Concluding remarks

The small difference between the ordinary and extraordinary refractive indices of the quartz crystal allows us to resolve the deviation in the incident angle for the rotating-element ellipsometry. The other two primary errors in a rotating PSA el-lipsometric system, the azimuthal misalignment and degradedness of polarizers, can be reduced by intensity ratio technique [12]. Since all three primary errors in a ro-tating PSA ellipsometry can be reduced, we can substitute a prism polarizer with a low cost dichroic sheet polarizer without loosing its accuracy in a PSA ellipsometric system. In addition to determining the deviation of incident angle in a rotating ele-ment ellipsometry, the following three parameters can be obtained by fitting the

measured tanΨ to the analytic solution of uniaxial crystals: the absolute value of no, ne and directions of optical axis (

θ

a and

θ

c) in the laboratory frame. Since the re-solving power of the system can be increased as the incident angle moves closer to the Brewster angle (the reflected intensity at 50^o will be about 0.4% of the incident intensity), the system can be improved by using a sensitive detector or a higher power light source. It is our interest to extend the system to measure a material, which consists of both linear and circular birefringence.

6.6 References

[1] J. R. Beattie, Philos. Mag. 46, 235 (1955).

[2] E. A. Taft and H. R. Philipp, Phys. Rev. A 138, 197 (1965).

[3] V. P. Tomaselli, R. Rivera, D. C. Edeweard, and K. D. Möller, Appl. Opt. 20, 3961 (1981).

[4] B. J. Stagg and T. T. Charalampopoulos, Appl. Opt. 30, 4113 (1991).

[5] R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized light (Amster-dam: North-Holland, 1992)

[6] M. I. Alonso and M. Garriga, Appl. Phys. Lett. 67, 596 (1995).

[7] R. W. Collins, Rev. Sci. instrum. 61, 2029 (1990).

[8] J. R. Zeidler, R. B. Kohles, and N. M. Bashara, Appl. Opt. 13, 1938 (1974).

[9] F. L. McCrankin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J. Res. Natl.

Bur. Stand. A. 67, 363 (1963).

[10] Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao, Jpn. J. Appl. Phys.

34, 5016 (1995).

[11] J. Lekner, J. Phys.: Condens. Matter 3, 6121 (1991).

[12] Y. F. Chao, W. C. Lee, C. S. Hung, and J. J. Lin, J. Phys. D: Appl. Phys. 31, 1968 (1998).

[13] D. E. Aspnes, J. Opt. Soc. Am. 70, 1275 (1980).

θc

θa

Y

X

Z

OA

θ_b θ_i

Fig. 6.1. The reflection geometry:

θ

i is the incident angle, xy plane is the reflecting face of the crystal, zx plane is the incident plane, the z axis is the normal line. OA is the optical axis of the crystal.

ψ

Fig. 6.2. The numerically simulated Ψ as a function of azimuth angle of

θ

a

while

θ

c=90^o: (a) quartz crystal: no=1.544, ne=1.553 at the incident angle of 45^o (line), and 44.94^o (dot); (b) yttrium orthovanadate crystal:

no=1.9929, ne=2.2154 at the incident angle of 45^o (line), and 44.5^o (dot).

Quartz: near principl angle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 50 100 150 200 250 300 350 400

57 56.94 Ψ

(deg)

θ_a(deg)

Fig. 6.3. The numerically simulated ψ as a function of azimuth angle of

θ

a

while

θ

c = 90^o, quartz crystal of no = 1.544, ne = 1.553 at the incident angle of 57^o (line), and 56.94^o (dot), respectively.

θi

P C D A/D

P A

Sample L

Fig. 6.4. A schematic set-up of the PSA ellipsometer: L, light source (He-Ne laser);

P, polarizer; A, analyzer; D, detector.

