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Design of an apparatus for polarization measurement in soft X-ray region
Spectrochimica Acta Part B 65 (2010) 147–151
Contents lists available at ScienceDirect
Spectrochimica Acta Part B j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s a b
Design of an apparatus for polarization measurement in soft X-ray region☆ Takashi Imazono a,⁎, Yoji Suzuki a, Kazuo Sano b, Masato Koike a a b
Quantum Beam Science Directorate, Japan Atomic Energy Agency, 8-1, Umemidai, Kizugawa, Kyoto, 619-0215 Japan Shimadzu Emit Co. Ltd., 2-5-23, Kitahama, Chuo-ku, Osaka, 541-0041 Japan
a r t i c l e
i n f o
Article history: Received 10 November 2007 Accepted 14 December 2009 Available online 24 December 2009 Keywords: Soft X-ray Polarimeter Ellipsometer Polarization analysis
a b s t r a c t A novel apparatus for polarization measurement in the soft X-ray region has been designed, constructed, and installed in the evaluation beamline for soft X-ray optical elements (BL-11) at the SR Center of Ritsumeikan University, Shiga, Japan. It allows us to perform conventional reflection and transmission measurements including rocking curve measurement as well as polarimetric and ellipsometric measurements based on the rotating-analyzer method by using six independently movable motorized stages. As a preliminary test of the apparatus, the reflection profile of a Mo/SiO2 multilayer mirror prepared by an ion beam sputtering technique, which is designed as a reflection polarizer for use of 13.9 nm, has been measured by the apparatus. The result is compared with that by an existing reflectometer, and the azimuth angle dependence of the reflection intensity has been demonstrated. Consequently, it is shown that the apparatus has the capability to perform the rotating-analyzer ellipsometry. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The increasing demand for comprehensive polarimetric measurements is pressing in the soft X-ray (SX) region. In the energy range between 0.7 and 1 keV in which the L absorption edges of transition metals are located, circularly polarized SX is useful for studies of magnetic properties of materials such as magnetic circular dichroism (MCD) measurements. In order to discuss the experimental results quantitatively, experimenters need information on the actual polarization state of the probe light. It is because the MCD signal is proportional to the degree of circular polarization of the probe beam used. It should also be kept in mind that the rotation of the plane of polarization and the degradation of the degree of polarization might result from reflection and diffraction of the beamline optics. Therefore the polarization state of the probe light should be characterized in advance of the experiment by polarization measurement. Quantitative evaluation of the actual polarization state of light requires a combination of phase shifter (or phase shifting polarizer) and analyzer usable at the same energy as the probe light. In the energy range between 100 eV and 300 eV, polarization measurements have been performed by using a polarimeter or ellipsometer equipped with multilayer phase shifter and analyzer such as Mo/Si, Ru/Si and Cr/C [1–4]. Recently development of polarizing elements for use in the higher region has been progressed [5,6]. A W/B4C multilayer has been
☆ This paper was presented at the 19th “International Congress on X-ray Optics and Microanalysis” (ICXOM-19) held in Kyoto (Japan), 16–21 September 2007. ⁎ Corresponding author. E-mail address: [email protected] (T. Imazono). 0584-8547/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2009.12.009
reported to work as the practicable polarizer for 710 eV, although the reflectance for s-polarization at 850 eV remarkably decreases to 0.4% from 5.2% [7]. In the higher energy range than about 0.7 keV, it becomes difficult to develop practicable phase shifters, even polarizers, and consequently to perform polarization measurements. On the other hand, in the higher energy region than 6 keV, single crystals, e.g., Si, Ge, and diamond, in Bragg or Laue geometry are of advantage rather than multilayers, and they are utilized for the evaluation and generation of linearly and circularly polarized x-rays, and helicity switching [8–10]. In our previous study [11,12], mica crystalline has been clarified to work as a high-efficiency polarizer at 880 eV. The linear polarization degree of light emerged from an undulator has been evaluated by using a versatile apparatus for polarimetry and ellipsometry (ELLI) [13] equipped with micas as the polarizers. Furthermore, mica film of ∼5 μm thickness has been found to be a promising candidate as a transmission quarter-wave plate at around 1 keV by simulation calculation [14]. It means that, in principle, it allows us to determine completely the polarization parameters by use of mica. To certify these features, it should be verified by the polarization measurements. Unfortunately one of the six drive shafts equipped in the ELLI, i.e., the detector arm is mechanically coupled to the incident angle of the analyzer. It is inconvenient to the alignment and the polarization measurements in the energy range of around 1 keV. It is because the reflection band width becomes narrower than that in low energy region [11,12]. From this viewpoint, it should be more profitable for the polarization measurement to have the capability to change all axes independently to perform conventional reflection and transmission measurements including rocking curve measurement. Therefore, referring to the ELLI, we decided to develop a polarimeter
148
T. Imazono et al. / Spectrochimica Acta Part B 65 (2010) 147–151
and ellipsometer equipped with fully independent drive shafts to realize the complete polarization analysis in the SX region.
