*3.1. Results of Regulation*

Firstly, in order to evaluate the linewidth uniformity of each grating line, ten grating lines in the standard were selected and their linewidths were calculated and analyzed. A length of L = 2000 nm was intercepted from each grating line, where 20 positions were chosen uniformly from top to bottom. The linewidth at each position of the grating line was the difference between the threshold line calculated by the gravity center method [27] and the two intersection points generated by left and right edges of grating line. The results of the linewidth of 10 grating lines for the three samples after ALD are shown in Figure 2a, while the position deviation curves of the linewidths are shown in Figure 2b. The inset in Figure 2a shows the AFM image of sample B after ALD. As evident from the figure, the 1D grating standard possesses well-distributed grating lines and excellent parallelism. However, there are a few particles or defects introduced by the tensile stress on Au with high ductility, during the lift-off process. It is shown in Figure 2a that the linewidths of the ten grating lines of each sample are close to each other with a slight degree of fluctuation. The deviation between the linewidths of 10 grating lines of sample A is the largest, but the maximum deviation is still only 2.1 nm (Figure 2b), which accounts for only 0.3% of the linewidth, thereby indicating the uniformity of linewidths of multiple grating lines in this structure. Hence, the user can select any grating line for the linewidth calibration, which certainly improves the repeatability of the calibration results. *Micromachines* **2022**, *13*, 995 5 of 11

**Figure 2.** (**a**) Calculated linewidths of the 10 grating lines of samples A, B and C, after ALD. (**b**) The position deviation curves of the calculated linewidths. **Figure 2.** (**a**) Calculated linewidths of the 10 grating lines of samples A, B and C, after ALD. (**b**) The position deviation curves of the calculated linewidths.

The average value of the linewidths of 10 grating lines was taken as the linewidth calibration value of each sample. The AFM images and comparison of the linewidths of

since ALD was growing the film simultaneously in the 3D direction. Here, the actual in‐ crease in the linewidths of three samples was 13.4, 19.6, and 29.7 nm, respectively. Evi‐ dently, the actual increase in the linewidths of samples B and C was close to the estimated value, while the actual increase in the linewidth of sample A deviated from the expected increment by 3.4 nm. This is because the linewidth uniformity of sample A is worse than the other two samples, as shown in Figure 2b. Further, the line edge roughness (LER) of the three samples was calculated according to Equation (1) [28] as LERA = 18.9 nm, LERB = 16.4 nm, and LERC = 15.9 nm, respectively. Thus, the final evaluation results are likely to be disturbed by many parameters such as the selection of linewidth evaluation position, quality of grating line edge, and linewidth evaluation algorithm when measuring and cal‐

ൌ 3 ൌ 3ඨ∑ ሺ െ ̅ሻ ே <sup>ଶ</sup> ୀଵ

where ̅is the average edge of grating line, *xi* is the intersection of threshold line and grating profile, *N* is the number of intersections, and σ is the standard deviation of line

െ1

(1)

⎩ ⎪ ⎨

⎪

⎧̅ൌ ሺ∑ ே ୀଵ ሻ 

culating the linewidth of this standard.

edge.

The average value of the linewidths of 10 grating lines was taken as the linewidth calibration value of each sample. The AFM images and comparison of the linewidths of the three samples before and after ALD are shown in Figure 3. It is shown in Figure 3a,b that the height of the grating was not changed and only the grating lines were widened since ALD was growing the film simultaneously in the 3D direction. Here, the actual increase in the linewidths of three samples was 13.4, 19.6, and 29.7 nm, respectively. Evidently, the actual increase in the linewidths of samples B and C was close to the estimated value, while the actual increase in the linewidth of sample A deviated from the expected increment by 3.4 nm. This is because the linewidth uniformity of sample A is worse than the other two samples, as shown in Figure 2b. Further, the line edge roughness (LER) of the three samples was calculated according to Equation (1) [28] as LER<sup>A</sup> = 18.9 nm, LER<sup>B</sup> = 16.4 nm, and LER<sup>C</sup> = 15.9 nm, respectively. Thus, the final evaluation results are likely to be disturbed by many parameters such as the selection of linewidth evaluation position, quality of grating line edge, and linewidth evaluation algorithm when measuring and calculating the linewidth of this standard.

