tungsten multilayers for X-ray-UV optics deposited by laser evaporation: Preparation and interface characterization

Thin Solid Films, 203(1991) 77 86 PREPARATION AND CHARACTERIZATION

77

C A R B O N / T U N G S T E N M U L T I L A Y E R S FOR X - R A Y - U V OPTICS D E P O S I T E D BY LASER EVAPORATION: P R E P A R A T I O N A N D INTERFACE CHARACTERIZATION PH. MACQUART, F. BRIDOU AND B. PARDO lnstitut d'Optique, L. A. 14 du CNRS, Centre Universitaire d'Orsay, Bat. 503, B.P. 147, 91403 Orsay Ckdex (France) (Received October 2, 1990; accepted February 28, 1991)

Using the laser ablation method thin films were evaporated in order to obtain W/C multilayers for X-ray-UV mirrors. The parameter determinations (thickness, roughness, complex index), were made by analysing the reflectivity curve (at 0.154 nm) and fitting with a computer program. The roughness (0.4 nm) of the C - W interface was low enough for a good reflectivity to be obtained. Disparities in thickness were observed.

1. INTRODUCTION

In order to make X-ray-UV interference mirrors, which function with a close to normal incidence, we have tried to create periodic multilayers with thin layers of two materials: a high index material for reflectivity, and a low absorption material for spacing the other in order to obtain the required periodicity. In particular, for Xr a y - U V mirrors working at 2 = 4.47 nm, the best combination of materials is W/C. The classical method of deposition is thermal evaporation. Here, we have used laser ablation similar to that used some years ago by Gaponovl.The main results of the two deposition methods will be compared. We have shown in preceding papers 2' a that the thin film density obtained by laser ablation is approximately equal to the bulk value. Consequently we hoped to obtain a better reflectivity than that obtained by classical thermal evaporation processes, where the density is always lower than the bulk value. Another important parameter is the roughness of different interfaces in multilayers. Chauvineau 4 has shown that, for amorphous materials during thermal evaporation, this parameter increases as the square root of the deposited thin film thickness of a given material. Our simulations tend to prove that by the laser ablation method we obtain constant roughness on a given type of interface layer. A good reflectivity of the multilayer for X-ray-UV optics can be obtained when the roughness of one interface is low.

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Prt. MACQUART,F. BRIDOU,B. PARDO

78 2.

LASEREVAPORATIONMETHOD

Pulsed laser ablation is used to produce thin films in an ultrahigh vacuum system. The characteristics of particles obtained by this vaporization technique are different from those obtained by classical thermal evaporation processes. A pulsed N D - Y A G laser gives a power density larger than 108 W cm -2 on the target. A plasma is created and evaporated particles are deposited on a substrate (Fig 1). SUBSTRATE~

YAG LASER

WINDO~ W ~ TARGETS 7 QUARTZ ./.

VAEUUH SYSTEM ~ i

Fig.1.

ii

Laser evaporation:experimentalprinciple.

The characteristics of the laser are as follows: wavelength, 1.06 ~tm; bandwidth, 7 0 m - 1 ; frequency, 30Hz; pulse duration, between 12 and 15 ns; m a x i m u m pulse energy, 0.8 J; beam diameter, 7 mm; energy stability, 2~o. The laser beam is focused onto the targets by means of an optical system which consists of divergent and convergent lenses, and a polished copper mirror. The substrate is placed 20 cm from the targets parallel to the surface of the targets and in the same axis. The deposited thickness is controlled by a quartz microbalance which is located as near to the substrate as possible. The system is computer controlled and pumped cryogenically to a residual pressure of approximately 1txPa. To scan the whole of their surfaces, the targets are moved backwards and forwards, with the convergent lens moving perpendicular to this direction of motion. After an experimental run, the ablated target surface obtained is a 1 0 m m × 8 m m rectangle. The evaporation rates are 4.7 × 10 4 nm pulse -1 for tungsten and 8.4 × 10 -4 nm pulse i for carbon; that is, 0.02 nm s - 1 and 0.38 nm s - 1 respectively. 3.