polarization ellipse of the incident light, and C is the contrast factor of the incident light defined as
2. Rotating-analyzer method with a phase shifter
C = ðImax −Imin Þ = ðImax + Imin Þ:
Rotating-analyzer ellipsometry by means of an analyzer A and a detector D is one of the well-known polarization measurements as shown in Fig. 1(A). When the azimuth angle η is rotated along the optical axis of a probe beam fixing the incident angle ω and the detection angle θ, the intensity I(η) of the reflected light from A follows the modified Malus' equation expressed as IðηÞ = Ia ð1 + C cos 2ðη−δÞÞ;
ð2Þ
We can obtain C and δ by applying the fitting function Eq. (1) to the measured data. The polarizance Z, which represents the polarizing ability of the analyzer, is defined using the reflectivities for s- and p-polarization components (Rs and Rp) of A as Z = ðRs −Rp Þ = ðRs + Rp Þ:
ð3Þ
ð1Þ
where Ia is the average of the maximum Imax and minimum Imin of the reflected light, δ is the azimuth angle of the major axis of the
If the value of Z is given, the degree of linear polarization PL can be derived from PL = C = Z:
ð4Þ
If the incident light is completely unpolarized or circularly polarized light as well as Z equals zero, then I(η) is independent of η, so that PL cannot be determined. Thus, when both Z and PL are unknown, another polarizer (or a phase shifter) is needed. Fig. 1(B) shows a double-reflection geometry using both a polarizer (or a phase shifter), P, and an analyzer, A. The contrast factor of the reflected beam from P fixed at the azimuth angle χ = δ ± π/4 is obtained by azimuth rotation of η, then PL can be derived from 1=2
PL = ðC1 C2 = C3 cos 2η3 Þ
;
ð5Þ
where C1 (or C2) is the contrast factor of the incident beam evaluated by A (or P) in the configuration in Fig. 1(A). Also C3 and η3 are the contrast factor and the azimuth angle of the major axis of the polarization ellipse of the reflected beam from P in the configuration in Fig. 1(B), respectively. The above scheme makes it possible to determine simultaneously Zi (i = 1, 2) of A and P, and PL and δ of the incident light by using Eqs. (4) and (5). If some pairs of (η3, χ) are obtained by the measurements in the configuration shown in Fig. 1(B), then the polarization degree P and the ellipticity angle ε of light, and the extinction ratio ρ defined as the ratio of the complex amplitude for s-polarization to that for p-polarization and the phase difference Δ between s- and p-polarization components of P can be determined as fitting parameters by the following equation:
tan 2η3 =
2ρPðcos2ε cosΔ sin2ðδ−χÞ− sin2ε sinΔÞ : ρ2 −1 + Pðρ2 + 1Þcos2ε cos2ðδ−χÞ
ð6Þ
The degree of circular polarization PC can be derived from PC = P sin 2ε
Fig. 1. Schematic diagrams of single-reflection geometry with an analyzer A and detector D (A), and double-reflection geometry based on the rotating-analyzer method with a phase shifter (or polarizer) P (B). The azimuth and incident angles of P (or A) are χ (or η) and φ (or ω), respectively. θ means a detection angle. ψ moves the position of A and D with those relative positions fixed.
ð7Þ
It is of importance that the polarization state of the incident light and the characteristics of the two polarizing elements used can be completely, simultaneously determined [15]. From the above argument, it is found that a sophisticated apparatus needs six fully independent drive shafts (η, ω, θ, χ, φ, and ψ). If so, it allows us to perform not only conventional reflection measurements (two-dimensional scans ω–θ and φ–ψ, where θ and ψ are fixed at 2ω and 2φ, respectively) but also one-dimensional scans such as rocking curve and transmission measurements. Furthermore, it is convenient to adjust the angular alignment between the optical axis and the sample position.
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149
Fig. 2. Projection drawing of the inside mechanism of a newly designed apparatus for SX polarimetry and ellipsometry. GSP and GSA represent goniometric stages to be able to mount a phase shifter (or polarizer) P and an analyzer A, respectively. Six motorized rotary stages (χ, φ, ψ, η, ω, and θ) and three motorized linear stages (H, X, and T) are employed to realize the configurations in Fig. 1 and to move the positions of P, A, and the inside mechanism in the x direction, respectively. The T stage is located under the U-shaped basement of the GSP (not shown in the figure).
3. Design and construction of a soft X-ray polarimeter and ellipsometer Fig. 2 shows the projection drawing of the inside mechanism of a soft X-ray polarimeter and ellipsometer (SXPE) which we have developed. This consists of two goniometric stages GSP and GSA to be able to mount
a phase shifter (or polarizer) P and an analyzer A, respectively, and is equipped with six motorized rotary stages (χ, ψ, φ, η, θ, and ω) to realize the configurations shown in Fig. 1, and the three motorized linear stages (H, X, and T) as auxiliary drive shafts to adjust the positions of P, A, and the inside mechanism. All motorized stages are made by Suruga Seiki Co., Ltd., Japan, of which the details are listed in Table 1.
