Device for detecting a magnification error in an optical imaging system

A device is described for detecting a magnification error in an optical imaging system comprising a lens system (L.sub.1, L.sub.2) which is telecentric at one side. Two gratings (RG.sub.1, RG.sub.2) arranged in the object plane (MA) are imaged onto two gratings (WG.sub.1, WG.sub.2) arranged in the image plane (W; WT) and the radiation beams (b.sub.1, b.sub.2) by means of which these images are formed are incident on two radiation-sensitive detection systems (D.sub.1, D.sub.2) which supply periodic signals (S.sub.1, S.sub.2). By phase comparison of these signals a magnification error (S.sub.ME) and, if desired, a focussing error can be measured very accurately.

The invention relates to a device for detecting a magnification error in an 
optical imaging system comprising a main lens system for conjugaing an 
object plane and an image plane to each other, which main lens system is 
telecentric at one side. 
In general, such a device may be employed in an imaging system by means of 
which an object of extremely fine detail is to be imaged without 
dimensional errors and is particularly suitable for use in an apparatus 
for repeatedly imaging a mask pattern on a substrate, which apparatus is 
employed in the fabrication of integrated circuits or ICs. 
Such an apparatus, often referred to as "Wafer stepper" in the literature, 
is described in the article "Optical Aspects of the Silicon Repeater" in 
"Philips' Technical Review", 41, 1983+84, No. 9, pages 268-278. This 
article describes an apparatus for imaging a mask pattern, for example the 
pattern of an integrated circuit, repeatedly and to a reduced scale on the 
same substrate, the mask pattern and the substrate being moved relative to 
each other in two mutually perpendicular directions in a plane parallel to 
the substrate plane and the mask plane between two successive exposures. 
Integrated circuits are fabricated by means of diffusing and masking 
techniques. In this process a plurality of masks having different mask 
patterns are successively imaged at the same location on a semiconductor 
substrate. Between consecutive imagings at the same locations the 
substrate must be subjected to the desired physical and chemical changes. 
For this purpose, after it has been exposed by a first mask pattern, the 
substrate must be removed from the apparatus and, after it has been 
subjected to the desired process steps; it should be replaced therein at 
the same location in order to expose it by a second mask pattern etc. 
During this process care must be taken that the image of the second mask 
pattern and of the succeeding mask patterns are positioned accurately 
relative to the substrate. 
Diffusion and masking techniques can also be employed in the fabrication of 
other structures with details having dimensions of the order of 
micrometers. Examples of these are structures of integrated optical 
systems or conduction and detection patterns of magnetic-domain memories. 
In view of the multitude of electronic components per unit area of the 
substrate and the resulting small dimensions of these components, 
increasingly stringent requirements are imposed on the accuracy with which 
integrated circuits are fabricated. Therefore, the repeated imaging of a 
mask pattern on a substrate requires the use of a projection lens system 
of a very high quality. The known apparatus described in the above article 
employs a projection lens system which is telecentric at two sides, that 
is a system which is telecentric both at the object side or mask side and 
at the image side or substrate side. A lens system is telecentric at a 
specific side if at this side the plane of the pupil, that is the entrance 
pupil or the exit pupil, is situated at infinity. This means that the 
image of the actual pupil, which image is formed by the lens elements 
which at this side are situated before the actual pupil, is situated at 
infinity. At a telecentric side of the lens system the chief ray of a 
beam, that is the ray passing through the center of the pupil, is always 
incident perpendicularly relative to the object plane or image plane 
corresponding to this side. In the known projection apparatus, which 
comprises a lens system which is telecentric at both sides and whose 
object plane coincides with the plane of the mask pattern and whose image 
plane coincides with the substrate surface in the ideal case, a 
displacement along the optical axis of the mask pattern or of the 
substrate relative to the projection-lens system will not result in a 
magnification error. 
The apparatus for the repeated imaging of mask patterns, described in the 
aforementioned article in "Philips' Technical Review", 41, No. 9, pages 
268-279, has proved to be very suitable for the repeated formation of 
images with a specific image format and with minimal details or line 
widths of the order of one micrometer or larger. However, there is an 
increasing demand for integrated circuits providing more electronic 
functions. Such circuits not only cover a larger surface area but their 
components have even smaller dimensions. Therefore, there is a growing 
need for an apparatus which is capable of making repeated images whose 
image format is larger and whose details or line widths are smaller than 
one micrometer. The projection lens system for such an apparatus is 
required to have a very high resolution, whilst the image field should be 
comparatively large, for example of a diameter of the order of 23 mm. Such 
a lens system, which has recently become available, is telecentric at the 
image side but not at the object side. 
When this projection-lens system is employed, a problem which until now was 
not serious may play an important part. This problem is that the 
performance of the lens system depends on ambient influences. In the case 
of varying ambient parameters, specifically air pressure, the relative 
refractive indices in the projection-lens system may change to such an 
extent that the magnification of this system changes. Thus, the need 
arises to detect the magnification error in order to enable it to be 
corrected. 
In addition to the magnification error which arises as a result of 
deviations in the projection lens system itself, it is also possible that 
during imaging of the mask pattern onto the substrate dimensional errors 
will arise which have the same effect as magnification errors. These 
dimensional errors may result from dimensional variations in the mask 
pattern caused by temperature variations and mask deformations and from 
thermal expansion of the suspension means of the projection-lens system 
and the mask in the exposure apparatus. Moreover, dimensional variations 
in the substrate, which also play part in the known apparatus, also exert 
a substantial influence on the quality of the mask-pattern image. 
The problem of a varying magnification under the influence of ambient 
conditions may also occur in other optical systems by means of which 
regular patterns must be imaged with a high dimensional accuracy. 
Usually several apparatuses of the type intended here for the repeated 
imaging of a mask pattern onto a substrate, also referred to as exposure 
apparatuses, will be installed in a plant for the fabrication of 
integrated circuits. It may be desirable, for example, to carry out the 
exposures required for the various process steps of a specific substrate 
by means of different apparatuses. Also when it is in principle the 
intention that the individual exposures of a substrate be carried out by 
means of the same exposure apparatus, it should be possible to change to 
another apparatus if the first apparatus requires maintenance or has 
become defective. When a plurality of exposure apparatuses are used for 
the same substrate it should be possible to make the imaging dimensions of 
these apparatuses equal to one another. 
A substantial length of time may elapse between a first exposure and a 
subsequent exposure of the same substrate by means of the same exposure 
apparatus. In the meantime the magnification of this apparatus may have 
changed. It should then be possible to adjust the magnification of the 
apparatus to the same value with which the structure already formed on the 
substrate has been imaged. 
In general, the exposure apparatus should have a possibility of adjusting 
the magnification in order to ensure that the image dimensions of the 
successive images formed on the substrate by means of the same apparatus 
or a plurality of apparatuses are the same. In order to enable such an 
adjustment to be carried out, it should be possible to detect a 
magnification error. 
It is the obiect of the present invention to provide a device for 
generating a magnification-error signal, which signal can be used as a 
control signal in a servo system for eliminating this magnification error. 
The device in accordance with the invention is characterized by a first 
and a second object grating which are arranged in the object plane and 
which are intended to be imaged by the main lens system on a first and a 
second image grating respectively, which image gratings are arranged in 
the image plane and have a grating period proportional to that of the 
associated object grating, by a radiation source for illuminating the 
gratings, and by a first and a second radiation-sensitive detection system 
respectively arranged in the path of an illumination beam originating from 
the first object grating and the first image grating and in the path of an 
illumination beam originating from the second object grating and the 
second image grating, for converting these beams into periodic electric 
signals whose phase differences are representative of the magnification 
error. 
If the magnification with which the main lens system images the object 
gratings onto the image gratings, or vice versa, is correct, the images of 
the object gratings are exactly in register with the image gratings. This 
is not the case if the magnification is not correct and a moire pattern of 
dark and bright bands will appear behind the gratings, the period of this 
pattern depending on the degree to which the images of the object grating 
are in register with the image gratings. If the magnification changes the 
frequency of the moire pattern, that is the number of bands per unit of 
length will vary, so that the bands apparently move relative to the 
associated stationary radiation-sensitive detection systems whose 
radiation-sensitive surfaces have a width smaller than that of the moire 
bands. 
