Despite considerable recent effort in research andtechnology, the limited reflectivity of soft-x-ray opticsremains an obvious restriction in the development ofsoft-x-ray instrumentation. This limitation is severeat near-normal incidence in the high absorptionwavelength range of � � 2.4–4.4 nm, the so-calledwater window. The advancement in the multilayer(ML) mirror optics in this energy range is still beyondthe desire, mainly due to the extreme demands oninterface roughness, limited material choice, andtechnical as well as physical limitations in the growthprocess. The chemical and optical properties of se-lected materials have a significant influence on re-
flectance at particular wavelengths. For example,three-dimensional (3-D) transition metals such as ScTi, V, and Ni can be used for high reflectivity normalincidence MLs by utilizing anomalies in optical con-stants at their respective absorption edges.
This work is an effort to study Ti-based multilayersthat can be used as focusing mirrors in tabletop in-struments with soft-x-ray sources based on transitionand Cherenkov radiation1 at the Ti–2p absorptionedge at E � 452 eV �� � 2.74 nm�. These multilayermirrors can act as reflecting optics both at normaland oblique incidence in any x-ray imaging instru-ment designed for this particular wavelength, e.g.,x-ray microscopes and x-ray telescopes. These mir-rors also have potential applications in synchrotronbeam line instrumentation as reflection polarizersand monochromators. Previously, Ni–Ti and W–Timetal systems were investigated by Mertins et al.2 fornear-normal incidence reflectance and transmittanceon the basis of the largest possible reflection coeffi-cients3 of Ni and W at their boundaries with Ti. In ourdesign, Cr was selected in combination with Ti be-cause of a maximum theoretical reflectance of �46%,calculated by the IMD code4 by use of Henke opticalconstants,5 for semi-infinite Cr–Ti multilayers, whichis comparable with the other material combinations
N. Ghafoor ([email protected]), P. Persson, and J. Birch are withthe Department of Physics, Materials Science, Thin Film PhysicsDivision, Linköping University, 581 83 Linköping, Sweden. F.Eriksson is with the Department of Astrophysics, Columbia Uni-versity, 550 West 120th Street, New York, New York 10027; F.Schäfers is with BESSY GmbH, Albert Einstein Strasse 15, D-12489 Berlin, Germany.
Received 12 April 2005; revised 25 June 2005; accepted 29 June2005.
just mentioned. Cr has a lower absorption coefficient� compared with Ni and slightly less contrast in thedispersion coefficient (��), which in turn gives aslightly lower reflectance from a single interface ac-cording to6
R �(��)2 � (��)2
4 . (1)
Although Ni–Ti gives a higher reflectance of approx-imately N � 250 bilayers (because of the higher con-trast in �) and thereafter saturates, Cr–Ti allowsmore than 250 bilayers to contribute to the reflectiv-ity, and hence the reflectivity increases beyond N� 250 because of the lower overall absorption.7Therefore, we explored the Cr–Ti material combina-tion to achieve normal-incidence ML mirrors withlarge N, giving as high reflectivity as possible nearthe Ti edge.
Even the best-selected material combination (ac-cording to the optical, chemical, and physical param-eters) exhibit in reality poor mirror performance,mainly restricted by the present inability to fabricateperfect ML interfaces. A highly reflecting mirror re-quires abrupt and sharp interfaces, preferably ofstructurally amorphous layers, throughout the MLstack. To have minimal accumulated roughness, im-proved interface flatness, and to avoid intermixing atthe interfaces, a novel technique of modulated ion-assisted growth was used in which each individuallayer was engineeredby use of two-stage ion assis-tance. Initially, during the first 0–0.4 nm growth ofeach layer, very low ion-assistance energy was usedto produce an abrupt interface without intermixing.In the final part of the deposition of each layer, higherion energy was used to create a dense layer with asmooth surface. A detailed description of the schemehas been presented elsewhere.8
Here we describe the interface-engineered growthof smooth Cr–Ti multilayers with abrupt interfaces.We focused mainly on the roughness evolution inmultilayers with an increased number of periods,quantitatively and qualitatively investigated by useof x-ray reflection (XRR) and transmission electronmicroscopy (TEM). Each bilayer is approximately1.4 nm thick with interface widths near 0.3–0.4 nm.Polarizing power of a ML designed for reflection atthe Brewster angle is also investigated for this ma-terial system.