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Table 1 Details of motorized stages employed as drive shafts of two goniometric stages GSP and GSA. The resolution per pulse of each axis is a nominal value in the atmosphere.
GSA
GSP
Axis name
Assignment of axis
Working range
Resolution per pulse
Motorized stage
η ω θ X χ φ ψ H T
Azimuth angle of A Incident angle of A Angle of detector arm Height position of A Azimuth angle of P Incident angle of P Angle of arm Height position of P Horizontal position of the inside mechanism
− 95 to 280° − 5 to 180° − 5 to 120° − 5 to 5 mm − 95 to 280° − 5 to 180° − 5 to 120° − 5 to 5 mm − 15 to 15 mm
0.00125° 0.001° 0.001° 0.5 μm 0.001° 0.001° 0.001° 0.5 μm 1 μm
U10698 KS401-60-L KS401-60-L KS101-20-L KS402-100-L KS401-60-L KS402-100-L KS101-20-L KX0830C-L-L
The GSP has three rotary stages (χ, ψ, and φ) and two linear stages (H and T). The azimuth rotation of GSP is operated by the χ stage connected to a rectangular frame made of aluminum alloy supported by a U-shaped basement with a bearing. The ψ stage on the U-shaped arm with a bearing shaft is used for moving the position of GSA. A counter weight made of stainless steel is attached on the opposite side of the GSA. The φ stage can change the incident angle of P. The height position of P can be changed by the H stage connected just below the φ stage. The T stage located just below the bottom plate of the U-shaped basement of the GSP (not shown in the figure) is used to move the inside mechanism parallel to the x direction. The GSA is connected to the arm on the ψ stage and is composed of three rotary stages (η, θ, and ω) and a linear stage (X). The azimuth rotation of GSA is operated by the η stage. The incident angle of A can be changed by the ω stage located on the X stage for moving and adjusting the height position of A, where the ω and X stages are the same specifications as the φ and H stages, respectively. The θ stages are used for changing the detector arm where a microchannel plate (MCP) assembly (F4655CsI, Hamamatsu Photonics K.K.) is attached. The sample holder for P and its holder housing are the same specifications as those for A. Each back plate of the holder and its housing has a 5-mm diameter hole. A sample having a size of up to 15 × 15 × 5 mm3 can be mounted on this holder. Therefore, transmission experiments can be also performed by detaching P or A from the light source by means of the H or X stages. Furthermore, the rotor shaft that supports the rectangular frame of the GSP has a 2-mm pinhole. The 0-th order light from a monochromator can be observed directly via this pinhole when both P and A are detached from the optical axis, so that it is easy to realize not only the configurations as shown in Fig. 1 but also the transmission geometries and the position alignment. The vacuum chamber made of stainless steel is a cylindrical tube with an 845-mm diameter and an 800-mm total length. A base pressure of 8 × 10− 5 Pa is achieved using a turbo molecular pump of 800-L/s and a scroll pump of 250-L/min. A four-quadrant slit located upstream of this chamber is equipped to form an incoming beam. The control software has been also developed by the National Instruments LabVIEW® along with the apparatus. It allows us to perform the following measurements: (1) conventional reflection and (2) transmission measurements including rocking curve, and (3) polarization measurements based on the rotating-analyzer method, i.e., doublereflection and transmission measurements, and reflection-transmission measurement and vice versa. All connection wirings of nine motorized stages to stepping motor drivers are connected through multi-pin electrical feedthroughs. The motor drivers are controlled by a stepping motor controller. The signals from the anode of the MCP and the beam current of a storage ring are read out by two electrometers via a GPIB bus with a noise level lower than 0.3 pA. They are automatically recorded in comma separated value (CSV) file format in every measurement.
Fig. 3. Reflectivities for s-polarization of the Mo/SO2 multilayers at 13.8 nm measured by SXPE (open circles) and the MRD (solid squares) as a function of the grazing angle.
4. Preliminary test of the soft X-ray polarimeter and ellipsometer A preliminary test of the soft X-ray polarimeter and ellipsometer (SXPE) was carried out at BL-11 of AURORA, a superconducting compact storage ring [16], at the SR Center of Ritsumeikan University, Shiga, Japan. BL-11 is an evaluation beamline for soft X-ray optical elements by means of a modified θ–2θ reflectometer/diffractometer (MRD) [17]. The incident light was set at a wavelength of 13.8 nm of which the resolving power has been estimated to be approximately 200. A Mo/SiO2 multilayer mirror optimized as a polarizer for 13.9 nm was prepared in this study. It was grown to 30 bilayers with topmost SiO2 layer on the surface of a commercial Si(111) substrate with a 2-in. diameter and a 1-mm thickness at ambient temperature using an ion beam sputtering method. By use of a high-resolution x-ray diffractometer (SLX-2000, Rigaku Co.), the periodic length and the ratio of the Mo layer thickness to the multilayer period were evaluated to be 10.44 nm and 0.56, respectively. The fabricated multilayer mirror was cut into half size pieces. One was used for the reflection measurement using the MRD. The other was also cut into a size of 15 × 15 mm2 and used as the analyzer in the preliminary test of the SXPE. Fig. 3 shows the reflection curves for s-polarization of the Mo/SiO2 multilayer measured by the SXPE (open circles) and the MRD (Solid
Fig. 4. Azimuth angle dependence of reflection intensity of Mo/SO2 multilayer at the angle of incidence of 48.75° measured in the configuration shown in Fig. 1(A) (solid circles). Solid line shows the result of the curve-fitting analysis.