In order to enable the magnification error to be determined very accurately 
and independently of all kinds of possible variations in the measuring 
system, such as intensity variations of the radiation source, local 
reflection or transmission differences in the gratings, or other optical 
components, care is taken that the detector signals are periodic signals 
which vary in time and whose phase differences depend on the magnification 
error. By measuring the phase differences positional deviations smaller 
than one period of the grating can be determined. Phase differences can be 
determined very accurately by electronic means as a result of the high 
degree of interpolation which is possible. 
In order to obtain the periodic detector signals the device in accordance 
with the invention may be characterized further in that the grating lines 
or strips of an object grating and those of an associated image grating 
are moved periodically relative to each other in a direction perpendicular 
to the longitudinal direction of the grating lines or strips. 
Owing to this periodic movement the moire pattern of two associated 
gratings will move periodically relative to the detection system 
associated with these gratings. After every displacement of the 
effectively moving grating over a distance equal to its grating period the 
signal from this detection system has passed through a maximum and a 
minimum. If the grating period is sufficiently small the detector signal 
will be substantially sinusoidal. If the period of the moire pattern is 
infinitely large, that is if the gratings are imaged onto each other with 
the correct magnification, the detector signals will be in phase. If the 
magnification is not correct, phase differences between the detector 
signals will occur. 
In order to obtain the periodic movement of the grating strips of the 
object grating and the image grating relative to each other, the device 
may be characterized by a drive means for one of two associated object and 
image gratings for periodically moving said gratings relative to each 
other. 
In this embodiment it is, in principle, adequate to use only one radiation 
sensitive detector for each grating pair. However, the situation may occur 
that the detector signals are in phase although the image gratings are 
shifted by roughly one whole grating period relative to the associated 
grating. In order to mitigate this drawback, the present embodiments of 
the invention may be characterized further in that at least one of the 
detection systems comprises two detectors, a phase difference between the 
output signals of these detectors indicating a coarse magnification error 
which corresponds to a displacement of the grating strips of a grating 
relative to those of a grating imaged thereon by at least half a grating 
period. This step enables a pre-adjustment of the magnification to be 
obtained. Moreover, in the case of a displacement of the imaged grating 
relative to an associated grating by, for example, three quarters of the 
grating period, the sign of the magnification error can be determined. 
A preferred embodiment of the invention, in which two associated gratings 
are moved relative to one ancther, is characterized in that the grating to 
be moved and the associated radiation-sensitive detection system together 
comprise an array of radiation-sensitive detectors, which array covers m 
grating periods of the grating imaged thereon and comprises n detectors 
for every grating period and in that each detector of the sequence number 
i is interconnected to a detector of the sequence number i+n, where i=1, 
2, 3, . . . n(m-1). 
By applying a special electronic processing of the detector signals it is 
possible to simulate a moving grating and eventually two signals can be 
obtained whose phase difference depends on the magnification error. 
The device in accordance with the invention may operate in the transmission 
mode or in the reflection mode. The device which operates with transmitted 
radiation is characterized in that the object gratings and the image 
gratings are transmission gratings, and in that the radiation source is 
arranged at one side of the main lens system before the gratings disposed 
at this side, and the radiation-sensitive detection systems at the other 
side of this lens system are arranged behind the gratings disposed at this 
other side. 
The device which operates with reflected radiation is characterized in that 
either the image gratings or the object gratings are reflection gratings 
and the other gratings are transmission gratings, in that the 
radiation-sensitive detection systems are arranged at that side of the 
transmission gratings which is remote from the reflection gratings, and in 
that in each of the illumination beams a beam splitter is arranged for 
separating from the illumination beam a radiation beam which originates 
from the reflection grating and which has twice traversed the main lens 
system and for directing the second-mentioned beam towards the 
radiation-sensitive detection system. 
In the embodiments described so far the illumination beams have a 
comparatively large aperture angle, such that the sub-beams diffracted in 
various diffraction orders by the gratings overlap each other and are not 
detected separately. 
Another category of embodiments have the common characteristic feature that 
the illumination beams have an aperture angle which is smaller than the 
diffraction angle at which the first-order sub-beams are diffracted by the 
gratings and in that for each illumination beam there are provided at 
least two radiation-sensitive detectors, the first detector being arranged 
in the path of both the (0,+1)-order sub-beams and one of the (+1,0)- and 
(+1,-1)-order sub-beams, whilst the other detection is arranged in the 
path of both the (0,-1)-order sub-beam and one of the (-1,0) and 
(-1,+1)-order sub-beams, the firstt and the second numeral referring 
respectively to the first and the second grating in the radiation path of 
the relevant illumination beam. 
The object gratings and the image gratings may have effectively the same 
grating period, that is the grating period of the image gratings is equal 
to that of the object gratings multiplied by M, where M is the 
magnification factor of the main-lens system, for example 1/5 or 1/10. In 
that case the (0,+1) and (+1, 0) order sub-beams and the (0,-1) and (-1,0) 
order sub-beams are utilized for magnification-error detection. 
However, suitably the device is characterized further in that the period of 
an object grating is equal to 2/M) times that of the associated image 
grating and in that the detectors are arranged in the path of the (+1,-1) 
and (0,+1) order sub-beams and in the path of the (-1,+1) and (0,-1) order 
sub-beams respectively. Irregularities in the grating structures or the 
fact that the width of the grating strips is not equal to that of the 
intermediate strips can then no longer affect the detector signals. 
In order to obtain time-modulated detector signals the device in which the 
sub-beams of different diffraction orders are utilized may be 
characterized further by a drive means for periodically moving one of two 
associated image gratings and object gratings relative to each other. 
However, preferably the magnification-error detection device utilizes other 
possibilities of time modulating the detector signals, so that moving an 
image grating or object grating to and fro is not necessary. The device is 
then characterized in that in the radiation path of each of the 
illumination beams a v. .lambda./2 plate is arranged in the zero-order 
sub-beam originating from the first grating, where v is an odd number and 
.lambda. is the wavelength of the radiation used, for converting the state 
of polarisation of this sub-beam into the orthogonal state relative to the 
state of polarisation of the first-order sub-beams originating from said 
grating. 
In the most general case of two elliptically polarised beams orthogonal 
states of polarisation are to be understood to mean that 
a. the azimuth of the polarisation of one beam is rotated through 
90.degree. relative to that of the other beam, 
b. the ellipticities of the polarisations are identical, and 
c. the sense of rotation of the polarisations is opposite. 
In the special case of two linearly polarised beams the orthogonality means 
that the directions of polarisation extend perpendicularly to each other. 
As a result of this, it becomes possible to obtain orthogonally polarised 
beams in the detection branches of the device, that is in those parts of 
the radiation paths which are traversed by the illumination beams after 
these beams have passed through a pair of associated gratings, which beams 
after further processing exhibit a phase difference which depends on the 
magnification error. Moreover, it is then also possible to detect a 
focussing error and an alignment error. An alignment error is an error in 
the alignment of two associated gratings relative to each other. 
A first embodiment comprising v..lambda./2 plates is characterized further 
in that for each illumination beam two .lambda./4 plates and a rotating 
polarisation analyser are arranged in the radiation path between the last 
grating traversed and the associated detectors. The rotating analyser 
generates periodic detector signals which exhibit phase differences which 
depend on a magnificaticn error. 
However, suitably the time modulation of the detector signals is obtained 
electronically. This is effected in a device which is characterized 
further in that each entrant illumination beam comprises two components 
having mutually perpendicular directions of polarisation and having 
different radiation frequencies, in that for each illumination beam there 
are provided four radiation-sensitive detectors, and in that 
polarisation-separating elements are arranged in the radiation path of the 
sub-beams between the last grating traversed and the detectors. In the 
detection branch the two frequencies of an illumination beam produce a 
signal having a beat frequency whose phase depends on a magnification 
error. 
Another embodiment, in which the time modulation of the detector signals is 
obtained electronically, is characterized further in that each entrant 
illumination beam is a linearly polarised beam whose direction of 
polarisation varies periodically between two mutually perpendicular 
states, in that for each illumination beam there are provided four 
radiation-sensitive detectors, and in that polarisation-separating 
elements are arranged in the radiation path of the sub-beams between the 
last grating traversed and the detectors. 
In the foregoing it is assumed that the v..lambda./2 plate is arranged in 
the radiation path between an image grating and an object grating. In 
practice, this may imply that this plate has to be arranged in the main 
lens system, which may complicate the design and manufacture of this lens 
system. This problem is precluded in an embodiment of the invention which 
is characterized further in that the grating period of an object grating 
is equal to k/M times the grating period of the associated image grating, 
where k is a number smaller than one, and in that in the detection branch 
for each illumination beam in each sub-beam which is diffracted in a first 
order by the last grating traversed there are arranged, in this order: the 
v..lambda./2 plate, a lens which images the grating plane on an auxiliary 
grating between said lens and the detectors, and a polarisation separating 
element between the auxiliary grating and the detectors. 