$$\begin{cases} \overline{\mathfrak{x}} = \frac{\left(\sum\_{i=1}^{N} \mathbf{x}\_{i}\right)}{N} \\\\ LER = \mathfrak{3}\sigma = \mathfrak{3}\sqrt{\frac{\sum\_{i=1}^{N} (\mathbf{x}\_{i} - \overline{\mathbf{x}})^{2}}{N-1}} \end{cases} \tag{1}$$

where *x* is the average edge of grating line, *x<sup>i</sup>* is the intersection of threshold line and grating profile, *N* is the number of intersections, and *σ* is the standard deviation of line edge.

The results here reveal that the linewidth of the standard can be regulated by the ALD process, nevertheless there are some certain requirements for the standard fabrication and measurement process: (1) The regulation scheme is unidirectional since ALD can only increase the linewidth of the convex structures or decrease the linewidth of the concave structures. Thus, it is necessary to confirm the desired range of linewidths when processing the grating structure with EBL, according to the type of grating structure (convex or concave). (2) The effect of regulation is related to the linewidth uniformity and the edge straightness of grating line. The better the linewidth uniformity and edge straightness of grating line, the better the regulation performance. (3) The linewidth evaluation algorithm can be further optimized by filtering out various noises as well as the disturbances of particles at the edge of the line. The actual increase in the calculated linewidth in this case will be more reliable and can be fed back to the ALD process, to further improve the experimental parameters and form a closed-loop control.

While aiming to compare the changes in the pitch before and after the regulation, all raw data of 10 scanning lines were obtained uniformly from top to bottom along the y-direction within the scanning range of the sample, and the average pitch of each sample was calculated by the gravity center method. Meanwhile, the measurement uncertainty of each sample was evaluated according to the International Bureau of Weights and Measures (BIPM), the International Electrotechnical Commission (IEC), the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC), the International Organization for Standardization (ISO), the International Union of Pure and Applied Chemistry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), and the International Organization of Legal Metrology (OIML)-1993 Guide to the Expression of Uncertainty in Measurement [29], and the corresponding results are provided in Figures 3 and 4, and Table 1. The average pitch of three samples A, B and C changed by 1.8, 5.5 and 4.9 nm, respectively, before and after ALD. Theoretically, ALD should not change the pitch of the grating, and a small variation in the actual results may be caused by the fact that the quality of ALD depends on the quality of the substrate surface [30]. Hence, when there are large raised particles of several nanometers in size at the edge of grating lines, the surface of such raised particles is uniformly covered with a layer of Al2O<sup>3</sup> film after ALD due to the three-dimensional conformal property of ALD. The shape of the particles is still retained, which would change the line width of the grating and affect the accuracy of the calculated

data in turn. Here, the change in the pitch is small, where the maximum variation is only about 0.5% of the average pitch, which still indicates that the Al2O<sup>3</sup> films deposited by ALD have a great uniformity in terms of film thickness and almost do not change the average pitch of the grating standards. As shown in Table 1, the measurement uncertainty of the standards after ALD is less than 0.16% of the average pitch, thus the calibration reliability is quite satisfactory. Certainly, the uncertainties introduced by the surface uniformity and measurement repeatability of the standards are largely minimized here compared with those before ALD, which validates that the surface quality of standard can be optimized and the measurement uncertainties can be reduced by utilizing ALD. *Micromachines* **2022**, *13*, 995 6 of 11

**Figure 3.** (**a**) The image of sample A before ALD by AFM. (**b**) The image of sample A after ALD by AFM. (**c**) Comparison of linewidths and pitches of samples A, B, and C, before and after ALD. **Figure 3.** (**a**) The image of sample A before ALD by AFM. (**b**) The image of sample A after ALD by AFM. (**c**) Comparison of linewidths and pitches of samples A, B, and C, before and after ALD.