T. Imazono et al. / Spectrochimica Acta Part B 65 (2010) 147–151
squares) as a function of the grazing angle. The efficiency, reflection width, and peak position measured by the SXPE well coincide with those by the MRD. This result means the SXPE has satisfactory performance as well as a conventional reflectometer. Fig. 4 shows the azimuth angle dependence of reflection intensity of the analyzer fixed at the angle of incidence of 48.75° in the configuration of Fig. 1(a) (solid circles). Solid line shows the result of the curve-fitting analysis. The fitting parameters have been evaluated to be C = 0.698 ± 0.008 and δ = − 4.55° ± 0.30°, although the best fitting curve seems to be in disagreement with the measured data due to misalignment between the center of the azimuth rotation of the SXPE and optical axis. As described in Section 2, it is impossible to determine PL from only this experiment, as well as Z, but the value of PL can be estimated to be close to C because the calculated Z ∼ 0.997. In the preliminary test, we did not determine PL and Z accurately and demonstrate any other polarization measurements such as a double-reflection measurement. However, from the results of the comparison measurement of the reflection profiles and the azimuth angle dependence of the reflection intensity, that is, the rotatinganalyzer ellipsometry, the apparatus has been shown to have the performance required for the polarization measurements. Acknowledgement We would like to thank Dr. H. Kimura of SPring-8, Japan Synchrotron Radiation Research Institute for his fruitful discussion. We wish to thank Prof. T. Ohta and his staff of the SR Center, Ritsumeikan University for their technical support. References [1] J.B. Kortright, H. Kimura, V. Nikitin, K. Mayama, M. Yamamoto, M. Yanagihara, Soft x-ray (97-eV) phase retardation using transmission multilayers, Appl. Phys. Lett. 60 (1992) 2963–2965. [2] S.D. Fonzo, W. Jark, F. Schäfers, H. Petersen, A. Gaupp, J.H. Underwood, Phaseretardation and full-polarization analysis of soft-x-ray synchrotron radiation close to the carbon K edge by use of a multilayer transmission filter, Appl. Opt. 33 (1994) 2624–2632.
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[3] H. Kimura, T. Miyahara, Y. Goto, K. Mayama, M. Yanagihara, M. Yamamoto, Polarization measurement of SR from a helical undulator using a quarter-wave plate for a wavelength of 12.8 nm, Rev. Sci. Instrum. 66 (1995) 1920–1922. [4] S.D. Fonzo, B.R. Müller, W. Jark, A. Gaupp, F. Schäfers, J.H. Underwood, Multilayer transmission phase shifters for the carbon K edge and the water window, Rev. Sci. Instrum. 66 (1995) 1513–1516. [5] H.-C. Mertins, F. Schäfers, H. Grimmer, D. Clemens, P. Böni, M. Horisberger, W/C, W/Ti, Ni/Ti, and Ni/V multilayers for the soft-x-ray range: experimental investigation with synchrotron radiation, Appl. Opt. 37 (1998) 1873–1882. [6] F. Schäfers, H.-C. Mertins, A. Gaupp, W. Gudat, M. Mertin, I. Packe, F. Schmolla, S.D. Fonzo, G. Soullié, W. Jark, R. Walker, X.L. Cann, R. Nyholm, M. Eriksson, Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light, Appl. Opt. 38 (1999) 4074–4088. [7] S. Braun, P. Gawlitza, M. Menzel, A. Leson, M. Mertin, F. Schäfers, Reflectance and resolution of multilayer monochromators for photon energies from 400–6000 eV, AIP Conf. Proc. 879 (2007) 493–496. [8] K. Hirano, T. Ishikawa, I. Nakamura, M. Mizutani, S. Kikuta, Transmission-type x-ray phase retarder using Ge crystal in Laue diffraction geometry, Jpn. J. Appl. Phys. 33 (1994) L689–L692. [9] K. Hirano, T. Mori, A. Iida, R. Colella, S. Sasaki, Q. Shen, Determination of the Stokes–Poincaré parameters for synchrotron x-ray beam by multiple Bragg scattering, Jpn. J. Appl. Phys. 35 (1996) 5550–5552. [10] L.E. Berman, Q. Shen, K.D. Finkelstein, P. Doing, Z. Yin, G. Pan, Characterization of a diamond crystal x-ray phase retarder, Rev. Sci. Instrum. 73 (2002) 1502–1504. [11] T. Imazono, M. Ishino, M. Koike, H. Kimura, T. Hirono, K. Sano, Performance of a reflection-type polarizer by use of muscovite mica crystal in the soft x-ray region of 1 keV, Rev. Sci. Instrum. 76 (2005) 023104. [12] T. Imazono, T. Hirono, H. Kimura, Y. Saitoh, Y. Muramatsu, M. Ishino, M. Koike, K. Sano, Polarizance of a synthetic mica crystal polarizer and the degree of linear polarization of an undulator beamline at 880 eV evaluated by the rotatinganalyzer method, Rev. Sci. Instrum. 76 (2005) 126106. [13] H. Kimura, T. Hirono, T. Miyahara, M. Yamamoto, T. Ishikawa, A new beamline appatatus for polarimetry and ellipsometry using soft X-ray multilayers, AIP Conf. Proc. 705 (2004) 537–540. [14] T. Imazono, M. Koike, Theoretical investigation of transmission-type phase shifter made with muscovite mica crystal for 1-keV region, AIP Conf. Proc. 879 (2007) 690–693. [15] H. Kimura, 1992. Polarization measurement of synchrotron radiation with use of multilayers in the soft x-ray region, Doctoral thesis, The Graduate University for Advanced Studies, Japan. [16] H. Iwasaki, Y. Nakayama, K. Ozutsumi, Y. Yamamoto, Y. Tokunaga, H. Saisho, T. Matsubara, S. Ikeda, Compact superconducting ring at Ritsumeikan University, J. Synchrotron Radiat. 5 (1998) 1162–1165. [17] M. Koike, K. Sano, O. Yoda, Y. Harada, M. Ishino, N. Moriya, H. Sasai, H. Takenaka, E. Gullikson, S. Mrowka, M. Jinno, Y. Ueno, J.H. Underwood, T. Namioka, New evaluation beamline for soft x-ray optical elements, Rev. Sci. Instrum. 73 (2002) 1541–1544.