STACKPARAMETERCHARACTERIZATION METHOD

After fabrication, we use an 0.154 nm X-ray goniometer in grazing incidence mode to establish the reflectivity of the sampleS' 6. The principle of the goniometer is shown in Fig. 2: the sample is positioned on a fixed stand, and the source unit and the detector are fixed on arms which move around the same axis. The reflectivity curve is obtained by varying the grazing angle while tracking the reflected beam. The angular accuracy is less than 0.005 ° .

C/W MULTILAYERSFOR X-RAY--UV OPTICS

79

[ounfer

Attenuator

UF k Cu

-----7

-

Slit

6RX2 Fig. 2. X-ray goniometer (diagrammatic).

3.1. Theoretical reflectivity computing: the matrix method" 8 The reflection of waves by stratified media can be computed using the so-called matrix formalism. One considers vectors the components R and T of which are the complex amplitudes of reflected and transmitted plane waves:

The matrix 1~ is the product of matrices of two types: the dioptre crossing (DC) type l~; thepropagation type P. (a) The DC-type matrix involves the components of the wavevectors in the two media. For instance, in the case of transverse electrical polarized electromagnetic plane waves, a DC matrix has the following form:

+__

1

k23-

k,± k2±

l_k,±l k2±

/ /

k2±J

k± denotes the normal component of the wavevector. The subscript indexes the medium. When the interface is rough this matrix has to be modified by the so-called Debye-Waller (DW) factor. This D W factor simply multiplies the extra-diagonal components of the DC matrix: DW factor = exp(-- 8/z2o'2kl±k2± ) where a is the r.m.s, roughness. In the case of transverse magnetic polarization the k± component has to be divided by the squared complex index. In the case of X-rays, the indices are very close to 1, so that the correction is not necessary, particularly when the grazing angle is far from Brewster's angle.

80

Prt. MACQUART, F. BRIDOU, B. PARDO

(b) Propagation matrices are diagonal and have the simple form

p=[exp(~kld)

0 exp(-ik±d)]

Here d is the thickness of the layer and i is the square root of - 1. Taking into account the fact that the initial vector in the substrate has a null reflection component, the reflectance intensity coefficient I is computed as

I-

RR* TT*

The reflected intensity is obtained by multiplying I by the incident number of particles.

3.2. Fitting The parameters of a multilayer (index, thickness, roughness) are obtained by fitting the curve of reflectivity vs. grazing angle. The fitting is calculated by computer code 9 using Box's method 1°. The code is written in the F O R T R A N language for the 9375/60 IBM computer of the Institut d'Optique. This machine works with a 32-bit microprocessor, and is able to perform 0.4 million statements on double-precision real numbers every second. 4.

DETERMINATION OF THE MULTILAYER PARAMETERS

When the reflectivity curve obtained for a multilayer does not correspond to a perfect theoretical case with identical parameters for each period, it is very difficult, in spite of the computer program, to fit this curve automatically and to retrieve a large number of parameters (three parameters for each layer). Therefore, to simplify the search, we began to study simple stacks. The results can be extrapolated for multilayers.

4.1. Study of simple C~W stacks We first studied a basic stack: a silica glass substrate covered with a carbon layer, followed by a tungsten and a carbon layer on one half as shown in Fig. 3. ZONE B

ZONE A

-

CARBON

03

n*2 -

o"2

TUNGSTEN CARBON

-

ol

-

oO

n°1

S I L I C E SIJBSTRATE

Fig. 3. Diagram of the simple stack.

