Instantaneous thickness measurement of multilayer films by single-shot angle-resolved spectral reflectometry

Young-Sik Ghim; Young-Sik Ghim; Hyug-Gyo Rhee; Hyug-Gyo Rhee

doi:10.1364/OL.44.005418

An ellipsometer [1–3] is widely used for the investigation of multilayer film stacks in the semiconductor industry. It is capable of measuring very important film parameters such as the thickness and refractive index, which can be used as a quality check of the films. However, the ellipsometer is difficult to use as production inspection equipment because of being configured off-axis and low spatial resolution due to the large spot size of 25 µm or greater. Moreover, it takes long measurement times, because it needs many measurement steps in order to measure the changes in the state of polarization of reflected lights by changing the incident angle and wavelength. In response to these continuous industrial demands for high spatial resolution and high speed, many studies have been performed in the film measurement field [3–9]. Among them, the beam profile reflectometer technique [4–6] can be a suitable candidate to fulfill these needs. Its on-axis configuration with a high NA objective provides submicron resolution, and it measures multi-angular reflectance for various polarization states in real time. However, this approach is limited to monochromatic light. In order to obtain multi-angular reflectance over various wavelengths, we need to vary the wavelength of the light source sequentially. For simultaneous measurements of both the spectral and angular variations of reflectance, angle-resolved spectral reflectometry was developed [10]. However, it measures only p-polarized or s-polarized reflectance according to the polarization state of the incident light and the direction of a line slit. In order to overcome all the technical limitations described above, we suggest a new concept of angle-resolved spectral reflectometry. Our proposed method can obtain the absolute reflectance data of the sample over a broad spectral range and a wide incident angle according to various polarization states in a single-shot measurement.

Fig. 1. Optical configuration of single-shot angle-resolved spectral reflectometry for instantaneous thickness measurements of multilayer films. BS, beam splitter; BFP, back focal plane.

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Figure 1 shows a schematic diagram of our proposed single-shot angle-resolved spectral reflectometry. A broad-spectrum light source focuses on the sample through a high numerical aperture objective. The focused light beam consists of many ray bundles with the angle of incidence ranging from $ - {{\rm \sin}^{ - 1}}({\rm NA})^\circ $ to ${{\rm \sin}^{ - 1}}({\rm NA})^\circ $, and each ray strikes the sample surface at its incident angle. Thus, a high NA objective lens is required to measure a wide range of angular reflectance according to the incident angle. The focused incident beam undergoes an infinite loop of multiple reflections within the sample, and it creates the interference fringe pattern. Then the back-reflected beam forms an angular reflectance fringe pattern at the back focal plane of the objective lens, and the radial direction of this circular-fringe interferogram represents the incidence angle. This angular interferogram results from the sum of monochromatic individual interference patterns over a broad spectral range.

Fig. 2. Basic principle of single-shot angle-resolved spectral reflectometry: (a) radial-circular interference fringe image produced by a multilayer dielectric film at the conjugate back focal plane; (b) pixelated polarizer mask array and its unit cell structure, and four angle-resolved spectral reflectance images corresponding to each sub-array with 90° polarizer pixel, 45° polarizer pixel, 135° polarizer pixel, and 0° polarizer pixel for a (c) bare-Si wafer and (d) multilayer film, respectively.

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Relay optics is used to deliver the interference fringe pattern formed at the back focal plane of the objective into an entry line slit of the imaging spectrometer, and the line slit passes only the selected line of the radial-circular interference pattern, as shown in Fig. 2(a). The relation between the radial pixel position ($r$) and the incident angle ($\theta $) can be expressed as follows:

(1)$$\theta = {\sin ^{ - 1}}\left( {\frac{r}{{{r_{\max }}}}{\rm \sin}{\theta _{\max }}} \right),\quad{\rm NA} = \sin {\theta _{\max }}.$$

