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Multilayer diffraction grating properties
A. Erko, V. Martynov, D. Roshchoupkin, A. Yuakshin, B. Vidal, P. Vincent, M. Brunel
To cite this version:
A. Erko, V. Martynov, D. Roshchoupkin, A. Yuakshin, B. Vidal, et al.. Multilayer diffraction grating properties. Journal de Physique III, EDP Sciences, 1994, 4 (9), pp.1649-1658. �10.1051/jp3:1994217�.
�jpa-00249214�
J. Phy.< III Frciiice 4 (1994) 1649-1658 SEPTEMBER 1994, PAGE 1649
Classification Phy.<ic.< Ah.<tracts
07.85 78.65E 78.70C
Multilayer diffraction grating properties
A. Erko('. *). V. Martynov ('), D. Roshchoupkin ('), A. Yuakshin ('), B. Vidal (2),
P. Vincent (2) and M. Brunel (~)
(') Laboratory of X-ray Optic~ and Technology, Institute of Microelectronics Technology and High Purity Materials, Ru~sian Academy of Sciences, 142432. Chernogolovka, Moscow region,
Ru;sia
(2) Facultd de~ Sciences de St Jdrome, URA 843. Universitd d'Aix-Marseille III, avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France
(~) Laboratoire de Cristallographie, CNRS, 25 avenue des Martyr~, 166X38042 Grenoble
Cedex, France
(Receii>ed 19 Noieniher 1993, ieii.<ed12 April 1994, accepted 27 April 1994)
Abstract. In the paper the diffraction properties of multilayer static and dynamic gratings are
discussed using reciprocal space and dispersive surfaces representation. A strong dependence of the multilayer grating properties on the lamellar period and the optical characteristics of multilayer grating materials are shown. Important points in the grating fabrication, computer simulation, and
tests also described.
1. Introduction.
Recently it was shown in several papers the possibility of using for the focusing, imaging and spectroscopy a kind of « grooved » diffraction optics on a flat multilayer substrate ii instead of a curved substrate. This is now known as Bragg-Fresnel Multilayer Lenses (BFML) [2, 3].
Gratings etched in multilayer are the basic type of Bragg-Fresnel Optics. Once the properties
of those elements are known, it will be possible to predict the major properties of more
complicated structures, such as the BFML.
This paper describes important points in the fabrication, computer simulation, and testing of
the lamellar multilayer gratings (LMG). LMG can be very interesting as a spectroscopic
device [4] with a relatively high dispersion and efficiency.
2. Theoretical calculations.
In our calculations we use a rigorous theory based on Maxwell's equations which take into
account this interaction (dynamic theory). Computations can be done using differential
method [5, 6] and modal theory [7] techniques. Recently both methods were used by the
authors to calculate LMG parameters. Using differential method developed in reference [8]
(~) Fie.<eiit a(I(fi.e.<.< BESSY G-m-b-H-, Lentzeallee100, D-14195 Berlin. Germany
calculations are carried out layer-by-layer making it suitable for any kind of profile [9]. In the modal theory, the solution is searched for the whole structure. Therefore structures with any number of layers can be calculated at the same time. In addition, using this method, one can quickly compute the dispersive curves in reciprocal space and the &~ scanning of the diffracted
orders. However, this method is valid only for a lamellar grating. That is why it is not
applicable, e.g., for a triangular profile grating. The results of application of the modal theory
for multilayer gratings is published [10]. In this paper some theoretical results from the
publications mentioned above have been used.
3. Experimental tests of the lamellar multilayer gratings.
3. I FABRICATION oF THE LAMELLAR MULTILAYER GRATINGS. LMG were made by magnet-
ron sputtering, optical lithography, reactive ion etching technique. A Fe~O~ mask of a grating with period of 4 ~m on a glass substrate was obtained by electron beam lithography and wet
etching. This mask was used for UV lithography on the multilayer substrate coated with
photoresist. Finally, an RF-excited ion beam source was used to etch the multilayer through the
photoresist mask. All steps of the technological process were rigidly controlled. An optical
interferometer and tally-step measurements were used to control the substrate wafer quality
and etching depth.