The invention not only relates to a magnification-error detection device 
but also to an apparatus for the repeated imaging of a mask pattern onto a 
substrate comprising a mask table, a substrate table and a projection lens 
system interposed between said tables, in which apparatus the 
magnification-error detection device may be used advantageously. This 
apparatus is characterized further in that the main-lens system comprises 
the projection-lens system and in that the axial position of the mask 
table is adjustable relative to the projection-lens system and the 
substrate table by means of the magnification-error signal supplied by the 
magnification-error detection device. 
Suitably, the apparatus is characterized further in that the radiation 
source for the magnification-error detection device is constituted by the 
radiation source employed for the repeated imaging of the mask pattern 
onto the substrate.

FIG. 1 shows a known apparatus for the repeated imaging of a mask pattern 
onto a substrate. The principal parts of this apparatus are a projection 
column, in which a mask pattern C to be imaged is mounted, and a movable 
substrate table WT, by means of which the substrate can be positioned 
relative to the mask pattern C. 
The projection column incorporates an illumination system which may 
comprise a lamp LA, for example a mercury lamp, a mirror EM, an element 
IN, also referred to as an integrator, which ensures a homogeneous 
radiation distribution within the projection beam PB, and a condensor lens 
CO. The beam PB illuminates the mask pattern C present in the mask MA, 
which mask is arranged on a mask table MT. 
The beam PB passing through the mask pattern C traverses a projection-lens 
system PL which is shown only schematically, which is arranged in the 
projection column, and which forms an image of the pattern C on the 
substrate W. The projection-lens system has a magnification of, for 
example, M=1/10, a numerical apertures N.A.=0.42, and a diffraction 
limited image field of a diamter of 23 mm. 
The substrate W is arranged on a substrate table WT, which is supported, 
for example, on an air cushion. The projection-lens system PL and the 
substrate table WT are arranged in a housing HO, which is closed by a base 
plate BP, made of for example granite, at the bottom and by the mask table 
MT at the top. 
For aligning the mask and the substrate relative to each other, as shown in 
FIG. 1, the mask MA comprises two alignment marks M.sub.1 and M.sub.2. 
Suitably, these marks comprise diffraction gratings, but alternatively 
they may comprise other marks such as squares or strips which differ 
optically from their environment. These alignment marks are two 
dimensional, that is they comprise sub-marks which extend in two mutually 
perpendicular directions, the X and the Y direction in FIG. 1. The 
substrate W, onto which the pattern C is to be imaged several times 
adjacent each other comprises a plurality of alignment marks, preferably 
also two dimensional diffraction gratings, of which two gratings P.sub.1 
and P.sub.2 are shown in FIG. 1. The marks P.sub.1 and P.sub.2 are 
situated outside the areas on the substrate W where the images of the 
pattern C are to be formed. Suitably, the grating marks P.sub.1 and 
P.sub.2 are phase gratings and the grating marks M.sub.1 and M.sub.2 are 
amplitude gratings. 
An apparatus as shown in FIG. 1, which is suitable for forming images on 
the substrate whose details or line widths are smaller than 1 .mu.m, for 
example equal to 0.7 .mu.m, comprises a projection lens system PL which is 
telecentric at the image side, that is the side of the substrate W, but 
which is non-telecentric at the object side, that is the side of the mask 
MA, so that magnification errors may arise during imaging if no further 
steps are taken. These magnification errors can be eliminated by moving 
the mask table MT in the direction of the optical axis of the 
projection-lens system relative to this system PL and the substrate table 
WT. For the desired highly accurate control of this displacement a signal, 
referred to as the magnification-error signal, must be generated which 
very accurately defines the magnitude of the deviation between the actual 
and the desired magnification and which also indicates the direction of 
this deviation. 
In accordance with the invention it is possible to obtain this 
magnification-error signal when two gratings arranged at an accurately 
defined distance from each other in the mask and two gratings also 
arranged at an accurately defined distance from each other in the 
substrate itself or in the substrate table are imaged onto one another by 
means of the main lens system PL. The magnification-error measurement and, 
if necessary, the axial movement of the mask table relative to the lens 
system PL and the substrate table, are performed before the repeated 
imaging of the mask pattern C is started. How many times this measurement 
is to be performed will depend on the variations of the ambient 
parameters. If one day substantially no variations are anticipated, it may 
suffice to perform one measurement at the beginning of this day. In the 
case of more variations the magnification error may be measured, for 
example, when mounting each new mask pattern by means of which a large 
number of substrates is to be exposed. The magnification-error measurement 
may also be performed if it is envisaged that the substrates are subject 
to changes or if the substrate already exhibit structures formed by means 
of another exposure apparatus. 
FIG. 2 shows a device in accordance with the invention in the simplest 
embodiment, which is preferably used if the construction of the exposure 
apparatus allows this. The object gratings comprise the gratings RG.sub.1 
and RG.sub.2 in a test mask MA.sub.T and the image gratings comprise the 
gratings WG.sub.1 and WG.sub.2 in the substrate table WT. The gratings are 
represented by short vertical lines. In reality, the grating strips extend 
in a direction perpendicular to the plane of the drawing. The gratings are 
amplitude gratings or deep phase gratings which behave as amplitude 
gratings. The projection-lens system is represented schematically by two 
lenses L.sub.1 and L.sub.2 ; in reality, this lens system comprises a 
large number of lens elements. The optical axis 00' is indicated in broken 
lines. 
The lens system PL images the grating RG.sub.1 onto the grating WG.sub.1 
and the grating RG.sub.2 onto the grating WG.sub.2. For the beam b.sub.2 
which images RG.sub.2 on WG.sub.2 the two marginal rays in addition to the 
chief ray are shown, whilst for the beam b.sub.1 which images RG.sub.1 
onto WG.sub.1 only the chief ray is shown. These beams may form part of a 
single broad beam, which is suitably the same beam as the beam PB in FIG. 
1, which subsequently images the mask pattern C onto the substrate. This 
is because the lens system PL is fully corrected for aberrations only for 
the specific wavelength, for example 365 nm, of the exposure beam PB. When 
another wavelength is used for magnification measurements minor deviations 
in the grating images may occur. However, in practice these deviations are 
so small that they may be considered to be constant. As a result of this, 
it is possible to correct for the shift of the zero point in the curve 
representing the magnification error signal, which shift is caused by said 
deviations. 
A radiation-sensitive detection system D.sub.1 and D.sub.2 respectively is 
arranged in the path of each of the beams b.sub.1 and b.sub.2 passing 
through the gratings WG.sub.1 and WG.sub.2. In the present embodiment the 
detection systems comprise simple detectors. The detectors are arranged in 
the substrate table. 
If the gratings RG.sub.1 and R.sub.2 are imaged on the gratings WG.sub.1 
and WG.sub.2 with the correct magnification M, for example 1/10, the 
periods of the grating images RG'.sub.1 and RG'.sub.2 are equal to those 
of the gratings WG.sub.1 and WG.sub.2, as is indicated in FIG. 3. The 
detectors D.sub.1 and D.sub.2 then receive a specific amount of radiation 
which is the same for both detectors if the gratings are aligned correctly 
relative to one another. If a magnification error occurs the imaged 
grating RG.sub.1 and the substrate grating WG.sub.1 are no longer exactly 
in register with each other, as is shown in FIG. 3b. This gives rise to a 
moire pattern, designated I.sub.2, that is a pattern of light and dark 
areas which in practice gradually merge into one another and whose period 
P.sub.MR is substantially larger than the period P.sub.RG'.sbsb.1 and 
P.sub.WG.sbsb.1 of the gratings RG'.sub.1 and WG.sub.1. The magnitude of 
the period P.sub.MR is determined by the magnification error. If the 
magnification error is zero the period of the moire pattern is infinite, 
as is indicated by the line I.sub.1 in FIG. 3a. 
In order to enable the magnification error to be determined the mask 
gratings and the substrate gratings are periodically moved relative to 
each other in the X-direction. For this purpose, as is shown schematically 
in FIG. 2, the substrate table WT may be coupled to a drive means DR for 
periodically moving this table in the X-direction. This drive means may 
comprise a drive means already present in the exposure apparatus for 
bringing the image of the gratings P.sub.1 and P.sub.2 in FIG. 1 in 
register with the gratings M.sub.1 and M.sub.2 to align the mask and the 
substrate relative to one another. The alignment device of the exposure 
apparatus cooperates with an interferometer system designated IF in FIG. 