Then this selected line signal is resolved into an angle-resolved spectral interference pattern after passing through an imaging spectrometer consisting of dispersive imaging optics and a line slit. This imaging spectrometer allows us to obtain the spectral interference information of the pixels on the incident angle, as well as the angular interference information of the pixels on wavelength, simultaneously. In order to obtain the angle-resolved spectral interferograms at various polarization states in a single-shot measurement, we use a pixelated polarizing camera. The pixelated polarizer camera is composed of a pixelated polarizer mask and 2D sensor array. As shown in Fig. 2(b), the pixelated polarizer mask consists of a repeated pattern array of a ${2} \times {2}$ unit cell over the entire mask. This ${2} \times {2}$ unit cell is a micro-polarizer pattern array with four discrete polarizations (90, 45, 135, and 0 deg). Each pixel of a 2D sensor array is well aligned to each individual polarizer element of mask array, so the interference pattern captured by the pixelated polarizer camera corresponds to four sub-arrays with each of four polarization states. Therefore, this 2D sensor array simultaneously captures the four angle-resolved spectral reflectance images with different polarization states according to the micro-polarizer angle. Figures 2(c) and 2(d) show the angle-resolved spectral reflectance images reflected from the bare-Si reference and the multilayer film sample, respectively. Sub-arrays with 90°, 45°, 135°, and 0° polarizers correspond to s-polarized, p- and s-mixed polarized, p- and s-mixed polarized, and p-polarized reflectance images, respectively. Therefore, various polarized reflectance data over a wide spectral and angular region can be obtained in a single-shot measurement. The angle-resolved spectral interferogram obtained by the pixelated polarizer camera can be expressed as [5]

Fig. 3. Schematic illustrations of a five-layer film structure, of which ${{\rm Si}_3}{{\rm N}_4} {\text -} {{\rm SiO}_2} {\text -}{\rm SiON}{\text -} {{\rm SiO}_2}{\text -}{{\rm Si}_3}{{\rm N}_4}$ are deposited on a Si wafer.

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(2)$$\begin{split}\!\!\!\!\!{{I}_{o}}( d;\theta ,\lambda ,\phi )=&{{I}_{i}}( \theta ,\lambda ,\phi)[|\Re_p|^2\cos^2(\phi)+|\Re_s|^2\sin^2(\phi)\!\!\!\\&+|\Re_p||\Re_s|\sin(2\phi)\sin(\Delta)],\!\!\end{split}$$

where $\theta $ is the incident angle, $\lambda $ is the wavelength, $\phi $ is the micro-polarizer angle, and $d$ is the thickness of the multilayer films. ${I_i}$ is the incident beam intensity, and ${\Re _p}$ (${\Re _s}$) and $\Delta $ are the Fresnel reflection coefficients of p-polarized (s-polarized) light and the phase difference induced by reflection between p- and s-polarized light, respectively [1,2]. Based on Eq. (2), we can derive dominant ellipsometric parameters for the sample given by

(3)$$\begin{split}| {\Re _p^{{\rm sam}}} | =& \sqrt {\frac{{I_o^{{\rm sam}}( {0^\circ } )}}{{I_o^{{\rm ref}}( {0^\circ } )}}} \times | {\Re _p^{{\rm ref}}} |,\\ | {\Re _s^{{\rm sam}}} | =& \sqrt {\frac{{I_o^{{\rm sam}}( {90^\circ } )}}{{I_o^{{\rm ref}}( {90^\circ } )}}} \times | {\Re _s^{{\rm ref}}} |, \\ \sin ( {{\Delta ^{{\rm sam}}}} ) =& \frac{\Lambda }{{2| {\Re _p^{{\rm sam}}} || {\Re _s^{{\rm sam}}} |}}, \\ \Lambda =& \frac{{I_o^{\rm sam}( {45^\circ } )}}{{I_o^{\rm ref}( {45^\circ } )}} \times \left[ \frac{1}{2}{{| {\Re _p^{\rm ref}} |}^2} + \frac{1}{2}{{| {\Re _s^{\rm ref}} |}^2}\right.\\&\left. + | {\Re _p^{\rm ref}} || {\Re _s^{\rm ref}} |\sin ( {{\Delta ^{\rm ref}}} ) \right]- \frac{{I_o^{\rm sam}( {135^\circ } )}}{{I_o^{\rm ref}( {135^\circ } )}}\\ &\times \left[ \frac{1}{2}{{| {\Re _p^{\rm ref}} |}^2} + \frac{1}{2}{{| {\Re _s^{\rm ref}} |}^2} - | {\Re _p^{\rm ref}} || {\Re _s^{\rm ref}} |\sin ( {{\Delta ^{\rm ref}}} ) \right].\end{split}$$

