Determination of layer structure in Mo/Si multilayers using soft X-ray reflectivity

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Determination of layer structure in Mo/Si multilayers

using soft X-ray reﬂectivity

M.H. Modi, G.S. Lodha*, M. Nayak, A.K. Sinha, R.V. Nandedkar

Synchrotron Utilisation Division, Centre for Advanced Technology, Indore 452 013, India

Received 20 August 2002; accepted 19 September 2002

Abstract

The soft X-ray reflectivity characterization of Mo/Si multilayer deposited by electron beam evaporation is discussed. The measurements are performed on Indus-1 synchrotron storage ring. The interdiffusion of two-layer materials in multilayer leads to the formation of interlayers. To understand the influence of interlayers and interfacial roughness on soft X-ray reflectivity profile, simulation studies are performed. The roughness parameter leads to reduction in peak reflectivity whereas the interlayers significantly change the reflectivity profile. For fitting the angle-dependent soft X-ray reflectivity profile, a four-layer model accounts for the interlayers formed at the interfaces. Asymmetry at the two interfaces, viz. Si-on-Mo and Mo-on-Si needs to be considered for a good model fitting of the soft X-ray reflected profile. The mechanism, which could lead to the formation of interlayers in Mo/Si multilayer is discussed.

PACS: 81.15.Ef; 41.50.+h; 68.65.Ac; 68.35.Fx; 68.35.Ct

Keywords: Multilayer; X-ray reﬂectivity; Interdiffusion; Soft X-ray; Synchrotron radiation

1. Introduction

Realization of normal incidence optical devices for imaging applications in soft X-ray, extreme ultra-violet (EUV) region have become feasible with the advent of multilayer optical elements [1,2]. It fulfills the requirement of high-reflected intensity and gives moderate spectral resolution at near normal incidence. Since the amplitude of reflected radiations add in phase upon reflection from successive interfaces, the intensity of reflected

light becomesN2_{times, where}_N_{is the number of}

periods in the multilayer [3]. Period length ‘d’ can be tailored according to the wavelength of interest depending upon application.

The efficiency of any optical devices, i.e. reflectance and resolution, is most sensitive to coating parameters [4]. The structural morphol-ogy, interface quality, interdiffusion and chemical reactivity significantly affect the performance in the soft ray region. Structural parameters of X-ray multilayers are mostly obtained using X-X-ray reflectivity, X-ray diffuse scattering and cross-sectional transmission electron microscopy [5–8]. Complete model fitting of soft X-ray reflectivity profiles for structural determination are scarce. *Corresponding author. Tel.: 731-488002; fax:

+91-731-488000.

E-mail address:[email protected] (G.S. Lodha).

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Most of the authors only report the reflectivity performance evaluations in soft X-ray region [9–11]. Ravet et al. [12] used soft X-ray radiation ðl¼126AÞ( for the analysis of B/Si multilayers. They have compared the results with X-ray measurements at l¼1:54A(: Values of thickness and roughness obtained from both measurements are in good agreement. Here, we report a detailed interface analysis of Mo/Si multilayer using soft X-ray reflectivity at l¼80A(: The complete angle-dependent reflectivity profile is fitted.

Mo/Si multilayer is one of the most efficient mirrors in the soft X-ray region of 130–300A( [7,11]. Due to its technological applications in soft X-ray projection lithography, it has exten-sively been studied. Various studies are carried out to understand the interface behaviors [13–15]. Different groups have investigated thermally induced structural modification [15–18]. Studies on sputter-deposited Mo/Si multilayers show that Mo layers are crystalline and textured, the Si layers are amorphous, and that the pure layers are separated by asymmetric interlayers composed of an amorphous mixture of Mo and Si [19]. Yakshin et al. [14] report the formation of interlayer in electron beam evaporated Mo/Si multilayer using hard X-ray reflectivity measure-ments. In spite of the importance of Mo/Si system in soft X-ray projection lithography, no detailed characterization using soft X-ray radiation is reported.

In this paper, the possibilities of structural analysis in soft X-ray region has been discussed by presenting a detail simulation study and a representative measurement for one Mo/Si multi-layer sample measured atl¼80A(:The soft X-ray measurements are carried out on Indus-1 synchro-tron source using reflectivity beamline. For a model fitting of the experimental data a four-layer model is considered to take into account the interlayers formed at the interfaces. Model fitting of the reflected profile in soft X-ray region suggests asymmetry in two different interfaces, viz. Si-on-Mo and Si-on-Mo-on-Si. This asymmetry at the two interfaces is in good agreement in comparison with previous studies on Mo/Si multilayers using high-resolution transmission electron microscopy [15].