The two types of specimens where prepared for the experimental tests :
ii the lamellar grating with a period of 4 ~m, aperture I mm x lo mm and a variable depth of profile was prepared by etching of C/W 80-period multilayer. lo steps of a grating depth on
the grating area have been fabricated. Small irradiated area (1800 ~m allow us to measure the diffracted intensity from a local part of the grating having a constant period
iii several specimens W/Si 4 ~m period multilayer gratings with different profile depths and aperture I mm x mm each were prepared. The period of the W/Si bilayer was 3.05 nm with 121 layers being coated. The depth of the profile was varied in the range of 40 nm-165 nm.
3.2 OPTICAL SCHEME. In the CNRS Crystallography Laboratory of Grenoble, a rotating
copper anode X-ray generator was used as the X-ray source. The experimental scheme is
shown in figure I. A monochromatic beam of the CUK~ line, with a characteristic wavelength
of 0.154 nm, was collimated by two 20 ~m horizontal slits.
detector
~
A B
~'°~°Ch~°~'~t°~ ~~~~ ~°
~~'~f~
sot 20 ~m ~'" "II m=0
slit 20 pm /
~
_ +
i~~ / /
~
m= +I
X-ray /
source X
Fig. I. Optical scheme of the experiment.
N° 9 MULTILAYER DIFFRACTION GRATING PROPERTIES 1651
One of the slits was placed at the focal plane of the curved graphite crystal monochromator and the other at 60 cm from the object under study. Diffraction orders were registered by a
scintillator-photo-multiplier detector. The 20 ~m horizontal slits were placed before the detector.
All experimental measurements were performed in the two-dimensional scan mode. During
the experiment, an X-ray goniometer having a step accuracy of 20 arc,s. was used.
3.3 EXPERIMENTAL RESULTS. Ten points on the same grating (Sample (I II with a variable
profile have been experimentally tested. For each part of the grating, a 3-D graph of the diffracted efficiency distribution versus incident 6~, as well as the diffracted 6~ angle are
measured and plotted. Figure 2 represents the result of the grating measurements in the so- called detector scan mode for the 230 nm profile depth. In this mode, for each incident angle 6~, the diffracted field was scanned with the detector slit. The angle of incidence was scanned
in the range between 1.5° to 1.65° with a step of 0.05°. For each incident angle
6~, the diffracted field was scanned with the detector slit in the same range with the step of 6~ equal to 0.01°. Using such a method, diffraction orders 2, 1, 0, + 1, + 2 can be easily
resolved.
40%
O or4er -1 or4er -2 or4er
2 or4er or4er
/
-
20%
/
1,55°
~
1~65°
W I
J"
~4'
J'
#4
Fig. 2. Three-dimentional plot in detector scan mode for the grating depth 230 nm.
As can be seen from this plot, the maximum intensity for the minus first diffraction order corresponds to the minimum of the zero order. This phenomena can be illustrated in figure 3 where one can see the diffracted orders for the two incident angles coincide with the maximum
efficiency of the zero and minus one orders.
When the minus one order exceeds the maximum value, the zero order is almost totally
suppressed. Practically all the diffracted energy is directed to the minus first order. For the first order, the situation is not the same. Due to the roughness of the multilayer mirror, the measured wing of the zero-order curve is larger than the calculated one. Thus, experimentally
it was impossible to observe a « pure » peak in the first order diffraction without significant
zero order intensity.
That is, experimentally one can find a « blaze » effect for the multilayer grating having a rectangular profile. The value of the « blaze » angle exactly corresponds to the Bragg condition
it Incident angle 1.475°
j 0 order I order
c ~
_y cZQ
i#
liu
1i
~
~t
1.3 1.4 1-S
Diffraction angle (deg)
Fig. 3. Integral inten~ity of the diffracted orders for the value of incident angle of 1.475°
for a proper order. The Bragg condition is satisfied when the diffraction vector in reciprocal
space is equal to the sum of the multilayer structure vector and the surface (lamellar) grating
vector.
A similar result was also described by Neviere ill for multilayer coated on large period
blaze echelette grating. In Neviere s paper, the system is totally different of our system which is a short period lamellar gratings etched in a multilayer.
The absolute diffraction efficiency for the minus first order i'eisus the depth of the profile
was measured and plotted in figure 4. The first curve (I) is the calculated efficiency for a
grating period of 20 ~m.
The property of the large-period multilayer grating is analogous to a simple superposition of
a plane phase grating and a multilayer reflector.