Here we omitted several symbols of $d$, $\theta $, $\lambda $ to simplify the above equations, and $I_o^{{\rm sam}}( \phi )$ and $I_o^{{\rm ref}}( \phi )$ represent the angle-resolved spectral intensities for the sample and the reference specimen at $\phi $ of 0°, 45°, 90°, and 135°, respectively. We used a bare crystalline silicon wafer as the reference specimen, of which the optical constants are well known in the literature, so the Fresnel reflection coefficients ($ \Re _p^{{\rm ref}} $, $ \Re _s^{{\rm ref}} $) and the phase shift ($ {\Delta ^{{\rm ref}}} $) can be calculated theoretically. After obtaining the ellipsometric quantities (${\Re _p}$, ${\Re _s}$, and $\Delta $) for the sample, we can search the true film thickness of each layer of multilayer film by minimizing the sum of the biased error function [11] over a wide range of wavelengths and incident angles expressed by

(4)$$\begin{split}&\zeta ( {{d_1} \cdots {d_n};\theta ,\lambda } ) = \frac{1}{{L - P - 1}}\\&\quad\times\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^k {\left[ {{{\left| {\frac{{\left| {\Re _p^{\exp }( {{\theta _i},{\lambda _j}} )} \right| - \left| {\Re _p^{{\rm cal}}( {d;{\theta _i},{\lambda _j}} )} \right|}}{{\sigma _{\left| {{\Re _p}} \right|}^{\exp }( {{\theta _i},{\lambda _j}} )}}} \right|}^2}} \right.} } \\&\quad + {\left| {\frac{{\left| {\Re _s^{\exp }( {{\theta _i},{\lambda _j}} )} \right| - \left| {\Re _s^{{\rm cal}}( {d;{\theta _i},{\lambda _j}} )} \right|}}{{\sigma _{\left| {{\Re _s}} \right|}^{\exp }( {{\theta _i},{\lambda _j}} )}}} \right|^2}\\&\quad \left. { + {{\left| {\frac{{\sin {\Delta ^{{\rm exp}}}( {{\theta _i},{\lambda _j}} ) - \sin {\Delta ^{{\rm cal}}}( {d;{\theta _i},{\lambda _j}} )}}{{\sigma _{\sin \Delta }^{\exp }( {{\theta _i},{\lambda _j}} )}}} \right|}^2}} \right],\end{split}$$

where ${L}( = {m} \times {k})$ is the total number of measured angular and spectral experimental data, and P is the number of unknown parameters. $ \sigma _{| {{\Re _p}} |}^{\exp } $, $ \sigma _{| {{\Re _s}} |}^{\exp } $, and $ \sigma _{\sin \Delta }^{\exp } $ represent the standard deviations on $|{\Re _p}| $, $ |{\Re _s}| $, and $\sin\Delta $ for each experimental data point, respectively.

To verify our proposed method, we fabricated a multi-stacked dielectric film layer patterned by a photolithography process. Figure 3 shows details of the internal structure of the sample. Three types of films with various thicknesses are sequentially stacked on a patterned silicon wafer in the order of ${{\rm Si}_3}{{\rm N}_4} {\text -} {{\rm SiO}_2} {\text -} {\rm SiON} {\text -} {{\rm SiO}_2} {\text -} {{\rm Si}_3}{{\rm N}_4}$. We performed measurement on two spots at T1 and T2 positions, of which the nominal thickness sets are (300, 350, 450, 700, 600 nm) and (300, 550, 350, 500, 1300 nm), respectively.

In this experiment, we used commercial products for an imaging spectrometer (V8E, SPECIM) and a pixelated polarizing camera (BFS-U3-51S5, FLIR), respectively. Table 1 shows details of our optical system used in the experiments. Once four angle-resolved spectral reflectance images corresponding to each sub-array in the pixelated polarizer camera are measured, we can obtain the angle-resolved spectral images of p- and s-polarization reflectance and sine of the phase difference between p- and s-polarized light, respectively, using Eq. (3).

