Aspect ratio-dependent etching in silicon using XeF2:
experimental investigation and comparative analysis
with dry etching methods

Baptiste Baradel, Olivier Léon, Fabien Méry, Philippe Combette, Alain Giani

► To cite this version:

Baptiste Baradel, Olivier Léon, Fabien Méry, Philippe Combette, Alain Giani. Aspect ratio-dependent etching in silicon using XeF2: experimental investigation and comparative analysis with dry etching methods. Journal of Micromechanics and Microengineering, 2024, 34 (12), pp.125002. 10.1088/1361-6439/ad8c52. hal-04818083

HAL Id: hal-04818083

https://hal.science/hal-04818083v1

Submitted on 4 Dec 2024

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Aspect Ratio-Dependent Etching in Silicon using XeF₂: Experimental Investigation and Comparative Analysis with Dry Etching Methods

Baptiste Baradel<sup>1,2*</sup>, Olivier Léon<sup>2</sup>, Fabien Méry<sup>2</sup>, Philippe Combette<sup>1</sup> and Alain Giani<sup>1</sup>

<sup>1</sup> IES, Université de Montpellier, France

<sup>2</sup> DMPE, ONERA, Université de Toulouse, France

E-mail: baptiste.baradel@umontpellier.fr

This work is licensed under a license CC-BY 4.0.

**Abstract.** Silicon machining plays a crucial role in shaping three-dimensional structures for Micro-Electro-Mechanical Systems (MEMS) applications. This study investigates Aspect Ratio Dependent Etching (ARDE) across various silicon etching processes, with a particular focus on Xenon Difluoride (XeF₂) etching, in comparison to Reactive Ion Etching (RIE) and Deep Reactive Ion Etching (DRIE). By exploring different etching parameters, the study highlights the presence of ARDE in both plasma and non-plasma etching processes. Additionally, it is demonstrated that ARDE can be modeled by a saturating exponential function through experimental adjustment of parameters, enabling the estimation of etching profiles.

*Keywords:* Silicon dry etching; ARDE; XeF₂; Plasma etching.

Submitted to: *J. Micromech. Microeng.*

## 1. Introduction

In the fabrication of Micro-Electro-Mechanical Systems (MEMS), silicon machining is a crucial step for shaping three-dimensional devices. Over the years, various silicon etching techniques have been explored, ranging from wet to dry methods
involving chemical or physical etching processes [1, 2, 3]. The selection of a par-
ticular technique depends on factors such as selectivity, etching shape (isotropic or
anisotropic), and desired etching depth. One key parameter in silicon etching is
the aspect ratio, defined as the depth-to-width ratio, with a value of 10:1 typically
considered high [2]. For achieving high aspect ratio etching, Reactive Ion Etching
(RIE) and Deep Reactive Ion Etching (DRIE) are commonly employed [4]. These
techniques entail creating a gas plasma within a chamber where the sample is po-
sitioned, with the plasma species reacting with silicon to induce etching. Typically,
the gas mixtures used in this type of etching process consist of fluorine-based gases
such as SF<sub>6</sub>, C<sub>4</sub>F<sub>8</sub> or CHF<sub>3</sub>, among others.

Advancements in lithography techniques have facilitated the creation of intri-
cate shapes for MEMS, bringing to light the phenomenon of Aspect Ratio Dependent
Etching (ARDE) in silicon etching [5, 6]. ARDE refers to the influence of the open-
ing size in the mask material on the depth of etching, arising from the physical and
chemical interactions between ions, neutrals, and matter at a microscopic scale. Al-
though the understanding of this phenomenon has been under investigation for years
[7, 8, 9, 10], plasma physics remains complex and dependent on various parameters
such as gas species, materials, pressure and power supply. Consequently, accurately
predicting the relationship between opening size and etching depth is challenging,
often necessitating experimental approaches to elucidate the specific characteristics
of each case.

While RIE and DRIE are commonly used as dry etching techniques for silicon,
Xenon Difluoride (XeF₂) etching presents an alternative method. In this process,
fluorine atoms react with silicon without any ionized species to create the SiF₄
volatile species, offering the advantage of natural reactivity at room temperature
in a low-pressure chamber [11, 12]. However, XeF₂ etching tends to exhibit high
isotropy, resulting in mask undercutting that can be as large as vertical etching
[13]. Nevertheless, it has found application in various MEMS fabrications [14, 15].
Matsutani et al. [15] conducted a study focusing on small holes with opening
sizes ranging from 60 nm to 500 nm, revealing a dependence of etching depth on
opening size and suggesting that XeF₂ etching may be subject to ARDE. Despite
this, according to the knowledge of the authors, no other literature exists on ARDE
in XeF₂ silicon etching. This motivates the present study to further investigate XeF₂
silicon etching, notably for larger opening sizes. Additionally, this research aims to
compare this etching technique with other dry etching techniques like RIE and DRIE
to identify potential similarities and trends.