(2) 4prr lamellar period, ~ccrefic~
(1) 20prr lamellar period, ~ccmfic~
-,x.- (3) 4~m lamellar period, expefimen~l
(4) same as (3), assunung a 0.4nm roughness
~
_;-...
~ /
/
~
i 1
oi "' 4
~j "",
%4 / ~
4J , "
# J
' f
- . J
~ ' J ,
~ ' Z
Q ' T
~ l' ""_
*~ '
0
epth of profile (nm)
Fig. 4. Absolute efficiency of the diffraction order iei.<u.< the depth of grating profile fot the iamellar groove period of 20 ~m (theoretical)1 4 ~m (theoretical) ; 4 ~m (experimental).
N° 9 MULTILAYER DIFFRACTION GRATING PROPERTIES 1653
Another result was calculated for short-period or « deep » gratings where the depth value
becomes comparable with the effective period value. This case is illustrated in figure 4
(curves (2) and (3)). Curve (2) corresponds to the data calculated with the computer simulation
program using the parameters mentioned before lamellar grating period 4 ~m and incident
angle equal to 1.475°. This value of the incident angle corresponds to the maXimum of the minus first order intensity like it was found in figure 3 for the + order. Curve (3) shows
eXperimental data for the seven grating diffraction efficiency measurements with those same parameters. For this calculation, the values
= + p for the optical indices of tungsten
and silicon are taken from the Henke tables [12]. For tungsten, = 4.57 x10~~ and
p
=
4 x 10~~ For silicon,
= 7.56 x 10~~ and p
=
1.7 x 10~~ One
can see that the shapes
of the two curves (2) and (3) are very similar. The difference in the absolute values of the
efficiency can be explained by the roughness of the multilayer grating. Multilayer roughness
(~r can be accounted for the multilayer by using the classical Deby-Waller formula
Ij/Io
= exp(- 16gr ~~r~sin~ MIA ~) where Ii is the first order efficiency and lo the input beam intensity.
In figure 4 curve (4) gives the corrected efficiency assuming a 0.4 nm iultilayer roughness.
The difference between curves (3) and (4) is very small.
Indeed, even 18 % absolute efficiency of the LMG eXperimentally found might open a wide
application of such gratings for spectroscopic devices.
4. Physical interpretation of the LMG properties.
Using the differential method for short period gratings, we found two different behaviors in
comparison to the behavior of large period gratings. First, we found a blaze effect due to the
grating period and not to a specific angle as for conventional gratings. We also observed an increased reflectivity as indicated in figure 4. This increase was confirmed by experimental
results. EXplanation of such behavior can be made easier by defining the eXtinction length (dynamical meaning) and by using dispersive curves in the reciprocal space.
Let us describe a multilayer grating as a two-dimensional crystal with two different
translation vectors, D in the.< direction and d in the z direction
When taking into account optical geometry of the system, we also have to consider the different radiation penetration depths in the,i and ? direction. Evidently, for a given incident angle, this penetration depends on both the D and d values as well as the etched depth. Such a
macro crystal has two main crystallographic directions along the = and x aXis. In geometry,
shown in figure 5, we have a so-called « Bragg-Laue » diffraction case. That is, a Bragg
reflection in the z direction and a Laue transmission in the,i direction. But existence of the Laue diffraction depends on the ratio between t, and D, whose t~ is defined as the distance along the surface between the ray s entrance and exit points as indicated in figure 5 and
figure 7. Let us consider two limiting cases :
4. LARGE PERIOD GRATINGS (t~ W D ).
4.I.I Real space. In this case effective diffraction take place only between waves
diffracted from the top and the bottom of the grooves (Fig. 5). From the physical point of view,
a phase shift between these waves depends only on the different optical paths in a vacuum.
Multilayer mirrors act as a monochromatic reflector with the phase reflecting grating on the top. This case was described as a « combined dispersion grating » in [2].
Looking at the efficiency dependence i>eisus the depth of the etched profile (Fig. 4,
curve I), we can see an increase in the reflectivity up to 25 §& which corresponds to the phase
maximum (gr phase shift between diffracted waves (see curve of the Fig. 4)).
,
",, ,,jl",,[,5«,,,,,
",, ,,jl",,iljlj[,j,,,"
o "', ,'11'),'l~[~[l",'I"' x
~~~×~ jsl~l-(--?iff°??--o-
. ~---~' i
tX '
---,---,---~,
Z D; pedo4 Gradng '
Fig. 5. -Multilayer grating scheme showing extinction length. The path corresponds to the case t~ MD-
Supermirrors (mirrors having variable bilayers periods) can increase the reflectivity and will be ideal multilayer substrates (region 3) for such gratings. In this case, the t, value is smaller
than the period.
