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Reconstruction of sub-wavelength

features and nano-positioning of gratings

using coherent Fourier scatterometry

Nitish Kumar,1,∗Peter Petrik,1,2Gopika K P Ramanandan,1Omar El

Gawhary,1,3Sarathi Roy,1Silvania F Pereira,1Wim M J Coene,4and

H. Paul Urbach1

1Optics Research Group, Department of Imaging Physics, Faculty of Applied Sciences, Delft

University of Technology, Van der Waalsweg 8, 2628CH Delft, The Netherlands

2Research Centre for Natural Sciences, Institute for Technical Physics and Materials Science,

Hungarian Academy of Sciences, H-1121 Budapest, Konkoly Thege Mikl´

os ´

ut 29-33, Hungary

3VSL Dutch Metrology Institute, Thijsseweg 11, 2600 AR Delft, The Netherlands

4ASML Netherlands B.V., De Run 6501, 5504 DR Veldhoven, The Netherlands

∗N.Nitishkumar-1@tudelft.nl

Abstract: Optical scatterometry is the state of art optical inspection

technique for quality control in lithographic process. As such, any boost in

its performance carries very relevant potential in semiconductor industry.

Recently we have shown that coherent Fourier scatterometry (CFS) can lead

to a notably improved sensitivity in the reconstruction of the geometry of

printed gratings. In this work, we report on implementation of a CFS instru-

ment, which conﬁrms the predicted performances. The system, although

currently operating at a relatively low numerical aperture (NA =0.4)

and long wavelength (633 nm) allows already the reconstruction of the

grating parameters with nanometer accuracy, which is comparable to that

of AFM and SEM measurements on the same sample, used as reference

measurements. Additionally, 1 nm accuracy in lateral positioning has been

demonstrated, corresponding to 0.08% of the pitch of the grating used in

the actual experiment.

© 2014 Optical Society of America

OCIS codes: (120.3940) Metrology; (290.5820) Scattering measurement; (180.5810) Scanning

microscopy; (050.1950) Diffraction gratings.

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European patent (WO/2012/126718) and US patent US 20120243004 A1 (2012).

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in coherent fourier scatterometry using scanning,” JEOS:RP 8, 13048 (2013).

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1. Introduction

The demand for faster, smaller, lighter and, at the same time, high-data density electronic de-

vices sets stringent requirements for nanolithography, the science of writing small features into

a photo-sensitive resist layer on top of a silicon wafer [1]. Already for the current 45 and 32 nm

technology nodes, the uniformity of the line-width or critical dimension (CD) over the wafer as

produced by lithographic scanners must be improved for an optimal yield and performance of

the electronic components. In order to obtain the intended line shapes and sizes, a reliable in-

line process control has to take place. This is achieved by printing special targets on the wafer,

typically gratings, which are successively measured in order to adjust dose, exposure time, over-

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6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24679

lay/alignment and other relevant process parameters of the photo-lithographic machine [2,3].

Currently, the metrology task of this process control is achieved by means of Incoherent Optical

Scatterometry (IOS). In this technique, which is a very well established method for the inspec-

tion of periodic structures like gratings, an incoming beam is shone on the target and the part of

the light which is scattered by it in reﬂection is measured in the far ﬁeld. Given some a priori

knowledge of the target, one can achieve high accuracies in the reconstruction of the shape of

the grating. The advantage over other competing inspection techniques, such as imaging, Scan-

ning Electron Microscopy (SEM) or Atomic Force Microscopy (AFM), is that IOS is a very

fast technique which does not suffer from the Rayleigh diffraction limit, is easily integrable in a

lithographic machine, and can cope with the high throughputs of today’s scanners, in the order

of 200 wafers per hour.

The way near ﬁeld techniques utilize coupling of probe and sample cannot be utilized in

production environment without decreasing the throughput. Rigorous far ﬁeld techniques are in

this sense a good alternative. However, such advantages also have a price since scatterometry

falls into the category of inverse problems in electromagnetism, which are known for being

severely ill-posed. Inverse problems occur in many other branches of science and technology

as well. Ill-posedness in this context means that the successful reconstruction of grating param-

eters from the far ﬁeld may not be possible, or may not be unique [4,5]. This implies that even a

very precise and accurate experimental far ﬁeld signal does not always provide enough informa-

tion content for reconstruction. It is the presence of some

a priori

information (as for example

an approximate grating structure) that enormously reduces the impact of the ill-posedeness and

makes scatterometry feasible in practice.

