Direct detection of polystyrene equivalent nanoparticles with diameter of 21 nm (&#x223C;&#x03BB;/19) using coherent Fourier scatterometry: erratum

D. Kolenov; D. Kolenov; I. E. Zadeh; R. C. Horsten; S. F. Pereira

doi:10.1364/OE.470101

Abstract

We present an erratum to our article Kolenov, D., et al. “Direct detection of polystyrene equivalent nanoparticles with a diameter of 21 nm ( ∼ λ/19) using coherent Fourier scatterometry.” Opt. Express 29, 16487 (2021) [CrossRef] .

1. Erratum

There were mistakes that occurred in the Eq. (18–20) in the original article [1]. The correct equations are:

(18)$$\frac{1}{6}\pi d^{3}=wlh_{resist}=\frac{\pi}{4}d^{'2}h_{resist},$$

(19)$$d_{sphere-equiv}=\left(\frac{6}{\pi}wlh_{resist}\right)^\frac{1}{3}=\left(\frac{3}{2}d^{'2}h_{resist}\right)^\frac{1}{3},$$

(20)$$LSE = d_{sphere-equiv}\ast\left(\frac{(m_{resist}^2-1)(m_{psl}^2+2)}{(m_{resist}^2+2)(m_{psl}^2-1)}\right)^{1/3}.$$

Accordingly, the estimates of the LSE in Table 1, column 4 should be:

Table 1. Resit particle types for which the LSE is estimated

View Table

The values of the third column of Table 1, are luckily correct.

The changes in the text associated with this wrong estimation are as follows:

• The title should be corrected to: Direct detection of polystyrene equivalent nanoparticles with diameter of 29 nm ($\sim \lambda /14$) using coherent Fourier scatterometry
• Abstract of the paper, last two lines: We demonstrate the detection of polystyrene equivalent nanoparticles of diameter of 29 nm with a signal-to-noise ratio of 4 dB using the illuminating wavelength of 405 nm.
• Page 16488, line 9 and 10: ${\ldots }$ with corresponding Latex Sphere Equivalent (LSE) sizes down to a diameter of 29 nm. This paper presents, for the first time, the detection of low contrast nanoparticles with diameter of 29 nm with a signal-to-noise ratio $SNR \approx 4$ dB at a wavelength of 405 nm ($\sim \lambda /14$) using CFS.
• Page 16493, first line: particles are $46$ and $42.5$ nm for nominal $50$ nm square prisms and cylinders, respectively.
• Page 16493, paragraph 2, line 6: we validate the detection of nanoparticles of diameter $LSE \approx 29$ nm.
• Page 16498, 4. Conclusions, paragraph 4, line 3: detection of nanoparticles with 29 nm ($\lambda /14$) LSE diameter.
• Page 16498, 4. Conclusions, paragraph 4, line 7: detection of $LSE \approx 29$ nm particle is achieved with $SNR \approx 4$ dB.

Accordingly, the x-axis of Fig. 1 should be corrected:

Fig. 1. The peak-to-peak amplitude of the signal (blue diamonds with error bar of $\sigma$), fitted power-law (red curve) as function of the latex sphere diameter. Inset shows experimental background level of the spin-coated particles samples (black line) and samples with particles fabricated with the EBL (magenta line). The background level is further split into the detector noise in light cyan, shot noise in green, and worst-case scenario roughness signal from the EBL-made and spin-coated sample in yellow and purple respectively.

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The text under the Fig. 1, related to the change in x-axis and corresponding best power fit, corrected as:

• Page 16497, line 8: The solid red line in the plot is the fourth-power law curve with the best fit based on the error sum of squares criterion.
• Page 16498, line 2: The crossing between the fitted power curve and the background measured for the EBL sample indicates the smallest detected particle that comes close to experimental one $d_{predEBL} = 31$ nm. Assuming a perfectly flat surface, the intersection between the fitted power law curve and present detector noise is at $d_{pred} = 24$ nm particle.

The authors regret these wrong estimations. Reassuringly, the detection results of the resist-made non-spherical particles and related analysis of noise and vibration in the system remain correct.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. D. Kolenov, I. Zadeh, R. Horsten, and S. Pereira, “Direct detection of polystyrene equivalent nanoparticles with a diameter of 21 nm ( λ/19) using coherent fourier scatterometry,” Opt. Express 29(11), 16487–16505 (2021). [CrossRef]

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Figures (1)

Fig. 1.

Fig. 1. The peak-to-peak amplitude of the signal (blue diamonds with error bar of

$\sigma$

), fitted power-law (red curve) as function of the latex sphere diameter. Inset shows experimental background level of the spin-coated particles samples (black line) and samples with particles fabricated with the EBL (magenta line). The background level is further split into the detector noise in light cyan, shot noise in green, and worst-case scenario roughness signal from the EBL-made and spin-coated sample in yellow and purple respectively.

View in Article | Download Full Size | PDF

Tables (1)

Table 1. Resit particle types for which the LSE is estimated

View Table

Equations (3)

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\frac{1}{6} π d^{3} = w l h_{r e s i s t} = \frac{π}{4} d^{^{'} 2} h_{r e s i s t},

d_{s p h e r e - e q u i v} = {(\frac{6}{π} w l h_{r e s i s t})}^{\frac{1}{3}} = {(\frac{3}{2} d^{^{'} 2} h_{r e s i s t})}^{\frac{1}{3}},

L S E = d_{s p h e r e - e q u i v} * {(\frac{(m_{r e s i s t}^{2} - 1) (m_{p s l}^{2} + 2)}{(m_{r e s i s t}^{2} + 2) (m_{p s l}^{2} - 1)})}^{1 / 3} .

Volume of resist particle [ $n m^{3}$ ]	Shape of particle	Sphere diam. equiv. [nm]	LSE [nm]
50 $\times$ 50 $\times$ 25	Square Prism	49.23	46
50 $\times$ 25	Cylinder	45.42	42.5
25 $\times$ 25 $\times$ 25	Cube	31.02	29

Direct detection of polystyrene equivalent nanoparticles with diameter of 21 nm (∼λ/19) using coherent Fourier scatterometry: erratum