4.1.2 Reciprocal spat-e. In addition, very useful explanations are given by the dispersive
curves of multilayer gratings in reciprocal space be shown in figure 6. The reciprocal space
technique is explained, for example, in [7].
-1
+ 0
_ ' K
~0 '~"'~ '
'
~~
.> ' '
,~'
',~ i
',~ i
6j ad *'(
(,i, ii ' ' (i, ii '~
(o,o)
.i ~
BiBo~+i e
N° 9 MULTILAYER DIFFRACTION GRATING PROPERTIES 1655
For the sake of simplicity let us consider only the and + I diffraction orders. The case of
large period gratings is characterized by h, ~ A, where h,
=
2gr/D, (D-grating period), and A is the forbidden gap (see Fig. 7) corresponding to the dispersion surface splitting value. The reciprocal space and the section of the dispersion curve within the incident plane for this region 2 are shown in figure 6. In the crossing points of Ko n, where n is the average optical
index of the media, radius spheres of the node pairs [(0, 0) (1, 1)], [(0, 0) ; (0, -1)] ; [(0, 0) (- 1, 1II has a split center due to the interaction between the diffraction orders
which occurs in the rigorous dynamic theory.
' t~
<---~
' ~>D
,
X
'~j--w '
o P~~~i
Grating
Fig. 7. -Muhilayer grating scheme showing extinction length. The path corresponds to the case : t, ~D.
For long period gratings, nodes (- I, I) and (I, I) are located near the node (0, ). In figure 6, the split diffraction orders of these nodes are the inside the main Bragg peak of the multilayer minor. The reflected intensity versus the incident angle show two
intensity peaks of and + I diffraction orders merged inside the main peak corresponding to the zero order. For this reason, and for a given incident angle, we can observe together the
three diffraction orders.
On the other hand, dispersion curves of and + diffracted orders are located inside the
gap between the dispersion curves of the zero order. The gap values are very close to these
corresponding to the value of a flat multilayer. This fact indicates an absence of a lamellar
grating influence on the value of the extinction depth of a multilayer substrate (region 3). In
particular this is valid for the one-dimensional optical grating.
In this case, re-radiation takes place only inside one period as shown in figure 6. This is a
typical case of diffraction by thin amplitude-phase gratings with an optical index equal to the average one of the structure.
4.2 SHORT PERIOD GRATINGS (t, ~ D ).
4.2.I Real space. In such a case, radiation penetrates through several periods in the X-
direction and a more or less effective Laue diffraction takes place as indicated in figure 7. As the depth of the grooves is increased, Laue diffraction takes more place, and thus more energy
JfiURN~L DE PHYSIQUE lH T 4 N'9 SEPTE~BER lv~4 b«
is located in one diffracted order. Like in a real crystal, in addition to lo, Id) reflections, we
can also find (- ID, Id and IID, Id reflections when the system rotate as it is the case in
a crystal.
The efficiency of these reflections for the ideal case c-an be as large as the =era aider Bt.agg dijfiiaction fi.om the flat miiltilaj,ei as it is shown in figure 3.
4.2.2 Reciprocal space. A reciprocal space for this case is shown in figure 8. Forbidden
gaps corresponding to the diffracted orders ( and + ), are located outside of the zero order for the small period gratings. In this case, nodes (- I, ), and (- I, ), are located far from
the node lo, due to the fact that h~ ~ J.
The interaction between the diffraction orders of nodes pairs (- I, ) and (- I, ) are
located outside the main Bragg zone drawn in figure 8 with ~. This is due to the interaction between the waves of the nodes (0, and lo, 0). The electrical componant along the.< axis must be identical for every diffraction order. This gives the excitation point on the dispersion
curve. When the incident angle is increasing, the excitation point move along the dispersion
-1
, + o
', ,K~
~ " ''
o , <, +1
j'( ' '
8. i"
d '
;
X j~ hx i).oi>
' ' i-1, i>
~~~
(o, oi
I ol
,i +i
8
~ B~ 8~~ 8j
Fig. 8. Reciprocal space for short period grating (D ~ 4 ~m).