Many variations of the idea behind a scatterometer have emerged in the last decades [6].

Some of the most widely used conﬁgurations are single incidence angle reﬂectometry, 2-Θ

scatterometry, spectroscopic ellipsometry, Fourier scatterometry, interferometric Fourier scat-

terometry,etc., [7–15] with a wide range of applications [16–20]. In an earlier paper, it has been

predicted theoretically how, and under which conditions, CFS can be more sensitive than the

classical IOS [21]. In this paper, we demonstrate the reconstruction of the parameters of a peri-

odic grating using Coherent Fourier Scatterometry (CFS), which represents a step towards the

further improvement of sensitivity of scatterometry in the sub-nanometer regime. Beside pro-

viding an accurate reconstruction of the grating’s parameters, CFS also carries the strong po-

tential of being used as subnanometer wafer alignment tool since the scattered signal is highly

sensitive to the grating position as well. Last, but not least, CFS with focused spot is not limited

to measuring periodic structures but can be applied to analysis of multilayer structures, mate-

rial sciences, photonics industry, biosensing, detection of isolated structures and other formsof

non-contact metrology.

2. Simulation and experimental considerations

2.1. Coherent Fourier scatterometry

In CFS, light from a coherent source is focused on periodic structures (typically gratings) on the

wafer. The focused spot interacts with the grating and the farﬁeld is recorded [22]. In this way,

the angular spectrum for all scattered waves is recorded at once for all incident plane waves

within the focused spot. In the event of overlapping reﬂected orders in the lens pupil, there is

interference between them and some phase information is also registered [23]. This is achieved

by scanning the grating by means of a tightly focused beam, which allows resolving the phase

information in practice. The number of scanning positions needed to resolve the phase depends

upon the number of overlapping orders in the pupil of the focusing lens. Since the technique

relies on the acquisition of the diffracted far ﬁeld, methods to model the interaction between

incident focused spot and the grating, which gives rise to such far ﬁeld, must be implemented.

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6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24680

This task, called forward problem, is typically performed by means of a rigorous electromag-

netic solver for a set of geometrical and physical parameters of the grating (Fig. 1.) under the

predeﬁned illumination conditions. In this way, the overall expected sensitivities of IOS and

CFS have been computed and compared [24,25].

2.2. Grating model and the illumination scheme

Let us consider an inﬁnitely long one-dimensional grating with period Λ, which is invariant

along the y-axis as shown in Fig. 1. The geometrical shape of the grating is deﬁned by the pa-

rameters midCD (width of the grating lines at half of the total height), height and side wall angle

(SWA). An additional metrology parameter, which we call bias, is also deﬁned here. Bias is the

measure of the grating displacement from its nominal position with respect to the illumination

spot. Deﬁned in this way, such parameter directly provides information on the alignment of the

wafer which the grating has been printed on. The zero bias position can be chosen arbitrarily,

and in our case, we choose it at the position where the optical axis of the microscope objective

bisects the midCD (assuming a symmetrical grating proﬁle). These parameters and the basic

principle of data acquisition in CFS are shown in Fig. 1.

Period

MidCD

Height

SWA

Bias=0

Bias=0

Incident

field

Scattered

field

CCD Beam

Splitter

Focusing

lens

Translation of the grating

x

zy

Fig. 1. Scheme of the CFS illumination, data acquisition system and the grating parameters.

A collimated light beam with a well-deﬁned polarization state in the pupil of the lens is

focussed on the grating and the scattered light is collected and collimated by the same lens, and

detected by the CCD as illustrated in Fig. 1. Any change in the grating parameters results in a

nonlinear change of the reﬂected far ﬁeld. The total number of detected propagating diffracted

orders depends on the wavelength (

λ

) of the incident light, the numerical aperture (NA)ofthe

lens and the period (Λ) of the grating. The amount of overlap between the diffracted orders in

the lens pupil is given by the overlap parameter F, deﬁned as:

F=

λ

NA∗Λ.(1)

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F<1 1<F<2 F>2

+1 +2

-1-2 0-1 +1

0-1 +1

0

Fig. 2. Overlap between the diffracted orders depending upon the value of the overlap

parameter F. The NA of the lens is marked with black circles.

As shown in Fig. 2, at the lens pupil, for 1 <F<2, there is an overlap between the 0th and

±1st orders of the grating but no overlap between the −1st and +1st order. For F<1, however,

there is an overlap between the higher diffracted orders, and for F>2, there is no overlap

between the orders.

