investigation of distortion and damage of molybdenum†silicon multilayer reflective coatings with...

Investigation of distortion and damage ofmolybdenum-silicon multilayer reflective coatingswith high-intensity ultraviolet radiation

Howard A. Bender, William T. Silfvast, Kenneth M. Beck, and Rajiv K. Singh

Studies are performed to determine an upper limit on the optical damage threshold of a soft-x-raymolybdenum-silicon multilayer reflective coating by the use of a 308-nm, 15-ns pulse from a Xe-Clexcimer laser in order to simulate the potential damage induced by the x-ray flux from a pulsedlaser-produced plasma. Experimental results yield a value of 0.26 J/cm 2 to produce visible signs ofdamage as determined by optical microscopy. Experiments are conducted first on silicon, as a referencepoint of a bulk material, and then applied to molybdenum-silicon in an effort to facilitate a theoreticalcomparison between a simple and a more complicated material. Theoretical predictions are inreasonable agreement with experimental results, but suggest that a lower value of 0.085 J/cm 2 mightcause significant thermal-induced damage.

1. IntroductionThe maximum soft-x-ray radiation flux that soft-x-ray multilayer reflective coatings can withstand with-out damage or distortion determines their appropri-ateness for certain applications. High fluxes wouldbe encountered in x-ray laser cavities, synchrotronradiation applications, and imaging with laser-produced plasmas (LPP's). The laser-producedplasma (LPP) x-ray source has become one of theleading candidates for soft-x-ray projection lithogra-phy (SXPL). Depending on the design of the SXPLsystem, multilayer mirrors or multilayer coated re-flecting masks could be subjected to damaging fluxlevels. The criteria for satisfactory performance aredependent on allowable tolerances for distortion ordeformation of the optical surfaces and thus theconcept of failure can vary.

Multilayer mirrors can fail by various means, includ-ing deformation induced by stress relaxation, interdif-

H. A. Bender and W. T. Silfvast are with the Department ofPhysics, Center for Research in Electro-Optics and Lasers, Univer-sity of Central Florida, 12424 Research Parkway, Orlando, Florida32826. K. M. Beck is with the Departments of Chemistry andPhysics, University of Central Florida, Orlando, Florida 32816.R. K. Singh is with the Department of Materials Science, Univer-sity of Florida, Gainesville, Florida 32611.

Received 16 July 1992.0003-6935/93/346999-08$06.00/0.o 1993 Optical Society of America.

fusion of layers, or mixing of layers by the formationof intermediate compounds.' In previous work, lat-tice expansion and x-ray reflectivity changes resultingfrom absorption of radiation were observed.2 Re-cently, real-time reflectivity decreases and wave-length shifts of the Bragg peak have been measuredunder high-intensity pulsed x-ray flux for applica-tions related to x-ray lasers.3

In SXPL, any damage to the primary optical compo-nent (i.e., a condenser optic) would have detrimentaleffects on the overall imaging system. Reflectivitydecreases would alter the flux reaching the resist andthereby alter the exposure time. Likewise wave-length shifts caused by lattice expansion (e.g., increas-ing the d spacing) would affect the spectrum and theamount of collected radiation thus degrading theimaging performance of a multiple-optic SXPL sys-tem.

Here we discuss some preliminary experimentalresults and theoretical predictions to determine thelimiting damage threshold for molybdenum-silica(Mo-Si) multilayers using high-intensity pulsed308-nm laser radiation. Preliminary tests were firstmade on bulk crystalline (c-Si) to establish a base linefor comparison with theory. Subsequently, damageexperiments were conducted on Mo-Si and thencompared with a theoretical multilayer model. Inconclusion, we discuss possible damage mechanismsand extrapolate the results to the soft-x-ray region.

1 December 1993 / Vol. 32, No. 34 / APPLIED OPTICS 6999

2. Silicon Reflectivity MeasurementsIn order to understand the thermodynamic proper-ties of the more complex Mo-Si multilayer structure,studies we first undertook on bulk c-Si. This wasdone to evaluate the technique of in-situ time-resolved reflectivity, and second, to establish theenergy density of 308-nm radiation required formelting bulk c-Si. The latter data are used (sectionbelow) to compare and test the accuracy of ourlaser-material interaction computer code.