1. This interferometer system may also be used for controlling the 
periodic movement of the substrate table for the purpose of 
magnification-error measurement. 
Owing to the periodic movement of the substrate grating WG.sub.1 relative 
to the imaged mask grating RG.sub.1 the amount of radiation incident on 
the detector D.sub.1 and consequently the signal S.sub.1 supplied by this 
detector will vary periodically. In the case of sufficiently small grating 
periods P.sub.RG1 and P.sub.WG.sbsb.1 the detector signal S.sub.1 as a 
function of the position X of the substrate table WT is substantially 
sinusoidal, as is shown in FIG. 3c. The detector D.sub.2 also supplies a 
periodic signal S.sub.2 having the same waveform as the signal S.sub.1. In 
the event of a magnification error and, consequently, a moire pattern of 
finite period, a phase difference .DELTA..phi. occurs between teh signals 
S.sub.1 and S.sub.2. The signals are applied to a phase comparator circuit 
FC whose output signal constitutes the magnification-error signal 
S.sub.ME. This signal is utilized for correcting the axial position of the 
substrate table in such a way that the signals S.sub.1 and S.sub.2 are 
substantially in phase. The period of the moire pattern is then infinite 
and the magnification error is reduced to substantially zero. 
The phase comparator circuit may be constructed in a way similar to that 
used for measuring linear displacements of an object by means of gratings, 
as is described in the article: "Accurate digital measurement of 
displacements by optical means" in "Philips' Technical Review" 30, 1969, 
No. 6/7, pages 149-160. As set forth in said article, a comparison of the 
phases of the beams originating from gratings which are imaged onto one 
another enable displacements of said gratings relative to each other to be 
determined very accurately and independently of variations in the 
measurement system. 
If a phase difference .DELTA..phi.=.epsilon. between S.sub.1 and S.sub.2 
can still be measured accurately by electronic means and if the residual 
magnification error after correction of the magnification gives rise to a 
positional error not greater than 0.05 .mu.m at the edge of the substrate 
area within which the mask pattern is to be imaged repeatedly, the 
following relationship is valid 
##EQU1## 
The factor 2 in the right-hand part of this equation results from the fact 
that said positional errors have opposite signs for the two substrate 
gratings. If P.sub.WG.sbsb.1 =2 .mu.m the phase difference will be 
.epsilon..ltoreq.0.31 rad. The minimum phase difference which should be 
detectable is then approximately 18.degree., which corresponds to 
approximately 1/20 of the period of the signals S.sub.1 and S.sub.2. This 
fairly large phase difference can already be detected by means of gratings 
which extend over a length corresponding to only a few times the grating 
period. The stroke of the periodic substrate-table movement may then be 
limited to some tens of .mu.m. When longer gratings are used it is 
possible to detect even smaller phase errors. 
The desired time modulation of the detector signal can be obtained by a 
periodic movement of the substrate gratings relative to the mask grating, 
but it can also be obtained by replacing each of the substrate gratings 
and the associated detector by an array of radiation sensitive detectors 
in the form of photodiodes. The detector array may be arranged in such a 
way that in one period of the grating image RG'.sub.1, which image is 
again assumed to be sinusoidal on account of the fine detail of the 
grating structure, there are for example four photodiodes, as is shown in 
FIG. 4. The first four detectors bear the reference numerals 1, 2, 3 and 4 
and form a first group. This group is followed by a second group and 
further groups of detectors. For the sake of simplicity only two groups of 
detectors are shown in FIG. 4. The detectors of the first group are 
interconnected to the corresponding detectors of the second group and 
those of the next groups. Corresponding detectors of the groups bear the 
same reference numerals. 
Since four detectors fit exactly in one period of the intensity profile of 
an imaged grating, the phase difference between the signals from two 
successive detectors is .pi./2 rad. Therefore, the detector signals may be 
represented by: 
EQU SI.sub.1 (x)=I. cos (x+.phi..sub.1)+I.sub.1 
EQU SI.sub.2 (x)=I. sin (x+.phi..sub.1)+I.sub.2 
EQU SI.sub.3 (x)=-I. cos (x+.phi..sub.1)+I.sub.3 
EQU SI.sub.4 (x)=-I. sin (x+.phi..sub.1)+I.sub.4 
where the phase term .phi..sub.1 is caused by a shift of the image of a 
mask pattern relative to the detectors resulting from a magnification 
error, and I.sub.1 . . . I.sub.4 are direct current terms which, in 
principle are equal. 
FIG. 5 schematically represents the electronic processing of the signals 
from the detector arrays associated with the grating picture RG'.sub.1 and 
RG'.sub.2. Each of these arrays is represented by only four detectors, so 
that the output signal of the detector represents the sum of the output 
signals of a plurlity of detectors corresponding to the number of groups. 
The signals SI.sub.1 (x) and SI.sub.3 (x) are applied to a differential 
amplifier 10 and the signals SI.sub.2 (x) and SI.sub.4 (x) are applied to 
a differential amplifier 11, resulting in: 
EQU SI.sub.5 (x)=SI.sub.i (x)-SI.sub.3 (x)=2.I. cos (x+.phi..sub.1) 
EQU SI.sub.6 (x)=SI.sub.2 (x)-SI.sub.4 (x)=2.I. sin (x+.phi..sub.1) 
By means of multipliers 12 and 13 these signals are multiplied by the 
signal cos .omega.t and sin .omega.t, respectively, supplied by an 
oscillator 15. These multipliers then deliver the signals: 
EQU SI.sub.7 (x)=2.I. cos (x+.phi..sub.1). cos .omega.t 
EQU SI.sub.8 (x)=2.I. sin (x+.phi..sub.1) sin .omega.t 
which are applied to the inputs of a differential amplifier 14, whose 
output signal is: 
EQU SI.sub.9 (x)=2.I. cos (x+.phi..sub.1 +.omega.t) 
The signals from the detectors 1', 2', 3' and 4' representing the detector 
array associated with the grating image R'.sub.2 are processed in the 
similar way by means of the elements 10', 11', 12', 13', 14' and 15, 
resulting in a signal SI'.sub.9 (x)=2.I. cos (x+.phi..sub.2 +.omega.t). 
In the phase comparator circuit FC the phases .phi..sub.1 and .phi..sub.2 
of the signals SI.sub.9 (x) and SI'.sub.9 (x) are compared with each 
other, yielding a magnification-error signal S.sub.ME. 
In the embodiment shown in FIG. 2 each of the detectors D.sub.1 and D.sub.2 
may be replaced by two detectors. The purpose of this will be explained 
with reference to FIG. 6, which shows an embodiment which also utilizes 
this step. 
If it is not desired or not possible to arrange detectors in the substrate 
table, the magnification-error measurement should be effected by means of 
reflected radiation instead of transmitted radiation. The embodiments of 
the invention to be described hereinafter all operate with reflected 
radiation. 
The image gratings may be formed by gratings on the substrate table. On 
such a table it is always possible to arrange these small gratings outside 
the substrate. However, alternatively, the image gratings may be arranged 
on the substrate itself. This is preferred if it is anticipated that, for 
example, deformations of the substrate will occur or if it is desired to 
have the possibility of using different exposure apparatuses in the 
processing of a substrate. 
FIG. 6 shows a first embodiment of a magnification-error detection device 
employing a reflected radiation. Again two gratings RG.sub.1 and RG.sub.2 
are arranged on the mask MA at an accurately defined distance d from each 
other and two gratings WG.sub.1 and WG.sub.2 are provided in the substrate 
w at a distance d', which is exactly equal to d times the magnification M, 
for example 1/10, of the projection-lens system PL. The gratings RG.sub.1 
and RG.sub.2 are amplitude gratings and, suitably, the gratings WG.sub.1 
and WG.sub.2 are also amplitude gratings. The last-mentioned gratings may 
also be phase gratings. However, in that case steps have to be taken to 
image the phase gratings as amplitude gratings. For this purpose, as is 
described in European Patent Application No. 0,164,165, polarisation means 
and beam-splitting means may be employed which ensure that two sub-beams 
which are shifted relative to one another by half a grating period are 
incident on a phase grating and that the beams reflected by the phase 
grating are recombined. 
