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PROOF COPY 022703APL

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Broadband Mo/Si multilayer transmission phase retarders for the extreme

ultraviolet

Zhanshan Wang, a� Hongchang Wang, Jingtao Zhu, Zhong Zhang, Yao Xu, Shumin Zhang,

Wenjuan Wu, Fengli Wang, Bei Wang, Liqin Liu, and Lingyan Chen

Institute of Precision Optical Engineering (IPOE), Physics Department, Tongji University, Shanghai

200092, China

Alan G. Michette, Slawka J. Pfauntsch, and A. Keith Powell

Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom

Franz Schäfers and Andreas Gaupp

BESSY GmbH, Albert Einstein Straße 15, D-12489 Berlin, Germany

Mike MacDonald

CCLRC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom

PROOF COPY 022703APL

�Received 3 November 2006; accepted 11 December 2006�

Experimental results on aperiodic broadband transmission molybdenum/silicon multilayer phase

retarders for the extreme ultraviolet range are presented. The broadband phase retarders were

designed using a numerical method and made using direct current magnetron sputtering on silicon

nitride membrane. The polarization properties of these aperiodic transmission phase retarders have

been investigated using the soft x-ray polarimeter at BESSY-II. The measured phase shift was about

42° in the wavelength range of 13.8–15.5 nm, and the corresponding s-component transmission �Ts� decreased from 6% to 2% with increasing wavelength. © 2007 American Institute of Physics.

�DOI: 10.1063/1.2431761�

Photons in the extreme ultraviolet �EUV� and soft x-ray

regions have sufficient energy to ionize core atomic electrons.

This means that scattering of polarized x rays is a

valuable tool in studying magnetic and structural properties

in thin films and multilayers. 1 The requirement of using polarized

light as a probe for magnetic materials has produced

great interest in the development of phase retarders, 2 which

can introduce relative phase changes between the s- and

p-polarization components of the beam. In the EUV and soft

x-ray spectral regions, multilayers can function as phase retarders

or shifters and could also be key optical elements of a

beamline to provide full control of the polarization of the

incident photons in x-ray spectroscopy. 3 There have been

extensive studies of periodic multilayer phase retarders, 4–7

especially for transmission molybdenum/silicon �Mo/Si�

multilayers, which do not change the beam direction. Large

phase shifts sufficient for quarter-wave phase retarders have

also been developed for conversion between linear and circular

polarizations as required in magnetic material studies. 8

However, traditional periodic multilayers have narrow bandwidths,

which greatly limits their use in practice. The use of

aperiodic multilayer structures can overcome these

limitations; 9 such broadband reflection analyzers 10–12 23

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have

46 been developed, and the same method is used here to de-

47 velop Mo/Si broadband transmission phase retarders. The

48 aperiodic Mo/Si multilayers were made on silicon nitride

49 membranes using direct current magnetron sputtering. The

50 phase shifts of these multilayers were measured at BESSY-II

51 using the ultrahigh vacuum soft x-ray polarimeter.

52 The phases of the transmitted s ��s� and p ��p� electro-

53 magnetic fields can be calculated following the formalism of

a�

Author to whom correspondence should be addressed; electronic mail:

wangzs@mail.tongji.edu.cn

APPLIED PHYSICS LETTERS 90, 1�2007�

Vidal and Vincent, 13 in which the phase shift ��=� s−� p is

evaluated as a function of the wavelength, the grazing angle,

the optical constants of the materials, the number of layers,

and their thicknesses. Initially, the published criteria for selecting

material 14 and the number of bilayer 15 were used to

satisfy both the maximum phase shift and the transmission

intensity. Then, the grazing angle was set in the region between

the Bragg peak and the total reflection, 16 at which the

phase shift is maximum. The optical constants of molybdenum

and silicon were derived from the handbook edited by

Henke et al. 17 and the numerical approach was based on the

minimization of the usual merit function �MF�,

MF =� 1

n� n

��0 − ����j�� j=1

2�

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1/2

, �1�

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where ���� j� is the calculated phase shift at wavelength � j

and � 0 is the desired phase shift. Finally, the merit function

was optimized using a computer code based on the

Levenberg-Marquardt algorithm, 12,13 with 66 layers 14,15 at

grazing angle of 47°. The calculated results for a multilayer

phase retarder with � 0=90° and estimated interfaces roughnesses

of 0 and 1.0 nm are shown in Fig. 1, assuming that

phase shifts of 90° ±30° are acceptable for experimental requirements.

