# Compact Optical System Based on Scatterometry for Off-Line and Real-Time Monitoring of Surface Micropatterning Processes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{a}) of the surface [19]. In a similar approach, imaging systems to capture the diffraction patterns reflected from periodic or quasi-periodic surface textures have been developed and extensively studied. In this method, commonly known as scatterometry, the captured images are compared to analytical or numerical models to extract useful information from the surface, such as texture shape, spatial periods, structure height, or texture uniformity. There is a plethora of available modeling techniques for complementing the experimental data, for instance, rigorous couple-wave analysis (RCWA) [20,21], Fourier modal method (FMM) [22,23], finite-difference time-domain (FDTD) [24,25], or finite element method (FEM) [26,27], all of which are numerical rigorous models. Simpler yet effective analytical models based on Fourier optics or even the well-known grating equation can also be used for benchmarking the experimental data [28,29]. Scatterometry was successfully used to characterize LIPSS on stainless steel and to detect fluctuations in the spatial periods of LIPSS when the fluence and angle of incidence were varied [30]. In a recent work done by our group, a compact imaging system that can be easily integrated as an in-line monitoring unit was presented and used to record the diffraction patterns from DLIP-treated samples. The images were analyzed, accurately yielding the spatial period and providing information on texture homogeneity [15,31,32]. However, there are still several aspects of the method that need to be further tested to validate it as a reliable and practical monitoring system for DLIP texturing. Therefore, this study sought to investigate the detection limits of the method upon introducing patterning errors on the sample surface, to evaluate the acquired images when DLIP parameters are varied, and to extract useful information upon fluctuations in the process parameters.

## 2. Materials and Methods

^{2}, a thickness of 1 mm, and an initial roughness (R

_{a}) of 52 nm (according to DIN-ISO 25178 norm) was used for the DLIP structuring experiments.

^{2}, a pulse-to-pulse feed of 7.0 µm, a hatch distance of 15.0 µm, a repetition rate of 10 kHz, and an overlapping angle 2α = 10.2°, yielding a nominal spatial period of 3.0 µm. A total of seven samples was produced on the steel plate, and in each sample, different parameters or different strategies were applied to induce artificial errors or fluctuations in the process (see schematics in Figure 2 and Table 1 for details). The five set of experiments are described as follows.

^{2}was structured with calculated spatial periods ranging from 1.3 to 3.3 µm (sample A in Table 1). The minimum spatial period of 1.3 µm was selected because this is the minimum spatial period that the monitoring system can detect according to previous simulations [31], whereas the maximum used period is imposed by the limitation of the current DLIP setup.

^{2}were produced with varying focus shifts.

^{2}. In this case, 12 fields with an area of 7 × 7 mm

^{2}were structured.

^{2}, the probability of missing pulses increases linearly from top to bottom (see Table 1). In turn, sample G was patterned with a different strategy; namely, the pulse-to-pulse feed and hatch distance were set equal to the spot size, i.e., 50 µm, to avoid overlap between adjacent pulses. In addition, at each position, 10 pulses were applied. As in sample F, the probability of missing spots was increased from the top structured field to the one at the bottom (see Table 1). Although the probability of missing pulses in samples F and G is equivalent, these samples were processed with different structuring strategies that are commonly used in DLIP. The monitoring capabilities as a function of each strategy were thus tested.

## 3. Results and Discussion

#### 3.1. Morphology of Structured Surfaces and Associated Diffraction Patterns

_{f}(d: z

_{f}= +300 µm, e: z

_{f}= +30 µm, f: z

_{f}= −300 µm). For the case of a slight focus shift of 30 µm, significant changes in neither the topography nor in the CCD image relative to the reference texture (Figure 3a) were observed. However, for the maximum and minimum focus shifts studied in this work, a noticeable increase and then decrease, respectively, in the spatial period was observed when analyzing the topography. These fluctuations in the spatial period as function of the focus position were also observed as a shift of the diffraction peaks positions in the CCD images and will be analyzed in the next section. The third row of Figure 3 shows results corresponding to sample C, in which the laser fluence was varied (g: 0.75 J/cm

^{2}, h: 0.63 J/cm

^{2}, i: 0.22 J/cm

^{2}). The topography images reveal a decrease in the structure height as the fluence decreases; however, the diffraction patterns in the CCD images do not show a significant variation.

