Schieber, M. Michman, and S. Patai, J. Elec. Chem. Soc. 126, 1203 (1979)
38.S. H. Bae, C. H. Lee, R. Clark, and D. L. Kwong, MOS characteristics of ultrathin CVD HfAlO gate dielectrics,IEEE Electron Device Lett. 24, 556 (2003)
39.M. Lee, Z.-H. Lu, W.-T. Ng, D. Landheer, X. Wu and S. Moisa, Interfacial growth in HfOxNy gate dielectrics deposition using [(C2H5)2N]4Hf with O2 and NO, Appl. Phys. Lett. 83, 2638 (2003)
40.C. H. Choi, S. J. Rhee, T. S. Jeon, N. Lu, J. H. Sim, R. Clark, M. Niwa and D. L. Kwong, Thermally stable CVD HfOxNy advanced gate dielectrics with poly-Si gate electrode, Int. Electron Devices Meet., 857 (2002)
41.C. S. Kang, H. J. Cho, K. Onishi, R. Nieh, R. Choi, S. Gopalan, S. Krishnan, J. H. Han and J. C. Lee, Bonding state and electrical properties of ultrathin HfOxNy gate dielectrics, Appl. Phys. Lett. 81, 2593 (2002)
42.S. Stemmer et al., Jpn. J. Appl. Phys., Part 1 42, 3593 (2003). first citation in article
43.S. Stemmer et al., Appl. Phys. Lett. 83, 3141 (2003). first citation in article
44.Z. M. Rittersma et al., J. Electrochem. Soc. 151, C716 (2004). first citation in article
45.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. 81, 2053 (2002)
46.M. A. Quevedo-Lopez, M. El-Bouanani, B. E. Gnade, R. M. Wallace, M. R. Visokay, M. Douglas, M. J. Bevan, and L. Colombo, Interdiffusion studies for HfSixOy and ZrSixOy on Si, J. Appl. Phys. 92, 3540 (2002)
47.B. Y. Tsui and H. W. Chang, Formation of interfacial layer during reactive sputtering of hafnium oxide, J. Appl. Phys. 93, 10119 (2003)
48.M. Oshima, S. Toyoda, T. Okumura et al., Chemistry and band offsets of HfO2 thin films for gate insulators, Appl. Phys. Lett. 83, 2172 (2003)
49.A. Kumar, D. Rajdev, and D. L. Douglass, Effect of oxide defect structure on the electrical properties of ZrO2, J. Am. Chem. Soc. 55, 439 (1972)
50.H. Takeuchi, D. Ha, and T.-J King, J. Vac. Sci. Technol. A 22, 1337 (2004)
51.Wanderlã L. Scopel, Antônio J. R. da Silva, and A. Fazzio, Phys. Rev B 77, 172101 (2008)
52.D. R. Hamann, M. Schlüter. and C. Chiang, Phys. Rev. Lett. 43, 1494-1497 (1979)
53.D. Vanderbilt, Phys. Rev. B 41, 7892 (1990)
54.J.Alder, and T.E. Wainwright, J. Chem. Phys. 27, 1208 (1957)
55.R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)
56.G. Kresse and J. Hafner, Phys. Rev B 47 ,R558 (1993); G. Kresse and J. Furthműler, ibid. 54, 11169 (1996); see also http://cms.mpi.univie.ac.at/vasp/
57.see http://accelrys.com/references/
58.Kresse G., Hafner J., Phys. Rev. B 47 , 558 (1993) ; Kresse G., Technischen Universität Wien, Thesis, 1993
59.Blöchl P. E., Phys. Rev. B 50, 17953 (1994)
60.Kresse G., Joubert D., Phys. Rev. B 59, 1785 (1998)
61.P. E. Blöchl, Physical Review B 50, 17953 (1994)
62.K. Kukli, J. Ihanus, M. Ritala, M. Leskela, Appl. Phys. Lett. 68, 3737 (1996)
63.J. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
64.Peter Broqvist and Alfredo Pasquarello, Appl. Phys. Lett. 90, 082907 (2007)
65.T.B. Massalski, Binary Alloy Phase Diagrams, second ed., ASM International, Materials Park, OH, 1990
66.J. Wang, H.P. Li, and R. Stivens, J. Mater. Sci. 27, 5397 (1992)
67.A.A. Demkov, Phys. Status Solidi B 226, 57 (2001)
68.J. Adam and M.D. Rodgers, Acta Crystallogr. 12, 951 (1959), R.E. Hann, P.R. Suttch, and J.L. Pentecost, J. Am. Ceram. Soc.68, C-285 (1985)
69.X. Zhao and D. Vanderbilt, Phys. Rev. B 65, 075105 (2002)
70.Wanderlã L. Scopel, Antônio J. R. da Silva, and A. Fazzio, Phys. Rev B 77, 172101 (2008)
71.Katharina Vollmayr, Walter Kob, and Kurt Binder, Phys. Rev. B 54 , 15808-15827 (1996)
72.Davide Ceresoli and David Vanderbilt, Phys. Rev. B 74 , 125108 (2006)
73.C. Kaneta, T. Yamasaki, Microelectronic Engineering 84, 2370-2373 (2007)
74.H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976)
75.J.C. Garcia, A. T. Lino, L. M. R. Scolfaro, J. R. Leite, V. N. Freire, G. A. Farias, and E. F. da Silva, Jr, Phys. Stat. Sol. (c) 1, No. S2, S236-S240 (2004)
76.J. Perdew, M. Ernzerhof, K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105, 9982 (1996)
77.M. Modreanu, J. Sancho-Parramon, O. Durand, B. BServet, M.Stchakovsky, C. Naudin, A. Knowles, F. Bridou, M.-F. Ravet, Investigation of thermal annealing effects on microstructural and optical properties of HfO2 thin films, Appl. Surf. Sci. 253, 328 (2006)
78.Peter Broqvist and Alfredo Pasquarello, Microelectronic Engineering 84, 2022-2027 (2007)
79.H. Takeuchi, D. Ha, and T.-J King, J. Vac. Sci. Technol. A 22, 1337 (2004)
80.Peter Broqvist and Alfredo Pasquarello, Appl. Phys. Lett. 90, 082907 (2007)
81.Ragesh Puthenkovilakam and Jane P. Chang, J. Appl. Phys. Vol. 96, No5, 2701-2707 (2004)
82.A. Callegari, E. Cartier, M. Gribelybelyuk, H. F. Okorn-Schmidt, and T. Zabel, J. Appl. Phys. 90, 6466 (2001)
83.H. Kato, T. Nango, T. Miyagaewa, T. Katagari, K. Soo Seol, and Y. Ohki, J. Appl. Phys. 92, 1106 (2002)
84.Jin, S. K. Oh, H. J. Kang, and M.-H. Cho, Appl. Phys. Lett. 89, 122901 (2006)
85.Van Elshocht, U. Weber, T. Connard, V. Kaushik, M. Houssa, S. Hyun, B. Seitzinger, P. Lehen, M. Schumacher, J. Lindner, M. Caymax, S. DeGendt, and M. Heyns, J. Electrochem. Soc. 152, F185 (2005)
86.Tomida, K. Kita, and A. Toriumi, Appl. Phys. Lett. 89, 142902 (2006)