The optimized thicknesses of Mo and Si layers

are in the range of 3.4–4.3 and 4.7–6.1 nm, respectively.

The calculated phase shifts are between 85° and 60° in the

wavelength range of 13.5–15.5 nm, where the transmission

ratio T p/T s is in the range of �0.65–0.95 with perfect interface

��=0 nm�. As shown in Fig. 1�c�, the p-component

transmission T p keeps nearly constant for different roughnesses,

and the phase shifts and s-component transmission T s

decrease with increasing the roughness. Although the transmitted

intensities are only 2%–8% in this wavelength range,

PROOF COPY 0003-6951/2007/90�3�/1/0/$23.00 022703APL

90, 1-1

© 2007 American Institute of Physics

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PROOF COPY 022703APL

1-2 Wang et al. Appl. Phys. Lett. 90, 1�2007�

PROOF COPY 022703APL

FIG. 1. �Color online� Calculated s- and p-transmission profiles of a Mo/Si

multilayer phase retarder as a function of the wavelength at a fixed grazing

incident angle of 47°, and the roughnesses � of the interfaces are estimated

to be 0 and 1.0 nm, respectively.

such phase retarders are suitable for high intensity light

sources such as synchrotron radiation.

The Mo/Si multilayer phase retarder was made using an

ultrahigh vacuum magnetron sputtering deposition system.

PROOF COPY 022703APL

18

The base pressure was 2�10−4 Pa before deposition. Argon

gas �99.999% purity� was used at a constant pressure of

0.08 Pa during deposition, and the operating powers for molybdenum

and silicon were regulated at 20 and 35 W, respectively.

The Mo/Si multilayers were deposited on the silicon

nitride membranes with thickness of 100 nm and size of

5�5 mm2 . In order to calibrate the deposition rate of each

sputtering target and determine the multilayer structure, the

multilayers were measured using small angle x-ray diffraction

�D1 system, Bede Ltd., UK� working at Cu K� line

�0.154 nm�.

The performance of the phase retarder was evaluated

using the high precision ultrahigh vacuum eight-axis soft

x-ray polarimeter on beamline UE56/1-PGM at BESSY-II. 19

In order to simplify the polarization measurements, a broadband

analyzer was also used in the experiment. 11,12 A

400 line mm−1 grating and horizontally polarized undulator

radiation were used to characterize the transmission of the

phase retarder. A full polarization analysis was performed by

recording the intensity behind the polarizer and analyzer at

four different analyzer azimuth angles ��� and for 37 polarizer

azimuth angles ���, corresponding to full rotation over

360°. 19–22 A typical polarimeter spectrum of the transmitted

intensity normalized by the incident intensity is shown in

Fig. 2. These data were analyzed using the least squares fitting

method with seven free parameters, i.e., three Poincaré

parameters �P1, P2, P3� equal to the Stokes’ parameters normalized

with respect to the total intensity S0 �Pi=S i/S 0�, a

scale factor f =S0/I 0 �I0 is the normalized intensity of incident

beam�, the transmission and reflection ratios Tp/T s and

Rp/R s for the phase retarder and analyzer, respectively, 19 85

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and

120 the phase shift �� �=39°� of the phase retarder which was

121 the most sensitive fitting parameter.