2.3. Grating fabrication

The periodic structure used in the experiment is an etched silicon grating. To fabricate the grat-

ing, a cleaned silicon wafer was spin-coated with e-beam sensitive resist polymethyl methacry-

late (PMMA). The grating pattern was written into the resist using electron beam lithography.

After development of the resist, the grating pattern was etched into the silicon wafer using a

reactive ion etching system (F1 Leybold Fluor ethna), with SF6gas as the etchant. The remain-

ing resist layer was removed using dry oxygen plasma etch. The target parameters of grating

fabrication are pitch=1300 nm, midCD=560 nm, height=115 nm, and SWA=90 degrees.

2.4. Experimental setup

SMF1

S1

FC

SMF2

L2

P1

BS1

BS2

L1

L3 L4L5

L6

P2

DP

CCD

BFP

MO

TS OP

LED

L7

(b)

S

MF1

S

MF2

L

2

P

1

BS

1

BS

2

L3

L

4

L5

6

BFP

M

O

T

S

OP

LED

L7

(

b

)

SMF1

MO

TS

OP

SMF2

LED

CCD

LASER

FIBER

COUPLER

Computer

(a)

Fig. 3. Schematics of the experimental setup. (a) Ray diagram of the experimental scheme

(S1: He-Ne laser, FC: Fiber coupler, SMF: Single mode ﬁber, LED: Light emitting diode,

BS: Beam splitter, P: Polarizer, L: lens, DP: Detector plane, BFP: Back focal plane, OP:

Object plane (grating), MO: Microscope objective, TS: Piezo-controlled translation stage).

(b) 3D illustration of the laboratory setup.

Figure 3 represents the schematics of the coherent Fourier scatterometer. Light from a He-

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6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24682

Ne laser (

λ

=633 nm) is coupled into a ﬁber which is then divided into two arms by a ﬁber

coupler (FC). SMF1 and SMF2 are the illumination and the alignment arm, respectively. Light

from SMF1 is collimated and polarized to provide a well-deﬁned illumination of the sample

through the microscope objective (MO). The incident light is selected to be either in TE or TM

polarization conﬁguration in the entrance pupil of the lens. The denomination TE(TM) here

refers to the incident electric (magnetic) ﬁeld in the pupil being oriented parallel to the grooves

of the grating. The incident focused spot can be decomposed into plane waves with varying

incident angles. The maximum angle of incidence is limited by the numerical aperture NA of

the microscope objective MO. In the actual experiment, we used an objective with NA =0.4.

Each allowed incident angle contributes to the reﬂected diffraction orders which propagate

back through the MO to the CCD. The diameter of the collimated reﬂected beam is reduced by

a telescopic system, which images the back focal plane (BFP) of the MO onto the CCD with

a demagniﬁcation of 2.5X to ﬁt into the CCD area (1600 ×1200 pixels, size of 3.75

μ

m×

3.75

μ

m per pixel). In the Fourier or back focal plane (BFP) there is an interference between

the reﬂected orders for the chosen Fnumber (1 <F<2, see Fig. 2). The polarizer P2 in the

experimental setup can be used to detect a selected polarization at the CCD. SMF2 is used to

align the telescopic system. The red LED light source is only used to image the grating on the

CCD camera for alignment purposes during the preparation of the experiment. Components

BS2 and L6 are removed during data acquisition. The solid red line in the ray diagram of Fig.

3(a) is the data acquisition path and the black dotted paths are used only for alignment and

imaging. In the setup, the telescopic lenses L4 and L5 are used for data acquisition; and lens

L6, beam splitter BS2, and lenses L4 and L5 are used for alignment and imaging.

3. Results and discussion

3.1. Diffracted far ﬁeld intensity maps

Along with the acquisition of experimental data, scatterometry also requires an accurate mod-

elling of the interaction between ﬁeld and sample. We used the rigorous coupled wave analysis

(RCWA) as the rigorous solver to compute the ﬁeld diffracted by the grating [26–28]. In order

to make the simulations as faithful as possible, the measured amplitude and phase distribution

of the incident ﬁeld is included in the RCWA simulations as well. The amplitude for the in-

coming beam is practically uniform (measured by CCD and SHS) and the phase in the entrance

pupil of the lens is measured with a Shack-Hartmann wavefront sensor (SHS) [29]. In Figs.