If the grating period of the phase gratings is small enough these gratings 
cause diffractions at such large angles that a substantial portion of the 
radiation falls outside the projection lens system. In that case phase 
gratings may be used for magnification-error measurement of the substrate 
without a conversion of the phase gratings to amplitude gratings. 
As is shown in FIG. 6 an illumination beam b.sub.1 having a small aperture 
angle .alpha. traverses the mask gratings RG.sub.1. Suitably, this beam is 
aimed at the centre of the entrance pupil IP of the projection lens system 
PL, because this minimizes aberrations caused by this system. The beam 
b.sub.1 traverses the projection-lens system PL and is incident on the 
substrate grating WG.sub.1. A part of the radiation of the beam b.sub.1 is 
reflected, traverses the projection lens system again, and is incident on 
the grating RG.sub.1. A part of the radiation transmitted by this grating 
is directed to the detection system S.sub.1 by a beam splitter BS, for 
example a semitransparent mirror. The auxiliary lens L.sub.3 ensures that 
the grating RG.sub.1 is imaged on the radiation-sensitive surface of this 
detection system. By means of a second radiation beam b.sub.2, of which 
only the chief ray is shown for the sake of simplicity, the substrate 
grating WG.sub.2 is imaged on the mask grating RG.sub.2. A part of the 
radiation transmitted by this grating is received by a detection system 
D.sub.2. 
This device operates in a way similar to that shown in FIG. 2; as a result 
of the periodic movement of the substrate in the X-direction periodic 
detector signals are generated and by phase comparison of these signals it 
is ascertained whether a moire pattern having a non-infinite period 
occurs. Subsequently, the magnification is adapted by moving the mask MA 
relative to the projection-lens system and relative to the substrate along 
the optical axis 00' of this system until the detector signals are in 
phase. 
Preferably, the illumination beams b.sub.1 and b.sub.2 have the same 
wavelength as the projection beam PB in FIG. 1. The beams b.sub.1 and 
b.sub.2 may be portions of the projection beam. Since the aperture angle 
.alpha. of the beams b.sub.1 and b.sub.2 is small relative to the field 
angle or angle of view .beta. of the projection-lens system, the detection 
systems D.sub.1 and D.sub.2 can be screened effectively from radiation 
reflected from the front of the mask when a diaphragm with a narrow 
aperture is arranged in the radiation path behind the two gratings. Such a 
diaphragm may be formed by the beam-splitting mirror BS if the reflecting 
surface of this mirror is small. 
When an imaged substrate mask is shifted relative to a mask grating as a 
result of a magnification error over a distance equal to the period of a 
mask grating this corresponds to a phase shift of 2 .pi. rad in a detector 
signal. If it is required that, after detection and correction, the 
resulting magnification error is allowed to give rise to a maximum 
displacement of 0.05 .mu.m of a line imaged on the substrate and if the 
phase difference between the detector signals which can still be detected 
accurately is .epsilon. rad, the following requirement should be met: 
##EQU2## 
Consequently, in the case of a grating period P.sub.R =20 .mu.m, it is 
required that: 
EQU .epsilon..ltoreq.0.31 rad. 
This corresponds to 18.degree. or 1/20 period of the detector signals. Such 
a phase difference can still be measured correctly by electronic means 
when gratings are used having a length corresponding to some grating 
periods. The displacement of the substrate grating in the X-direction may 
be limited to this number of periods of the substrate gratings, that is to 
some tens of .mu.m. 
In principle, the radiation-sensitive detection systems D.sub.1 and D.sub.2 
may each comprise one detector. However, suitably these systems each 
comprise two detectors D'.sub.1, D".sub.1 and D'.sub.2, D".sub.2. By phase 
comparison of the signals from the detectors D'.sub.1 and D".sub.1 it is 
possible to determine whether the parts of the mask grating observed by 
these detectors and the substrate gratings imaged thereon coincide 
exactly. However, if this is the case it is still possible that the 
gratings are displaced by a full grating period relative to one another. 
However, in the case of, for example, a centre-to-centre distance of 60 mm 
between the gratings RG.sub.1 and RG.sub.2 and a distance of 5 mm between 
the detectors D'.sub.1 and D".sub.1 such a displacement results in a phase 
difference between the signals from the detectors D'.sub.1 and D".sub.1, 
which phase difference corresponds to 1/12 of the period of the signals of 
the detectors D'.sub.1 and D".sub.1 and can be measured even more simply 
than the above-mentioned phase difference of 1/20 period. Thus, said 
displacement by a full grating period can be detected by phase comparison 
of the signals from the detectors D'.sub.1 and D".sub.1 or from the 
detectors D'.sub.2 and D".sub.2. 
An axial-position error of the mask larger than the depth of focus of the 
lens system L.sub.1 L.sub.2 causes a deviation of the d.c. level of the 
detector signal and a deviation in the modulation depth of these signals. 
One of these parameters may be utilized for detecting a focussing error 
larger than the depth of focus. A focussing error can be eliminated by 
moving the substrate in an axial direction relative to the projection-lens 
system. The magnification-error measurement by means of the device shown 
in FIG. 6 is not affected by a focussing error. 
As is known, a radiation beam which is incident on a grating will be split 
into a plurality of sub-beams of different diffraction orders by this 
grating, namely into a non-diffracted zero-order sub-beam, two first-order 
sub-beams which are diffracted at a specific angle determined by the 
grating period, two second-order sub-beams which are diffracted through 
twice this angle, and higher-order sub-beams. If, as is assumed in the 
description with reference to FIGS. 2 and 6, the beams b.sub.1 and b.sub.2 
have an aperture angle .alpha. which is large relative to the angle at 
which the sub-beams are diffracted, the sub-beams of the various 
diffraction orders will overlap each other and the sub-beams cannot be 
detected separately. However, in the embodiments to be described 
hereinafter the gratings are illuminated by beams which have a 
substantially smaller aperture angle, for example ten times as small. In 
that case the sub-beams can be detected separately, so that it is possible 
to generate a focussing-error signal in addition to a magnification-error 
signal. Moreover, it is then possible to employ different methods for 
generating time-modulated detector signals. 
FIGS. 7a and 7b respectively show a plan view and a side view of a device 
utilizing this possibility. In this device the illumination beams b.sub.1 
and b.sub.2 can no longer enter the imaging systems by the mask gratings 
RG.sub.1 and RG.sub.2, because the first passage through these gratings 
would also give rise to diffraction orders, so that after diffraction by 
the substrate gratings WG.sub.1 and WG.sub.2 and further diffraction 
caused by the secondpassage through the mask gratings so many different 
diffraction orders would occur that these could not longer be detected 
separately. For this reason the beams b.sub.1 and b.sub.2 enter the 
imaging system by a mirror MR, as is shown in FIG. 7a. This Figure only 
illustrates how the beam b.sub.1 enters. The beam b.sub.2 which is 
situated before or behind the plane of the drawing of FIG. 7a enters by 
the same mirror MR. 
As is shown in FIG. 7b, the beam b.sub.1 traverses the projection-lens 
system L.sub.1, L.sub.2 and the chief ray of this beam is perpendicularly 
incident on the substrate grating WG.sub.1. The beam reflected by this 
grating is split into a zero-order sub-beam b.sub.1 (0) and two 
first-order sub-beams b.sub.1 (+1) and b.sub.1 (-1). The beams of higher 
diffraction orders may be ignored because their intensity is low, or they 
fall largely outside the pupil of the projection lens system, or they can 
be filtered out after passage through this lens system. The radiation 
reflected by the grating WG.sub.1 again traverses the lens system and 
reaches the mask grating RG.sub.1. This grating splits the zero-order and 
first-order sub-beams each into a zero-order sub-beam and two first-order 
sub-beams. These sub-beams are shown in FIG. 8. In this Figure WG.sub.1 ' 
is the image of the grating WG.sub.1. It may occur that the plane in which 
this grating is imaged does not coincide with the plane of the mask 
grating: then a focussing error .DELTA.Z occurs. Of the large number of 
sub-beams produced during passage through the mask grating RG.sub.1 only 
four sub-beams are employed which are incident in pairs on one of the 
detectors D.sub.10 and D.sub.11. As is shown in FIG. 8, it is possible to 
ensure by means of suitable filters or a suitable arrangement of the 
detectors that the detector D.sub.10 is hit by, for example, the sub-beams 
b.sub.1 (+1,0) and b.sub.1 (0,+1) and the detector D.sub.11 by the 
sub-beams b.sub.1 (-1,0) and b.sub.1 (0,-1). 