**2. Materials and Methods**

This section details the methodology used in the present study to
comprehensively investigate ARDE in XeF₂ silicon etching, RIE and DRIE. We
notably provide descriptions for the substrate used, the various opening sizes
employed, the parameters associated with each etching technique and the methods
used for measuring different etching depths.

2.1. Silicon substrate and mask material

The primary substrate used is (100)-oriented silicon with a thickness of 200 µm. For XeF₂ etching, the mask material is SiO₂, chosen for its low etching rate compared to silicon [16] (near infinite selectivity). Due to reactor's contamination constraints and the impossibility to introduce metals within it, the same material is employed for DRIE, although with a thicker layer deposited onto the Si substrate to compensate for the reduced selectivity. Specifically, layers thicknesses of 200 nm and 3 µm are deposited by Low Pressure Chemical Vapor Deposition (LPCVD) for XeF₂ etching and DRIE, respectively. These thicknesses ensure that the mask material is always present above Silicon during the entire etching process for both samples. Conversely, for the RIE process, a different approach is adopted due to the strong reactivity of the plasma gases with SiO₂. Instead, a chromium (Cr) mask layer is employed. For this purpose, a 100 nm Cr layer is deposited by sputtering.

After lithography, each mask layer is etched to transfer the mask patterns as
described in the following section. The SiO₂ layer undergoes RIE process, with
careful attention given to etching the 3 µm thick layer to ensure anisotropic etching.
The Cr layer is etched using a chromium etchant solution.

2.2. Mask openings

To investigate the impact of opening size on etching depth, various mask
openings were created. These openings are circular in shape, with diameters ranging
from 1.5 µm to 36 µm and spacings varying from 10 µm to 50 µm. These openings are arranged in a matrix of 25 × 25 mm to ensure adequate statistical estimation of etching depths and facilitate the identification of holes, as illustrated in Figure 1.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Partial view of the photo-mask with different opening size.</figcaption></figure>

## 2.3. Etching techniques

Three different etching techniques were employed, each with specific parameters tailored to their respective processes.

### 2.3.1. Reactive Ion Etching
The RIE system used, an ICP-RIE 210IL by Corial, exploits an inductively-coupled plasma (ICP) etch configuration to achieve deeper etching and uses mixtures of SF$_{6}$ and O$_{2}$. As noted by Legtenberg et al. [17], numerous etch parameters can influence etching characteristics such as anisotropy and etch rate. Therefore, various proportions of SF$_{6}$ and O$_{2}$ ranging from 60%/ 40% to 80%/ 20%; chamber pressures ranging from 30 mTorr to 70 mTorr; and RF generator power, operating at 13.56 MHz, ranging from 150 W to 250 W are explored to assess their potential impact on ARDE and to optimize etching speed. The only parameter kept constant is the etching time, which is fixed at 45 minutes. For each etching
process, the samples were affixed to a graphite plate using Fomblin oil, and the plate was maintained to a temperature close to 20°C through helium cooling to prevent any substrate temperature increase. All experiments are conducted at the Centrale de Technologie en Micro et Nanoélectronique (CTM) of the University of Montpellier.

### 2.3.2. Deep Reactive Ion Etching
The DRIE process was conducted in the clean room at LAAS-CNRS laboratory, Toulouse. For availability reasons, etching parameters could not be varied. The samples were etched using an Alcatel AMS4200 system with a tri-pulsed Bosch process to achieve deep, anisotropic etching. The recipe employed is commonly used for traversing silicon wafers and consists of three cycles: an etching phase with $SF_6$, a passivation phase with $C_4F_8$, and a removal phase of the passivation layer using $O_2$. Each cycle was maintained at a constant duration until an etching depth of 190 µm was achieved, corresponding to an etching time of approximately 20 minutes. Additionally, the samples were affixed with Fomblin oil onto a wafer coated with thermal silicon dioxide (1.6 µm) to facilitate silicon etching. A representative result showing ARDE using DRIE, but obtained for rectangular opening shapes, is illustrated in Figure 2. This figure highlights the significant differences in etching depths between apertures of small and large sizes.