The time-resolved optical reflectivity measure-ments are analogous to those of Auston et al.4However, earlier work was based on a 1.06-pm inci-dent laser pulse or heating pulse instead of the308-nm radiation from a Xe Cl excimer laser, asemployed in this experiment. The experimentalsetup is shown in Fig. 1. It consists of a He-Ne(632.8-nm) probe beam incident at 450 upon thesample and centered on the area to be irradiated.The reflected light is detected by the photomultipliertube. The heating pulse induces melting at thesurface for sufficiently high laser intensities. As wasfirst shown by Auston et al., we observed a reflectivityincrease of approximately 30% for the molten Si layerproduced by the absorbed energy. Figure 2 showsthe time-resolved reflectivity signal as recorded bythe oscilloscope. The duration of the elevated reflec-tivity (which is due to the liquid Si layer) wasobserved to be a function of the energy absorbed bythe sample above the critical energy required forinducing melting. The magnitude of the reflectedsignal remains constant, as would be expected for aconstant reflectivity, but the duration lengthens forhigher laser pulse energies. The time duration forwhich the layer remains molten was found to be asshort as 100 ns and as long as 500 ns for our range oflaser intensities.

The threshold energy to induce melting of this thinlayer, as deduced from the threshold to produce areflectivity change at 632.8 nm, was found to be 700mJ/cm2 for a 15-ns pulse duration. This corre-sponds to an intensity of 4.7 x 107 W/cm2. This

Filter

Sample[ Excimer Beam

Fig. 1. Schematic diagram of experimental configuration used fortho timo-resolved roflectivity measurements. PMT, photomulti-plier tube.

value is consistent with that of Narayan et al., whodetermined a threshold of 750 mJ/cm 2 for a 248-nm,24-ns pulse from a KrF excimer laser.5 However,that work relied on cross-sectional TEM examinationof the annealed samples to determine melt depth andsubsequent extrapolation of the data to determine thethreshold.

3. Molybdenum-Silicon Multilayer ExperimentsExperiments to determine the damage threshold forMo-Si and to observe melting consisted of focusingthe beam of a XeCl excimer laser onto a Mo-Simultilayer sample (spot diameter 1 mm). Thesample used was a 40-bilayer, 78-nm period Mo-Sicoating on a Si (100) substrate.6 The thicknesses ofthe Mo and Si layers were 37 A and 41 A, respectively.The output energy of the laser could be continuouslyadjusted by changing the input voltage, and exter-nally, by attenuating the beam.

Results of a series of experiments yielded a lowerlimit of 260 mJ/cm2 to produce visible signs of changeof the multilayer under inspection with an opticalmicroscope. This was also found to correspond to adecrease in the thickness of the multilayer coating.Figure 3 shows a photomicrograph of the changescaused by this energy density. A series of contactprobe profilometer measurements was made on theseirradiated areas that showed a nominal depression of500 A. No changes could be discerned under micro-scopic examination for energy densities lower than260 mJ/cm2 . Gross damage, i.e., complete delamina-tion of the layers, occurred near 500 mJ/cm 2 and isshown in the photomicrograph of Fig. 4. Profilome-ter measurements confirmed removal of the coatingdown to the Si substrate.

An attempt was made to melt the surface of theMo-Si and hence use time-resolved optical reflectivityto ascertain structural changes to the multilayer inreal time. However, after no reflectivity changeswere observed, it was deduced that the energiesrequired for melting Mo (Tm = 2800 K) were too highfor the underlying Si layers to withstand. No time-dependent reflectivity signal such as that for bulk Siwas observed up to energies great enough to causedelamination. This could be explained by consider-ing that the energies sufficient to melt Mo, whichwould thus create temperatures of 2800 K at thesurface, would cause explosive ablation of the Si as aresult of its reaching its boiling point of 2890 K.This is reasonable since the temperature at the firstSi layer, 37 A below the surface, should not be muchlower than the surface temperature as a result ofthermal conduction.