When a focussing error .DELTA.Z occurs there will be phase difference 
.DELTA..phi. between the sub-beams b.sub.1 (0) and b.sub.1 (+1) or b.sub.1 
(-1) as a result of the difference in the optical pathlengths traversed by 
these beams between the gratings WG'.sub.1 and RG.sub.1. In the case of a 
pathlength difference .DELTA.W this phase difference is: 
##EQU3## 
It follows from FIG. 8 that 
EQU .DELTA.W=.DELTA.Z (1-cos .theta.) 
For small angles .theta. the following applies: 
##EQU4## 
In the case of a periodic displacement of the imaged grating in the 
X-direction the signals from the detectors are moreover modulated with a 
time frequency where X' is the velocity in the X-direction and 
P.sub.WG'.sbsb.1 is the grating period of the image grating WG'.sub.1. 
A magnification error produces an additional phase difference between the 
signals from the detectors D.sub.10 and D.sub.11. 
The a.c. signals supplied by the detectors D.sub.10 and D.sub.11 may be 
represented as 
EQU SI.sub.10 =cos (.omega.t+.gamma.F+.gamma.M) 
EQU SI.sub.11 =cos (.omega.t-.gamma.F+.gamma.M) 
FIG. 8 relates to the image of the grating WG.sub.1 formed on the grating 
RG.sub.1 by the beam b.sub.1. It will be evident that a similar Figure 
applies to the imaging of the grating WG.sub.2 onto the grating RG.sub.2 
by means of the beam b.sub.2. If the latter figure detectors D.sub.12 and 
D.sub.13 are arranged at the locations of the detectors D.sub.10 and 
D.sub.11 in FIG. 8, the signals from the detectors D.sub.12 and D.sub.13 
comply with: 
EQU SI.sub.12 =cos (.omega.t+.gamma.F-.gamma.M) 
EQU SI.sub.13 =cos (.omega.t-.gamma.F-.gamma.M) 
In this expression 
##EQU5## 
The phase term .gamma.F as a result of the focussing error is given by 
##EQU6## 
The grating diffraction angle .theta. complies with 
##EQU7## 
i.e. for small angles .theta. this angle is 
##EQU8## 
and, consequently, 
##EQU9## 
The depth of focus s of the projection lens system PL complies with: 
##EQU10## 
where NA is the numerical aperture of the lens system or sin .beta., cf. 
FIG. 7b. If the angles .beta. are small and if .theta.=C..beta., where C 
is a constant smaller than 1, this yields 
##EQU11## 
A focussing error equal to one time the depth of focus s results in a phase 
difference 2 .gamma.F=2 rad between the signals SI.sub.10 and SI.sub.11 
and between the signals SI.sub.12 and SI.sub.13 if C=1. This means that 
focussing errors smaller than the depth of focus of the projection-lens 
system can be detected. 
Since the signals SI.sub.10 and SI.sub.11 differ only from one another with 
respect to the phase term .gamma.F a phase comparison of these signals in 
a phase comparator circuit enables the magnitude and the direction of a 
focussing error to be detected. 
The phase term .gamma.M is determined by the magnification error. If 
.DELTA.X is the distance, which depends on the magnification error, 
between the actual position q and the desired position q' in the plane of 
the mask of the image of a point p on the substrate, the phase difference 
2 .gamma.M between the signals SI.sub.10 and SI.sub.12 or between the 
signals SI.sub.11 and SI.sub.13 is equal to: 
##EQU12## 
where P.sub.RG is the period of the mask gratings. If an X of 0.5 .mu.m is 
permissible and if P.sub.RG =20 .mu.m it should be possible to detect a 
phase difference between the detector signals of 
##EQU13## 
which corresponds to 1/20 of the period of the signals SI.sub.10 and 
SI.sub.12, which presents no problem. The magnification error can be 
detected by phase comparison of the signals SI.sub.10 and SI.sub.12 or the 
signals SI.sub.11 and SI.sub.13 in a phase-comparator circuit. 
A displacement of the mask in the Z-direction over a distance .DELTA.Z 
gives rise to a displacement of the grating images in the X-direction of 
EQU .DELTA.X'=tan .beta.. .DELTA.Z. 
Since tan .beta.=d.sub.1 /Z, in which d.sub.1 is the distance between the 
centres of the mask gratings, see FIG. 6, and Z is the distance between 
the plane of the pupil and the plane of the mask, see FIG. 7b, this 
yields: 
##EQU14## 
In the case of a distance d.sub.1 =65 mm and Z.sub.1 is 384 mm a 
displacement .DELTA.Z =1 .mu.m results in a displacement of 0.17 .mu.m of 
the imaged gratings the mask plane. In view of the large depth of focus 
##EQU15## 
of the projection lens system, for example 200 .mu.m for an NA=0.32 and 
.lambda.=0.4 .mu.m, such a focussing error is negligible. In this 
projection system the magnification is more critical than the focussing. 
In the foregoing it is assumed that the mask gratings have a grating period 
equal to 1/M times the grating period of the substrate gratings. The mask 
gratings may also have a period which is twice as large, i.e. a period 
equal to 2/M times the period of the substrate gratings. The detector 
D.sub.10 or D.sub.11 is then arranged in such a way that it is hit by the 
sub-beams b.sub.1 (+1,-1) and b.sub.1 (0,+1) and the sub-beams b.sub.1 
(-1,+1) and b.sub.1 (0,-1) respectively. The advantage of this is that 
second-order sub-beams which may be produced by the mask grating if the 
width of the grating strips of these gratings is not equal to that of the 
intermediate strips, or which may be produced as a result of deformations 
of these gratings, can no longer overlap with the zero-order sub-beam and 
the first-order subbeams at the location of the detectors. Such overlaps 
may give rise to a slight distortion of the detector signals. 
Instead of by a periodic movement of the substrate or the mask the time 
modulation of the detector signals can also be obtained by using sub-beams 
which are polarised perpendicularly to each other and means for modulating 
the phase between these beams. Modulation may be effected at the detector 
side, that is in the detection branch, or at the object side. FIG. 9a is a 
plan view and FIG. 9b a side view of a device operating with polarised 
sub-beams. These Figures differ from FIGS. 7a and 7b only in that 
.lambda./2 plates HWP are arranged in the radiation path between the 
substrate gratings WG.sub.1, WG.sub.2 and the mask gratings RG.sub.1, 
RG.sub.2, .lambda. being the wavelength of the radiation which is used. 
The operation of the device employing polarized beams is best illustrated 
by means of FIG. 10 which shows an imaged substrate grating WG'.sub.1 and 
the associated mask grating RG.sub.1, as well as the sub-beams formed by 
these gratings. The sub-beams b.sub.1 (0), b.sub.1 (+1) and b.sub.1 (-1) 
originating from the substrate grating are linearly polarised beams whose 
direction of polarisation, indicated by the arrow 30, is situated in the 
plane of the drawing. A .lambda./2 plate HWP is arranged in the path of 
the zero-order beam b.sub.1 (0) to rotate the direction of polarisation of 
this beam through 90.degree. in the direction indicated by the arrow 31 
which extends perpendicularly to the plane of the drawing. As a result of 
this, the sub-beams b.sub.1 (+1,0) and b.sub.1 (0,+1) are also polarised 
perpendicularly to each other, which is also the case with the sub-beams 
b.sub.1 (-1,0) and b.sub.1 (0,-1). In the path of each pair of sub-beams 
which are polarised perpendicularly to each other a .lambda./4 plate QWP 
is arranged in a diagonal position. "Diagonal position" is to be 
understood to mean that the optic axis of this plane extends at an angle 
of +45.degree. or -45.degree. to the directions of polarisation 30 and 31. 