Table 1. Specification of Optical System Used for Experiments

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Before measurement, we performed the preliminary work of calibrating both the vertical axis and the horizontal axis of the angle-resolved spectral interferogram. First, we calibrated the wavelength of the vertical axis by finding the relation between the pixel position and wavelength using a mercury argon (HgAr) source. We used three narrow, intense peaks (404.66, 435.84, 546.07 nm) from the source to determine the wavelength calibration equation, a third-order polynomial fitting model for mapping the pixel to wavelength. Next, we calibrated the incident angle of the horizontal axis by mapping the pixel position to the incident angle using Eq. (1). Here ${\theta _{{\rm max}}}$ can be determined by finding the pixel position (${r_B}$) corresponding to Brewster’s angle (${\theta _B} = {56.6}^\circ $) of BK 7 glass with a refractive index of 1.5185 at 550 nm using the relation of ${{\theta }_{\max }}={{\sin }^{-1}}( {r}_{\max }/{r}_{B}\times \sin {{\theta }_{B}}).$ After these calibration works, we performed measurements for the multilayer sample and compared our results with other conventional ellipsometer techniques. Figure 4 shows the comparison results of experiments and simulations of ${\Re _p}$, ${\Re _s}$, and ${\rm \sin}\Delta $, respectively, for the five-layer film sample.

Fig. 4. Comparison results of measurements and simulations: measured and simulated angle-resolved spectral reflectance images for p-polarization and s-polarization are (a), (b), (c), and (d), respectively; comparisons of our measured angular reflectance (black solid line) for (e) p-polarization and (f) s-polarization with the simulation (red “x” mark) at a wavelength of 587.6 nm; comparisons of our measured spectral reflectance (black solid line) for (g) p-polarization and (h) s-polarization with the simulation (red ”x” mark) at an incident angle of 52.4°; (i) measured and (j) simulated angle-resolved spectral images of sine of the phase difference between p- and s-polarization; comparisons of our measured sine $\Delta $ (black solid line) with the simulation (red “x” mark) at (k) a wavelength of 587.6 nm and (l) an incident angle of 52.4°.

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The optimal sets of the film thickness of each layer of the sample at T1 and T2 positions (${d_1}$, ${d_2}$, ${d_3}$, ${d_4}$, ${d_5}$), were numerically determined by minimizing the merit function of Eq. (4) by a global optimization technique. Each theoretical model for p-polarized reflectance, s-polarized reflectance, and phase difference are well matched to the measurements. However, the experimental measurements tend to be less sharp than the simulated data at critical points, because the measured angular spectra data at each pixel with finite size actually is the response containing the contribution of a small range of angles and wavelength, rather than a single angle and wavelength. If reflecting these considerations in the simulations, the simulations will agree better with the measurement results. Table 2 shows the comparisons of our measurement results with a commercial instrument, the KLA-Tencor SpectraFx 100 ellipsometer. The thickness deviation of each layer between the two methods is less than ${\sim}11.3\;{\rm nm}$, and the comparison results show good agreement with each other.

Table 2. Summary of the Comparisons of Our Measurement Results with a Commercial Ellipsometer

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To conclude, we have proposed and verified a new method of single-shot angle-resolved spectral reflectometry by comparing our measurement results with an ellipsometer; our method shows performance equivalent to the conventional methods. Our method acquires only a single image, which simultaneously provides the changes in the phase and amplitude of p-and s-polarized light reflected from the sample. Hence, we can measure the film thickness corresponding to each layer of multilayer film in real time. Moreover, its on-axis configuration provides higher spatial resolution and a relatively compact setup. We expect that our proposed technique will be widely used as an in-line metrology tool, especially in the semiconductor industry in terms of high measurement speed, robustness to external noises, and high spatial resolution.

Funding

Korea Research Institute of Standards and Science (19011086); Ministry of Trade, Industry and Energy (18201022).

Disclosures

The authors declare no conflicts of interest.

REFERENCES

1. R. M. A. Azzam and N. M. Bashra, Ellipsometry and Polarized Light (North-Holland, 1987).

2. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (Wiley, 1999).