A. Experimental Details
A dual-cathode dc magnetron sputter deposition sys-tem with circular magnetron sources having unbal-anced type-II magnetic configuration with oppositepolarities was used to deposit all the MLs. The two 75mm diameter magnetrons were mounted at off-axispositions and formed an angle of 25° with the sub-strate normal. An electrically isolated �-metal shieldbetween the magnetrons serves to protect the targetsfrom cross-contamination and also to extend the mag-netic field lines closer toward the substrate. This con-
figuration leads to strong magnetic fields from theouter poles extending into the chamber in which theycouple to a separate solenoid that surrounds the sub-strate. The solenoid consists of 220 turns of Kapton-insulated Cu wire ( � 2 mm) wound on a stainless–steel frame with an inner diameter of 125 mm. Thesolenoid current was constant at 5 Å with a directionthat couples the magnetic field of the solenoid to thatof the magnetron being used for deposition. Thesemagnetic field lines guide the secondary electronsfrom the magnetrons to the substrate region to en-hance ionization of the working gas in the vicinity ofthe growing film. This enhanced ion density plays acentral role in engineering smooth and abrupt inter-faces between growing layers. The substrate is biasedwith a negative voltage, Vs, to attract a high flux ofions from the surrounding plasma to the growing filmin a controlled manner with desired energies. A moredetailed description of the deposition system can befound in Refs. 9 and 10. All the depositions werecarried out by use of chemically cleaned Si(001) sub-strates (40 mm 20 mm 0.5 mm) mounted on theelectrically isolated substrate table, rotating at a con-stant rate of 60 rpm and placed at a distance of120 mm from each magnetron. The background pres-sure prior to deposition was �2 10�7 Torr and alow working sputtering gas pressure of �3 mTorr Arwas maintained during all depositions.
Plasma probe measurements were carried out toobtain a quantitative estimation of the average num-ber of Ar gas ions and their corresponding energytransfer to each deposited atom during each part ofthe growing Ti and Cr layers. Current–voltage char-acteristics of the plasma were measured in both re-gimes dominated by ion currents and electroncurrents by use of two different electrical probe ge-ometries; a flat stainless-steel probe (area Apr �1.77 cm2), and a cylindrical Langmuir probe (a tung-sten wire probe, 5 mm long, 0.25 mm diameter), re-spectively.
The MLs were intended for the first-order reflec-tions at near-normal incidence and oblique incidenceat the Brewster angle of �45°, just below the Ti-2pemission line. Simulations made with the IMD codepredicted optimal periodicities of � � 1.379 nm and� � 1.99 nm, respectively, and layer thickness ratiosof � � 0.5 for this wavelength. No separate cappinglayer was used, but growth was designed, on purpose,to end with Cr as the top layer because of its abilityto form a passive oxide layer over the highly reactiveTi.
Determination of deposition rates, measurements oflayer thickness, and optimization of ion energy as wellas multilayer design affirmation were all carried outby measuring Bragg-peak positions and�or intensitiesfrom low-angle x-ray reflectivity scans with a line-focus copper anode source (Cu-K , � � 0.154 nm op-erating at 0.8 kW). Taking into consideration thefirst-order reflection at high angles �5°, the effect ofrefraction could be neglected in applying Bragg’s lawfor determination of bilayer period �.
We took soft-x-ray reflectivity measurements atthe Ti-2p absorption edge by using an ultrahigh-vacuum polarimeter with an energy resolution of ap-proximately E��E � 2500 in both s and p geometriesat beamline UE56�1 at BESSY II. The exact positionof the Ti-2p absorption edge was determined by per-forming a so-called Bragg scan, for which the �–2�scans were made to vary photon energies around theabsorption edge. These two-dimensional scans werealso performed in both s and p polarization to deter-mine the polarizing power of the multilayers in-tended to work at the Brewster angle.