### 2.3.3. $XeF_2$ etching
With this type of etching approach, the number of tunable parameters is more limited compared to RIE system. Specifically, only the gas pressure, which determines its quantity, and the duration of each pulse can be adjusted. Consequently, the scope for conducting a comprehensive parametric study is restricted. Instead, the focus is given on ensuring optimal etching conditions by maintaining a consistent gas quantity for the duration of each pulse. To achieve this, a brief parametric study was conducted to determine the optimal parameters. We conclude that neither the $XeF_2$ pressure nor the pulse duration significantly influenced the outcome. Ultimately, the $XeF_2$ pressure was set to 3 Torr, the duration of each cycle was fixed at 30 seconds and a total of 25 cycles was applied. The process was conducted at room temperature, with the temperature measured throughout. A maximum increase of +1°C was observed. These etchings are performed at the CTM of the University of Montpellier with a XACTIX e1 Series etching system.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Scanning Electron Microscope image of a DRIE of Silicon illustrating ARDE for rectangular apertures ranging from 2 µm to 60 µm in width.</figcaption></figure>

## 2.4. Data collection and analysis

ARDE is mainly assessed by estimating the etching depth. However, since XeF₂ etching is purely isotropic, estimation of the mask undercutting is also important for this process. This is achieved by cleaving the etched samples to expose the openings in a cross-sectional view. Subsequently, the cleaved samples are examined using a Scanning Electron Microscope (SEM). Figure 3 depicts typical SEM images obtained after cleavage for each etching method, illustrating the etching shapes resulting from the different processes. For DRIE (Figure 3 (a)), the etching is clearly anisotropic with straight sidewalls, indicating precise and directional etching. Conversely, XeF₂ (Figure 3 (b)) etching is characterized by a purely isotropic process, resulting in a half-circular etching profile where the etching depth is equal to the lateral etching. In the case of RIE (Figure 3 (c)), the resulting etch is also anisotropic like DRIE. However, unlike DRIE, the resulting shape is not straight but conical with a larger lateral etching at the beginning that narrows towards the bottom of the hole.

Different sources of uncertainty can be identified in this approach to measure etching depths. First, cleaving must be precisely centered on the opening to obtain
accurate measurements. Additionally, manual observation using SEM may introduce inaccuracies due to the positioning of the measurement line and the alignment of the sample on the holder, which can cause perspective errors. All measurement errors are quantified to ensure the reliability of the results. In that case, the measurement error is quantified to ±4 pixels and the perspective error is approximately 1%. The reported etching depths represent the mean of at least four measurements, along with their respective dispersions and errors.

To facilitate comparison between different etching techniques, the etching depths were normalized by the maximum depth achieved for each process. Additionally, the mask thickness, was subtracted from the total measured thickness with SEM. As a result the relative etching depth $R_d$ is defined as : $R_d = (D - t_m)/D_{max}$, where D is the measured depth, $t_m$ the mask thickness specific to each process and $D_{max}$ is the maximum etching depth.

Moreover, it is observed that the etching depths exhibit a saturation point, representing the maximum achievable depth for a given etching time. To model this behavior, we propose using a saturating exponential function, as it effectively captures both the rapid initial increase and the subsequent saturation. The function is expressed as follows :

$$f(x) = 1 - e^{-Ax} \qquad (1)$$

where x represents the opening diameter and A is a positive rate constant. This model accurately reflects the dynamics of the etching process, where initial etching progresses quickly but slows as the depth approaches its maximum limit. Furthermore, this function describes the response of first-order systems, commonly found in chemical kinetics and other physical processes. As such, it can help to identify the reduced-order dynamics underlying the complex processes studied in this work. The validity of this model will be investigated and discussed in the following section.

### 3. Results & Discussion

This section focuses on the various experiments conducted and their interpretations. Two main studies are of interest: the application of the saturating
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Cross-sectional view of etching samples highlighting the shape and etching depth measurement : (a) DRIE for an opening size of *d* = 16 µm, (b) XeF₂ etching for an opening size of *d* = 20 µm and (c) RIE for an opening size of *d* = 10 µm and spaced from 25 µm.</figcaption></figure>
exponential function introduced earlier and the study of ARDE in relation to XeF₂
etching. For the first study, it is known that ARDE occurs during the RIE process
and that the parameters of the etching process influence the ARDE profile, as
discussed in the introduction. To validate the application of the function, we aim to
vary the RIE parameters and investigate its effectiveness in following the trend of
ARDE profiles. This will constitute the first part of this section. The second study
involves comparing XeF₂ etching with RIE and DRIE techniques.

3.1. Assessment of the application of the saturating exponential function

Regarding the range and the parameters that can be modified in RIE, it was
decided to conduct etching by varying one parameter while keeping the other two
constant to observe their potential impact on ARDE and on the function fit. The
results are presented in Figure 4.

