行政院國家科學委員會補助專題研究計畫成果報告
行政院國家科學委員會補助專題研究計畫成果報告
行政院國家科學委員會補助專題研究計畫成果報告
行政院國家科學委員會補助專題研究計畫成果報告
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光彈調變式橢圓偏光儀(㆒) 反射面之校正
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計畫類別：v 個別型計畫 □整合型計畫
計畫編號：NSC89-2112-M-009-032
執行期間：88 年 8 月 1 日至 89 年 7 月 31 日
計畫主持㆟
：趙于飛
計畫參與㆟員：王夢偉 交大光電所 博士
本成果報告包括以㆘應繳交之附件：
□赴國外出差或研習心得報告㆒份
□赴大陸㆞區出差或研習心得報告㆒份
□出席國際學術會議心得報告及發表之論文各㆒份
□國際合作研究計畫國外研究報告書㆒份
執行單位：國立交通大學光電所
㆗ 華 民 國 89 年 9 月 18 日
行政院國家科學委員會專題研究計畫成果報告
光彈調變式橢圓偏光儀(㆒) 反射面之校正
計畫編號：NSC 89-2112-M-009-032
執行期限：88 年 8 月 1 日至 89 年 7 月 31 日
主持㆟：趙于飛 國立交通大學光電所
㆒ ㆒㆒ ㆒、㆗文摘要、㆗文摘要、㆗文摘要、㆗文摘要 本計畫利用㆔個亮度量測技術以校正 偏光片,析光片及光彈調變制器等之偏光 角的位置。先用穿透式將偏光片,析光片及 光彈調變制器等之偏光角的相對位置，再 將此元件放在返射面㆖利運用㆔個亮度量 測技術量測偏光角, 本計畫並證明利用同 樣的㆔個亮度量也可量出其橢圓參數 ψ。 關鍵詞 關鍵詞關鍵詞 關鍵詞：橢圓偏光儀，彈調變制器，校正 技術Abstract Instead of nulling method, a three-intensity-measurement technique is proposed to determine the azimuth deviation of the polarizer (P), photoelastic modulator (PEM) and analyzer (A) with respect to the specimen surface for ellipsometric measurements. After the initial alignment in a straight- through set-up, we adjusted the azimuth of P at 45o to the strain axis of the PEM. Arranging a PPEMSA ellipsometry by subjecting a specimen at the required incident angle, we measured a set of three DC radiances at zero point of the zero-order Bessel function. In addition to the azimuth deviation, the ellipsometric parameter ψ can also be determined from the same measurements.
Keywords: Ellipsometry, photoelastic
modulator, alignment
㆓ ㆓㆓
㆓、、、、Introduction
Recently, the photoelastic modulator (PEM) has been used to replace the wave plate in an ellipsometric system [1-3]. The PEM is a device that utilizes the photoelastic effect to modulate the phase retardation in a harmonic form [3]. This ability allows not only the use of PEM for a wide range of wavelengths, but also the chopping of the light beam at reasonable frequencies for
synchronous detection. Moreover, in the PEM ellipsometric system the orientations of the polarizer and analyzer are fixed with respect to the plane of incidence while the ellipsometric parameters are obtained by modulating its phase retardation. This is in contrast to a conventional ellipsometric system, in which the ellipsometric parameters are obtained by rotating one of the optical components, such as the polarizer, analyzer or compensator. It is known that this rotating setup may cause beam deviation [4] and thus produce parasitic error, which can be avoided in the PEM ellipsometric. The azimuth alignment of the optical components in the ellipsometer is essential to the accuracy of measurements because any improper azimuth setting in the system can cause significant errors [5,6]. The nulling method [7,8] has been the most frequently used technique in polarization-related measurements. McCrackin et al. [9,10] suggested some systematic alignment techniques for aligning the azimuth angles of the optical components in ellipsometer. Because the minimum intensity must be precisely located, a highly sensitive detecting system and high- extinction-ratio polarizers are required in those techniques. In a previous study [11], we improved Steel’s intensity ratio technique [12] for aligning the azimuths of the polarizer and analyzer to the specimen surface in a Polarizer-Sample-Analyzer ellipsometric system, but only determined [13] the relative azimuth position of the strain axis of a PEM to the transmission axes of the polarizer and the analyzer in a straight-through (polarizer-PEM-analyzer, PPEMA) setup. In this paper, we continue our efforts by applying a similar technique to align all of the optical components (namely P, PEM and A) to the
reflective surface of a specimen in a PEM ellipsometer. Initially, the relative positions of P, PEM and A can be directly determined [13] in a straight-through arrangement with the specimen removed. The specimen is then positioned and arranged at the required angle of incidence in a PPEMSA type ellipsometer. The small azimuth deviation from the incident plane is determined by applying a three-intensity-measurement technique [14] to its DC component at the zero point of the zero-order Bessel function, under the condition that the azimuth of the PEM and polarizer are set at 0 and 45o, respectively. This direct determination technique can be operated at any incident angle with the specimen in situ. Without any additional measurement, this technique can also determine one of the ellipsometric parameters, ψ.