ticles at the edge of the line. The actual increase in the calculated linewidth in this case will be more reliable and can be fed back to the ALD process, to further improve the ex‐

While aiming to compare the changes in the pitch before and after the regulation, all raw data of 10 scanning lines were obtained uniformly from top to bottom along the y‐ direction within the scanning range of the sample, and the average pitch of each sample

The results here reveal that the linewidth of the standard can be regulated by the ALD process, nevertheless there are some certain requirements for the standard fabrica‐ tion and measurement process: (1) The regulation scheme is unidirectional since ALD can only increase the linewidth of the convex structures or decrease the linewidth of the con‐ cave structures. Thus, it is necessary to confirm the desired range of linewidths when pro‐ cessing the grating structure with EBL, according to the type of grating structure (convex or concave). (2) The effect of regulation is related to the linewidth uniformity and the edge straightness of grating line. The better the linewidth uniformity and edge straightness of grating line, the better the regulation performance. (3) The linewidth evaluation algorithm

perimental parameters and form a closed‐loop control.

**Figure 4.** The standard uncertainty of major uncertainty components of samples A, B, and C, before and after ALD. **Figure 4.** The standard uncertainty of major uncertainty components of samples A, B, and C, before and after ALD.

was calculated by the gravity center method. Meanwhile, the measurement uncertainty of each sample was evaluated according to the International Bureau of Weights and Measures (BIPM), the International Electrotechnical Commission (IEC), the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC), the International Or‐ ganization for Standardization (ISO), the International Union of Pure and Applied Chem‐ istry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), and the In‐ ternational Organization of Legal Metrology (OIML)‐1993 Guide to the Expression of Un‐ certainty in Measurement [29], and the corresponding results are provided in Figures 3 and 4, and Table 1. The average pitch of three samples A, B and C changed by 1.8, 5.5 and 4.9 nm, respectively, before and after ALD. Theoretically, ALD should not change the pitch of the grating, and a small variation in the actual results may be caused by the fact that the quality of ALD depends on the quality of the substrate surface [30]. Hence, when there are large raised particles of several nanometers in size at the edge of grating lines, the surface of such raised particles is uniformly covered with a layer of Al2O3 film after ALD due to the three‐dimensional conformal property of ALD. The shape of the particles is still retained, which would change the line width of the grating and affect the accuracy of the calculated data in turn. Here, the change in the pitch is small, where the maximum variation is only about 0.5% of the average pitch, which still indicates that the Al2O3 films deposited by ALD have a great uniformity in terms of film thickness and almost do not change the average pitch of the grating standards. As shown in Table 1, the measurement uncertainty of the standards after ALD is less than 0.16% of the average pitch, thus the calibration reliability is quite satisfactory. Certainly, the uncertainties introduced by the surface uniformity and measurement repeatability of the standards are largely minimized here compared with those before ALD, which validates that the surface quality of stand‐ ard can be optimized and the measurement uncertainties can be reduced by utilizing

**Table 1.** The evaluation results of the one‐dimensional grating standards. **Table 1.** The evaluation results of the one-dimensional grating standards.


<sup>1</sup> *k* is the coverage factor. *k* is the coverage factor.

### *3.2. Application*

1

ALD.

To verify the calibration applicability of the sample obtained from this method in different measurement instruments, the AFM and SEM were used to measure sample B. The data obtained from the two measurement instruments were analyzed to provide a reference for the nano-geometry measurements between different instruments. The linewidth and pitch of sample B were measured by SEM system (SU8010, Hitachi, Tokyo, Japan), calculated by the gravity center method, and then evaluated for the uncertainties. The comparison of the SEM and AFM images, along with the evaluation results, is shown in Figure 5. The linewidth of the standard measured by AFM was evaluated as (589.4 ± 2.8) nm (*k* = 2) while the pitch was evaluated as (990.1 ± 1.5) nm (*k* = 2). On the other hand, the linewidth of the standard measured by SEM was evaluated to be (585.7 ± 3.1) nm (*k* = 2), whereas the pitch was (990.5 ± 1.8) nm (*k* = 2). Clearly, the pitch measured by the both instruments is very close. However, the difference in the linewidths is more obvious.