4. Heat Conduction CalculationsTo understand the thermal effects caused by pulsedlaser heating in the bulk c-Si and in the Mo-Simultilayer, we examine the one-dimensional heatflow in both cases. We attempt to determine whethertemperatures sufficient to induce melting are reached.The basis for our calculations relies on the assump-

7000 APPLIED OPTICS / Vol. 32, No. 34 / 1 December 1993

(a) (b)

(c) (d)Fig. 2. Oscilloscope traces of the increased reflectivity signals (flattop portion) for 632.8-nm light versus time. Photograph (a) shows anincident 308-nm laser pulse (top) and a reflected 632.8-nm probe signal (bottom) simultaneously. Additional traces (b), (c), and (d) showthe increasing duration of the flattop portion corresponding to the duration of the molten phase with increasing incident pulse energy.The time scale is 50 ns/div.

tion that thermal degradation caused by extremetemperatures in the multilayer is the dominantmechanism for damage. First, we use an analyticalapproximation for surface temperature produced bylaser heating to serve as a benchmark for our experi-mental results. Second, we present calculationsbased on a computer solution of the one-dimensionalheat conduction equation to investigate the thermalresponse of both c-Si and our multilayer compositemodel more accurately.7

A. Linear Diffusion ApproximationIt is possible to estimate8 the intensity I necessary toraise the surface of a pulsed laser-heated sample tosome temperature T by using the following linearheat diffusion relationship:

T rrCK 1/2

2A t / (1)

where A is the absorptance, T is the surface tempera-ture, At is the laser pulse duration, and C and K areheat capacity and thermal conductivity, respectively.To calculate the energy density necessary to raise thesurface temperature to the melting temperature forbulk c-Si the following values are used: A = 0.4 at

= 308 nm (calculated),9 T = 1687 K, C = 2.3J/cm 3/K, t = 15 ns, and K 0.25 W/cm/K. Thetemperature dependence of A is unknown but isexpected to decrease for liquid Si (i.e., increasedreflectivity), and therefore a larger intensity would beobtained. In addition, the thermal conductivityquoted above is an average for the approximatetemperature range 800-1685 K. Substituting thevalues given above into Eq. (1) yields I = 23 MW/cm 2

or an energy density of 350 mJ/cm2 to reach Tmelt atthe Si surface. The actual energy required for melt-ing the surface will be the sum of the energies to raise


(a)

(b)Fig. 3. Photomicrographs of the distortion of a Mo-Si multilayerat 260 mJ/cm2 for (a) a single pulse and (b) two pulses overlaid.

the volume to the melting point and the latent heat offusion.

In order to estimate the volume of material melted,we must calculate the melt depth. The thickness ofthe molten layer should be somewhere between theoptical absorption depth at 308 nm and the thermaldiffusion distance d = (Kt/C )1/2. The simple calcula-tion gives a range of 70 to 4000 A. The actual meltdepth has been calculated to be approximately 500 Awith our computer code SLIM (which is discussedbelow) for an energy density of 700 mJ/cm 2 (see Fig.5). Considering the heat of fusion for Si and thevolume of material, as calculated by the spot size andmelt depth, the additional energy or latent heat isfound to be negligible. Thus the approximationdetermined by Eq. (1) is within a factor of 2 of theexperimentally determined value of 700 mJ/cm2 ,which is within reasonable agreement, consideringthe uncertainty in the value of A and the averagednontemperature-dependent approximation to the con-ductivity.

B. Simplified Multilayer Composite Model

In order to examine the effects of laser heating on theMo-Si multilayer we have developed a simplifiedmodel of the multilayer structure. We have as-sumed that the 40-bilayer Mo-Si structure on Si canbe modeled as a two-component system comprisingan approximately 3200-A (80A x 40) compositelayer on top of the Si substrate. The properties ofthe composite layer represent an average of thethermophysical properties of amorphous Si (a-Si) andMo. The microstructural state of the interstitial Silayers has been confirmed to be amorphous by cross-sectional TEM studies and electron-diffraction analy-sis.10 To determine the average thermal conductiv-ity, we have used the harmonic average of the twoelements, Mo and a-Si. The values of the thermaland the optical properties" used in our calculationsare summarized in Table 1. The table shows thatthe thermophysical properties of c-Si are a strong

0.2 0.4 0.6 0.8 1.0 1.2

Fig. 4. Photomicrograph showing delaminationmultilayer caused by a flux loading of 500 mJ/cm 2.

of the Mo-Si

Energy Density (/cm 2)Fig. 5. Maximum melt depth as a function of energy density forcrystalline Si. Results from SLIM calculations are shown. Thethreshold density to induce melting occurs near 500 mJ/cm 2 .