4(a) and (a) the measured wavefronts for TE and TM polarizations on the lens pupil expressed

in units of wavelength of the incident light are shown. The far ﬁeld intensity maps for a ﬁxed

bias shown in Fig. 4 are the simulated and measured data obtained for a silicon etched grating

having an overlap parameter F=1.2 (see Fig. 2) for NA =0.4 at the wavelength of 633 nm.

Far ﬁeld intensity maps b, c and d (b,c

and d) represent respectively the simulation, exper-

iment and the difference between them for best matched ﬁt for TE (TM) incident light on the

lens pupil and mixed output polarization (i.e., no polarizer is used in the detection path). In the

simulations, the measured wavefront with a Shack-Hartmann sensor (SHS) is used to compute

the diffracted far ﬁeld intensity maps. The camera has been tested for noise by measurements,

where each far ﬁeld intensity map is averaged over 10 frames. Also, we consider the measured

noise of the CCD camera as normally distributed with standard deviation given by measured

uncertainties of

σ

=1×10−3. While the energy in the diffracted order depends upon the grat-

ing parameters, the extent of overlap between the diffracted orders in the far ﬁeld is given by

the overlap parameter F.

It is to be noted that the sensitivity of grating parameters (change of the far ﬁeld maps) is dif-

ferent for TE and TM incident polarized light. In CFS,in the overlap region there is interference

between the grating orders and the phase change due to the shift of the grating can be related to

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−0.3

−0.2

−0.1

0

0.1

−0.3

−0.2

−0.1

0

0.1

λ

λ

0

0.5

1

0

0.5

1

−0.2

−0.1

0

0.1

0.2

0.3

0

0.5

1

0

0.5

1

−0.2

0

0.2

0.4

0.6

(a) (b) (c) (d)

(a’) (b’) (c’) (d’)

Fig. 4. Simulated and experimental far ﬁeld intensity maps for a ﬁxed bias value and the

difference between the simulation and experiments. Wavefront for TE (a) and TM (a)

incident polarizations on the lens pupil. Far ﬁeld intensity maps b, c and d (b,c

and d)

represent the simulation, experiment and the difference between them for best matched ﬁt

for TE (TM) incident light on the lens pupil and mixed output polarization. The diameter

of the pupil in a and ais 8 mm.

the change in far ﬁeld intensity maps for different bias values. The amount of phase shift in the

non-zero order due to translation distance

δ

xis given by

δφ

=2

π

m

δ

x

Λ,(2)

where mis the order number of the reﬂected order.

3.2. Bias correlation

Wafer positioning is an important issue in the industrial manufacturing process. Being a phase

sensitive technique CFS introduces a change in the far ﬁelds with scanning position on the

grating. In the experiments, far ﬁeld intensity maps for consecutive scan positions (bias) of

20 nm difference were recorded over the length of several periods of the grating. The ability to

distinguish between the intensity maps deﬁnes the sensitivity to bias of the present experimental

setup. The degree of correlation ’r’ (correlation coefﬁcient) is used as a measure to distinguish

experimental images:

r=∑x∑yIref

xy −¯

Ire f (Ixy −¯

I)

∑x∑yIref

xy −¯

Ire f 2∑x∑y(Ixy −¯

I)2

.(3)

Here, Iref and I(xand yare pixels) are the far ﬁeld intensities corresponding to the starting

bias position called reference and the other scanning positions. ¯

Iref and ¯

Iare the corresponding

mean values for Iref and I. The correlation coefﬁcient rhas values between −1 to 1. When

the intensity maps are completely correlated, r=1, while r=0 implies no correlation and there

is complete anti correlation between the intensity maps for r=-1. In Fig. 5, value of correlation

coefﬁcient derived from the experimental far ﬁeld intensity maps is shown for bias values rang-

ing from 0 to 1.3

μ

m (one period of the grating). Figure. 5(a) plots the correlation coefﬁcients

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for scanning positions within one period of the grating. Figure 5(b) is the color label adjusted

plot to highlight the sensitivity of bias.

Bias (nm)

Bias (nm)

200 400 600 800 1000 1200

200

400

600

800

1000

1200 −0.2

0

0.2

0.4

0.6

0.8

(a)

Bias (nm)

Bias (nm)

200 400 600 800 1000 1200

200

400

600

800

1000

1200

0.9

0.92

0.94

0.96

0.98

1

(b)

Fig. 5. Degree of correlation between experimental far ﬁeld intensity maps. (a) Correlation

coefﬁcients for positions separated by 20 nm for bias values within one period of the grating

(b) The same as a), but only showing the range points where 0.9<r<1.