17.5 17.7 17.9 18.1 18.3 18.5

0 100 200 300 400

45

experimental Ψ

(deg)

(a)

θa(deg)

17.5 17.7 17.9 18.1 18.3 18.5

0 100 200 300 400

44.94 experimental 17.8

17.9 18 18.1

210 230 250

Std = 0.02^o

Ψ (deg)

θa(deg)

(b)

Fig. 6.5. Ψ verses

θ

_a : Quartz

θ

_c=90^o, n_o=1.544, n_e=1.553: (a)

θ

_i = 45^o (line: calculated •:

measured) and

θ

_a = 0^o ; (b)

θ

_i = 44.94^o (line: calculated •: meas-ured) and

θ

_a = -1.78^o . Subplot: portion of the main plot, “ I ” is the standard deviation of the measured value to its calculated value.

17.2 17.3 17.4

0 50 100 150 200 250 300 350 400

Ψ

(deg) Error bar=0.02^o

θ_a(deg)

Fig. 6.6. Ψ verses

θ

_a : BK7

The standard deviation is 0.02^o. The line indicates the mean value which is 17.29^o.

22 23 24 25 26 27

0 100 200 300 400 500

44.94 experimental 24.5

25.5

200 220 240

std =0.06^o

Ψ (deg)

θa(deg)

Fig. 6.7 Ψ verses

θ

a : YVO4

θ

c=136.01^o for YVO4 with no=1.9929 and ne=2.2154,

θ

i = 44.94^o (line: c culated •: measured) and

θ

a = 7.24^o .

al-, Subplot: portion of the main plot

“ I “ is the standard deviation of the measured value to its calculated value.

Chapter 7 Conclusion

Multi-wavelength photoelastic modulation (PEM) ellipsometry, based on phase modulation, have been presented. From the spectroscopic point of view, they can cover visible range. Like other ellipsometric techniques, PEM ellipsometry is non invasive and can be used in any ambient atmosphere. Nevertheless, the main characteristic of PEM ellipsometry is the fast, whose measuring speed is provided by a photoelastic modulator (50kHz). This leads that PEM ellipsometry superior to the low frequency ellipsometric techniques (100Hz), such as the rotating element ellipsometry at the tens of millisecond scale. Furthermore, PEM ellipsometry can be easily combined with other low frequencies of modulations leading to double modulation techniques. For reducing the error of DC signal, one can combined with mechanical rotating chopper or modulated diode laser light source

We have developed in situ alignment techniques to align all of the optical components (namely P, PEM and A) to the reflective surface of a specimen in a PEM ellipsometer at fixed incident angle. In addition to the azimuths of polarizer and analyzer, the strain axis of PEM can also be determined at the same incident angle by intinsity ratio technique. This intensity ratio technique not only can reduce the error caused by the intensity fluctuation, it also simultaneously determine the ellipsometric parameter Ψ, which can be used to determine the incident angle on-line. Just like two incident-angle-alignment technique, it requires at least two testing samples or two-wavelengths to align the system prior to any measurement at a working incident angle. This technique is particularly suitable to a pre-designed closed system, in which a multi-incident-angle technique is not possible.

We also introduce a real time calibration technique for the modulation amplitude

∆o of PEM in ellipsometry by a Multiple Harmonic Intensity Ratio (MHIR) technique with a data acquisition (DAQ) system. By reflection and transmission set up, it can be verify that MHIR technique is independent of frequency. In addition to confirm our calibration by the digitized oscilloscope waveform, we also obtain a set of ellipsometric parameters Ψ and ∆ under various values of modulation magnitude ∆o. However, in an etching/deposition process, a preliminary study is necessary under the chemistry of etching/deposition process, instead of using the MHIR, we introduce a correction factor to calibrate the modulation amplitude. This correction technique provides us a pair of dependable ellipsometric parameters for monitoring the etching process. After comparing the measured value of Ψ and ∆ under etching, we are confident to propose that one should study the traces of Ψ and ∆ verses the thickness for controlling instead of calculating the thickness in real time.