2000

is 15000

i 1000

.E 500.H

00

77M't N

Cl:

Y1

Table 1. Values of the Thermal and the Optical Properties of c-Si, a-Si, and the Mo-Si Composite Used in Calculations

Parameters c-Si a-Si Mo-Si Composite

Thermal conductivity 1585/T"229 (300 < T < 1370 K) 0.0212,13 (300 < T < 1400 K) 0.04 (300 < T < 2000 K)(W/cm/K) 0.221 (1370 < T < 1685 K)

Melting point (K) 1685 1400 1400 (for a-Si)Specific heat capacity 1.98 + 2.54 x 10-4 T (see Ref. 14) 2.55 (300 < T < 2000 K)

(J/cm3/K) -3.68 x 104 T-2 (T < 1685 K)Reflectivity ( = 308 nm) 0.60 0.40 (Ref. 15)

(solid)Absorption coefficient 1.5 x 106 1.25 x 106 > 1.0 x 106

(cm-') (at 308 nm)

function of temperature. For example, the thermalconductivity varies over almost an order of magni-tude (1.6 W/cm/K at 300 K and 0.221 W/cm/K at1685 K) when raised from room temperature to itsmelting point. However, it is expected that thethermal conductivity of a-Si does not exhibit a signifi-cant variation with temperature compared with c-Si.12

With the above considerations taken into account,the relevance of our composite model can be discussed.Since this model essentially neglects the details of theperiodic nature of the structure, i.e., the multilayerstack, one must qualify the results that are obtained.Comparing the average K for Mo and a-Si at 1.0W/cm/K and 0.02 W/cm/K, we see that most of theheat conduction will be impeded by the a-Si layers.If one were to compare two bulk samples of Mo versusa-Si, the higher thermal conductivity of Mo wouldresult in lower temperatures farther into the samplein contrast with higher temperatures at shorterdepths for a-Si for the same input energy. Ourcomposite model uses an average conductivity of 0.04W/cm/K, which is weighted toward the lower valueof a-Si. Thus we would expect to get slightly highertemperatures that do not penetrate as deeply for thecomposite in comparison with an exact temperatureprofile solution that takes into account the periodicity.It is reasonable to suggest that the thermal responseof the multilayer, as far as heating is concerned, isdominated by the a-Si layers, which have a muchlower thermal conductivity.

To obtain realistic simulations, we must take thetemperature dependence of the thermophysical prop-erties into account. Yet for the composite Mo-Si,which is at elevated temperatures except for timesmuch shorter than the laser pulse duration, we canassume a constant average value without signifi-cantly sacrificing accuracy in the calculations. Also,because the thermal conductivity of a-Si does not varysignificantly from approximately 300 to 1000 K, ourconstant value assumption is even more realistic.In addition to the temperature-dependent thermalparameters of the multilayer structure, other compli-cations such as the time-dependent laser intensity,make an analytical solution of the heat conductionproblem difficult. Thus numerical methods havebeen adopted to obtain a solution for this problem.

C. One-Dimensional Numerical SolutionTo determine the time-dependent heat conduction inthe Mo-Si composite model, we have employed acomputer program called SLIM16-1 8 (simulation of la-ser interaction with materials). SLIM is designed tomodel effects of nanosecond laser pulses on complexmaterial systems. By employing an accurate im-plicit finite difference scheme with varying spatialand temporal node dimensions, SLIM can accuratelyand quickly determine the time-dependent thermalhistory of laser-irradiated material. This programcan take into account the temperature-dependentoptical and thermal properties of the solid, time-dependent laser pulse intensity and formation andpropagation of the melt or vaporization interfacesinduced by the laser radiation.

The results of these numerical method solutions onour composite model for energy densities of 0.05,0.075, and 0.1 J/cm2 are shown in Figs. 6, 7, and 8.These values were chosen because at energy densitiesgreater than 0.1 J/cm 2, extremely high temperaturesabove the melting point (1685 K) of c-Si occurred atthe surface and inside the composite model. Theabove range was found to be suitable to predictcritical temperatures near the reduced melting point(1400 K) of a-Si.