122 The measurement of angular dependence was performed

123 at a fixed wavelength of 14.1 nm. As shown in Fig. 3�a�, the

124 theoretical phase shift with an interlayer roughness of 1.0 nm

125 coincides with a fitting to the measurements with a maxi-

126 mum phase shift of up to 90°. This shows that the deposition

127 rate calibration was well controlled. In addition, a broadband

FIG. 2. �Color online� Polarization measurements with Mo/Si multilayers at

14.1 nm, showing the angular distribution of the transmitted intensity as a

function of the polarizer azimuthal angle � for four settings of the analyzer

azimuthal angle �. The scale factor F, three fitted Poincaré parameters of the

incident radiation, and the polarizing properties of the two optical elements

are F=17.9, P 1=−0.027, P 2=−0.009, P 3=−0.995, ��=39°, T p/T s=1.3,

and R p/R s=0.02.

angular phase shift of about 40° is observed with an angular

width of 10°. Figure 3�b� shows that the fitted transmission

ratio agrees with the absolute measurement of the same

quantity, except the difference at the grazing incident angle

of 56°, which is mainly caused by the correlation of the

parameters as the phase shift is very small. 19 128

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The transmitted 133

intensities Ts and Tp are approximately constant in the range 134

of 40°–50°, as shown in Fig. 3�c�.

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The wavelength dependence was measured at the design 136

grazing angle of 47°, and the fits to the measurements along 137

with the calculated values for a roughness of 1.0 nm are 138

shown in Fig. 4�a�. The measured phase shift is approxi- 139

mately constant at 41.7° ±4.3° over the wavelength range of 140

13.8–15.5 nm. It is worth noting that when a phase shifter is 141

used to analyze elliptical polarization, a phase shift angle of 142

a few tens of degrees is sufficient.

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The results show that broadband phase shifts can be re- 144

alized using aperiodic multilayers. From Fig. 4�b�, it can be 145

seen that the transmitted intensity Ts decreases from 6% to 146

2% with increasing wavelength. The sample was also mea- 147

FIG. 3. �Color online� �a� Calculated �solid line �=1.0 nm� and fitted ���

phase shifts as function of the grazing incidence angle at a fixed wavelength

of 14.1 nm. �b� The fitted and measured transmission ratios T p/T s. �c� The

measured s and p transmissions as function of the grazing incidence angle at

a fixed wavelength of 14.1 nm.


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1-3 Wang et al. Appl. Phys. Lett. 90, 1�2007�

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FIG. 4. �Color online� �a� Calculated �solid line� and fitted ��� phase shifts

and �b� the measured transmission T s as function of the wavelength at grazing

incidence angles of 47° and 54°.

148 sured at 54°, and the results show the similar trends as at 47°.

149 This demonstrates that useful phase shifts could be obtained

150 in the longer wavelength range so long as the phase retarder

151 is used at larger grazing angles.

152 In conclusion, an aperiodic broadband Mo/Si transmis-

153 sion phase retarder has been designed, prepared, and mea-

154 sured. Its polarization properties were evaluated using the

155 polarimeter at BESSY-II. The measured phase shift was

156 about 42° with bandwidth of about 2 nm at grazing angles of

157 both 47° and 54°. Although the transmitted intensities and

158 the phase shifts cannot simultaneously be maximized, by ad-

159 justing the number of layers and their thicknesses approxi-

160 mately constant phase shifts and high transmission intensities

161 can be obtained over large bandwidths using the aperiodic

162 multilayers. Broadband phase retarders can greatly simplify

163 polarization analysis experiments without the necessity of

164 changing the components. The design and preparation meth-

165 ods described here are generally applicable for other material

166 combination and wavelength ranges in EUV and soft x-ray

167 regions.

168 The authors are indebted to Hongjun Zhou and Tonglin

169 Huo at NSRL and Mingqi Cui and Lijuan Sun at BSRF for

170 their assistance with initial measurements at NSRL and

171 BSRF. This work was supported by the National Natural Sci-

ence Foundation of China �Contract Nos. 60378021 and

10435050�, by National 863-804 Sustentation Fund, by the

Program for New Century Excellent Talents in University

�No. NCET-04-0376�, by the Royal Society, London �Contract

No. NC/China/16660�, and by the European Union

through the BESSY-EC-IA-SFS contract �BESSY-

ID.05.2.165�.

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