1. Introduction

The rapid development of nanotechnology, in particular for the mass production of silicon chips, requires simple and effective methods for inspection of objects with characteristic dimensions of several dozen nanometers. Conventional measuring tools such as the scanning electron microscope (SEM), scanning tunneling microscope (STM) and atomic force microscope (AFM) provide near-atomic level imaging resolution, but cannot be used in a mass production environment due to low throughput and the destructive nature of inspection. Rapid inspection of nanochips is particularly necessary at the quality control stage.

In order to solve this problem, several simple and high performance optical methods have been developed. These methods, being based upon such techniques as ellipsometry [1], scatterometry [2] and reflected light spectroscopy [3], allow a quantitative estimation of the critical dimension (CD) of periodic structures (such as gratings) with a 0.2–1 nm accuracy. Although these methods are used at the final stages of semiconductor manufacturing processes, they can hardly be applied to the inspection of non-periodic or isolated structures. Therefore, the development of new optical methods for the inspection of semiconductor structures that combine spatial local measurements, high performance, and simplicity, irrespective of structure type, is of significant interest in the semiconductor industry [4].

The authors in [5–8] report numerical simulations of electromagnetic field scattering from isolated semiconductor structures with CD values of several nanometers. These previous works have also shown that a change of several nanometers in CD values results in a change in the intensity distribution of scattered light in the defocused position. As stated in [8], this fact could be used for the development of through-focus scanning optical microscopy (TSOM), a new optical method for inspection of nanoscale objects. However, the practical implementation of this experimental technique faces a number of challenges. For instance, the accuracy of scattered light intensity measurements is strongly affected by imaging system noise. In addition, in order to obtain reliable estimates of the CD under inspection, aberration in the imaging system and misalignment must be taken into account for comparisons between experiments and simulations. The present work discusses the practical implementation of an optical method for the inspection of isolated nanoscale objects based upon the analysis of defocused object images obtained during a shift along the optical axis.

2. Methods

The optical scheme for measurements is presented in Fig. 1(a). The experimental setup allows us to obtain images of opaque micro-objects using bright field microscopy using the Kohler illumination scheme [9]. This scheme is based on a fiber coupled light emitting diode (LED) operating at λ = 660 nm with Δλ = 20 nm. A fiber output of 400 μm in diameter is imaged using a relay system composed of L1 and L2 lenses with 1x magnification at the back focal plane of a 50x (NA = 0.75) Olympus micro-objective. Images are registered with ~70x magnification (tube lens with focal length F = 250 mm) using an Ophir-Spiricon Beam Gage CCD matrix laser beam analyzer (4.65 × 4.65 μm² pixel size, 12 bit). For the controllable movement of the sample along the optical z-axis within an 80 μm range with a 50 nm step size, a piezoelectric nanopositioner with closed loop operation is used.

 

Fig. 1 (a) Experimental setup, (b) SEM images of test objects.

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Calibrated samples fabricated by NTT Advanced Technology Corporation have 12 lines with the outside area etched in a monocrystalline silicon substrate with a 40 µm gap between adjacent lines. The lines have the following geometry: height 50 nm, length 100 μm and width (the CD or parameter of interest for the present study) of 40–150 nm (deviation less than 2 nm) with a 10 nm step size. Thus, lines widths are at least several times smaller than the Rayleigh limit (approximately 540 nm) for the current optical imaging system. SEM images of test objects with 40, 100, and 150 nm are shown in Fig. 1(b).

Experimental measurements were performed as follows: test objects were shifted along the z-axis (coincident with the optical axis) within a −15–15 μm range. The position with the best focus was at approximately 0 µm. At each focus position a diffraction pattern with 232x232 pixel size was obtained. In order to exclude the possible influence of different illumination conditions, diffraction patterns were obtained at fixed positions within the optical system field of view, with size equal to that of the detector of 1600 × 1200 pixels.

The next step includes averaging of obtained diffraction patterns along the y-axis parallel to the sample plane (Fig. 1(b)), with subsequent construction of a through-focus diffraction pattern. Typical normalized through-focus diffraction patterns, obtained for two test objects with 40 and 50 nm in width are shown in Figs. 2(a) and 2(b).