The sensitivity of soft X-ray reflectivity technique to structural characterization, particularly to the four-layer model, is demonstrated by systematic simulation study. The reflectivity formulation is presented which has not been explored in the literature for soft X-ray study. The simulation study shows that the effect of interlayer is very different compared to statistical RMS roughness parameters. The interlayer, which takes into account the formation of compound on interfaces, causes the redistribution of reflectivity pattern whereas the roughness parameters reduce the reflected intensity.

2. Model calculation

The reﬂection and refraction taking place at the interfaces is basically governed by optical index contrast. The reﬂectance of multilayer system, consisting of N layers can be calculated using recursive formalism given by Parratt [20]. Let nj be the refractive index of the jth layer

deﬁned as

nj ¼1djibj; ð1Þ

wheredjandbjare the real and imaginary parts of

refractive index, also referred as optical constants. These optical constants for thejth layer consisting of Nj number of atoms per unit volume are

deﬁned as dj ¼ rel2 2p NjðZjþDf 0_Þ ; ð2Þ b_j¼rel 2 2p NjDf 00_; _ð3Þ

where re is the electron classical radius, Df0 and

Df00 are the resonance and absorption correction terms to atomic scattering factor arising from anomalous dispersion. For s-polarized radiation where the electric field vector is perpendicular to the plane of incidence, the Fresnel coefficient for reflection from the interface between j and jþ1 layer is given by Fj;jþ1¼ ER j Ej ¼kj;zkjþ1;z kj;zþkjþ1;z ð4Þ

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with kj;z¼ 2p lðn 2 j cos2yÞ1=2;

where Ej and ERj are the amplitude of electric

vector of incident and reﬂected waves on the interface j and jþ1 and in medium j: Recursion relation for reﬂection can be obtained with the boundary condition that tangential component of electric vector is continuous:

Rj;jþ1¼a2j

Rjþ1;jþ2þFj;jþ1

1þRjþ1;jþ2Fj;jþ1

; ð5Þ

whereaj¼expðikj;zdjÞis the amplitude factor for

half the perpendicular distancedj;the thickness of

jth layer. The final reflectivity from multilayer system, the ratio of reflected intensity to incident intensity can be written as

jR1;2j2 ¼ IR I0 ¼ E R 1 E1 2 : ð6Þ

The recursion method starts from bottom layer with the assumption thatRN;Nþ1 ¼0;since there is

no reﬂection from inﬁnite thick substrate.

If a continuous refractive index proﬁle is assumed between layers j and jþ1 with error function, then Eq. (5) is to be multiplied with the factor [21]

Sj¼expð2kj;zkjþ1;zs2jÞ; ð7Þ

where sj is the root mean square deviation of

interface atoms with respect to a smooth interface. Using this formalism reﬂectivity pattern is simu-lated for a given multilayer system. The ﬁtting of the measured data yields the information about layer thickness, interface roughness and composition.

In any real multilayer system the interfaces are imperfect due to interdiffusion and reactivity of materials. Because of these imperfections the reflectivity pattern gets modified. Imperfect inter-faces can be dealt either by statistical approach or multiple layer model with the incorporation of interlayers between the two-layer system. In statistical approach, the Fresnel reflection coeffi-cient is multiplied by a factor given in Eq. (7). In this case, the composition gradient at the inter-faces is usually modeled using either sinusoidal, linear, step profile, or error function [22]. In the

case when a compound material is formed at the interface, multiple layer model gives a better model fitting of the reflected profile than the model based on statistical approach. In this paper, we show that a four-layer model gives better experimental fit to the soft X-ray reflectivity data on Mo/Si multilayer than a statistical model. In Fig. 1 the model of the four-layer system is shown to describe the forma-tion of interlayers at the imperfect boundaries due to interdiffusion. The thickness of the interlayers separating the layers of materials ‘1’ and ‘2’ at two different interfaces are d12 and d21: Hence, the

period of the multilayer isd ¼d1þd12þd21þd2:

The thickness of the interlayersd12andd21may or

may not be same. If it is not the same, then this asymmetry significantly modifies the reflectivity profile. We now discuss the presence of interlayers and the effect of asymmetry on the soft X-ray reflectivity pattern.