81

C / W MULTILAYERS FOR X-RAY--UV OPTICS

The carbon layers numbered 1 and 2 are made to the same thickness, with evaporation parameters the same in both cases. The latter condition makes it possible to reduce the number of parameters for the computer program. The fit of the experimental reflectivity curve of the free substrate gives the roughness a0 of silica glass. In the same manner, we found the roughness oftrl of carbon (zone A) and then the roughnesses tr 1, 0 2 and 0"3 of the three-layer interface (zone B). Results are summarised in Table I. TABLE I ROUGHNESSRESULTSCORRESPONDINGTO THE SIMPLESTACKS(FIG. 3) Layer i

Roughness ~ri (nm) for the following zones

0 1 2 3

Zone A

Zone B

0.7 0.5

0.7 1.2 0.3 0.5

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oo

o o oI

I

oooo"looooolz @ o?oooo?ooo 0

0

0

0

0

0

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I

0

0

0 i

I

io o o oi-I o o o o

/oooo 10000

iooooooooo IO 0

0

0

0

0

0

0

0

Fig. 4. Index profile ofa W ~ interface.

Interface roughness can be assimilated to a transition layer between the two layers (Fig. 4), where the index varies as the error function between nl and n2. The roughness tr 1 is 0.5nm in zone A (free carbon) and 1.2nm in zone B (tungsten-carbon interface). This difference may be caused by the existence of a transition area between carbon and tungsten that produces the same effect as interface roughness in grazing X-ray reflectometry 11. As this transition zone does not appear at the following interface (carbon-tungsten), it is possibly formed with the implantation of energetic tungsten particles (atoms or ions) in the carbon substrate during deposition. We have

82

Prt. MACQUART, F. BRIDOU, B. PARDO

calculated that tungsten atoms having a kinetic energy of 100 eV penetrate into the carbon substrate to an average depth of 0.75 nm. The roughness value is also 0.75 nm. This fact appears to confirm the predicted implantation of tungsten particles in carbon. On the contrary, the tungsten layer surface covered with carbon has a low roughness (0.3 nm) which confirms the hypothesis that the excess kinetic energy of particles can induce a reduction of surface roughness by rearranging condensed atoms. Similar layers made by classical thermal evaporation have a greater roughness (about 1 nm). Taking into account the low roughness of the carbon-tungsten interface we assume that the kinetic energy of carbon particles incident onto the tungsten is not sufficient for their implantation. The small tungsten surface roughness has been confirmed by the study of the reflectivity curve of one simple tungsten layer on a float glass substrate, tested immediately after its production to avoid superficial oxide. We found tro ~ 1 nm for the substrate and al ~ 0.5 nm for the surface material.

4.2. Multilayer study Using these results, we have tried to fit the W/C multilayer reflectivity curves on the assumption that the observed phenomena in the three-layer stack C/W/C are the same in the multilayer. We have supposed that interface roughnesses are constant during the evaporation, but we have introduced a dissymmetry between C/W and W/C layer interfaces. Nevertheless, the assumption that the stack is strictly periodic was shown to be false. We therefore had to assume a slight disparity in the thickness between the different layers. Modification of the surface state of the carbon target possibly influences the repartition of the evaporated material. In the vacuum system the substrate and the quartz microbalance are not in the same place, and for the same variation of the quartz microbalance, the thickness deposited on the substrate is not the same. The disparity in thickness may not only be random but also be continuously changing during the deposition. These hypotheses allow us to suppose that the variation in thickness, to a first approximation, is a linear function of the layer number. Thus, we assumed that the layer thickness decreases linearly. The laser ablation of tungsten induces no significant modification on the target surface; therefore we considered that the tungsten thickness is constant in the multilayer. Furthermore, we assumed that the increase in roughness is small enough to be considered as being linear. Table II gives the different values calculated by the computer for the roughnesses and the indices of different layers in the W/C multilayers. All these values correspond to the following ten fitted parameters: two indices (tungsten and carbon); three roughnesses (C1/substrate, W2//CI, C3/W2); two rates of roughness increase (W/C, C/W); two thicknesses (C1, WE); one rate of thickness increase (carbon). The fit confirms the following (1) There is a drift in carbon thickness which is certainly due to the modification