For structural characterization cross-sectionaltransmission electron microscopy (XTEM) was per-formed in a CM 20 UT microscope equipped with aLaB6 filament, operated at 200 kV with a point res-olution of 0.19 nm for structural characterization. Weprepared cross-sectional samples by mechanical thin-ning and polishing from both sides. Low-angle (4°) ionmilling in a BalTec RES 010 rapid ion etch that op-erated at 8 kV was used to make the samples electrontransparent. A final polishing stage that uses low-energy ions at 2 kV was applied to remove any amor-phous surface layer formed in the previous stage.
2. Results and Discussion
By use of magnetron-solenoid magnetic coupling a rel-atively large negative floating potentials of the sub-strate, Vf � �22 V, recorded for both materials,indicated the presence of a large number of secondaryelectrons and hence a large fraction of ionized Aratoms in the substrate vicinity. The ion-to-metal fluxratios � at the substrate for the two magnetrons were�Ti � 3.3 and �Cr � 2.2, as determined by electricalprobe measurements taken with the known deposi-tion rates � and assuming nominal densities � of thefilm as
� �ji
jn�
IiM�NA�Aprq
, (2)
where Ii is the ion current, M is the molar mass of theneutral atoms, Apr is the area of the probe, q is the ioncharge, and NA is Avogadros constant. The plasmapotentials were measured with a Langmuir probe fordeposition of the two materials Vp�Ti� � 1.69 V andVp�Cr� � �1.29 V. The energy of the ions that arrivedat the growing surface can thus be determined by
Eion � q�Vp � Vs�, (3)
where Vs is the applied substrate bias potential.The modulated high-flux low-energy ion-assisted
growth was optimized for average ion energies [Eq.(3)] as well as for initial layer thicknesses in the Tiand Cr layers by growing several different MLs thatcontain 20 bilayers with initial layer thicknesses be-tween 0 and 0.4 nm and with different ion energies inthe initial and final part of each layer varied in therange from 0 to �40 eV. The optimization was basedon the comparison of low-angle hard-x-ray reflectance
of the multilayer peak, the appearance of Kiessigfringes, and the profile of nonspecular rocking curves.We achieved the best MLs by using a 0.3 nm initialthickness with a 1.7 eV ion and 1.3 eV electron bom-bardment for Ti and Cr, respectively; the remainingparts of the layers were deposited with 23.7 and21.2 eV ions, respectively. Figure 1 shows the modu-lated substrate potential with respect to the plasmapotential during growth of each part of the Ti and Crlayers. Figure 1 also shows the various thicknessesand ion–electron energies involved.
The electron bombardment shown for the initialgrowth of the Cr layer is the result of a large second-ary electron irradiation from the sputtering processat the target in combination with a slightly positivesubstrate potential that attracts the electrons. Thishigh-flux low-momentum bombardment has no ad-vantage in displacing surface atoms and can there-fore result in increased roughness. Since thishappens in the initial part of each Cr layer, it can becompensated by 21 eV ion bombardment in the finalpart. Electron irradiation can cause a slight temper-ature increase of the growing film with a possiblethermal interdiffusion as a consequence. Once theseconditions were established, all the MLs were grownby use of the same optimal parameters.
The successful growth of Cr–Ti MLs with extremelythin layer thicknesses (�0.7 nm) is illustrated in Fig.2 by the hard-x-ray reflectivity curve along with asimulation for a multilayer with 100 bilayers. Thevisibility of 98 Kiessig fringes (distinct destructiveinterference fringes that are due to the finite thick-ness of the ML being 100 times the period) is clearevidence of a very high layer conformity. The individ-ual layer thicknesses dTi � 0.697 nm and dCr �0.690 nm, corresponding to a modulation period of� � 1.39 nm, were determined from simulations,which also revealed an average interface width of �
Fig. 1. Potential ion energy versus growth diagram for a singlebilayer of a Cr–Ti ML with a modulation period of 1.38 nm. Initial,d�initial�, and final, d�final�, thicknesses of individual Ti and Cr layersare labeled together with ion energies in the corresponding re-gions.