From the above analysis of the experimental data, it is evident that CFS is highly sensitive to

grating position. However, for a symmetric grating, absolute positions may also be determined

regarding the symmetric position within a period of the grating (like the middle of the midCD,

for which the far ﬁelds are also symmetric). In CFS, nm and sub-nm positioning within a single

period of the grating can be reached in wafer alignment in semiconductor industry, also shown

in the reconstructed values (see Table 1 further in the text). This feature can also be used in

other application as in imprint technology.

3.3. Model based optimization

Solving the inverse problem of grating reconstruction with CFS amounts to the determination

of the values of the grating parameters for which the computed scattered far ﬁeld maps ﬁt best

the experimentally measured images. The grating parameters deﬁned in Fig. 1 lie in certain

intervals obtained from a priori information and from the design speciﬁcation of the grating.

Starting from the nominal values of the grating parameters, the deviation between the experi-

mental and simulated images are minimized, using a least square function (merit function) by

varying the grating parameters. The diffracted far ﬁeld of the grating depends on the known

experimental conditions and the unknown grating parameters. Let adenote the grating param-

eters and I(m)

i,jand I(s)

i,jthe measured and simulated far ﬁeld intensities at the ith CCD pixel and

jth scan position. The merit function to be minimized is the difference between the simulated

and experimental far ﬁeld intensities summed over all the incident angles in the entrance pupil

and pixels over the detector. The merit function is thus given by

f(a)=

S

∑

j=1

1

N

N

∑

i=1I(m)

i,j(a)−I(s)

i,j(a)2

,(4)

where Sis the total number of scan positions and Nis the total number of pixels at the detector

for a single far ﬁeld intensity map. We use a gradient-based non-linear optimization method to

minimize the merit function deﬁned in Eqn. 4 [30]. It can be minimized using library search or

real time optimization methods [31]. In library search, several sets of far ﬁelds for approximate

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Received 30 Jun 2014; revised 17 Aug 2014; accepted 19 Aug 2014; published 1 Oct 2014

(C) 2014 OSA

6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24685

grating parameters lying in the deﬁned intervals are computed. Subsequently, the set of grating

parameters for the minimal value of the merit function (Eqn. 4) is selected as the desired value

of the grating parameters. It is to be noted that the optimization algorithm ﬁnds only the local

minima. Here we use a gradient based non-linear least squares real time optimization method

implemented in MATLAB. As a priori information in optimization, the target parameters of

grating fabrication (listed in the text in section 2.3) are used. Figure 6 shows a set of simulated

and experimental far ﬁelds for bias values lying within a single period of the grating obtained

with TE incident light on the lens pupil and no polarizer at the detector for the grating parame-

ters corresponding to the minimized merit function. Consecutive far ﬁelds (numbered 1 to 12)

correspond to consecutive grating positions for a bias difference of 100 nm.

Simulations

1

2

3

4

5

6

7

8

9

10

11

12

Experiment

1

2

4

5

6

7

8

9

10

11

12

Fig. 6. Simulated and experimental far ﬁeld for TE incident polarization on the lens pupil

and no polarizer at the detector for the grating parameters corresponding to the minimized

merit function. The bias position is changed by 100 nm between consecutive far ﬁelds

(numbered 1 to 12).

3.4. Parameters reconstruction and discussion

The reconstructed grating parameters are listed in Table 1 (for all the grating parameters includ-

ing bias are ﬁtted together in the optimization). The far ﬁeld intensities used for the reconstruc-

tion algorithm is a set of data such as shown in Fig. 6 but the incident ﬁelds are TE and TM

polarized and no polarizer at the detector side. To verify the results, the grating was also meas-

ured by SEM and AFM. The SEM measurement was performed with a Hitachi S 400 scanning

electron microscope at 4 kV with a magniﬁcation of 35000. The uncertainties of the CFS and

SEM were determined from repeated evaluations. In the case of the SEM, the uncertainty of

the measured midCD was determined from measurements at different parts of the image (so the

uncertainties are partly caused by line edge roughness). The bright edges of the grating lines

were the main cause of the uncertainties. This edge is clearly seen in Fig. 7(a). The uncertainty

of the height measurement with the AFM can be estimated using the histogram of Fig. 7(c). The

uncertainties are in the “few nanometers” range for all techniques. A low-uncertainty measure-

ment with AFM (without the 3D option) and SEM (without cutting the sample) is only possible

for height and CD, respectively. The 3−

σ

uncertainty in the grating parameters reconstruction

by means of CFS is lower compared to that obtained through SEM and AFM measurements. We

notice higher relative uncertainties in SWA reconstruction as compared to height and midCD

uncertainties, which are also reported by others [13].