㆔ Theoretical Background
The basic setup of the ellipsometric system is shown in Fig. 1.
2 ) ( ) ( M R M P R A I I = o −θ S θ PEM . cos t o ω ∆ = ∆
As the zero-order Bessel function (Jo) equals
zero, i.e., ∆o=2.405, the appendix provides
the calibration technique of the zero point of the zero-order Bessel function in a PEM system, and intensity can be further simpli-fied as
A three-intensity-measurement technique [13] can be easily applied to determine the azmuth position of θ. Measuring three radiances through three analyzers evenly spaced 60o apart in half a cycle, one can use the following relation
)] 120 ( ) 60 ( ) ( 2 [ )] 120 ( ) 60 ( [ 3 ) ( 2 tan + − + − + − + − = − A I A I A I A I A I A DC DC DC DC DC θ
One can also obtain one of the ellipsometric parameters, ψ, by the relation of
κ κ ψ + − = 1 1 tan2 , where )] 120 ( ) 60 ( ) ( )[ ( 2 sin )] 120 ( ) 60 ( [ 3 + + + + − + − + = A I A I A I A A I A I θ κ ,
through the same measurements.
㆕ Experimental Results
The azimuth deviation of P, PEM and A with respect to the specimen surface was deduced from the reflected intensity measurements; the deviations were evaluated before and after the adjustment, and were -0.60±0.02o and 0.008±0.02o, respectively, as shown in Fig 2. The azimuth angle of the system can be arranged within 0.01o of the specimen surface in our system. The ellipsometric parameter ψ was also obtained from the same measurements, and our results are comparable with those measured by using a conventional null ellipsometer. The ellipsometric parameter ψ of a thick platinum film and a standard SiO2/Si thin film are tabled in Table 1 at an
incident angle of 700 by this PEM ellipsometer. The ellipsometric parameter
ψ of thick Pt film measured using a Rodulph AutoEL III is 34.15 ± 0.01o. However, the ellipsometric parameter ψ of the standard SiO2/Si thin film is 50.58o, which is
calculated by considering its thickness as 1133 Å and refractive index as 1.462.
Concluding Remark
The three-intensity-measurement tech-nique [14] can directly determine the azimuth deviation of the PPEMA system to the specimen surface by high-level intensity measurements instead of the time-consuming measurements in which the angular positions of the analyzer as well as
)}. ( cos tan ) ( {sin 2 ) ( = 2 −θ + 2ψ 2 −θ A A I A I i DC
the polarizer corresponding to the intensity minimum are required to be determined. Since the azimuth position is determined by an intensity ratio technique, it cannot only reduce the error caused by the imperfection of the analyzer, but also determine the parameter ψ simultaneously. Because this method can determine the azimuth position at the working angle of incident with the specimen in situ, a prior testing sample for alignment is not required in the system. The major problem in this system is the intensity fluctuation. Because the multiple reflection effect [17] can be avoided in the reflective arrangement, the standard deviation of the reflected system (∆θ=0.02o) is less than the straight-through measurements [13] (∆θ=0.05o). Further study will be devoted to measure the tilting angle of the reflective surface.
Acknowledgments
This work was supported by the National Council of the Republic of China under Grant No. NSC 88-2112-M-009-040. We would like to thank professors M. C. Chen and K. Y. Hsu of the National Chiao Tung University for their advice on the manuscript. We are also grateful to Mr. Fwu-Jen Cheng of the Chung Shan Institute of Science and Technology for his measurement of the sample using the Rodulph AutoEL III.
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Fig. 1 Schematic view of the experimental setup: L:light source, P:polarizer, A:analyzer, D: detector.
Fig. 1 Schematic setup of photoelastic modulation ellipsometry
Fig. 2 θ, the azimuth deviation (◆: before adjustment, ■ after adjustment) of P, PEM and A with respect to the surface of reflection. Table 1 Pt thick film ψ (deg) θ (deg) 1 34.15 0.007 2 34.17 -0.014 3 34.09 0.002 4 34.18 -0.036 5 34.16 -0.035 Mean (std) 34.16(0.02) 0.01 (0.02) SiO2/Si std thin film ψ (deg) θ (deg) 1 50.58 -0.01 2 50.63 0.03 3 50.60 -0.01 4 50.61 -0.04 5 50.58 0.04 Mean (std) 50.60(0.02) 0.002(0.03) -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0 2 4 6 8 10 12
before adj after adj.
