Corrector of quasi-static large-scale and nano-type optical distortions
for EUV projection lithography at 13.5 nm.
S.A. Dimakov, B.V. Kislitsyn, S.I. Klimentiev, A.P. Zhevlakov, D.I. Zhuk
Institute for Laser Physics Scientific and Industrial Corporation Vavilov State Optical
Institute, Birzhevaya 12, St. Petersburg 199034 Russia
ABSTRACT
Extreme Ultraviolet Lithography is a new R&D field aimed at creation of high-quality
imaging systems operating at the wavelength up to 13.5 nm.. When creating imaging
devices at such a wavelength the main problems are high optical quality of the
elements under using and rigid requirements to service conditions of the device
(vibration, temperature stability etc.). For systems operating in the 13-nm wavelength
range, their optical distortions should not exceed 1 nm in magnitude. Large price of
EUV projection system is defined, in particular, by serious costs for optical elements
and for the system of parameters stabilization. Requirements to the optics quality and
to its service conditions can be essentially decreased if the corrector of optical
distortions is used in the projection system. Large-scale distortions (20 % of diameter
of the element) of operating surface of optical elements with the amplitude of several
wavelengths considerably reduce the resolution of the imaging system. However such
small distortions (dozens nanometers) can be compensated by artificial thermogradients caused by additional light. Basing, namely, this idea the corrector of quasistatic large-scale optical distortions, intended for EUV range, and developed by us
operates .Such a corrector can be used without special imaging optics because
diffraction effects at the wavelength of 13.5 nm are negligible and the amplitude of
distortions under correction is little. Use of the corrector can essentially decrease the
price of optical elements because distortions with the value of 10-40 nm are corrected
up to residual distortions of 0.5-0.7 nm (λ/20 for EUV).
Keywords: Optical reducing systems, extreme ultraviolet projection lithography,
correction for distortions, thermal deformation, EUV.
1. INTRODUCTION
Technical progress and, in particular, present development of computer technique put
stricter requirements to the devices which are applied in chips production. Creation of
microchips of the next generation requires a lithographic equipment operating at 13.5
nm wavelength with high image quality. High quality image maintenance is possible
only subject to observance of ideality of the lithograph optical elements.
2-34
Fig. 1. Block diagram of the correction system
In particular, deviations of the working surface from the required shape have not to
exceed λ0/20. For λ0=13,5 nm it comes to ~0,7 nm. Fabrication of optical elements
with such high quality requires, obviously, considerable financial expenses. Besides
the requirement on manufacture of the practically ideal optical elements it is
necessary to provide high stable conditions of their operation as well. But this is
insufficient again. In the case when even the high-stable service conditions differ from
the one wherein final processing of the optical element has been executed then the
optical distortions of the working surface inevitably appear. In the paper [1] it was
made an assumption that the most undesirable distortions are the quasi-static largescale ones which exist at the stages of the optical elements processing or/and which
appear at optic operation as a result of insignificant declinations from the required
conditions of its use.
In the paper [1] it was made an assumption that the price for the last stage of a mirror
processing and final adjustment of the operating parameters, is an essential share of
the EUV lithographer price. Study of the ways of correction for these quasi-static nonuniformities has shown that no one of well-known actuators for linear method of
correction will not allow providing required high accuracy of correction (fractions of
a nanometer). From the other part nonlinear methods are really inadaptable here for
instance because of absence of acceptable nonlinear media operating in the EUV
range.
In its turn deliberate artificial thermo-deformation of the mirror allows us to remove
large-scale distortions of a small value. For that, in the paper [1] the distorted mirror
was illuminated by an additional light source (see Fig.1).
Spatial distribution of light intensity corresponded to distribution of the thermal
sources, which can strain the mirror so that it would have an ideal shape of the
working surface. This light was absorbed by the working surface of the mirror, and
distribution of the thermal sources needed for compensation of distortions was created
on the surface.
To demonstrate the operation capacity of the proposed idea for the mirror distortion
correction using the method of thermo-deformations, we have performed a numerical
simulation. The correction process under consideration represents a complex
mathematical problem of heating a thin surface layer of the mirror and deformation of
the mirror in a holder, which fixes its position. Variation of the mirror temperature is
described by a nonstationary heat transfer equation. As the paper [1] we have carried
out our studies by computer simulation solving together the heat transfer equation and
the nonstationary equation of thermoelasticity. The initial data for the calculations are