#### 3.2. Off-Line Evaluation

^{2}and beam divergence angle Θ are known [35]:

_{f}is the deviation from the optimum focus position (z

_{f}> 0 if the working distance is reduced), and z

_{0}= λM

^{2}/πΘ

^{2}. Assuming a quality factor M

^{2}= 1.3, as provided by the manufacturer, the divergence can be fitted with the data shown in Figure 6, yielding Θ = 8 mrad. Therefore, the method allows not only to detect fluctuations of the focus positions but also a methodology to extract the divergence (or quality factor if the divergence is given) of the beam from the measured data.

^{2}(fields 1–6), the structure depth oscillates around 220 nm ± 30 nm. However, when the fluence drops below 0.66 J/cm

^{2}, the depth decreases as well. Figure 7 shows that the intensities of the first and second diffraction orders as a function of the position y in the sample are essentially oscillating around a constant value for fields 1–8. For the zero-order intensity, the signal is constant up to the position corresponding to the field number 9 (with a fluence of 0.48 J/cm

^{2}), where its intensity starts to increase. For fields number 11 and 12, which have a very low structure depth of 48 nm and 21 nm, respectively, the first and second orders showed a clear decrease in the signal, accompanied by a steep increase in the zero-order intensity. The overall observed behavior of the diffraction orders as function of the structure depth seems not to correspond with the trends expected from the classical equations for the diffraction efficiency of sinusoidal diffraction gratings [28]. In addition, the measured intensities cannot be unequivocally correlated to the structure depths, let alone to the laser fluence. These results suggest that the algorithm implemented to detect the intensities of the diffraction orders based on calculating the area circumscribed by binary pixels associated with each order is not effective for this purpose. An improved version of the algorithm based on calculating the grayscale values of the pixels associated with each order is currently under evaluation.

#### 3.3. Real-Time Evaluation

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic setup of the (

**a**) DLIP station used to pattern line-like structures on the stainless steel plate and (

**b**) optical system employed to monitor the texture morphology of the different samples.

**Figure 2.**Schematics of the patterned steel plate (100 × 100 mm

^{2}) with the seven samples (A–G). In each sample, a different laser parameter was varied, or some areas were deliberately left unstructured by avoiding firing pulses at given positions (see Table 1 and text for details). The red color points at unstructured or partially structured areas.

**Figure 3.**Selected topography images from samples A–C and their corresponding diffraction patterns captured with the monitoring system. The first row shows patterned fields of sample A with varying spatial periods of (

**a**) 3.0 µm (reference texture), (

**b**) 1.4 µm, and (

**c**) 3.2 µm. In the second row, different fields belonging to sample B are shown, which were structured at different focus positions with respect to the reference texture: (

**d**) 300 µm, (

**e**) 30 µm, and (

**f**) −300 µm. The third row shows fields corresponding to sample C, in which the fluence was varied: (

**g**) 0.75 J/cm

^{2}, (

**h**) 0.63 J/cm

^{2}, and (

**i**) 0.22 J/cm

^{2}.

**Figure 4.**Selected topography images from samples D–G and their corresponding diffraction patterns captured with the monitoring system. In the first row, unpatterned stripes with line widths of (

**a**) 42 µm and (

**b**) 98 µm are displayed. The second row shows examples of untreated squares with edge lengths of (

**c**) 19.8 µm and (

**d**) 210 µm. In the third and fourth rows fields, different probabilities of skipping pulses are shown: (

**e**) 20% and (

**f**) 95% correspond to sample F, whereas (

**g**) 20% and (

**h**) 80% belong to sample G.

**Figure 5.**Spatial period extracted from the CCD images as a function of the position in sample A (black line). The symbols stand for the relative error between the measured spatial period with the monitoring system and the spatial period extracted from topographical images.