3. T. E. Jenkins, J. Phys. D 32, R45 (1999). [CrossRef]

4. A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, and J. T. Fanton, Appl. Phys. Lett. 60, 1301 (1992). [CrossRef]

5. J. T. Fanton, J. Opsal, A. Rosencwaig, and D. L. Willenborg, Proc. SPIE 2004, 313 (1993). [CrossRef]

6. J. M. Leng, J. Opsal, and D. E. Asppnes, J. Vac. Sci. Technol. A 17, 380 (1999). [CrossRef]

7. K. Wu, C.-C. Lee, N. J. Brock, and B. Kimbrough, Opt. Lett. 36, 3269 (2011). [CrossRef]

8. D. Kim, Y. Yun, and K.-N. Joo, Opt. Lett. 42, 3189 (2017). [CrossRef]

9. Y.-S. Ghim, H.-G. Rhee, and A. Davies, Sci. Rep. 7, 11843 (2017). [CrossRef]

10. J. Dong and R. Lu, Opt. Express 26, 12291 (2018). [CrossRef]

11. G. E. Jellison Jr., Appl. Opt. 30, 3354 (1991). [CrossRef]

Item	Specification
Light source	Tungsten halogen lamp
Microscope objective	100 magnification with 0.9 N.A.
Wavelengths to be used	477 to 648 nm
Incident angle to be used	−64° to 64°
Lateral resolution (spot size)	0.75 µm at 550 nm

Sampling Position		Ellipsometer	Our Method
${S i}_{3} N_{4}$ Layer (1st Layer)	T1 ①	300. 2 nm	300.1 nm
${S i}_{3} N_{4}$ Layer (1st Layer)	T2 ⑥	300.1 nm	302.2 nm
${S i O}_{2}$ Layer (2nd Layer)	T1 ②	338.6 nm	334.2 nm
${S i O}_{2}$ Layer (2nd Layer)	T2 ⑦	544.2 nm	532.9 nm
SiON Layer (3rd Layer)	T1 ③	461.4 nm	454.1 nm
SiON Layer (3rd Layer)	T2 ⑧	366.3 nm	364.2 nm
${S i O}_{2}$ Layer (4th Layer)	T1 ④	724.1 nm	725.6 nm
${S i O}_{2}$ Layer (4th Layer)	T2 ⑨	518.1 nm	518.8 nm
${S i}_{3} N_{4}$ Layer (5th Layer)	T1 ⑤	670.3 nm	666.4 nm
${S i}_{3} N_{4}$ Layer (5th Layer)	T2 ⑩	1347.4 nm	1353.5 nm

Item	Specification
Light source	Tungsten halogen lamp
Microscope objective	100 magnification with 0.9 N.A.
Wavelengths to be used	477 to 648 nm
Incident angle to be used	−64° to 64°
Lateral resolution (spot size)	0.75 µm at 550 nm

Sampling Position		Ellipsometer	Our Method
${S i}_{3} N_{4}$ Layer (1st Layer)	T1 ①	300. 2 nm	300.1 nm
${S i}_{3} N_{4}$ Layer (1st Layer)	T2 ⑥	300.1 nm	302.2 nm
${S i O}_{2}$ Layer (2nd Layer)	T1 ②	338.6 nm	334.2 nm
${S i O}_{2}$ Layer (2nd Layer)	T2 ⑦	544.2 nm	532.9 nm
SiON Layer (3rd Layer)	T1 ③	461.4 nm	454.1 nm
SiON Layer (3rd Layer)	T2 ⑧	366.3 nm	364.2 nm
${S i O}_{2}$ Layer (4th Layer)	T1 ④	724.1 nm	725.6 nm
${S i O}_{2}$ Layer (4th Layer)	T2 ⑨	518.1 nm	518.8 nm
${S i}_{3} N_{4}$ Layer (5th Layer)	T1 ⑤	670.3 nm	666.4 nm
${S i}_{3} N_{4}$ Layer (5th Layer)	T2 ⑩	1347.4 nm	1353.5 nm

Instantaneous thickness measurement of multilayer films by single-shot angle-resolved spectral reflectometry

Abstract

Funding

Disclosures

REFERENCES

Cited By

Figures (4)

Tables (2)

Equations (4)

Optics Letters