The directions of the optic axes of the plates QWP.sub.1 and QWP.sub.2 are 
indicated by the arrows a and b in FIG. 10. For the sake of simplicity 
these arrows are shown in the plane of the drawing; in reality these 
arrows extend at angles of +45.degree. and -45.degree. to the plane of the 
drawing. The .lambda./4 plate QWP.sub.1 converts the beam b.sub.1 (+1,0) 
into a clockwise circularly polarised beam and the beam b.sub.1 (0,+1) 
into a counter clockwise circularly polarised beam, as is indicated by the 
arrows 32 and 33. The .lambda./4 plate QWP.sub.2 performs the same 
function for the beams b.sub.1 (-1,0) and b.sub.1 (0,-1). As in reality 
the two sub-beams b.sub.1 (+1,0) and b.sub.1 (0,+1) and the sub-beams 
b.sub.1 (-1,0) and b.sub.1 (0,-1) practically coincide, these two 
oppositely circularly polarised sub-beams form one linearly polarised 
sub-beam whose azimuth or polarisation is determined by the phase 
difference between these beams. Before the linearly polarised sub-beams 
reach their respective detectors D.sub.10 and D.sub.11 they traverse a 
polarisation analyser AN which rotates with an angular velocity .OMEGA.t, 
thereby causing the detector signals to be time-modulated. The rotation of 
the analyser is indicated by the arrow 34, which has the same direction as 
the arrow 32. The signals from the detectors may now be represented by: 
EQU SI.sub.10 =cos (Qt-.gamma.F+.gamma.M,1) 
EQU SI.sub.11 =cos (Qt-.gamma.F+.gamma.M,1) 
FIG. 10 relates to the image of the grating WG.sub.1 formed on the grating 
RG.sub.1 by means of the beam b.sub.1. It will be obvious that a similar 
Figure applies to the image of the grating WG.sub.2 formed on the grating 
RG.sub.2 by means of the beam b.sub.2. If in the last-mentioned Figure 
detectors D.sub.12 and D.sub.13 are arranged at locations analogous to the 
locations of the detectors D.sub.10 and D.sub.11 in FIG. 10, the signals 
from the first-mentioned detectors comply with: 
EQU SI.sub.12 =cos (QT+.gamma.F-.gamma.M,2) 
EQU SI.sub.13 =cos (QT-.gamma.F-.gamma.M,2) 
In this expression for the detector signals 
##EQU16## 
is again the phase difference as a result of a focussing error .DELTA.Z, 
which can again be detected by phase comparison of, for example, the 
signals SI.sub.10 and SI.sub.11 and which can be eliminated by moving the 
substrate in the axial direction relative to the projection-lens system. 
The phase term .gamma.M,1 is caused by a deviation .DELTA.X.sub.1 between 
the actual position q' and the desired position q of the image of a point 
P of the substrate grating on the mask grating RG.sub.1. The phase term 
.gamma.M,2 is caused by a similar deviation .DELTA.X.sub.2 at the location 
of the grating RG.sub.2. Said deviation may be caused by an alignment 
error of a mask grating relative to the associated substrate grating or by 
a magnification error. The magnification error can be detected by 
comparing the phase term .gamma.M,1 with the phase term .gamma.M,2. The 
magnification error can be eliminated by applying the magnification-error 
signal thus obtained to a servo system by means of which the mask can be 
moved in the axial direction relative to the projection lens system and 
relative to the substrate. 
After the magnification error has been eliminated and hence 
.gamma.M,1=.gamma.M,2=.gamma.M,0 the alignment error can be detected by 
comparing the value of .gamma.M,0 with a reference value, which is for 
example given by the position of the analyser AN. The alignment error can 
be eliminated by moving the substrate in the X-direction relative to the 
mask. When two-dimensional gratings are used and additional detectors it 
is also possible to detect and eliminate an alignment error in the 
Y-direction perpendicular to and in the same plane as the X-direction. 
Instead of by means of a rotating polariser in the detection branch the 
time modulation of the detector signals is preferably effected by 
utilising incoming beams b.sub.1 and b.sub.2 which comprise two components 
which are polarised perpendicularly relative to each other and which have 
different frequencies or time-varying phases. A first possibility to 
achieve this is the use of a Zeeman laser as described in the article 
"Displacement measurement with a laser interferometer" in "Philips' 
Technical Review", Vol. 30, No. 6-7, pages 160-166. Such a laser produces 
a beam comprising two oppositely circularly polarised beam components 
having different radiation frequencies .omega..sub.1 and .omega..sub.2. In 
the detection branch a beat frequency .DELTA..omega.=.omega..sub.1 
-.omega..sub.2 is produced, whose phase depends on the magnitude to be 
measured. 
FIG. 11 shows the various directions of polarisation and frequencies of the 
sub-beams associated with the sub-strate-grating image WG'.sub.1 and the 
mask grating RG.sub.1. Each of the sub-beams b.sub.1 (0), b.sub.1 (-1) and 
b.sub.1 (+1) issuing from the substrate grating WG.sub.1, not shown, 
comprise two beam components having mutually perpendicular directions of 
polarisation, indicated by the arrows 30 and 31. The beam component having 
the direction of polarisation 30 has a radiation frequency .omega..sub.1 
and the beam component having the direction of polarisation 31 has a 
radiation frequency .omega..sub.2. In the path of the zero-order sub-beam 
b.sub.1 (0) a .lambda./2 plate HWP is arranged, which plate rotates the 
directions of polarisation of the beam components through 90.degree. 
relative to those of the corresponding components in the sub-beams b.sub.1 
(+1) and b.sub.1 (-1). Therefore, the directions of polarisation of the 
beam components of the frequencies .omega..sub.1 and .omega..sub.2 of the 
sub-beams b.sub.1 (0,+1) and b.sub.1 (0,-1) selected for detection are 
rotated through 90.degree. relative to the directions of polarisation of 
the corresponding components of the sub-beams b.sub.1 (+1,0) and b.sub.1 
(-1,0). 
In order to enable the different directions of polarisation to be spatially 
separated, polarisation analysers may be used which are situated in two 
mutually perpendicular positions, in which the directions of the optic 
axes correspond to the two directions of polarisation of the sub-beams. 
However, preferably use is made of polarisation-separating elements such 
as polarisation-separating prisms or Wollaston prisms. In FIG. 11 these 
Wollaston prisms bear the reference numerals 40 and 40' and the optic axes 
of these prisms bear the numerals 41 and 42. These prisms split each of 
the sub-beams in two sub-beam components having mutually perpendicular 
directions of polarisation. In the present embodiment four detectors 
D.sub.20, D.sub.21, D.sub.22 and D.sub.23 are provided for each 
illumination beam b.sub.1 and b.sub.2. On each of the detectors D.sub.20 
and D.sub.21 both the sub-beam b.sub.1 (+1,0) and the sub-beam b.sub.1 
(),+1) are incident and on the detectors D.sub.22 and D.sub.23 both the 
sub-beams b.sub.1 (0,-1) and the sub-beam b.sub.1 (-1,0) are incident. 
In FIG. 11 the angles at which the sub-beams are reflected by the Wollaston 
prisms and the focussing error .DELTA.Z are shown to an enlarged scale but 
in reality these angles .DELTA.Z are much smaller. For the image of the 
substrate grating WG.sub.2 formed on the mask grating RG.sub.2 by means of 
the beam b.sub.2 a Figure similar to FIG. 11 applies, four detectors 
D.sub.25, D.sub.26, D.sub.27 and D.sub.28 again being arranged at 
locations analogous to the locations of the detectors D.sub.20, D.sub.21, 
D.sub.22 and D.sub.23 in FIG. 11. In the device shown in FIG. 11 the 
sub-beams b.sub.1 (+1,-1), b.sub.1 (0,+1) and the sub-beam b.sub.1 
(-1,+1), b.sub.1 (0,-1) may also be used for detection instead of the 
aforementioned sub-beams, in the same way as in the device shown in FIGS. 
8 and 10. 
The time-dependent output signals from the detectors D.sub.20, D.sub.21, 
D.sub.22 and D.sub.23 may be represented by: 
EQU SI.sub.20 =A cos (.DELTA..omega.t+.gamma.F-.gamma.M,1) 
EQU SI.sub.21 =A cos (.DELTA..omega.t-.gamma.F-.gamma.M,1) 
EQU SI.sub.22 =A cos (.DELTA..omega.t+.gamma.F-.gamma.M,1) 
EQU SI.sub.23 =A cos (.DELTA..omega.t-.gamma.F-.gamma.M,1) 
Replacing .gamma.M,1 by .gamma.M,2 in this expression yields the detector 
signals SI.sub.25, SI.sub.26, SI.sub.27 and SI.sub.28. From the signals 
SI.sub.20 -SI.sub.23 and SI.sub.25 -SI.sub.28 the same information can be 
derived as is described with reference to FIG. 10. 