� 0.46 nm. Interface roughness, interdiffusion andintermixing are not separable in the simulations.
At-wavelength soft-x-ray reflectivity measure-ments made on the same sample by use of near-normal incidence photon energy of 452 eV �2.74 nm�,corresponding to the Ti-2p absorption edge, showed apeak reflectivity of 2.1% at � � 78.8° (Fig. 3). This isa high reflectance considering that the highest re-ported near-normal incidence reflectivity achieved atthis x-ray wavelength is 1.7% at 87° from W–Ti mul-tilayers and even lower for the Ni–Ti system.2
A simulation of the soft-x-ray reflectivity by use ofthe IMD code is shown along the experimental curve inFig. 3. It is in good agreement with the experiment aswell as the hard-x-ray reflectivity results. Hereagain we achieved the same layer thicknesses of dTi� 0.699 nm and dCr � 0.689 nm. However, the inter-face width of � � 0.33 nm measured here differs from
the hard-x-ray value of � � 0.46 nm. This differencein (Figs. 2 and 3) is due to different coherencelengths of the two probing x-ray wavelengths used,which consequently have different sensitivities to dif-ferent types of roughness. Short wavelength x rays (Cu-K � 0.154 nm) with a longitudinal coherencelength11 of �25 nm at glancing incidence are morereceptive to short range lateral roughness correla-tion, also known as jaggedness. On the other handsoft x rays at near-normal incidence, with 20 timeslonger and �1000 times larger transverse coher-ence length,11 are more responsive to long-range lat-eral correlation up to 10 �m, often called waviness.Soft-x-ray reflectivity is influenced by atomic scalejaggedness on length scales much shorter than thewavelength, in the same way as continuous intermix-ing influences hard x rays, i.e., reducing the absolutereflectivity without significant lateral or transversepeak broadening.
In Fig. 4 the TEM cross-sectional image is shownfor a ML that has a high structural order, as revealedby hard-x-ray reflectivity characterization and hasgiven the best reflectivity at near-normal incidence insoft-x-ray analyses, as illustrated in Figs. 2 and 3,respectively. The image shows the entire ML stack of100 bilayers with a modulation period of �� 1.39 nm. Although the atomic scale interface in-vestigation for roughness evaluation in such ex-tremely thin MLs is still not fully possible by electronmicroscopy, however, the highly ordered thin filmlayered structure is reasonably clear throughout thegrowth direction. The fiirst �30 layers in the stackexhibit smooth and abrupt interfaces without anysignificant roughness. Thereafter, a low spatial fre-quency roughness or waviness starts to evolve. Theroughness is correlated up to the surface, but indi-vidual layers with well-defined interfaces are clearlydistinguished even at the extreme end, near the sur-face. The occurrence of some large amorphous mate-rial areas comes from the ion milling preparationprocess.
The TEM observations immediately infer that localinterface widths are unaffected by the large numberof layers in the stack and the major cause of reducedML quality is an increased low spatial frequencyroughness with an increased number of bilayer-s.Therefore, to investigate the Cr–Ti ML system withrespect to the accumulated roughness with an in-creased number of layers, a series of four MLs with anumber of bilayers, N � 20, 50, 100, and 200, wasgrown in a row keeping the same deposition condi-tions and using the optimum design of modulatedion-assisted growth as described above (Fig. 1). Weaimed for the same ML period of � � 1.379 nm andlayer thickness ratio of � � 0.5 for all the samples. Allfour samples were characterized using grazing inci-dence hard x rays (� � 0.154 nm) as well as near-normal incidence soft x rays (� � 2.74 nm),investigating both specular reflectivity and non-specular diffuse scattering.
A quite similar behavior for the two probing photonenergies is shown in Fig. 5, where the specular re-
Fig. 2. Hard-x-ray reflectivity as a function of grazing incidenceangle 2� for a Cr–Ti multilayer with N � 100 periods. The presenceof distinct interference fringes is magnified in the figure. The in-dividual layer thicknesses and the average interface width ob-tained by simulations are given. The simulation was shiftedvertically for clarity.