2.1. Influence of interlayer

The reﬂectivity pattern in multilayer is modu-lated by structure factorðGÞ:In an ideal multilayer it is deﬁned as the ratio of thickness of high refractive index material to the period of multi-layer, i.e.d1=ðd1þd2Þ:The modulation of intensity

of Bragg peaks depends on G ratio. The weight factor of interlayer d12 and d21 decides the G

ratio in the four-layer model system [14]. The presence of interlayers significantly affects the reflectivity patterns as shown in Fig. 2. The reflectivity curves for Mo/Si multilayer with and without interlayers are simulated for soft X-ray radiationðl¼80AÞ( :We consider the five periods Fig. 1. Schematic of four-layer model assumed for Mo/Si multilayer is shown. The interlayers formed due to intermixing of Mo and Si at the imperfect boundaries are presented by crossed region.

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of Mo/Si coated on ﬂoat glass substrate. The thickness of Si and Mo layers are assumed to be 59 and 30A; respectively in case if there are no( interlayers present. As the thickness of interlayer increases the corresponding thickness is subtracted from Si and Mo layer thickness to keep the period of the multilayer constant. In addition to inter-layer, which takes into account the compound formation, the interface roughness of 5.5A is( assumed for continuous composition changes. The interlayer is assumed to be of MoSi2. The motive

behind these numbers taken for simulation is to match these with our experimental parameters as will be discussed later. From Fig. 2 it is seen that as the thickness of the interlayer increases the reflectivity of Bragg peak decreases as well as the position shifts to the higher angle side due to the change in refraction correction term. In Fig. 3, for comparison, the reflectivity curves are simu-lated for increasing the roughness with no-inter-layers. In case of increasing roughness (Fig. 3), the reduction of reflectivity is observed without affecting the distribution of intensities of indivi-dual peaks. It is to be noted here that the incorporation of interlayer leads to redistribution

of peak intensity, which is not the case when no interlayer is present and only roughness increases.

2.2. Effect of asymmetry

The thicknesses of interlayers for two interfaces, viz. Si-on-Mo and Mo-on-Si, may not be the same which lead to an asymmetric behavior. The degree of asymmetry is a sensitive parameter. In addition to material combination, it may depend on deposition techniques and ambient conditions. Different authors [14–16] have reported the asym-metric nature of interlayers for Mo/Si multilayers grown in different conditions. The interchange of two interlayer thicknesses, i.e. dSi-on-Mo and

dMo-on-Si affects the reﬂectivity pattern. The effect

of interchanging the thickness of asymmetric interlayer is simulated at 80A wavelength, and is( shown in Fig. 4. Where curve A corresponds to thickness dSi-on-Mo and dMo-on-Si 8 and 10A,(

respectively. Curve B corresponds to interchanging of these thicknesses for two interlayers. This interchange leads to change in peak reflectivity of B20% and a steep fall in reflectivity just before Fig. 2. Effect of interdiffused layer thickness upon reflectivity pattern of Mo/Si multilayer is calculated. As interdiffused layer thickness increases the Bragg peak reflectivity decreases.

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the Bragg peak in case B:This may be understood by the standing wave-ﬁeld intensity distribution inside the multilayer. The position of nodes and anti-nodes of standing wave ﬁeld leads to

significant change of reflectivity [23]. These simu-lation results for l¼80A suggest that the( interlayer formation and its asymmetric nature can be picked up in soft X-ray measurements. Fig. 3. Effect of statistical roughness parameter on reflectivity pattern is simulated. The increasing roughness causes the reduction in whole reflected intensity.

Fig. 4. The calculated spectra to see the effect of interchanging the thickness of interlayers. If the thickness of two interlayers are interchanged then the reﬂectivity changes byB20%.

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3. Experimental

Mo/Si multilayers have been deposited using an ultra-high-vacuum (UHV) electron beam evaporation system [24] at a base pressure of 4109mbar. The system has three electron guns of 3 kW power. Multilayer samples have been deposited on good-quality ﬂoat glass substrates. Prior to deposition, substrates are ultra-sonically cleaned with acetone. Proper care has been taken to avoid any contamination during the loading of substrate after cleaning.