Instead of a Zeeman laser it is possible to use a radiation source 
supplying a linearly polarised beam. A modulator MO, for example an 
elasto-optical modulator, should then be arranged in the path of this 
beam, as is indicated in FIG. 9a. Care is taken that the direction of 
polarisation of the beam b.sub.1 makes an angle of 45.degree. with the 
optic axis of the modulator. If the modulator is energised with periodic 
signal cos (.delta.t) the birefringence .psi. of the modulator changes in 
conformity with .delta.=.delta..sub.0 cos(.psi.t). The beam b.sub.1 
issuing from the modulator then has two components having mutually 
perpendicular directions of polarisation and exhibiting a phase difference 
which is time-modulated in conformity with .delta..sub.o cos (.psi.t). In 
the same way as is shown in FIG. 11, the sub-beams formed from this beam 
after traversing the gratings WG'.sub.1 and RG.sub.1 are separated in 
conformity with their directions of polarisation and are incident on four 
detectors. The output signals of these detectors are now: 
EQU SI.sub.20 =B cos (.delta..sub.o. cos (.psi.t)+.gamma.F-.gamma.M,1) 
EQU SI.sub.21 =B cos (.delta..sub.o. cos (.psi.t)-.gamma.F-.gamma.M,1) 
EQU SI.sub.22 =B cos (.delta..sub.o. cos (.psi.t)+.gamma.F-.gamma.M,1) 
EQU SI.sub.23 =B cos (.delta..sub.o. cos (.psi.t)-.gamma.F-.gamma.M,1) 
Replacing of .gamma.M,1 by .gamma.M,2 again yields the signals SI.sub.25 to 
SI.sub.28. Again the signals SI.sub.20 -SI.sub.24 and SI.sub.25 -SI.sub.28 
contain the same information as the corresponding signals obtained by 
means of the device shown in FIG. 11. 
A modification of the embodiment which is related to the embodiments 
described with reference to FIGS. 9, 10 and 11 will now be described with 
reference to FIGS. 12 and 13. This device has the advantage that the 
.lambda./2 plate HWP need no longer be arranged between the substrate and 
the mask, so that in the design of the projection-lens system no allowance 
has to be made for this plate and that for the magnification measurement 
the coupling mirror MR in FIG. 9a need no longer be arranged in the path 
of the projection beam PB. However, it is now necessary that the radiation 
source produces a beam of high intensity and that the elements, to be 
described hereinafter, in the detection branch can be positioned with high 
accuracy. 
In the device shown in FIGS. 12 and 13 the mask gratings have a smaller 
period than 1/M times the period of the substrate gratings. The angle at 
which the first-order sub-beams are diffracted by a mask grating are then 
larger than the angle at which the substrate grating diffracts the 
first-order sub-beams. The grating periods are selected in such a way that 
the sub-beams b.sub.1 (+1) and b.sub.1 (-1) formed by the substrate 
grating WG.sub.1 can just pass through the pupil PU of the projection-lens 
system PL. The first-order sub-beams b'.sub.1 (+1) and b'.sub.1 (-1) 
produced upon the first passage through the mask grating RG.sub.1 can then 
no longer pass through the projection-lens system. Therefore, the 
substrate gratings are only illuminated by the zero-order beams b'.sub.1 
(0) and b'.sub.2 (0) of the illumination beams b.sub.1 and b.sub.2 which 
are incident on the mask gratings RG.sub.1 and RG.sub.2 from the left. The 
beams b'.sub.1 (0) and b'.sub.2 (0) are again split into a zero-order 
sub-beam and two first-order sub-beams by the substrate gratings WG.sub.1 
and WG.sub.2, so that after the passage through the mask gratings RG.sub.1 
and RG.sub.2 each beam b.sub.1, b.sub.2 again has the same number of 
diffraction orders as in the devices shown in FIGS. 8, 10 and 11. FIG. 13 
shows the sub-beams b.sub.1 (0,+1), b.sub.1 (+1,0) and b.sub.1 (-1,0) and 
b.sub.1 (0,-1) employed for detection. This Figure also shows the 
additional elements used in the detection branch. 
Again the zero-order sub-beam b.sub.1 (0) and the first-order sub-beams 
b.sub.1 (+1) and b.sub.1 (-1) originate from the substrate grating, not 
shown and are diffracted at an angle .theta.. Each of these sub-beams has 
two components with directions of polarisation which are perpendicular to 
each other and with different radiation frequencies .omega..sub.1 and 
.omega..sub.2 if a Zeeman laser is used as the radiation source. Again it 
is possible to employ a combination of a radiation source emitting a 
linearly polarised beam and an elasto-optic modulator. The direction of 
polarisation of each sub-beam then varies periodically in time. The mask 
grating RG.sub.1 splits each of said beams into a zero-order sub-beam and 
two first-order sub-beams. Since the period of the mask grating is k/M 
times the period of the substrate grating, k being smaller than 1, for 
example 1/3, the diffraction angle .theta. of the mask grating is 1/k 
times the diffraction angle of the substrate grating. In order to provide 
a better overlap of the sub-beams b.sub.1 (0,+1) and b.sub.1 (+1,0) and 
the sub-beams b.sub.1 (0,-1) and b.sub.1 (-1,0), deflection elements, for 
example wedges WE, WE', may be arranged in the path of these beams. In 
order to ensure that only the desired sub-beams reach the detectors 
D.sub.20, D.sub.21, D.sub.22 and D.sub.23 a filter FI is provided, which 
filter stops the sub-beams b.sub.1 (-1,-1), b.sub.1 (+1,-1), b.sub.1 
(0,0), b.sub.1 (-1,+1) and b.sub.1 (+1,+1). The plane of the mask grating 
RG.sub.1 is imaged in the plane of an axiliary grating AG by means of a 
lens L.sub.4. The grating period of this grating is adapted to the period 
of the interference pattern which is formed at the location of this 
grating by the interfering sub-beams, which make specific angles with one 
another. The grating period of this auxiliary grating should be such that 
the diffraction angle .theta.' is equal to the angle (k'-1). .theta. 
between the beams b.sub.1 (0,+1) and b.sub.1 (+1,0). This grating period 
is given by: 
##EQU17## 
where M.sub.4 is the magnification of the lens L.sub.4 and k'=1/k. Now a 
.lambda./2 plate HWP is arranged behind the mask grating RG.sub.1 and only 
in the path of the sub-beam b.sub.1 (0,+1) and b.sub.1 (0,-1). This plate 
has the same function as the .lambda./2 plate in the device shown in FIGS. 
9, 10 and 11. Between the auxiliary grating AG and the detectors a 
polarisation-separating element, for example a Wollaston prism WP is 
arranged, which prism spatially separates the beam components having 
mutually perpendicular directions of polarisation, so that these 
components can be received by separate detectors in the same way as in the 
device shown in FIG. 11. 
The detector signals SI.sub.20 -SI.sub.23 and SI.sub.25 -SI.sub.28 are 
similar to the corresponding signals obtained in the device shown in FIG. 
11. 
The time modulation of the detector signals for the device shown in FIG. 2 
and described with reference to FIGS. 4 and 5 may also be employed in a 
device utilising reflected radiation. FIG. 14 shows such a device. This 
device does not employ mask gratings and polarisation means nor does it 
utilise movements of the gratings relative to each other. The substrate 
gratings WG.sub.1 and WG.sub.2 are illuminated by the beams b.sub.1 and 
b.sub.2 by windows WI.sub.1 and WI.sub.2 in the mask. The sub-beams of 
different diffraction orders reflected by the substrate gratings traverse 
the projection-lens system PL and image the gratings on the window. 
Semitransparent mirrors BS.sub.1 and BS.sub.2 are arranged in the paths of 
the beams b.sub.1 and b.sub.2 to direct a part of the radiation reflected 
by the substrate gratings towards an array of radiation-sensitive 
detectors DA.sub.1 and DA.sub.2. The lenses L.sub.5 and L.sub.6 and the 
lenses L'.sub.5 and L'.sub.6 respectively image the substrate gratings 
WG.sub.1 and WG.sub.2 on the associated detector array. Filters SF, SF' 
are arranged between these lenses and transmit only the desired 
diffraction orders. The detector arrays have the same construction and the 
signals from the detectors are processed in the same way as described with 
reference to FIGS. 2, 4 and 5. 
The fact that the invention has been described when utilized in an 
apparatus for the repeated exposure of a substrate by a mask pattern does 
not imply that it is limited thereto. The magnification-error detection in 
accordance with the invention may be employed in systems in which very 
fine details should be imaged with a high dimensional accuracy and in 
which ambient parameters can influence the imaging quality and in systems 
in which different patterns have to be imaged onto one another.