Contents lists available at ScienceDirect
Spectrochimica Acta Part B j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s a b
Design of an apparatus for polarization measurement in soft X-ray region☆ Takashi Imazono a,⁎, Yoji Suzuki a, Kazuo Sano b, Masato Koike a a b
Quantum Beam Science Directorate, Japan Atomic Energy Agency, 8-1, Umemidai, Kizugawa, Kyoto, 619-0215 Japan Shimadzu Emit Co. Ltd., 2-5-23, Kitahama, Chuo-ku, Osaka, 541-0041 Japan
a r t i c l e
i n f o
Article history: Received 10 November 2007 Accepted 14 December 2009 Available online 24 December 2009 Keywords: Soft X-ray Polarimeter Ellipsometer Polarization analysis
a b s t r a c t A novel apparatus for polarization measurement in the soft X-ray region has been designed, constructed, and installed in the evaluation beamline for soft X-ray optical elements (BL-11) at the SR Center of Ritsumeikan University, Shiga, Japan. It allows us to perform conventional reflection and transmission measurements including rocking curve measurement as well as polarimetric and ellipsometric measurements based on the rotating-analyzer method by using six independently movable motorized stages. As a preliminary test of the apparatus, the reflection profile of a Mo/SiO2 multilayer mirror prepared by an ion beam sputtering technique, which is designed as a reflection polarizer for use of 13.9 nm, has been measured by the apparatus. The result is compared with that by an existing reflectometer, and the azimuth angle dependence of the reflection intensity has been demonstrated. Consequently, it is shown that the apparatus has the capability to perform the rotating-analyzer ellipsometry. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The increasing demand for comprehensive polarimetric measurements is pressing in the soft X-ray (SX) region. In the energy range between 0.7 and 1 keV in which the L absorption edges of transition metals are located, circularly polarized SX is useful for studies of magnetic properties of materials such as magnetic circular dichroism (MCD) measurements. In order to discuss the experimental results quantitatively, experimenters need information on the actual polarization state of the probe light. It is because the MCD signal is proportional to the degree of circular polarization of the probe beam used. It should also be kept in mind that the rotation of the plane of polarization and the degradation of the degree of polarization might result from reflection and diffraction of the beamline optics. Therefore the polarization state of the probe light should be characterized in advance of the experiment by polarization measurement. Quantitative evaluation of the actual polarization state of light requires a combination of phase shifter (or phase shifting polarizer) and analyzer usable at the same energy as the probe light. In the energy range between 100 eV and 300 eV, polarization measurements have been performed by using a polarimeter or ellipsometer equipped with multilayer phase shifter and analyzer such as Mo/Si, Ru/Si and Cr/C [1–4]. Recently development of polarizing elements for use in the higher region has been progressed [5,6]. A W/B4C multilayer has been
☆ This paper was presented at the 19th “International Congress on X-ray Optics and Microanalysis” (ICXOM-19) held in Kyoto (Japan), 16–21 September 2007. ⁎ Corresponding author. E-mail address: [email protected] (T. Imazono). 0584-8547/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2009.12.009