83

C/W MULTILAYERS FOR X-RAY-U~¢ OPTICS

T A B L E II DETAILED PARAMETERS OF THE THEORETICAL REFLECTIVITY CURVE OF FIG. 5

Layer

d (nm)

tr (nm) 0.750

7.700 × 10 - 6

1.300 x 10 - 7

1

3.380

0.980

6.390 x 10 - 6

1.000 × 10 - s

2

3.068

0.350

4.260 x 1 0 - 5

4.000 x 10 - 6

3

3.308

0.986

6.390 × 10 - 6

1.000 x 10 - 8

4

3.068

0.359

4.260 x 1 0 - 5

4.000 x 10 - 6

0

1-n

k

5

3.236

0.994

6.390 x 10 - 6

1.000 x 10 - 8

6

3.068

0.370

4.260 x 1 0 - 5

4.000 × 10 - 6

7

3.165

1.000

6.390 × 10 - 6

1.000 × 10 - s

8 9

3.068 3.094

0.376 1.010

4 . 2 6 0 x 10 - 5 6.390 x 10 - 6

4 . 0 0 0 x 10 6 1.000 × 10 - s

10

3.068

0.385

4.260 >~ 10- 5

4.000 x 1 0 - 6

11

3.022

1.018

6.390 x 10 - 6

1.000 x 10 - 8

12

3.068

0.394

4.260 x 1 0 - 5

4.000 x 10- 6

13

2.951

1.026

6.390 × 10 - 6

1.000 × 10 - 8

14

3.068

0.403

4.260 × 1 0 - 5

4.000 x 10 - 6

15

2.879

1.034

6.390 x 10 - 6

1.000 × 10 - 8

16

3.068

0.412

4.260 x 10 -5

4.000 × 10 - 6

17

2.808

1.042

6.390 x 10 - 6

1.000 × 1 0 - s

18

3.068

0.420

4.260 × 10 - 5

4.000 × 10 - 6

19

2.736

1.051

6.390 x 10 - 6

1.000 x 10 - s

20

3.068

0.429

4.260 × 10 - 5

4.000 × 10 - 6

21

1.000

1.059

6.390 × 10 - 6

1.000 × 1 0 - s

of the spatial repartition of evaporated material, and also the very rough appearance of the ablated carbon area. (2) There is a dissymmetry between weak roughness at the C/W interface (near 0.4 nm) and high roughness (near 1 nm) at the other interface (W/C), probably caused by implantation of energetic tungsten particles in carbon. (3) The small increase in the two interface roughnesses is considered a function of the total thickness of each material. Figure 5 shows that there is good agreement of experimental and theoretical curves. To obtain a perfect fit it would be necessary to utilize 87 parameters, but this is impossible on the computer we used. Figure 6 shows the different curves that give the calculated reflection ratio as a function of the grazing angle for a 4.47 nm wavelength. Curve 1 indicates ideal stack reflectivity. Curve 2 corresponds to a periodic stack with roughnesses which we have found and without disparity in thickness. Curve 3 gives the realistically calculated stack reflectivity. All the parameters of these curves are given in Table III. Two sorts of defects induce different consequences. The interface roughness produces a significant decrease in the reflectivity, without modification of the peak position, whereas thickness variations produce a shift in the peak position without much decrease in intensity. Furthermore, there is a slight increase in the maximum reflectivity that is due to the fact that the variation in thickness in the real stack is closer to the optimum variation 12 than in the theoretical stack, where thicknesses are supposed to be equal according to the fabrication program.

84

PH. MACQUART, F. BRIDOU, B. PARDO

X2B I~,~

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~ o

J

z Ld

~j LJ J i, L~ 0

COURBE RJUSTEE PFIR PROGRRMME Br I dou-Pardo I

I

I

I

I

I

I

I

1000

2000

3000

4000

5000

6000

7000

8000

-I

GRRZING RNGLE

I

I

I

10000

11000

18008

(~ecol~d~)

) (with low periodicity variation) and experimental (...)

Fig. 5. Comparison between theoretical ( reflectivity curves. Lo=4.47 nm;

F

9000

10 Periods

N-C

15 14 13 12

>_

I/

11

\

I

> p-

u ,,, ,,J

0[. LJ

.09 .08

/

• 07

I/I

.86 .85 .84

/

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/

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.03 • 02

-

-

.01 0

17

18

19

20 GRRZING

21

22 RNGLE

23 (de

24

25

26

27

9)

Fig. 6. Calculated multilayer reflectivity at 4.47 nm wavelength: grazing incidence at approximately 21.5 °.