The main purpose of our research is trying to establish multiple wavelength ellipsometry for in situ / real time measurements, the modulation amplitude has to be set as a constant for a particular wavelength in the process of measurement. Since the physical path of PEM is invariant, the modulation amplitude should be inversely proportion to the wavelength. After considering the static retardation and taking the modulation amplitude at 0.383λ for 568.2 nm, we calculated the corresponding modulation amplitude for other wavelengths, and the measured values are well fitted to our expectation. To real time monitor etching processing, the instrumentation program dedicated to FFT computation can be employed for on-line control system.

Nevertheless, waveform measurement can be utilized to diagnose the sample dynamic behavior less than millisecond scale, for example, the dynamic response of etching system or the modulation of liquid crystal device.

The small difference between the ordinary and extraordinary refractive indices of the quartz crystal allows us to resolve the deviation in the incident angle for the

rotating element in ellipsometry. In addition, the degradedness of polarizers can be reduced by intensity ratio technique. After these calibrations, we believe there is enough information for the construction of an in situ / real time spectroscopic ellipsometry. On the other hand, the capability of PEM ellipsometry to provide real time control and monitoring of semiconductor processes has been prospective. Real time applications of PEM ellipsometry, combined with two alternative wavelength, for adaptive control in etching processing can be employed by hardware Digital Signal Process (DSP). In particular, it has been shown that the ability to diagnose the interruption of etching process for end point prediction.

In conclusion, it can be anticipated that the ellipsometric techniques, based on phase modulation, will be extensively used, in the near future, for process monitoring and control, as well as probing the fundamental semiconductor growth/etching mechanisms.

Appendices

Appendix A The samples for fixed incident angle alignment

One has to choose appropriate samples for fixed incident angle alignment. Chao [1] aligned the PSA system by two incident angles; one is less than the principle angle and the other one is greater than the principle angle. The reason of this choice is because changes sign across the principle angle. This basic concept can be substituted by two thin films, i.e., 105 nm and 5 nm SiO

∆ cos

2/Si, or two different wavelengths 488nm and 647nm for one thin film (SiO₂/Si 105 nm). For expressing the concept, we plot their ellipsometric parameters in the Ψ-∆ diagram, such as shown as Fig. A.1 and Fig A.2, respectively. From the diagrams, one can immediate identify two suitable thin films or two appropriate wavelengths for the thin film of 105 nm thickness at the incident angle of 70^o.

The reflected intensity ratio A and B of a typical SiO

2/Si thin film is shown in Fig.

A.3

.

One can obtain the position and value at the intersections of A and B by a polynomial fit. Two parameters can be obtained from the intensity ratio distribution : (a) the position of intersection (

α

,

β

), (b) the value of the intersection, . From Fig. A.3 one clearly observes that these intersections switch sides with respect to plane of incident when

β

changes its sign

.

This phenomenon provides a apparent indication to the plane of incident in the laboratory scale.

Ψ tan2

108

Fig. A.3 Intensity ratio of A and B plotted against angular position of polarizer (α) at a fixed angular position of analyzer (β) for the SiO₂/Si 105 nm thin film sample and native oxide 2 nm silicon sample. The intensity ratios are scaled according to different sample and denoted as (105 nm) and (2 nm), respectivily.

-5 0 5

Appendix B The analysis of etching process

To study of etching process, we are trying to build a model for monitoring the poly silicon etching process in real time; in the beginning, however, only a flat poly silicon layer on a oxide (about 1000 Å) on silicon substrate is measured. From our numerical simulation, we expect to observe a significant change in Ψ about 900 Å prior to the endpoint. This phenomenon did appear in the process of etching. In etching process, the thickness of film is determined by the measured value of Ψ(t) and

∆(t) through modeling. It is known that both parameters oscillate, especially at the wavelength where the material is less absorbing. Maynard[2] suggested choosing the wavelength with high extinction coefficient for monitoring and controlling.