reported to work as the practicable polarizer for 710 eV, although the reflectance for s-polarization at 850 eV remarkably decreases to 0.4% from 5.2% [7]. In the higher energy range than about 0.7 keV, it becomes difficult to develop practicable phase shifters, even polarizers, and consequently to perform polarization measurements. On the other hand, in the higher energy region than 6 keV, single crystals, e.g., Si, Ge, and diamond, in Bragg or Laue geometry are of advantage rather than multilayers, and they are utilized for the evaluation and generation of linearly and circularly polarized x-rays, and helicity switching [8–10]. In our previous study [11,12], mica crystalline has been clarified to work as a high-efficiency polarizer at 880 eV. The linear polarization degree of light emerged from an undulator has been evaluated by using a versatile apparatus for polarimetry and ellipsometry (ELLI) [13] equipped with micas as the polarizers. Furthermore, mica film of ∼5 μm thickness has been found to be a promising candidate as a transmission quarter-wave plate at around 1 keV by simulation calculation [14]. It means that, in principle, it allows us to determine completely the polarization parameters by use of mica. To certify these features, it should be verified by the polarization measurements. Unfortunately one of the six drive shafts equipped in the ELLI, i.e., the detector arm is mechanically coupled to the incident angle of the analyzer. It is inconvenient to the alignment and the polarization measurements in the energy range of around 1 keV. It is because the reflection band width becomes narrower than that in low energy region [11,12]. From this viewpoint, it should be more profitable for the polarization measurement to have the capability to change all axes independently to perform conventional reflection and transmission measurements including rocking curve measurement. Therefore, referring to the ELLI, we decided to develop a polarimeter
148
T. Imazono et al. / Spectrochimica Acta Part B 65 (2010) 147–151
and ellipsometer equipped with fully independent drive shafts to realize the complete polarization analysis in the SX region.
polarization ellipse of the incident light, and C is the contrast factor of the incident light defined as
2. Rotating-analyzer method with a phase shifter
C = ðImax −Imin Þ = ðImax + Imin Þ:
Rotating-analyzer ellipsometry by means of an analyzer A and a detector D is one of the well-known polarization measurements as shown in Fig. 1(A). When the azimuth angle η is rotated along the optical axis of a probe beam fixing the incident angle ω and the detection angle θ, the intensity I(η) of the reflected light from A follows the modified Malus' equation expressed as IðηÞ = Ia ð1 + C cos 2ðη−δÞÞ;
ð2Þ
We can obtain C and δ by applying the fitting function Eq. (1) to the measured data. The polarizance Z, which represents the polarizing ability of the analyzer, is defined using the reflectivities for s- and p-polarization components (Rs and Rp) of A as Z = ðRs −Rp Þ = ðRs + Rp Þ:
ð3Þ
ð1Þ
where Ia is the average of the maximum Imax and minimum Imin of the reflected light, δ is the azimuth angle of the major axis of the
If the value of Z is given, the degree of linear polarization PL can be derived from PL = C = Z:
ð4Þ
If the incident light is completely unpolarized or circularly polarized light as well as Z equals zero, then I(η) is independent of η, so that PL cannot be determined. Thus, when both Z and PL are unknown, another polarizer (or a phase shifter) is needed. Fig. 1(B) shows a double-reflection geometry using both a polarizer (or a phase shifter), P, and an analyzer, A. The contrast factor of the reflected beam from P fixed at the azimuth angle χ = δ ± π/4 is obtained by azimuth rotation of η, then PL can be derived from 1=2
PL = ðC1 C2 = C3 cos 2η3 Þ
;
ð5Þ
where C1 (or C2) is the contrast factor of the incident beam evaluated by A (or P) in the configuration in Fig. 1(A). Also C3 and η3 are the contrast factor and the azimuth angle of the major axis of the polarization ellipse of the reflected beam from P in the configuration in Fig. 1(B), respectively. The above scheme makes it possible to determine simultaneously Zi (i = 1, 2) of A and P, and PL and δ of the incident light by using Eqs. (4) and (5). If some pairs of (η3, χ) are obtained by the measurements in the configuration shown in Fig. 1(B), then the polarization degree P and the ellipticity angle ε of light, and the extinction ratio ρ defined as the ratio of the complex amplitude for s-polarization to that for p-polarization and the phase difference Δ between s- and p-polarization components of P can be determined as fitting parameters by the following equation:
tan 2η3 =
2ρPðcos2ε cosΔ sin2ðδ−χÞ− sin2ε sinΔÞ : ρ2 −1 + Pðρ2 + 1Þcos2ε cos2ðδ−χÞ
ð6Þ
The degree of circular polarization PC can be derived from PC = P sin 2ε
Fig. 1. Schematic diagrams of single-reflection geometry with an analyzer A and detector D (A), and double-reflection geometry based on the rotating-analyzer method with a phase shifter (or polarizer) P (B). The azimuth and incident angles of P (or A) are χ (or η) and φ (or ω), respectively. θ means a detection angle. ψ moves the position of A and D with those relative positions fixed.