C / W MULTILAYERS FOR X-RAY--UV OPTICS

85

T A B L E III PARAMETERSOF CALCULATEDREFLECTIVITYCURVESAT 4.47 n m (FIG. 6) Curve number

1

2

3

Layer

Surface roughnesses

Layer thicknesses

(nm)

(nm)

Substrate C W

0 0 0

3.1 3.1

Substrate C W

0.75 1.25 0.27

3.1 3.1

Substrate C W

0.75 0.35~).43 0.98-1.06

3.04-2.73 3.8-3.07

5. CONCLUSION

The study of the "sandwich" stack C/W/C has enabled us to observe great dissymmetry of roughness on either side of the tungsten layer; roughness is greater for the W/C interface than for the C/W interface. As the initial carbon roughness before tungsten deposition is very low, we conclude that laser deposition of tungsten leads to a transition layer with continuous index variation that is probably due to implantation of tungsten atoms with large kinetic energy (about 100 eV). Using the results of the "sandwich" stack study we have been able to fit a C/W multilayer reflectivity curve exhibiting a good reproducibility of interface roughness, contrary to that observed in classical thermal evaporations, where roughness increases with cumulative thickness of the layers. However, we have noticed a small continuous variation in thickness monitored by the quartz microbalance. This is attributed to the modification in the spatial repartition of evaporated particles from the carbon target, depending on the depth of erosion by laser ablation. Using laser ablation for multilayer fabrication is an interesting method because, for some materials, it can produce interfaces of lower roughness than classical thermal evaporation. However, it needs technical improvement leading to the stabilization of the spatial emission of particles during the experiment. REFERENCES 1 S.B. Gaponov, Pis'ma Zh. Teckh. Fiz., 6 (1980) 1413. 2 Ph. Macquart, J. Corno and C. Mahe, Fabrication de couches minces par 6vaporation sous vide avec un laser puls6, J. Opt. (Paris), 21 (1990) 107-110. 3 Ph. Macquart, Fabrication par ablation laser et caract6risation de couches minces de mat6riaux utilisables pour la fabrication de multicouches pour les optiques X-UV, Th~se PARIS X I (Orsay), Orsay, 1990. 4 J.P. Chauvineau, Soft X-ray reflectometry applied to the evaluation of surface roughness variation during the deposition of thin films, Rev. Phys. Appl., 23 (1988) 1645-1652.

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L. Nevot, B. Pardo and J. Corno, Analyse des mat6riaux stratifi6s par r6flectom6trie X, Analusis, 16 (7) (1988) 381-388. J. Corno, B. Pardo and A. Raynal, A new X-ray reflectometer, Proc. Soc. Photo-Opt. Instrum. Eng., 984 (1988) 199-123. T. Megademini, Optimisation de r6flecteurs multicouches absorbants. Mod61isation des interfaces rugueux et application au domaine X-UV, Thesis, Orsay, 1984. B. Pardo, T. Megademini and J. M. Andre, X-UV synthetic interference mirrors: theoretical approach, Rev. Phys. Appl., 23 (1988) 1579-1597. F. Bridou and B. Pardo, Automatic characterization of layer stacks from reflectivity measurements. Application to the study of the validity conditions of grazing X-ray reflectometry, J. Opt. (Paris), 21 (4) 183-191. J . M . Box, A new method of constrained optimization and a comparison with other methods, Comput. J., Vol. 8 (1965)42 54. L. Nevot and P. Croce, Caract6risation des surfaces par r6flexion rasante de rayons X. Application ~i l'6tude du polissage de quelques verres silicates, Rev. Phys. Appl., Vol. 15 (1980) 761 779. P. Croce, Sur l'optimisation du facteur de r6flexion des empilements de mat6riaux absorbants, J. Opt. (Paris), 12 (6) (1981).