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(C) 2014 OSA

6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24686

0 1 2 3

0

50

100

x (μm)

Height (nm)

0 50 100

0

5

10

Height (nm)

No. of Pixels

116nm

(b)

(c)

Pitch

MidCD

561nm 1.3μm

(a)

Fig. 7. (a) Top view of the SEM image. (b) AFM cross section in the direction perpendicular

to the grating lines. (c) Histogram of heights for each pixel of the AFM measurement.

Table 1. Comparative measurements of the grating parameters using different techniques.

Parameters CFS SEM AFM

MidCD (nm) 563±2 562±4 –

Height (nm) 116±1 – 116±3

SWA(◦) 89±3 – –

Bias (nm) 1190±1 – –

The results are compiled in table 1 for NA=0.4 and at

λ

=633 nm. Interestingly, the lateral

position of the grating can be retrieved with an accuracy at 1 nm level, which is an impressive

accuracy, considered the numerical aperture of the system and the wavelength used. Actually,

an accurate retrieval of the alignment parameter bias is a fundamental pre-requisite for CFS to

work. In fact, no reconstruction of the grating parameters would be possible without ﬁrst de-

termining the relative position between incident spot and grating. We have also performed sim-

ulations studies, in order investigate to which level of accuracy the alignment can be obtained

through CFS measurements. We have found that, by using an incident ﬁeld with

λ

=250 nm,

NA =0.95 and a grating with pitch 200 nm (all these values are very well representative of a

current state-of-the art industrial IOS) positioning accuracy at 10 pm level is attainable. Simula-

tion studies show that at such high NA and shorter wavelength the uncertainty in reconstruction

of the grating parameters can be further decreased as well. All these beneﬁts can be attributed

to the phase sensitive signal, as for F<2 CFS can be seen as a common path interferometer.

4. Conclusions

Grating reconstruction with coherent Fourier scatterometry (CFS) has been demonstrated. The

tool is capable of illuminating and measuring the response of the sample simultaneously over

a broad range of incident and reﬂected angles. The measurement for all radial and azimuthal

angles can be performed within one second. Due to the coherent illumination, the measuring

spot can be focused to a size smaller than one micron. Compared to incoherent scatterometry

the advantage of coherent Fourier scatterometry is that the measured response in the pupil plane

includes interference patterns caused by overlapping orders. The interference changes when the

spot is scanned perpendicularly to the grooves of the grating, and consequently the phase in-

formation contained in the overlapping orders can be determined accurately. The capabilities

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Received 30 Jun 2014; revised 17 Aug 2014; accepted 19 Aug 2014; published 1 Oct 2014

(C) 2014 OSA

6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24687

of the tool were demonstrated by reconstructing the parameters of grating with 1300 nm pitch

using a wavelength of

λ

= 633 nm and an objective lens of NA =0.4. The reconstruction was

performed by non-linear least squares gradient ﬁt of the grating parameters to minimize the dif-

ference between the measured and rigorously computed pupil images. The sensitivity of coher-

ent Fourier scatterometry was found to be comparable with the applied reference metrologies

(SEM and AFM). In addition, simulation studies show that positioning accuracy of the order of

10 picometer with NA =0.95 and

λ

in the UV can be achieved. Finally, it is worth mentioning

that accurate nano-positioning in combination with the reconstruction shape parameters of the

grating can be done in a single tool which is not possible in conventional optical scatterometry.

Acknowledgments

The authors acknowledge Mark Van Kraaij from ASML, Veldhoven. Peter Petrik is grateful

for the EMRP IND17 joint research project on scatterometry for ﬁnancial support. The EMRP

is jointly funded by the EMRP participating countries within EURAMET and the European

Union.

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Received 30 Jun 2014; revised 17 Aug 2014; accepted 19 Aug 2014; published 1 Oct 2014

(C) 2014 OSA

6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024678 | OPTICS EXPRESS 24688