In this work, the *E<sup>n</sup>* [31] was used to assess the level of agreement between the two measurements, which can be defined using Equation (2). When |*En*| ≤ 1, the consistency of the results is good and acceptable; whereas |*En*| > 1 indicates a poor consistency of the results, which is unacceptable. Based on this criterion, the |*En*|pitch = 0.17 and the |*En*|linewidth = 0.79 were calculated for the considered sample, illustrating high agreement between the pitch and linewidth values obtained using two measurement instruments.

$$E\_{\rm nl} = \frac{\chi\_{AFM} - \chi\_{SEM}}{\sqrt{\mathcal{U}^2{}\_{AFM} + \mathcal{U}^2{}\_{SEM}}} \tag{2}$$

where *xAFM* is the value measured by AFM; *xSEM* is the value measured by SEM; *UAFM* is the expanded uncertainty of the result measured by AFM; *USEM* is the expanded uncertainty of the result measured by SEM.

*3.2. Application*

instruments is very close. However, the difference in the linewidths is more obvious.

To verify the calibration applicability of the sample obtained from this method in different measurement instruments, the AFM and SEM were used to measure sample B. The data obtained from the two measurement instruments were analyzed to provide a reference for the nano‐geometry measurements between different instruments. The lin‐ ewidth and pitch of sample B were measured by SEM system (SU8010, Hitachi, Tokyo, Japan), calculated by the gravity center method, and then evaluated for the uncertainties. The comparison of the SEM and AFM images, along with the evaluation results, is shown in Figure 5. The linewidth of the standard measured by AFM was evaluated as (589.4 ± 2.8) nm (*k* = 2) while the pitch was evaluated as (990.1 ± 1.5) nm (*k* = 2). On the other hand, the linewidth of the standard measured by SEM was evaluated to be (585.7 ± 3.1) nm (*k =*

**Figure 5.** (**a**) The image of sample B after ALD by AFM. (**b**) The image of sample B after ALD by SEM. (**c**) Comparison of the calculation results of linewidth and pitch. **Figure 5.** (**a**) The image of sample B after ALD by AFM. (**b**) The image of sample B after ALD by SEM. (**c**) Comparison of the calculation results of linewidth and pitch.

In this work, the *En* [31] was used to assess the level of agreement between the two measurements, which can be defined using Equation (2). When |*En*| ≤ 1, the consistency of the results is good and acceptable; whereas |*En*| > 1 indicates a poor consistency of the results, which is unacceptable. Based on this criterion, the |*En*|pitch = 0.17 and the |*En*|lin‐ ewidth = 0.79 were calculated for the considered sample, illustrating high agreement be‐ tween the pitch and linewidth values obtained using two measurement instruments. ൌ ிெ െ ௌாெ ඥଶ ிெ ଶ ௌாெ (2) Compared with SEM, AFM can measure the 3D surface morphology of the sample more accurately, and the resolution of AFM in the horizontal and vertical directions is close to the atomic scale, hence the measurement uncertainty by AFM is lower. Meanwhile, the measurement uncertainty for SEM is higher, which is mainly introduced by the errors in the image resolution and the variation of electron beam spot diameter. However, the width of AFM probe cannot be neglected while measuring the linewidth, which can induce a spreading effect in the scanning image. As a result, the shape of AFM probe has a significant impact on the linewidth measurement, thereby resulting in a larger linewidth measured by AFM compared to SEM.