Fig. 3. Reflectivity of a Cr–Ti ML close to normal incidence. Thepeak reflectivity is 2.1%, and from simulations we found an aver-age interface width of 0.33 nm.
flectivity is plotted as a function of the number ofbilayers for both hard and soft x rays. For hard x rays,the maximum intensity is evident for the ML withN � 100, and when the film thickness is increased bymore than N � 200, a slight decline in the reflectancecurve can be observed. In contrast, the soft-x-ray re-flectance already begins to reach a saturation limitfor N � 50 and shows only a 4% increase in reflec-tance when the number of bilayers is doubled to N� 100. Further addition of bilayers could not enhancethe peak reflectance and followed the similar trend ofdeclining as in the case of hard x rays. The fact thatthe reflectivity saturates before the theoretical opti-mal value for highest reflectivity and subsequentlydecreases on adding more bilayers is a clear indica-
tion of accumulated interface roughness evolution.Another fact, that the longer wavelength reflectancealready saturates at a thickness of N � 50 bilayerswhereas the hard-x-ray reflectivity saturates at ap-proximatetly 100, is a consequence of a higher sensi-tivity of interface roughness and a higher absorptionof soft x rays. The smoothest layers and best inter-faces located at the bottom of the ML stack near thesubstrate contribute much less to the overall soft-x-ray reflectance. Moreover, the earlier saturation inreflectivity for soft x rays also indicates the existenceof long-range lateral roughness (waviness). Hard xrays, with a shorter coherence length in the lateraldirection, are virtually insensitive to lateral rough-ness with characteristic length scales larger than ap-proximately 25 nm, whereas soft x rays probe up totens of micrometers.
A better understanding of the reflectivity varia-tions is obtained from analyses of the diffuse scatter-ing around the Bragg peak of the MLs with adifferent number of bilayers in the stack. Figure 6shows the soft-x-ray rocking curves (a) along withestimated interface widths (b). The two probing x-raywavelengths show similar behavior, and we thereforelimit the discussion here to the soft-x-ray measure-ments. An immediate conclusion based on qualitativejudgment of the rocking curve data, as shown in Fig.6 (a), is a decrease in the diffuse scattering width withan increased number of bilayers N. Since the width ofdiffuse scattering is inversely proportional to the lat-eral correlation length, it can be concluded that lowspatial frequency roughness increased in lateral di-rections when N increased.12 The presence of smoothand abrupt interfaces by use of high-flux low-energyion-assisted growth is evident for N � 20 bilayers,where almost no diffuse scattering is observedaround the specular peak position. An outcome of theaddition of 30 bilayers is a sharp increase in reflec-tance from 0.32% to 2.02%, and a signature of diffusescattering in the form of shoulders around the spec-ular peak start to appear. Since the intermixing atinterfaces is induced during the creation of the inter-
Fig. 4. Cross-sectional HRTEM micrograph of a Cr–Ti ML con-taining 100 bilayers with a nominal period of � � 1.39 nm.
Fig. 5. Reflectivity comparison of a series of MLs, with a differentnumber of bilayers of N � 20, 50, 100, and 200 at two probingwavelengths.
faces, intermixing is independent of the increasednumber of bilayers, and the accumulation of roughnessof the interfaces is therefore the cause of increasedpeak shoulders whereas local abruptness of the inter-faces is maintained throughout the layer stack.