5. DiscussionExperiments conducted on Si indicated that thematerial melted under high-intensity pulsed radia-tion at 308 nm. SLIM calculations predicted that at700 mJ/cm2 a maximum melt depth of nearly 500 Awould be formed in bulk c-Si, as indicated in Fig. 5.Flux density calculations based on the approximationof Eq. (1) are also in reasonable agreement with theexperimentally determined threshold melting valuesfor c-Si. From the relative agreement between theoryand experiment for bulk c-Si, it is possible to considerthe effect on the Mo-Si multilayer.

As mentioned above, in analyzing pulsed heating ofthe composite model by using SLIM calculations, wefound that at energy densities near and above 0.1J/cm2 surface temperatures and temperatures wellwithin the multilayer model exceeded the meltingtemperature of c-Si and thus certainly exceeded themelting temperature of a-Si ( 1400 K).12 In Fig.


1000

4

2

300

Time (ns)

(a)

4)

aCU

S

E!4)

H

150

0 Distance (pm) 2.6

(b)

Fig. 6. (a) Surface temperature as a function of time, (b) tempera-ture profile versus depth for the composite model subjected to anenergy density of 0.05 J/cm2 . The curve separates the compositelayer from the c-Si substrate.

8(a), the surface temperature as a function of time isshown for an energy density of 0.1 J/cm2 . A maxi-mum surface temperature of 1598 K is achieved at t =20.2 ns. In all the calculations, we have used aGaussian input pulse with FWHM of 15 ns. Figure8(b) illustrates the temperature profile inside thecomposite multilayer model at t = 20.6 ns. Eventhough these temperatures may be exaggerated incomparison with the actual profile in the multilayerstack, which is based on the arguments given above,we still would not expect them to be in error by morethan 10-20%. Therefore at this energy density ex-tremely critical temperatures that may lead to melt-ing and resolidification and subsequent crystalliza-tion of the amorphous layers could be occurring.Considerable diffusion across the interfaces and theformation of silicides may also be occurring as thematerial reaches such elevated temperatures.

In Fig. 9, curve (a) we have plotted the surfacetemperature as calculated by SLIM for the energydensities of 0.05, 0.075, and 0.1 J/cm2 . A simplecurve fit shows a linear dependence of surface tem-perature on input energy density. Figure 9, curve(b), shows Eq. (1) with the values for the Mo-Sicomposite used as listed in Table 1. At the experi-mentally determined threshold of 0.26 J/cm 2 , extrapo-lation on Fig. 9, curve (a), yields nearly 3700 K andFig. 9, curve (b), yields 4500 K. Hence this result

1300

2

300

0 Time (ns)

(a)

150

0 Distance (,um) 2.6

(b)

Fig. 7. (a) Surface temperature versus time, (b) temperatureproffle versus depth for the composite model subjected to an energydensity of 0.075 J/cm 2. The curve separates the composite layerfrom the c-Si substrate.

predicts temperatures that are sufficient to causeboiling of the Si layers. This may explain the natureof the distortion shown in Fig. 3 and corroborateevidence of removal of layers.

Results of SLIM calculations indicate that at energydensities below the experimentally determined thresh-old there should be considerable thermal-induceddamage caused by melting of interstitial a-Si layers.If one accepts Tmelt = 1400 K for a-Si, then a betterestimate of the damage threshold based on the simu-lations and based on this measure would be approxi-mately 0.085 J/cm2, as obtained from the linearregression curve fit of Fig. 9.

6. Application of Results to the Soft-X-RaySpectral RegionAlthough this work was performed at 308 nm it ispossible to draw some conclusions concerning fluxlevel thresholds for wavelengths in the soft-x-rayregion. The values reported here suggest an upperlimit on the damage threshold for Mo-Si multilayers.This upper limit can be attributed to the underlyinga-Si layers that reach critical temperatures near theirmelting point. At these elevated temperatures, con-siderable diffusion can occur at the interfaces alongwith thermal expansion. Thus the threshold couldbe somewhat lower than the values reported here,


1300

1650

WiI

K

0 Time (ns)

(a)

W'/0m

000

0

0e

-~~ 4)

150 r.