 

Fig. 2 Test objects measurements. (a) Normalized through-focus diffraction pattern obtained for the object with 40 nm CD. (b) Normalized through-focus diffraction pattern for the object with 50 nm CD. (c) Differential through-focus diffraction pattern for test objects with 40 and 50 nm CD.

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To compare different objects we subtracted normalized through-focus diffraction pattern of one object (reference object) from that of the other (test object). The resulting pattern is referred to as differential through-focus diffraction pattern (DTDP). This pattern obtained for objects with 40 nm and 50 nm CD values is presented in Fig. 2(c).

To estimate DTDP quantitatively and distinguish between different objects under study a metric value was used. This value is determined as the sum of absolute values of all pixels within DTDP, normalized by the total amount of pixels. In our study the size of the pixel was the same both for experimental and simulated through-focus diffraction patterns. By using the metric value we can estimate the limit of measurements accuracy in the presence of measurements errors such as camera noise and possible errors of sample positioning. Figure 3 demonstrates some of the experimentally measured dependencies of metric value on CD value of the test objects. The presented dependencies were obtained for DTDP of reference objects with 40 and 90 nm CD values.

 

Fig. 3 Estimation of measurement accuracy. (a) Metric value curve measured for all test objects with use of 40 nm reference object; dashed lines denote ± 2σ standard deviation, blue for 40 nm CD value, red for 50 nm CD value (b) Metric value curve measured for all test objects with use of 90 nm reference object; dashed lines denote ± 2σ standard deviation, blue for 90 nm CD value, red for 100 nm CD value

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One can see from the Fig. 3 that metric value increases almost monotonically with increase in difference between CD values of test and reference objects. So it is convenient to use metric value for relative CD measurements with subsequent objects recognition.

To evaluate measurement accuracy limit a series of measurements of the metric value for each test object was carried out and standard deviation was estimated. Results obtained for objects with 40 nm and 50 nm CD values are presented in Fig. 3(a) and enlarged in the figure inset. Results obtained for objects with 90 and 100 nm CD are presented in Fig. 3(b). The spread in these metric values, as calculated using the ± 2σ standard deviation, determines the total measurement error and is shown in the Fig. 3 with dashed lines. These data demonstrate accuracy of the measurements sufficient for reliable recognition of object with 10 nm of CD difference. Comparison of the data in insets of Figs. 3(a) and 3(b) shows that difference between metric values measured for objects with 40 and 50 nm CD value is higher than that for the case of objects with 90 and 100 nm CD value. At the same time, spread of metric values measured for the first pair of objects is smaller than that for the second pair of objects. These facts allow us to draw a conclusion on higher accuracy of measurement of CD with smaller absolute values.

To prove this hypothesis a series of experiments with use of an experimental library composed of 12 through-focus diffraction patterns was performed. The results obtained are presented in Table 1, where the green cells correspond to successful recognition of object width and the red cell corresponds to erroneous recognition.

Table 1. Recognition of object width with use of experimental library

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One can see, some faults in recognition of objects with higher CD may occur. In our case the test object with 120 nm CD was erroneously recognized as object with 110 nm CD value.

In order to estimate the measurement accuracy limit, which can be reached for objects with smaller CD, we analyzed experimental data shown in inset of Fig. 3(a). As the measured difference between metric values is caused by the difference in object width only, and since the metric values increase with increasing object width, the measurement accuracy limit can be estimated as 10 nm divided by (N + 1). Here, N is the number of metric value curves that correspond to objects with intermediate width values which would occupy the gap shown by the arrow between mean values of the two data sets without an intersection of their spreads. Evaluated accuracy limit of measurements with this optical method within the 40–50 nm range for object widths is about 1 nm.

3. Numerical simulation

Use of library of the experimentally obtained through-focus diffraction patterns seems reasonable when we need to measure a single CD parameter, however, in the case of real inspection system that may be inadequate since there are at least several parameters to be measured; and the accuracy required for 22 nm node technology is equal to 0.2nm [4]. Taking this fact into account we made an attempt to use current method with the libraries of simulated through-focus diffraction patterns.