Since certain amount prior knowledge of the film is needed for deducing the thickness of the film, the basic etching behavior can be studied before the etching. Instead of deducing the thickness of the film in real time, one can provide the traces of Ψ(t) and

∆(t) with respect to the thickness of film in the process of etching and compare it with the real time recording traces of Ψ(t) and ∆(t). . For reference, we use two models (poly-silicon/SiO₂/silicon substrate) to illustrate the characteristic traces of Ψ(t) and

∆(t): (1) the gate oxide region, where the thickness of SiO2 less than 100 Å , such as shown in Fig. B.1; (2) the field oxide region, where the thickness of SiO2 more than 500 Å , such as shown in Fig. B.2. The oscillation of Ψ(t) and ∆(t) give the information of how thick the film has been etched for both cases.

0 1000 2000 3000 4000 5000 6000 7000 8000 16 9000

18 20 22 24

Ψ(deg)

0 1000 2000 3000 4000 5000 6000 7000 8000 170 9000

175 180 185 190

Thickness (Å)

∆(deg)

Ψ and ∆ for film during etching with 70 Å gate oxide

Fig. B.1 The distribution of Ψ and ∆ for film under etching with 70 Å gate oxide.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000 20 40 60 80

Ψ(deg)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000 100 200 300 400

Thickness (Å)

∆(deg)

Ψ and ∆ for film during etching with 800 Å gate oxide

Fig. B.2 The distribution of Ψ and ∆ for film under etching with 800 Å field oxide.

Appendix C Fresnel reflection coefficients of uniaxial crystals

The reflection geometry is shown in Fig. C.1. The direction of optical axis is specified by angles

θ

_a and

θ

_c relative to the laboratory xyz, if c is the unit vector of ^r at incident angle

θ

i. According to reference [3], we summarized the Fresnel reflec-tion coefficients for uniaxial crystals of ordinary refractive index no=

ε

_o and extraordnary refractive index ne=

ε

_e as follows;

D

The ordinary and extraordinary modes have wave vector normal components qo, and qe related to the medium as

where No, Ne are the normalization factor, respectively. For simplicity, we also state the collective parameters as follows;

o

References of appendices

[1] Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao, Jpn. J. Appl. Phys.

34, 5016 (1995).

[2] H. L. Maynard, N. Layadi, and J. T. C. Lee, J. Vac. Sci. Technol. B. 15, 109 (1997).

[3] J. Lekner, J. Phys.: Condens. Matter 3, 6121 (1991).

θ_c

θ_a

Y

X

Z

OA

θ_b θ_i

Figure C.1. The reflection geometry:

θ

i is the incident angle, xy plane is the reflecting face of the crystal, zx plane is the incident plane, the z axis is the normal line. OA is the optical axis of the crystal.

簡歷 (Vita)

一、 基本資料

Meng-Wei Wang

中 文 姓 名 王夢偉 英 文 姓 名

(First Name) (Last Name)

國 籍 中華民國 性 別 男

聯 絡 地 址 300 新竹市大學路 1001 號交通大學光電所偏光量測實驗室

聯 絡 電 話 (公).03-5731941 (宅). 0991271982

傳 真 號 碼 03-5716631 E-MAIL [email protected]

二、 主要學歷

畢 肄業學校 國別 主修學門系所 學位 起訖年月(西元年/月)

成功大學 R.O.C. 電機系 工學學士 1991/9 至 1995/6

交通大學 R.O.C. 光電所 工學碩士 1995/9 至 1997/6

交通大學 R.O.C. 光電所 工學博士 1997/9 至 2004/6

/ 至 /

三、專長

1. 偏極光量測 2. 線上校正即時監控 3. 光電信號處理 4.

CURRICULUM VITAE

GENERAL INFORMATION Meng-Wei Wang (王夢偉)

Addr.: Institute of Electro-Optics Engineering, National Chiao Tung University, No. 1001 Ta Hsueh Rd., Hsinchu, Taiwan, R. O. C.

Email: [email protected] Telephone: (886)-(3)-5731941 Fax: (886)-(3)-5716631

PERSONAL DATA

Academic Degree: Ph. D.