300\

Distance (um) 2.6

4)~~~~~~~~~~~~ba~~~~

Fig. 8. (a) Surface temperature versus time, (b) temperatureprofile versus depth for the composite model subjected to an energydensity of the curve 0.1 J/cm 2. The curve separates the compositelayer from the c-Si substrate.

I-

4)4Z

0.4

Energy Density (J/cm 2 )Fig. 9. (a) Linear regression fit to the surface temperature valuesfrom SLIM calculations for given energy densities of 0.05, 0.075, and0.1 J/cm2 ; (b) surface temperature, as clculated from Eq. (1),which we plotted as a function of energy density using constantvalues for the Mo-Si composite model from Table 1 (zero energydensity temperature set to 300 K).

v'I0

0.8 '!'

In-

0.6 -~)eno0

04)Oe

0.2 S

01500

Depth (A)Fig. 10. Energy deposition versus depth into the Mo-Si multi-layer (not the composite model) for both 308 nm and 135.5 A.

depending on the amount of tolerable degradation ofthe layers.

Given that the absorption depth of x rays can beconsiderably longer than that of the UV, dependingon the wavelength, the distribution of incident energyas it is initially absorbed would be significantly differ-ent. At 308 nm most of the absorbed energy isdeposited to a depth of 55 A. However, at thesoft-x-ray wavelengths near 130 A, the absorptiondepth is of the order of 1000 A. This energy deposi-tion is plotted against depth into the Mo-Si multi-layer for both 308 nm and 135.5 A in Fig. 10.9 19 InFig. 10 a reflectivity of 60% at 135.5 A, 40% at 308nm, and an incident energy density of 260 mJ/cm 2 forboth cases are assumed. As can be seen, there is amuch lower amount of energy deposition per unitvolume near the surface for 135.5 A radiation.However, the figure also illustrates that the absorbedenergy penetrates farther into the multilayer. Eventhough the large initial temperature increases wouldnot occur, as has been shown for 308-nm flux loading,a relatively lower temperature would be distributedthroughout the entire multilayer depth. This couldlead to significant thermal-induced distortion that isdue to expansion and to the larger volume subjectedto the radiation. Thus it is possible that distortionby this mechanism could occur at lower thresholdsbelow the 85- to 260-mJ/cm 2 range.

However, we must qualify these statements bysuggesting that for broadband sources such as laser-produced plasmas, the absorption depth varies consid-erably over the short wavelength spectrum. Dam-age thresholds would thereby have to be determinedby averaging flux values over various wavelengths.Nevertheless, since 308 nm is in the wavelengthrange at which maximum absorption occurs, then thedamage threshold obtained here is most likely theminimum threshold.

7. Conclusion

From experiments conducted on c-Si it was shownthat laser intensities greater than or equal to 700


1.0

mJ/cm2 induced melting. The time-resolved opticalreflectivity signal for this molten Si layer was con-stant in magnitude but increased in duration forincreasing incident laser pulse energies. When thistechnique was applied to the Mo-Si coating, nochanges in reflectivity were observed. However, in-tensities greater than 500 mJ/cm2 caused severedamage to the multilayer, resulting in delamination.In effect, it was impossible to induce melting in themultilayer before catastrophic damage occurred.It was also determined that visible distortion of themultilayer along with corresponding removal of somelayers occurred at 260 mJ/cm 2 and thereby set anexperimental limit on the damage threshold.

Theoretical predictions were tested on Si to deter-mine the intensity necessary to induce melting. Asimple calculation based on linear diffusion yielded350 mJ/cm2 compared with the SLIM value of 500mJ/cm2 . Both are relatively close to our experimen-tal result of 700 mJ/cm2 . Based on our Mo-Sicomposite, predictions of surface temperatures by alinear diffusion approximation and the numericalmethod solution for the temperature distributionindicated temperatures that were much higher thananticipated for the experimental threshold flux load-ing of 260 mJ/cm2 . At these levels there is evidencethat layer removal is occurring by vaporization ofunderlying Si layers. It was found that tempera-tures near the melting point of a-Si are being achievedin the multilayer for energy densities as low as 85mJ/cm2 . Thus significant damage is most likelytaking place near or below these levels. Furtherexperiments should entail a detailed TEM cross-sectional analysis of the damaged areas.

