隨著積體電路零件縮小至微/奈米尺度，啟動元件所需的臨界電壓愈
來愈容易受到細微環境因素的影響。在同一片晶圓上，由設計的圖樣
差異所引起的臨界電壓差異現象稱之為系統化臨界電壓變異。微/奈
米尺度下的載子分布是影響臨界電壓的關鍵因素。
我們設計一套系統化實驗流程，成功取得佈植區間從0.3 到 5 微米
的二維載子分布，並以人口成長模型為基準，提出一個非線性方程式，
模擬結果相當符合實驗數據。
我們設計一系列長條(一維)和方塊(二維)的離子佈植區域，在熱退火
製程之後，以平面掃描式電容顯微鏡觀測二維載子分布。透過比對佈
植窗口與實驗結果，我們得到一系列載子瞬態增強擴散長度。實驗數
據顯示(1)擴散長度隨著尺度縮小而減少以及(2)硼原子在方塊區域
內的擴散長度較在長條區域內為長。我們的模型顯示 (1)在大尺寸的
佈植區域有較多的間隙矽原子幫助擴散以及(2)間隙矽原子由離子佈
植的邊界射出，方塊和長條分別具有五個和三個維度的佈植邊界；方
塊內的硼原子與間隙矽原子的結合率較高，因此擴散得更多。簡單來
說，我們首先研究了系統化佈植區域內的瞬態增強擴散，並更進一步
的證實尺度和維度是兩項影響瞬態增強擴散的重要因素。

Current microelectronics chip can be composed of thousands of microarrays
that contain up to millions of physically identical transistors layout
in vastly different micro-environment. Systematic threshold voltage
(Vth) variation due to the detailed difference in the microenvironment has
been shown in many electrical assessments.
In this work, we have designed an experimental platform for investigating
the dependence of dimensionality in two dimensional boron diffusion
lengths (Ldi f f ). We systematically vary the ion implantation window
length scales in both length (l) and width (w) directions using photolithography
process. The two dimensional Ldi f f are measured with
plane view scanning capacitance microscopy (SCM). The Ldi f f in width
shrunk patterns exhibit stronger diffusion, especially in ion implantation
windows with larger l, namely, boron transient diffusion roll-off.
This observation suggest there is effectively more interstitial (Is) sources
within the proximity of B-Is interaction range during annealing and lead
to more significant transient enhanced diffusion (TED) at larger confinements.
The normalized Ldi f f for ion implantation boundaries length
scales ranging from 0.3 micron to 5 micron shows five folds difference.
The normalized curves for both categories of patterns overlap, indicating
similar physical mechanism in play for the two cases.
We have developed a non-linear logistics model. We can successfully
fit the experimental data with the above model by considering only the
difference in dimensionality. In particular, we found a 3/5 ratio for the
linear growth coefficients of effective Is supersaturation with respect to
the ion implantation boundary dimensions between the two patterns. We
relate this coefficient ratio to number of interstitial injection boundaries
available within B-Is interaction range.

1 Introduction 1
2 Background 5
2.1 Introduction of semiconductor . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 The intrinsic silicon . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 The extrinsic silicon . . . . . . . . . . . . . . . . . . . . . . 10
2.2 The Si based devices . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 The p-n junction . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Metal oxide semiconductor field effect transistor (MOSFET) . 13
2.3 Manufacturing process . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Photolithography . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 Doping process . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Post-implantation Annealing . . . . . . . . . . . . . . . . . 20
2.4 Challenges of shrinking devices . . . . . . . . . . . . . . . . . . . . 21
3 Literature survey 26
3.1 Normal diffusion and Fick’s law . . . . . . . . . . . . . . . . . . . . 27
3.2 A glance at transient enhancement diffusion (TED) . . . . . . . . . . 28
3.3 Historical survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 The mechanisms of TED . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 TED variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.2 Implanted dose . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.3 Time evolution . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.4 Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.5 Co-implantation . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 The plus-one model . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.7 The size effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8 Variation issues at nano-scale . . . . . . . . . . . . . . . . . . . . . . 40
3.8.1 Systematic layout pattern variation . . . . . . . . . . . . . . . 40
3.8.2 Random dopant fluctuation . . . . . . . . . . . . . . . . . . 42
4 Experimental methods 44
4.1 Evolution of measurement . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 SCM Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Working Principle . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2 SCM signal analysis . . . . . . . . . . . . . . . . . . . . . . 57
5 Experimental results and discussions 59
5.1 Plane view sample preparation for SCM . . . . . . . . . . . . . . . . 59
5.1.1 Clean process . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.1.2 Etching curve . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 SCM parameters tuning process . . . . . . . . . . . . . . . . . . . . 62
5.3 Dimensionality and size effects . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.2 The experimental results . . . . . . . . . . . . . . . . . . . . 70
5.3.3 The logistics model for population growth . . . . . . . . . . . 73
5.3.4 The improved logistics model in our work . . . . . . . . . . 74
6 Conclusion 78
7 Bibliography 81