the real geometry of the mirror, elastic and thermo-physical constants, conditions of
the convective heat transfer and mounting, and spatio-temporal variations of the
absorbed light power. The calculations allow one to obtain time dependence of the
field of temperature and displacements and to plot time dependence of the mirror’s
reflecting surface.
2-35
It was assumed in [1], for definiteness, that the objective of the lithograph comprises
two aspherical mirrors with apertures in the centers. Figure 2 shows an example of the
secondary mirror of the UV lithograph objective. For definiteness, let the mirror be
made of vitrocrystalline material and have a diameter of 300 mm. By means of
computer simulation, we created, on the reflecting surface of the mirror, a static
distortion, 15 nm in magnitude with a spatial scale of D/2, shown in Fig. 3. In the
paper [1] it was assumed that this distortion of the mirror arose in the process of its
manufacturing, and that further polishing of the mirror, to reduce the value of the
distortion to below 0.7 nm (λ0/20 for λ0=13,5 нм), is very expensive.
Fig. 2. Secondary mirror for the objective of the UV lithograph
Fig. 3 A model distortion produced on the surface of secondary mirror of the UV
objective
2-36
Fig. 4 Distribution of thermal sources over the mirror surface for compensation of the
model distortion (fig.3).
By special additional calculations, authors of the paper [1] have found the profile of
the light power density that creates the distribution of thermal sources over the surface
of the mirror needed to correct the distortion. (Fig. 4).
Fig. 5 Dynamics of the reflecting surface profile of the non-ideal quality mirror in the
process of thermal correction (spatial scale of the distortions is D/2).
Figure 5 shows the dynamics of the reflecting surface profile of the distorted mirror in
the process of thermal correction of the model quasi-static distortions. The mirror was
heated until 14th second, and then, from 14th to 18th second, the incident light power
did not exceed 10% of that of the correcting irradiation. As is seen, the distortions,
originally 15 nm in magnitude, in the process of the correction do not exceed 0.7 nm
practically over the whole surface of the mirror during 4 seconds (from 14th to 18th).
2-37
Only in peripheral zones of the mirror, several mm from the edge, the distortions
exceed the specified value. However, first, the area of the perturbed zones is small
and, second, the mirror can be intentionally manufactured with a slightly larger
diameter, and the perturbed zone can be blocked by a diaphragm.
Fig. 6. The mirror distortions for the lithograph operating between 14th and 18th
seconds.
In the same work it was also shown that thermo-compensation can be carried out in
pulse-periodic mode. In particular, re-compensation of nm distortions in 120 seconds
after the first stage of correction was introduced. Such a type of thermo-compensation
allows us to save heat energy spending it in portions. Besides, at such compensation it
is practically no need to worry about refrigerator. According to calculations the
process of compensation can be repeated several times up to evident raise of the
average temperature of the mirror under correction.
An important shortcoming of the correction process considered in [1] is its shortliving in time. According to [1] the mirror was illuminated by light with required
intensity distribution during ~ 14 sec and after that as a result of thermo-deformation
the mirror had an ideal non-distorted surface for the period of 4-6 sec. All residuary
time the mirror had annoying impairments for lithograph operation. To remove this
shortcoming the calculations on stationary thermo-correction were undertaken.
2. STATIONARY THERMO-CORRECTION.
Calculations on stationary correction were realized for the mirror where the inverse
surface had a contact with the fridge, and at constant illumination of the working
surface a heat flow continuously passed through the mirror’s body. Under the effect of
this heat flow one establishes in the mirror body stationary temperature distribution
which results in stationary artificial thermo-deformation of the required mirror. In
these calculations we considered a ceramized mirror with the diameter of 100mm and
thickness of 5 mm (heat conductivity coefficient -1.2 W/m*grad, linear expansion
coefficient 1,5*10-7, Young modulus 91 GPa, heat-transfer coefficient 4000
2-38
W/m2*grad, initial temperature of the mirror and the temperature of the heat-transfer
agent (coolant) 20oC.
Axisymmetric distortions depending only on radial coordinates were put by a
computer simulation on the working surface of the mirror (see Table1). A heat flow
changed in radial direction is absorbed on by the upper surface of the mirror. The
bottom surface of the mirror is cooled by the heat-transfer agent. Due to a heat flow
passing through the mirror it heats up and changes the shape. It is believed that the
bottom surface of the mirror does not move in vertical direction. Transfers of the
upper surface of the mirror partially compensate initial aberration.
The Table1 shows the dependences of the model distortions and compensative heat
flow being under consideration in this work from the mirror radius.
Table 1
Distortion, nm
Heat flow q0, W/mm2
 r 
Y  r   7.7Cos 