In relating the results to the soft-x-ray region toestablish a reasonable estimate of the damage thresh-old, we must be careful to consider all possiblewavelengths that might be incident upon such aMo-Si coating. The wavelength-dependent absorp-tion depth can have considerable effect on the distri-bution of energy absorbed by the sample. Greaterabsorption depths (as would be the case for shorterwavelengths) could distribute energy in a largervolume and hence increase damage thresholds.However, at shorter wavelengths energy absorptionis significant well into the layers, and thus thermal-induced distortion caused by expansion and diffusioncould be the crucial damage mechanism. This mecha-nism would then be the limiting factor and therebylower thresholds. These effects will be investigatedin future theoretical and experimental studies.

The authors thank D. Windt of AT&T Bell Labora-tories for providing the multilayer sample.

References and Notes1. A. V. Vinogradov, P. N. Lebedev Physics Institute, Moscow,

Russia (personal communication, 1991).2. A. Zigler, J. H. Underwood, J. Zhu, and R. W. Falcone, "Rapid

lattice expansion and increased x-ray reflectivity of a multi-layer structure due to pulsed heating," Appl. Phys. Lett. 51,1873-1875 (1987).

3. B. McGowan, Lawrence Livermore National Laboratories,Livermore, Calif. (personal communication, 1992).

4. D. H. Auston, C. M. Surko, T. N. C. Venkatesan, R. E. Slusher,and J. A. Golovchenko, "Time resolved reflectivity of ion-implanted silicon during laser annealing," Appl. Phys. Lett.33, 437-439 (1978).

5. J. Narayan, C. W. White, M. J. Aziz, B. Stritzker, and A.Walthius, "Pulsed excimer (KrF) laser melting of amorphousand crystalline silicon layers," J. Appl. Phys. 57, 564-567(1985).

6. Sample provided by D. Windt of AT&T Bell Laboratories.7. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids,

2nd ed. (Oxford U. Press, Oxford, 1959), pp. 466-474.8. M. Sparks, "Theory of laser heating of solids: metals," J.

Appl. Phys. 47, 837-849 (1976).9. Optical constant data for Mo, c-Si, and a-Si at 308 nm obtained

from: E. D. Palik, ed., Handbook of Optical Constants (Aca-demic, Orlando, Fla., 1985).

10. T. D. Nguyen, R. Gronsky, and J. B. Kortright, "Cross-sectional transmission electron microscopy of x-ray multilayerthin film structures," J. Electron Microsc. Tech. 19, 473-485(1991).

11. Y. S. Toulakian, ed., Thermophysical Properties of Matter (IFIPlenum, New York, 1969).

12. H. C. Webber, A. G. Cullis, and N. G. Chew, "Computersimulation of high speed melting of amorphous silicon," Appl.Phys. Lett. 43, 669-671 (1983).

13. D. H. Lowndes, R. F. Wood, and J. Narayan, "Pulsed lasermelting of amorphous silicon: time-resolved measurementsand model calculations," Phys. Rev. Lett. 52, 561-564 (1984).

14. The specific heat capacity of a-Si has been estimated to beslightly higher than c-Si and only weakly temperature depen-dent (see Ref. 12 for more details).

15. Measured near-normal incidence reflectivity at 308 nm for theMo-Si multilayer sample.

16. R. K. Singh and J. Narayan, "A novel method for simulatinglaser-solid interactions in semiconductors and layered struc-tures," Mater. Sci. Eng. B 3, 217-230 (1989).

17. SLIM is a copyrighted computer program written by R. K. Singhand J. Viatella of the Department of Materials Science andEngineering at the University of Florida.

18. R. K. Singh and J. Viatella, "SLIM: A computer program forsimulation of laser interaction with materials during anneal-ing and ablation," in Proceedings of the Photon and LowEnergy Particles in Surface Processing, C. Ashby, J. H.Brannon, and S. Prang, eds. (Materials Research Society,Pittsburgh, Pa., 1991), Vol. 236, pp. 533-538.

19. Optical constant data for Mo and a-Si at 135.5 A obtainedfrom: D. L. Windt, "XUV optical constants of single-crystalGaAs and sputtered C, Si, Cr3C2, Mo, and W," Appl. Opt. 30,15-25 (1991).


investigation of distortion and damage of molybdenum†silicon multilayer reflective coatings with...

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