**Figure 6.**Measured spatial period with the monitoring unit (black line) as a function of the position in sample B. The symbols represent the spatial period calculated with Equation (2).

**Figure 7.**Intensity of the diffraction peaks (lines; see legend) as a function of the position in sample C. The symbols stand for the structure depth (right axis) determined from confocal microscopy.

**Figure 8.**Intensity of the diffraction peaks (lines; see legend) as a function of the position in samples (

**a**) D and (

**b**) E.

**Figure 9.**Intensity of the diffraction peaks (lines; see legend) as a function of the position in samples (

**a**) F (overlapping pulses) and (

**b**) G (no overlap between pulses).

**Figure 10.**Real-time calculation of spatial period (colored symbols) on sample A at three axis speeds. The black lines correspond to the off-line results from Figure 5.

**Figure 11.**Real-time calculation of intensity of zero order on sample E at three axis speeds. The lines are guides to the eye.

Sample A | Sample B | Sample C | Sample D | Sample E | Sample F | Sample G | |||
---|---|---|---|---|---|---|---|---|---|

Field # | Spatial Period (µm) | Focus Deviation (mm) | Fluence (J/cm^{2}) | Unpatterned Line Width (µm) | Unpatterned Squares Edge (µm) | Unpatterned Line Width (µm) | Unpatterned Squares Edge (µm) | Error prob. (%) | Error prob. (%) |

1 | 1.3 | 0.31 | 0.751 | 35 | 35 | 7 | 7 | 0 | 0 |

2 | 1.4 | 0.15 | 0.741 | 70 | 70 | 14 | 9.9 | 10 | 10 |

3 | 1.5 | 0.07 | 0.728 | 140 | 140 | 28 | 19.8 | 20 | 20 |

4 | 1.7 | 0.03 | 0.708 | 210 | 210 | 42 | 29.7 | 30 | 30 |

5 | 1.8 | 0.01 | 0.682 | 280 | 280 | 56 | 39.6 | 40 | 40 |

6 | 2.0 | 0 | 0.657 | 350 | 350 | 70 | 49.5 | 50 | 50 |

7 | 2.3 | −0.01 | 0.632 | 420 | 490 | 84 | 59.4 | 60 | 60 |

8 | 2.5 | −0.03 | 0.535 | 490 | 560 | 98 | 69.3 | 70 | 70 |

9 | 2.9 | −0.07 | 0.481 | 560 | 630 | 126 | 79.2 | 80 | 80 |

10 | 3.1 | −0.15 | 0.362 | 630 | - | 140 | 89.1 | 90 | 90 |

11 | 3.3 | −0.31 | 0.216 | - | - | 154 | 99.0 | 95 | 95 |

12 | - | - | 0.031 | - | - | - | 108.9 | 97.5 | 97.5 |

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## Share and Cite

**MDPI and ACS Style**

Soldera, M.; Teutoburg-Weiss, S.; Schröder, N.; Voisiat, B.; Lasagni, A.F.
Compact Optical System Based on Scatterometry for Off-Line and Real-Time Monitoring of Surface Micropatterning Processes. *Optics* **2023**, *4*, 198-213.
https://doi.org/10.3390/opt4010014

**AMA Style**

Soldera M, Teutoburg-Weiss S, Schröder N, Voisiat B, Lasagni AF.
Compact Optical System Based on Scatterometry for Off-Line and Real-Time Monitoring of Surface Micropatterning Processes. *Optics*. 2023; 4(1):198-213.
https://doi.org/10.3390/opt4010014

**Chicago/Turabian Style**

Soldera, Marcos, Sascha Teutoburg-Weiss, Nikolai Schröder, Bogdan Voisiat, and Andrés Fabián Lasagni.
2023. "Compact Optical System Based on Scatterometry for Off-Line and Real-Time Monitoring of Surface Micropatterning Processes" *Optics* 4, no. 1: 198-213.
https://doi.org/10.3390/opt4010014