ð7Þ
It is of importance that the polarization state of the incident light and the characteristics of the two polarizing elements used can be completely, simultaneously determined [15]. From the above argument, it is found that a sophisticated apparatus needs six fully independent drive shafts (η, ω, θ, χ, φ, and ψ). If so, it allows us to perform not only conventional reflection measurements (two-dimensional scans ω–θ and φ–ψ, where θ and ψ are fixed at 2ω and 2φ, respectively) but also one-dimensional scans such as rocking curve and transmission measurements. Furthermore, it is convenient to adjust the angular alignment between the optical axis and the sample position.
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Fig. 2. Projection drawing of the inside mechanism of a newly designed apparatus for SX polarimetry and ellipsometry. GSP and GSA represent goniometric stages to be able to mount a phase shifter (or polarizer) P and an analyzer A, respectively. Six motorized rotary stages (χ, φ, ψ, η, ω, and θ) and three motorized linear stages (H, X, and T) are employed to realize the configurations in Fig. 1 and to move the positions of P, A, and the inside mechanism in the x direction, respectively. The T stage is located under the U-shaped basement of the GSP (not shown in the figure).
3. Design and construction of a soft X-ray polarimeter and ellipsometer Fig. 2 shows the projection drawing of the inside mechanism of a soft X-ray polarimeter and ellipsometer (SXPE) which we have developed. This consists of two goniometric stages GSP and GSA to be able to mount
a phase shifter (or polarizer) P and an analyzer A, respectively, and is equipped with six motorized rotary stages (χ, ψ, φ, η, θ, and ω) to realize the configurations shown in Fig. 1, and the three motorized linear stages (H, X, and T) as auxiliary drive shafts to adjust the positions of P, A, and the inside mechanism. All motorized stages are made by Suruga Seiki Co., Ltd., Japan, of which the details are listed in Table 1.
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Table 1 Details of motorized stages employed as drive shafts of two goniometric stages GSP and GSA. The resolution per pulse of each axis is a nominal value in the atmosphere.
GSA
GSP
Axis name
Assignment of axis
Working range
Resolution per pulse
Motorized stage
η ω θ X χ φ ψ H T
Azimuth angle of A Incident angle of A Angle of detector arm Height position of A Azimuth angle of P Incident angle of P Angle of arm Height position of P Horizontal position of the inside mechanism
− 95 to 280° − 5 to 180° − 5 to 120° − 5 to 5 mm − 95 to 280° − 5 to 180° − 5 to 120° − 5 to 5 mm − 15 to 15 mm
0.00125° 0.001° 0.001° 0.5 μm 0.001° 0.001° 0.001° 0.5 μm 1 μm
U10698 KS401-60-L KS401-60-L KS101-20-L KS402-100-L KS401-60-L KS402-100-L KS101-20-L KX0830C-L-L
The GSP has three rotary stages (χ, ψ, and φ) and two linear stages (H and T). The azimuth rotation of GSP is operated by the χ stage connected to a rectangular frame made of aluminum alloy supported by a U-shaped basement with a bearing. The ψ stage on the U-shaped arm with a bearing shaft is used for moving the position of GSA. A counter weight made of stainless steel is attached on the opposite side of the GSA. The φ stage can change the incident angle of P. The height position of P can be changed by the H stage connected just below the φ stage. The T stage located just below the bottom plate of the U-shaped basement of the GSP (not shown in the figure) is used to move the inside mechanism parallel to the x direction. The GSA is connected to the arm on the ψ stage and is composed of three rotary stages (η, θ, and ω) and a linear stage (X). The azimuth rotation of GSA is operated by the η stage. The incident angle of A can be changed by the ω stage located on the X stage for moving and adjusting the height position of A, where the ω and X stages are the same specifications as the φ and H stages, respectively. The θ stages are used for changing the detector arm where a microchannel plate (MCP) assembly (F4655CsI, Hamamatsu Photonics K.K.) is attached. The sample holder for P and its holder housing are the same specifications as those for A. Each back plate of the holder and its housing has a 5-mm diameter hole. A sample having a size of up to 15 × 15 × 5 mm3 can be mounted on this holder. Therefore, transmission experiments can be also performed by detaching P or A from the light source by means of the H or X stages. Furthermore, the rotor shaft that supports the rectangular frame of the GSP has a 2-mm pinhole. The 0-th order light from a monochromator can be observed directly via this pinhole when both P and A are detached from the optical axis, so that it is easy to realize not only the configurations as shown in Fig. 1 but also the transmission geometries and the position alignment. The vacuum chamber made of stainless steel is a cylindrical tube with an 845-mm diameter and an 800-mm total length. A base pressure of 8 × 10− 5 Pa is achieved using a turbo molecular pump of 800-L/s and a scroll pump of 250-L/min. A four-quadrant slit located upstream of this chamber is equipped to form an incoming beam. The control software has been also developed by the National Instruments LabVIEW® along with the apparatus. It allows us to perform the following measurements: (1) conventional reflection and (2) transmission measurements including rocking curve, and (3) polarization measurements based on the rotating-analyzer method, i.e., doublereflection and transmission measurements, and reflection-transmission measurement and vice versa. All connection wirings of nine motorized stages to stepping motor drivers are connected through multi-pin electrical feedthroughs. The motor drivers are controlled by a stepping motor controller. The signals from the anode of the MCP and the beam current of a storage ring are read out by two electrometers via a GPIB bus with a noise level lower than 0.3 pA. They are automatically recorded in comma separated value (CSV) file format in every measurement.