where *xAFM* is the value measured by AFM; *xSEM* is the value measured by SEM; *UAFM* is the expanded uncertainty of the result measured by AFM; *USEM* is the expanded uncertainty of the result measured by SEM. Compared with SEM, AFM can measure the 3D surface morphology of the sample more accurately, and the resolution of AFM in the horizontal and vertical directions is close to the atomic scale, hence the measurement uncertainty by AFM is lower. Mean‐ while, the measurement uncertainty for SEM is higher, which is mainly introduced by the errors in the image resolution and the variation of electron beam spot diameter. However, the width of AFM probe cannot be neglected while measuring the linewidth, which can On the basis of measurement results, the sample satisfies a cross-comparison of the measurement capabilities of two measurement instruments. Excellent 3D morphology measurements were realized in the AFM, and clear edges of grating lines along with a sharp contrast with the substrate were demonstrated in the SEM. In conclusion, it can be assessed that the consistency level of results obtained by both instruments is superior in this work, based on the *En*. Accordingly, this experiment demonstrates that the samples obtained via precise linewidth regulation based on ALD can be applied to many different types of measurement instruments, where simultaneous calibration of nanoscale pitch and linewidth can be achieved, thereby enhancing calibration efficiency substantially.

induce a spreading effect in the scanning image. As a result, the shape of AFM probe has

### a significant impact on the linewidth measurement, thereby resulting in a larger linewidth **4. Conclusions**

measured by AFM compared to SEM. On the basis of measurement results, the sample satisfies a cross‐comparison of the measurement capabilities of two measurement instruments. Excellent 3D morphology measurements were realized in the AFM, and clear edges of grating lines along with a In this work, we have studied the controllable regulation of the linewidth of a 1D grating standard with a pitch of 1000 nm, using ALD. The results reported herein show that the linewidth of the standard can be regulated precisely by utilizing a thin film with controllable thickness and 3D conformal structure, based on the self-limiting layer-by-layer deposition mechanism of ALD. Moreover, the better the edge straightness and linewidth uniformity of the grating line, the better the regulation performance. Evidently, the ALD process can improve the surface uniformity as well as the measurement repeatability of the standard, and restrict the measurement uncertainty of the grating standard below 0.16% of the average pitch, thus potentially guaranteeing the calibration reliability of the standard. Since the thickness of thin film grown by ALD generally does not exceed 100 nm, and the film and substrate bonding will be worse when the film is thicker. That is, the regulation value of this method for linewidth is typically less than 100 nm (film thickness is 50 nm), which requires that the deviation between the designed dimension and the actual fabricated dimension during the patterning process must not be larger than 100 nm. As a result, it is more appropriate for linewidth regulation of the grating standard with a pitch of 100 nm–10 µm.

> The results acquired here from the comparisons of linewidth and pitch of the same sample by AFM and SEM are consistent; therefore, the 1D nano-grating standard with controllable pitch and linewidth can be integrated with the calibration function of grating

and linewidth. It can be used not only to calibrate the magnification of the measuring instruments, but also to achieve the measurement of critical dimensions of micro- and nanodevices, thereby avoiding the repetitive errors introduced by frequent standard replacement and improving calibration efficiency significantly. Furthermore, it can also be adapted to the measurement requirements of different measurement instruments regarding the duty cycle of standard, easily and efficiently, by simply adjusting the duty cycle of the formed 1D nano-grating standard, which essentially expands the application range of the standard, and economizes the manufacturing expense.

The follow-up work will focus on further reducing the deviation between the actual and estimated regulation values of the linewidth by optimizing the parameters of the ALD process based on the molecular microscopic properties of thin film materials, and realizing precise regulation of the linewidth of 1D grating standards at the sub-nanometer scale.

**Author Contributions:** Conceptualization, Y.Z. (Yaxin Zhang) and C.W.; methodology, Y.Z. (Yaxin Zhang), S.W. and L.Z.; validation, Y.Z. (Yujing Zhang) and Y.W.; formal analysis, W.J. and N.Z.; investigation, Y.Z. (Yaxin Zhang); data curation, Y.Z. (Yijun Zhang); writing—original draft preparation, Y.Z. (Yaxin Zhang); writing—review and editing, C.W. and Q.L.; visualization, S.W.; supervision, W.J. and Y.Z. (Yifan Zhao); project administration, Z.J.; funding acquisition, C.W., Y.Z. (Yifan Zhao) and Z.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant Nos. 52175434, 62001366), 111 Program (No. B12016).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