Birth Place: Taipei, Taiwan, Republic of China Sex: Male

EDUCATION

Bachelor of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan,

R. O. C. 1995.

Focus: Electronics, Electromagnetic Wave, and Computer Organization.

Master of Electro-Optical Engineering, National Chiao Tung University, Hsinchu,

Taiwan, R. O. C. 1997.

Focus: Polarization Optics, Crystal Optics, Experimental Computing.

Master Thesis: Uniaxial Crystal and Its Ellipsometric Measurement.

Ph.D. of Electro-Optical Engineering, National Chiao Tung University, Hsinchu,

Taiwan, R. O. C.. 2004.

Focus : Polarization Measurement, Error Evaluation, Instrument Calibration.

Ph. D. Thesis: Multi-wavelength Photoelastic Modulation Ellipsometry.

著作目錄 (Publication List)

所有學術性著作分成三大類：(A)期刊論文 (B)研討會論文 (C)專利

(A)期刊論文 (Journal Paper)

1.Y. F. Chao, M. W. Wang and Z. C. Ko, “An error evaluation technique for the angle of incidence in a rotating element ellipsometer using a quartz crystal,” J. of Phys. D:

Appl. Phys. 32 (1999) 2246-2249

2.M. W. Wang, Y. F. Chao, “Azimuth alignment in photoelastic modulator ellipsometry at a fixed incident angle,” Jpn. J. Appl. Phys. 41 (2002) 3981-3986 3. M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen and Y. W. Liu,

“Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl.

Phys. 43 (2004) 827-832

4. M. W. Wang, F. H. Tsai and Y. F. Chao, ”In situ calibration technique for photoelastic modulator in ellipsometry,” Thin Solid film 355-356(2004) 78-83

(B)研討會論文 (Conference Paper)

1. 王夢偉, 趙于飛 “光彈調變式橢圓儀方位角線上校正” OPT 99, 台灣光電研 討會論文集(1999) 1251-1254

2. M. W. Wang and Y. F. Chao, “Azimuth alignment in photoelastic modulator ellipsometry at a fixed incident angle,” OSA Annual MEETING 2000, Oct 22-26, Providence, Rhode Island, USA

3. Yu-Faye Chao, Andy Lin and M. W. Wang, “Photoelastic modulation polarimetry and its measurement of twisted nematic liquid crystal,” ISPA photonics system and applications, Singapore 27-30 November 2001, SPIE proceedings, 4595, (2001) 43-51 4. 王夢偉, 蔡斐欣, 趙于飛,“光彈調變橢圓儀之相位調變線上校正”,OPT02, 2002 年台灣光電科技研討會論文集 I, TD1-5 (2002) 85-87

5. 王夢偉, 劉育維, 柳克強, 趙于飛, 林滄浪, “相位調變式橢圓儀應用於電漿蝕 刻製程”, OPT02, 2002 年台灣光電科技研討會論文集 I, TD1-7 (2002) 91-93 6. M. W. Wang, F. H. Tsai and Y. F. Chao, ”In situ calibration technique for photoelastic modulator in ellipsometry,” 3rd International Conference on Spectroscopic Ellipsometry, Vienna, Austria, July 6-11 (2003)

7. 柯 凱 元 , 王 夢 偉 , 趙 于 飛 “ 多 波 長 光 彈 調 變 式 橢 圓 偏 光 儀 之 即 時 量 測 ”, OPT2003 Proceedings I TG1-3, (2003) 267-269

8. 郭俊儀, 王夢偉, 趙于飛, 林滄浪, 柳克強 “光彈調變橢圓儀線上監控電漿 蝕刻製程”, OPT2003 Proceedings II FG1-6, (2003) 464-467

(C) 專利 (Patent)

1. 趙于飛, 王夢偉,“光彈調制式橢圓偏光儀之單角入射校正法”,中華民國發 明專利 145274 有效期 2001-2020

2. 趙于飛, 王夢偉, 寇人傑 ”利用石英量測轉動式橢圓偏光儀之入射角偏差 的方法”,中華民國發明專利 180743 有效期 2003-2020

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