Fig. 3. Reflectivities for s-polarization of the Mo/SO2 multilayers at 13.8 nm measured by SXPE (open circles) and the MRD (solid squares) as a function of the grazing angle.
4. Preliminary test of the soft X-ray polarimeter and ellipsometer A preliminary test of the soft X-ray polarimeter and ellipsometer (SXPE) was carried out at BL-11 of AURORA, a superconducting compact storage ring [16], at the SR Center of Ritsumeikan University, Shiga, Japan. BL-11 is an evaluation beamline for soft X-ray optical elements by means of a modified θ–2θ reflectometer/diffractometer (MRD) [17]. The incident light was set at a wavelength of 13.8 nm of which the resolving power has been estimated to be approximately 200. A Mo/SiO2 multilayer mirror optimized as a polarizer for 13.9 nm was prepared in this study. It was grown to 30 bilayers with topmost SiO2 layer on the surface of a commercial Si(111) substrate with a 2-in. diameter and a 1-mm thickness at ambient temperature using an ion beam sputtering method. By use of a high-resolution x-ray diffractometer (SLX-2000, Rigaku Co.), the periodic length and the ratio of the Mo layer thickness to the multilayer period were evaluated to be 10.44 nm and 0.56, respectively. The fabricated multilayer mirror was cut into half size pieces. One was used for the reflection measurement using the MRD. The other was also cut into a size of 15 × 15 mm2 and used as the analyzer in the preliminary test of the SXPE. Fig. 3 shows the reflection curves for s-polarization of the Mo/SiO2 multilayer measured by the SXPE (open circles) and the MRD (Solid
Fig. 4. Azimuth angle dependence of reflection intensity of Mo/SO2 multilayer at the angle of incidence of 48.75° measured in the configuration shown in Fig. 1(A) (solid circles). Solid line shows the result of the curve-fitting analysis.
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squares) as a function of the grazing angle. The efficiency, reflection width, and peak position measured by the SXPE well coincide with those by the MRD. This result means the SXPE has satisfactory performance as well as a conventional reflectometer. Fig. 4 shows the azimuth angle dependence of reflection intensity of the analyzer fixed at the angle of incidence of 48.75° in the configuration of Fig. 1(a) (solid circles). Solid line shows the result of the curve-fitting analysis. The fitting parameters have been evaluated to be C = 0.698 ± 0.008 and δ = − 4.55° ± 0.30°, although the best fitting curve seems to be in disagreement with the measured data due to misalignment between the center of the azimuth rotation of the SXPE and optical axis. As described in Section 2, it is impossible to determine PL from only this experiment, as well as Z, but the value of PL can be estimated to be close to C because the calculated Z ∼ 0.997. In the preliminary test, we did not determine PL and Z accurately and demonstrate any other polarization measurements such as a double-reflection measurement. However, from the results of the comparison measurement of the reflection profiles and the azimuth angle dependence of the reflection intensity, that is, the rotatinganalyzer ellipsometry, the apparatus has been shown to have the performance required for the polarization measurements. Acknowledgement We would like to thank Dr. H. Kimura of SPring-8, Japan Synchrotron Radiation Research Institute for his fruitful discussion. We wish to thank Prof. T. Ohta and his staff of the SR Center, Ritsumeikan University for their technical support. References [1] J.B. Kortright, H. Kimura, V. Nikitin, K. Mayama, M. Yamamoto, M. Yanagihara, Soft x-ray (97-eV) phase retardation using transmission multilayers, Appl. Phys. Lett. 60 (1992) 2963–2965. [2] S.D. Fonzo, W. Jark, F. Schäfers, H. Petersen, A. Gaupp, J.H. Underwood, Phaseretardation and full-polarization analysis of soft-x-ray synchrotron radiation close to the carbon K edge by use of a multilayer transmission filter, Appl. Opt. 33 (1994) 2624–2632.
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