[1] F.Giannazzo. Scanning capacitance microscopy of semiconducting materials,
PhD thesis, Universita’ Degli Studi Di Catania, 2002.
[2] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. Wiley Interscience, New
York 1981.
[3] J.F. Gibbons, Proc. IEEE 60, 1062 (1972).
[4] F. Giannazzo, F. Pirolo, V. Raineri, and V. Privitera, Appl. Phys. Lett. 78, 598
(2001).
[5] Hong Xiao, Introduction of Semiconductor Manufacturing Technology, Prentice
Hall. Inc., United States 2000
[SRIM] The Stopping and Range of Ions in Matter, http://www.srim.org/
[6] W. K. Hofker, H.W.Werner, D. P. Oosthoek, and H. A. M. de-Grefte, Appl. Phys.
Lett. 2, 165 (1973).
[7] C. L. Claeys, G. J. Declerck, and R. J. Van-Overstraeten, Rev. Phys. Appl. 13,
797 (1978).
[8] H. Bracht, MRS Bull. 25, 6 (2000).
[9] N. Cowern and C. Rafferty, MRS Bull. 25, 39 (2000).
[10] M. D. Giles, Appl. Phys. Lett. 62, 1940 (1993).
[11] A. E. Michel, W. Rausch, P. A. Ronsheim, and R. M. Kastl, Appl. Phys. Lett. 50,
416 (1987).
[12] N. E. B. Cowern, J. T. F. Janssen, and H. F. F. Jos, J. Appl. Phys. 68, 6191 (1990).
[13] A. E. Michel, W. Rausch, P. A. Ronsheim, and R. M. Kastl, Appl. Phys. Lett. 50,
416 (1987).
[14] N. E. B. Cowern, M. Jaraiz, F. Cristiano, A. Claverie, and G. Mannino, Tech. Dig.
Int. Electron Devices Meet. 333 (1999).
[15] H. J. Gossmann, C. S. Rafferty, H. S. Luftman, F. C. Unterwald, T. Boone, and J.
M. Poate, Appl. Phys. Lett. 63, 639 (1993).
[16] D. Skarlatos et al:, J. Appl. Phys. 97, 113534 (2005).
[17] M. D. Giles, Appl. Phys. Lett. 62, 1940 (1993).
[18] M. D. Giles, J. Electrochem. Soc. 138, 1160 (1991).
[19] The International Technology Roadmap for Semiconductors, http:// public.
itrs.net.
[20] F. Giannazzo, F. Pirolo, V. Raineri, and V. Privitera, Appl. Phys. Lett. 78, 598
(2001).
[21] E. Bruno, S. Mirabella, G. Impellizzeri, F. Pirolo, F. Giannazzo, V. Raineri, and
E. Napolitani, Appl. Phys. Lett. 87, 133110 (2005).
[22] F. Giannazzo et al:, J. Vac. Sci. Technol. B 24, 468 (2006).
[23] E. G. Roth, O. W. Holland, V. C. Venezia, and B. Nielsen, J. Electron. Mater. 26,
1349 (1997).
[24] K. C. Ku, C. F. Nieh, J. Gong, L. P. Huang, Y. M. Sheu, C. C. Wang, C. H. Chen,
H. Chang, L. T. Wang, T. L. Lee, S. C. Chen, and M. S. Liang, Appl. Phys. Lett.
89, 112104 (2006).
[25] R.G. Mazur and P.H. Dickey, J. Electrochem. Soc. 113, 225 (1966).
[26] Dieter K. Schroder, Semiconductor Material and Device Characterization,
Wiley-Interscience, New York 2006.
[27] Y. Martin, D.W. Abraham, and Kumar Wickramasinghe, Appl. Phys. Lett. 52,
131103 (1988).
[28] F. Giannazzo, S. Mirabella, D. De Salvador, E. Napolitani, A. Terrasi, A. Carnera,
A. V. Drigo, and F. Pirolo, Phys. Rev. B 66, 161310 (2002).
[29] Masafumi Miyamoto, Hiroyuki Ohta, Yukihiro Kumagai, Yasuo Sonobe,
Kousuke Ishibashi, and Yasushi Tainaka, IEEE Trans. Electron Devices 51, 3,
(2004).
[30] N. E. B. Cowern, P. C. Zlam, P. C. van der Sluis, D. J. Gravesteijn, and W. B.
Boer, Phys. Rev. Lett. 72, 2585 (1994).
[31] Yi-Ming Sheu, Sheng-Jier Yang, Chih-ChiangWang, Chih-Sheng Chang, Li-Ping
Huang, Tsung-Yi Huang, Ming-Jer Chen, IEEE Trans. Electron Devices 52, 1
(2005).
[32] Kelin Kuhn et al:,Intel® Technology Journal, 12, 01 (2008).