 2 R
r  0.1 r

q  r   0.007Cos  0.5  e R
R

r   0.1 r


Y  r   0.004  1  Cos  2.5   e R
R 


r 


Y  r   6.9  1  Cos  2.53  
R 


r 


Y  r   8.0  1  Cos  4.5  
R 


r   0.2 r


q  r   0.007  1  Cos  4.46   e R
R 


2.1 Calculation results
The Fig.7 - 9 show the results of calculation for compensation of model distortions,
by means of nonuniform stationary heating by a heat flow specified at the mirror
surface.
A
B
2-39
C
D
Fig.7 Model distortion #1 (A – initial distortions; B – a heat flow specified at the
mirror surface; C - temperature; D – residual distortions.
A
B
C
D
Fig.8 Model distortion # 2 (A – initial distortions; B – a heat flow specified at the mirror
surface; C - temperature; D – residual distortions.
2-40
A
B
C
D
Fig.9 Model distortion # 3 (A – initial distortions; B – a heat flow specified at the
mirror surface; C - temperature; D – residual distortions.
The figures 7 – 9 show the results of calculation which introduce that the stationary
heat flows allow creation of required temperature distribution that causes artificial
thermo-deformation so that the amplitude of distortions becomes less than the
required value of  practically along the whole surface of the mirror. Three
versions of aberration, considered in our calculations allow making a conclusion that
such a corrector allows us to compensate non-uniformities at least by the scale D/5
(See Fig.7) and may be less.
The executed studies confirm availability of this method of correction by means of
thermo-deformation both in pulse-periodic and continuous modes.
3. Experimental demonstration of possibility to improve optical quality of a mirror by
means of its thermal deformation by light.
The obtained results of numerical calculations allow us to hope the compensation for
nanometer optical distortions with the use of mirror’s artificial thermal deformation to
be feasible. To prove this theoretically obtained fact the experimental verification is
needed. The theoretical part of the work showed the correctable distortions to have a
large scale. However, exactly these distortions will probably require substantial
financial expenditure at a final stage of mirror manufacture. The distortion
compensation demonstrated was quasi-static. It could be realized either for several
2-41
seconds (only during the time of exposure the target in a lithographer to radiation) or
in steady-state conditions. In the first case the thermal compensation allows saving on
thermal energy which is taken a little at a time. Besides, in this case it is not needed to
trouble about a refrigerator. As calculations have shown, a compensation act can be
repeated in case of need some seconds later. More attractive of course is the second
mentioned mode of operation that is the static compensation mode. In this case the
light with a special power distribution over cross-section illuminates a mirror, the
mirror being a high quality one for an arbitrary long time. As it was mentioned above,
this mirror should be supplied with a refrigerator from the mirror’s rear.
In the course of our studies a demonstration experiment on correction of non-ideal
mirror’s optical quality with the use of correcting light illuminating the mirror has
been carried out. Both metallic and glass mirrors were subjected to the correction.
For simplicity the experiment was carried out in visible light and a slightly spherical
round mirror was subjected to the correction (Fig.10).
Fig. 10
In correction the correcting light power distribution was selected so that the studied
mirror after illumination should be flat at the most part of its central surface area. The
demonstration experiment layout is shown in Fig. 11.
2-42
Fig.11 The demonstration experiment layout (1- Ne-He laser; 2- flat turn mirror; 3, 4,
7, 11- lenses; 5- semitransparent mirror; 6-high quality reference mirror; 8- opaque
screen; 9-camera; 10-mirror corrected; 12- source of correcting radiation; 13spherical mirror).
The surface-monitoring layout of the mirror studied in our experiment is based on a
Michelson interferometer. This is routine interferometer layout for different
applications where spatial overlap of the objects giving rise to interfering waves is
either impossible or for some reason undesirable. In our case the Michelson
interferometer is used for remote testing of small deformations (departure from
flatness) of the mirror studied. This layout is rather convenient because close location
of an object and the reference surface is undesirable since the mirror corrected is
heated.
In the experiment a low-power continuously working He-Ne laser (wavelength
=0.633 m, power P=30mW) was employed for illuminating the interferometer.
Telescope 3.4 broadened a light beam up to 60mm in diameter. The output beam of
parallel rays was partially reflected by the semitransparent surface of a beam splitter 5
and partially passed through it. The first beam (reference) reflected by the reference
mirror 6, passed through the beam splitter 5, and hit opaque screen 8. The second
beam was reflected by the mirror 10 (this mirror being examined), then by the beam
splitter 5, and after that it propagated in the same direction as the reference beam and
interfered with it. The corresponding interference pattern can be seen on the opaque
screen (8). As correctable mirrors we used in our experiments both metallic and glass
(with aluminum coat) mirrors. As a source of radiation for artificial thermal
deformation of the mirror under consideration we used a lamp K220-1000 (voltage
U=220V, power consumption W=1000W) (12). Radiation from the lamp 12 reflected
by the examined mirror was returned to it by an auxiliary spherical mirror 13 so that
to increase thermal current absorbed by the mirror examined.
Figures 12 a,b show typical interference patterns characterizing the optical quality of
the considered mirror before thermal correction (Fig.12 a) and after it (Fig.12 b). In
2-43
EUV spectrum the distortions of our mirror are too large; as is seen in Fig.4a the ‘pit’
on the mirror’s surface are 1200nm in depth. The fact that the deformation is of ‘pit’
type was determined in dynamics of fringe displacement at shifting motion of the
reference and the examined mirrors. After correction the mirror’s central area is
virtually a plane one, distortions are available only at the periphery of the mirror’s
surface amounting to 320nm.
a)
b)
Fig.12 Interference patterns characterizing the surface shape of the mirror before (a)
and after (b) correction
6. CONCLUSIONS
The presented results of numerical calculations allow us to hope that compensation
for large-scale nanometer axial symmetric optical distortions with the use of artificial
thermal deformation of a mirror is realizable. The demonstration experiments on
correction of large-scale distortions of the mirror by means of thermal deformation of
its working surface have confirmed the numerical results. The work was performed at
partial financing by the Grant ISTC 0991.
Reference
1. Dimakov S.A., Kislitsyn B.V., "Thermo-correction of quasi-static optical
distortions in optical reducing systems for EUV projection lithography", Proc. SPIE
v.5553, #26, August 2004.
2-44