Library of through-focus diffraction patterns is simulated using the finite-difference time-domain (FDTD) [10] method, which is used for the calculation of spatial distribution of light field scattered by objects under inspection. Simulated defocused light intensity distributions are obtained by a light field expansion to plane waves and their subsequent free space propagation and optical system transformation to compose diffraction patterns for different object’s focus offsets. Simulation parameters corresponded to experimental parameters, including: numerical aperture of illumination NA_ill = 0.05, collecting numerical aperture NA_coll = 0.75, average wavelength λ = 660 nm, Δλ = 20 nm, and silicon substrate refractive index n = 3.9. Normalized through-focus diffraction patterns simulated for test objects with 150/90/40 nm widths are shown in Figs. 4(g)-4(i) correspondingly.

 

Fig. 4 Comparison between experimental and simulated normalized through-focus diffraction patterns. Left column corresponds to 150 nm CD value, middle column – 90 nm, right column – 40 nm. (a)-(c) Experimental results, (d)-(f) Simulation results with aberration correction. (g)-(i) Simulation results without aberration correction. (j)-(l) Difference between measured and simulated normalized through-focus diffraction patterns without aberration corrections. (m)-(o) Difference between measured and simulated normalized through-focus diffraction patterns with aberration correction.

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One can observe some difference between the experimental and simulated normalized through-focus diffraction patterns, shown in Figs. 4(a)-4(c) and 4(g)-4(i) correspondingly. This difference seems to be caused by aberrations in the optical system, non-uniform illumination and pattern noises which are not taken into account during simulation. In order to account for the axial chromatic aberration, its value was determined experimentally and corresponding corrections were introduced into the mathematical model. For the phase aberrations, we empirically introduce an additional phase shift to each plane wave until the best match conditions between experimental and simulated focus metrics simulated for a current object are found. The chosen phase shift offers offset values between experiments and simulations and is subsequently used for the simulation of light scattering from other objects. Normalized through-focus diffraction patterns simulated with consideration of optical system’s aberrations described are shown in Figs. 4(d)-4(f).

Thus, two sets of DTDP shown in Fig. 4(j)-4(l) and 4(m)-4(o) which correspond to ideal and aberrated optical system were obtained. One can see from the presented results that taking into account optical system’s aberrations lead to better match between the experimental and simulation results. We simulated 2 libraries of normalized through-focus diffraction patterns for CD value in the range from 30 nm to 160 nm with 1 nm step with and without aberration corrections in simulation model. Further inspection of the test objects based on simulated library was carried out. CD value of the inspected object was defined as the corresponding CD value of the simulated through-focus diffraction pattern which provides the minimum of the metric value with the experimental test object’s through-focus diffraction pattern as a reference. These results are summarized in Table 2. Green cells in the table correspond to CD value recognition within ± 5nm range for the CD value measured by SEM, while the CD values in red cells are outside ± 5nm range.

Table 2. Recognition of object width with use of simulated library

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The discrepancies between simulation and measurement data observed in Figs. 4(j)-4(o) may stem from test objects’ geometrical irregularities such as sidewall slope, curvature, line width roughness also known as LWR etc., which were not introduced into mathematical model. The influence of the sidewall angle value on measurement results was investigated in [7], and it was shown, that several degrees change in sidewall inclination results in several percent difference in differential through-focus diffraction patterns. Moreover, one can see from Figs. 4(j)-4(o) that DTDP are not symmetrical in x-axis direction, which is the result of non-uniform illumination of the test objects. This non-uniformity can be due to a misalignment of optical elements as well as inclination of the test object with respect to optical axis.

4. Conclusions

The practical implementation of an optical method for inspection of nanoscale isolated objects through defocused image analysis with a shift along the optical axis is presented. Experimental library composed of through-focus diffraction patterns for 40–150 nm CD values with 10 nm step was created. Reliable recognition of test objects with widths in 40-110 nm range was reached. Measurements accuracy limit for the case of the use of experimental library was estimated as 1 nm for 40-50 nm CD value.

Attempt to create the method, based on comparison between experimental data with simulated library was made. It was shown, that aberrations of optical system have significant effect on the method accuracy. By taking into account phase and axial chromatic aberrations of the optical system in the mathematical model, an improved correspondence between experimental and simulated data, which allows reliable recognition of objects with 10 nm CD difference, is achieved. In order to achieve higher accuracy of CD value inspection with the use of simulation library, phase aberrations in the optical system and the effects of non uniform illumination will be accurately evaluated and used in the simulation model. We also consider building simulation library which can account for possible changes in object’s parameters, other than line width value.