Soft X-ray reflectivity measurements are carried out on Indus-1 synchrotron facility using reflectiv-ity beamline [25]. The beamline delivers radiation in the range of 40–1000A with high flux and( moderate spectral resolution using a toroidal grating monochromator. Various absorption edge filters are provided in the beamline to suppress the higher order contamination from the monochro-mator. The experimental station operates in high vacuum environment (B5108mbar). To main-tain UHV environment of 1109mbar pressure of beamline, a differential pumping system has been incorporated between the experimental sta-tion and the beamline.

The goniometer assembly of reflectometer sta-tion comprises of two rotary stages and one linear stage. Two rotary stages are used to accomplish the standard y22y scan for normal reflectivity measurements. In the exiting configuration, the theta-stage movement of the goniometer was restricted to B451_{. In addition, both stages can} be moved in coupled and uncoupled modes to carry out different modes of reflectivity, i.e. detector scan, rocking curve scan, etc. The linear stage is employed to bring the sample in and out of direct beam, to facilitate the direct beam monitor-ing. This feature is useful for normalization of reflectivity data with incident beam intensity. Sample and detector can be aligned with a precision of 0.011. Silicon XUV photodiode has been used to monitor reflected beam intensity. The current output of detector is recorded using Keithley 485 Pico ammeter. All motions in reflectometer system are computer controlled. The data acquisition and motion control pro-gramme is written in C++ with a visual interface for user-friendly operation.

The detail ﬁtting of measured reﬂectivity data is carried out using the Parratt formalism discussed in Section 2. Since in soft X-ray region the optical

Fig. 5. Reﬂectivity spectra for an Mo/Si multilayer with ﬁve bilayers and a bilayer period of 89A (59( A Si/30( A Mo) measured at(

l¼80A(:Measured curve is represented by open circles. The dotted line ( ) shows calculated spectrum by assuming two-layer model. The best ﬁt represented by continuous line is obtained by assuming an interdiffused layer in between pure layers of Mo and Si.

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constants vary significantly, hence along with the thicknesses and roughnesses, the optical constants are also taken as fitting parameters. Optical constants from Henke’s tabulated values [26] are taken as a starting guess for fit.

4. Results and discussions

Angle-dependent reflectivity spectrum of Mo/Si multilayer deposited on a float glass substrate, of period 89A (30( A Mo/59( A Si), with five-layer( pairs and 0.33 G is shown in Fig. 5. Measured spectrum is shown by circles whereas the dotted line represents calculated spectrum assuming a two-layer model with no interdiffused layer, and the continuous spectrum assuming four-layer model as discussed earlier. It is clear from the figure that in the case of the two-layer model the disagreement between the calculated and the measured spectrum is quite distinct, whereas the four-layer model gives the best fit. The best fit is obtained with interlayer thicknesses of 8 and 10A( for Si-on-Mo and Mo-on-Si interfaces, respec-tively. The quantitative numbers for thicknesses, roughnesses and optical constants deduced from the fit are given in Table 1. The values of optical constants for silicon differ significantly from the tabulated values whereas the optical constants for molybdenum MoSi2 mixing layer are slightly

different from tabulated values, which can be attributed to density change. The variation of silicon optical constants particularly in high absorption region has been reported earlier [27]. In Fig. 6a, the proﬁle of the real part of optical index is plotted, as obtained from ﬁtting of experimental data. The minima and maxima

Table 1

Parameters of the ﬁt atl¼80A(

Layer Thickness (A)( Roughness (A)( Indicesa(103) Absorptiona(103)

Si 50 5.5 10.78 (6.34) 8.4 (14.49)

Si on Mo 8 5.5 12.61 (14.01) 15.42 (15.42)

Mo 21 5.5 18.18 (20.21) 3.69 (3.69)

Mo on Si 10 5.5 12.61(14.01) 15.42 (15.42)

Float Glass N 3.0 10.62 (10.62) 8.13 (8.13)

a_{In braces the tabulated values of optical constants from Henke et al. [26].}

Fig. 6. Optical index profile obtained after fitting of the reflectivity data. (a) Maxima and minima correspond to layers of pure Mo and Si, respectively. In between are the interface region arises from the formation of silicide. (b) Expanded view of one period in multilayer. The dashed (- - - -) line represents actual profile used for fitting assuming interlayers with Gaussian roughness. The dotted ( ) line represents the profile without Gaussian roughness. Interface width for Si-on-Mo and Mo-on-Si is shown with clear asymmetry on two sides.