The existence of increased accumulated roughness isfurther evidenced by a ML with N � 100, where aslight increase in peak reflectance and enhancedpeak shoulders appeared, and in multilayer N� 200, where the slight decrease in peak reflectanceis a consequence of a huge increase in roughnessaccumulation. An exact quantitative estimation ofthe roughness accumulating on the growing surfacesis a somewhat complicated task. Figure 6(b) showsthe evolution of an average interface width (calcu-lated by simulations of specular reflectivity by use ofthe IMD code), and nonspecular intensity with anincreased number of layers. The average interfacewidth, shown at the left axis, can be seen to increasefrom � � 0.26 to � � 0.41 nm as the N increases from20 to 200 bilayers. Nonspecular diffuse scatteringwas also estimated by measuring the ratio of inte-
grated intensities occupied by the nonspecular to thespecular part of the rocking curves and is representedin Fig. 6 by the dotted curve drawn at the right axis.For N � 20 this ratio is only 3%, indicating atomicallyabrupt and smooth interfaces without any accumu-lated roughness, but increases rapidly to 79% as Nincreased to 200 in the same way as the averageinterface width.
The accumulated roughness in these mirrors andthe accompanying saturation in reflectivity suggestthat the parameters for interface engineering wereoptimized with a too high emphasis on the local in-terface abruptness. This is an effect of using only 20bilayers for the optimization. It is possible that ahigher reflectance from mirrors with more than 100periods can be achieved if slightly higher ion assis-tance energy is used that promotes layer smoothnessat the expense of a slightly broader interface width.
A ML intended as an analyser for polarized syn-chrotron radiation was grown with 150 bilayers andcharacterized by use of the same polarimeter as forthe previous normal-incidence soft-x-ray measure-ments. Figure 7 shows the maxima of both s- andp-polarization angular reflectivity scans performed atvarious energies. The resulting curves exhibit theirmaximum just below the Ti-2p absorption edge withabsolute reflectivity of 4.3% for s polarization at42.2°. At the Brewster angle of �45°, the extinctionratio Rs�Rp was 266. A much higher extinction ratio isexpected if the reflectivity maximum is made to co-incide with the Brewster angle of �45°, which couldbe achieved by making a slightly thinner period of1.99 nm rather than 2.04 nm. This indicates thatCr–Ti MLs are also suitable as soft-x-ray polarizers.
3. Summary and Conclusions
Interface roughness hinders the achievement ofhighly reflective normal incidence soft-x-ray opticsparticularly in the high-energy region where inter-face width has a severe effect on the achieved reflec-tance. There are many kinds of roughness and it is
Fig. 7. Soft-x-ray reflectivity measurements of a ML that con-tains 150 bilayers intended for use at the Brewster angle. Bothin-plane and out-of-plane polarization reflectance is shown.
Fig. 6. (a) Soft-x-ray diffuse-scattering measurements at the first Bragg peak at near-normal incidence for a ML series with differentbilayers. Reflectivity is plotted on a log scale and was shifted vertically for clarity. (b) Roughness profile in terms of simulated interfacewidth (solid curve) and ratio of diffuse-to-specular integrated intensities (dotted curve) as a function of bilayers N.
not easy to gain control of, either during growth orwhen making analysis. We show here that interfaceengineering by modulated ion assistance with a highion-to-flux ratio can considerably overcome the prob-lem of intermixing Cr–Ti and to some extent produceabrupt interfaces, which is evident by x-ray reflectiv-ity and electron microscopy in Figs. 3 and 4. Theroughness evolution observation in the TEM imagesupports the conclusion drawn about roughness ac-cumulation from the x-ray reflectivity analysis. Atnear-normal incidence, at the Ti-2p absorption edgein the water window, a Cr–Ti multilayer with 100bilayers showed a high reflectance of 2.1%. However,the maximum reflectivity is limited by a correlatedlow spatial frequency roughness evolution with anincreased number of bilayers. Also the multilayerwith 150 bilayers exhibited a maximum reflectance of4.3% near the Brewster angle with an extinction ratioof �266. The obtained reflectances of 2.1 and 4.3%are comparable or higher than the reflectance ofstate-of-the-art condenser mirrors used in a tabletopmicroscope that operates at a longer wavelengthwhere more absorption occurs in the specimen.13 Wetherefore conclude that the Cr–Ti mirrors are of suf-ficient quality for implementation of an instrumentoperating at the Ti-edge.
These results clearly demonstrate the successfulimplementation of interface engineering by use of ionmodulation to make Cr–Ti a competitive system forx-ray mirrors.
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