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correspond to layers of pure Si and Mo, respec-tively. Interlayer region arising due to the combi-nation of silicide interlayers and layer roughness is shown by dashed line (- - - -) in Fig. 6b, whereas the dotted line ( ) represents the proﬁle without the Gaussian roughness. The interlayer regions as marked in Fig. 6b on two sides are asymmetric.

Earlier Stearns et al. [15] have shown in their high-resolution electron microscopy study that, in sputter deposited Mo/Si multilayer, pure layers of Mo and Si are separated by an amorphous interlayer of Mo–Si mixture. The work of Yakshin et al. [14] show the formation of silicide at interfaces in electron beam ion assisted Mo/Si multilayer. For ion-assisted energy of 300 and 2000 eV, the interlayer width of silicide layer at two interfaces are slightly different. In the case of 300 eV ion energy, the width of two interlayers are the same (8A).( For 2000 eV ion energy, the two widths are 11 and 13A for interlayers at Si-on-Mo and Mo-( on-Si interfaces respectively (multilayer period

d ¼75:4A). Feigl et al. [16] also reported the( asymmetric nature of two interlayers in sputter-deposited Mo/Si multilayer. The thickness of two interlayers reported is 6 and 10A for a multilayer( period of 65.8A (0.44( G). Different mechanisms have been proposed to explain the formation of interlayers and its asymmetry in Mo/Si multi-layer [13,28]. Liwen Wu et al. [13] have suggested a thermally activated model by considering the different thermal conductivities of the deposited Mo and Si surfaces. The thermal conductivity of Mo is higher than that of amorphous Si, so the heat produced by the Si adatoms on Mo surface will diffuse quickly compare to that for depositing Mo on Si surface. This leads to a lower local temperature in Si-on-Mo case and hence less probability for diffusion. This will lead to a thinner interlayer compared to Mo-on-Si case. The ratio of two interlayer thicknesses may also depend on the kinetic energy of the deposited particle. Morgan et al. [28] in their molecular beam dynamics study have tried to explain the thickness asymmetry of two interlayers. The different degree of penetration and interdiffusion of the ad atoms

during deposition are basic factor behind the asymmetry. Stearns et al. [15] have suggested that the Mo atoms can get embedded more easily into the relatively open and disordered lattice of amorphous Si than are the Si into the more compact crystalline Mo lattice. If the kinetic energy model is to play a role behind the formation of interlayers, then the results of electron beam deposited Mo/Si multilayer should have been different. Since, the formation of interlayers could be found in both electron beam deposited and sputtering deposited Mo/Si multi-layers where the kinetic energy of ad atoms are quite different. So we conclude that the thermally activated model should be responsible for the formation of interlayers and its asymmetric width in Mo/Si multilayer.

It is clear from earlier data on Mo/Si multi-layer that the intermulti-layers are formed during deposition and its asymmetric nature has been explored by various techniques. Our present work on soft X-ray reﬂectivity also conﬁrms the interlayer asymmetry in Mo/Si multilayer. This gives yet another proof of invocation of asymmetric interlayer model in Mo/Si multi-layer.

5. Conclusions

Mo/Si multilayer of period 89A is characterized( for structural parameters using soft X-ray radia-tion of Indus-1 synchrotron facility at reflectivity beamline. The detailed analysis of reflectivity data shows that the Mo/Si multilayer comprises an additional interlayer of Mo–Si in addition to a pure layer of Mo and Si. The interlayers formed at two interfaces, viz. Mo-on-Si and Si-on-Mo, are asymmetric. The simulation study reveals that the effect of interlayer is very different compared to that of statistical RMS roughness parameters. The roughness parameter leads to reduction in peak reflectivity only, whereas the interlayer effect redistributes the reflectivity pattern. Our soft X-ray characterization results are consistent with the results reported on Mo/Si multilayer characterized by hard X-ray radiation and transmission electron microscopy.

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Acknowledgements

The authors are thankful to Dr. K.J.S. Sawhney for helpful discussions. We acknowledge R.K. Gupta and M.N. Singh for their contributions in running the beamline.

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