To comment this results, the RF power variation affects the etching process, as
evidenced in Figure 4 (a), with higher power levels resulting in a lower etching rate
for smaller openings relative to larger ones. Although the effect is relatively minor.
In terms of pressure variations, Figure 4 (b) indicates that the impact is minimal.
Regarding the uncertainties, the negligible differences observed point out that the
influence of pressure on ARDE is not significant, at least for the tested pressure
range. The composition of the etching gas-mixture, particularly the proportion of
SF₆, plays a more critical role. As highlighted by Figure 4 (c), for increasing propor-
tion of SF₆ the etching rate for smaller openings decreases more noticeably compared
to larger openings. This impact underscores the importance of chemical composition
in controlling ARDE. It highlights that adjusting the SF₆ concentration can be a tool
for optimizing etching profiles. It is noteworthy to highlight that modifying these
parameters also influences the etch rate and the morphology of the etched features,
as presented by Legtenberg et al. [17]. However this study is out of the scope of
the present research and here the objective is simply to achieve the fastest etching.
Therefore, for comparison with other etching techniques, RIE is performed with the
following parameters: a SF₆/O₂ proportion of 80% and 20%, a chamber pressure
of 70 mTorr, a power supply set to 250 W, and an etch duration of around 45 minutes.

To investigate the reliability of the application of the saturating exponential
function, curve fittings were performed on each set of etching data, as shown in
Figure 4. The different parameters obtained through this operation are listed in Table 1. Upon closer examination, the function seems to accurately represent the experimental data, with good agreement between the two and a high coefficient of correlation ($r^2 > 0.93$). The only exception is the etching performed at a power of $P = 150$ W, where a dispersion in the collected data is observed, which may account for this difference. Thus, this exponential function can serve as a reliable model for fitting experimental data and determining etching depth based on opening size, thus facilitating the design of photo-masks. It should be noted that the observations were made only for apertures larger than 1.5 µm. Consequently, the assumption may be valid only for opening sizes above this threshold, although the strong correlation suggests that it may also be physically valid for smaller apertures.

<table><caption>**Table 1.** Parameter of the saturating exponential function fitted to the data for the different RIE parameters with their coefficient of correlation $r^2$.</caption><thead><tr><th></th><th>A (µm<sup>-1</sup>)</th><th>r<sup>2</sup></th></tr></thead><tbody><tr><td>P = 250 W</td><td>0.2055</td><td>0.9358</td></tr><tr><td>P = 200 W</td><td>0.2514</td><td>0.9578</td></tr><tr><td>P = 150 W</td><td>0.2604</td><td>0.8691</td></tr><tr><td>p = 70 mTorr</td><td>0.2055</td><td>0.9358</td></tr><tr><td>p = 50 mTorr</td><td>0.1966</td><td>0.9617</td></tr><tr><td>p = 30 mTorr</td><td>0.2337</td><td>0.9376</td></tr><tr><td>SF<sub>6</sub> / O<sub>2</sub> = 80%/ 20%</td><td>0.2055</td><td>0.9358</td></tr><tr><td>SF<sub>6</sub> / O<sub>2</sub> = 70%/ 30%</td><td>0.3166</td><td>0.9311</td></tr><tr><td>SF<sub>6</sub> / O<sub>2</sub> = 60%/ 40%</td><td>0.3196</td><td>0.9500</td></tr></tbody></table>

## 3.2. Comparison between XeF₂ etching and plasma etchings process

The results of the different etching processes are depicted in Figure 5. Firstly, the curve fitting using the exponential function, with the parameters presented in Table 2, once again closely aligns with the experimental data and has a high coefficient of
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Impact of RIE Parameters on ARDE. The graphs show the relative etching depth as a function of opening diameter *d*, with a fitted saturating exponential function curve. The following etching parameters were used:</figcaption></figure>

(a) Etching with $p = 70$ mTorr and mix $SF_6/O_2 = 80\%/20\%$;

(b) Etching with $P = 250$ W and mix $SF_6/O_2 = 80\%/20\%$;

(c) Etching with $p = 70$ mTorr and $P = 250$ W.
correlation. This reinforces the initial assumption that the function can effectively model the ARDE profile.

Upon examining the experimental data, XeF₂ etching and RIE exhibit nearly identical ARDE profiles, for the selected parameters. In contrast, the DRIE profile deviates from this trend. The reasons for these similarities and disparities are difficult to fully apprehend due to the multitude of mechanisms involved in silicon dry etching. Indeed, the chemical composition of the etchants differs slightly for each experiment, and micro-mechanisms involved are extremely complex to model and beyond our current reach. One factor that may partly explain these differences is that DRIE is a cyclic etch process, following the Bosch process. The removal phase of the polymer (passivation layer) in DRIE, which drives vertical etching, may be responsible for the more pronounced ARDE effect, as observed by Lai *et al.* [18]. Additionally, it should be noted that the mask materials used in the three etching techniques vary in both material and layer thickness. Since it is known that mask material can significantly influence the chemical etching process, notably affecting lateral undercutting [19, 20], it is conceivable that the ARDE phenomenon may also be modulated by the mask material, as suggested by Jansen *et al.* [21]. A comprehensive understanding of the impact of physical and chemical interactions between the matter and etchant on ARDE thus requires further investigation to elucidate the observed discrepancies. Nonetheless, the present experimental work clearly highlights the possibility of ARDE for XeF₂ etching of silicon, unambiguously showing the dependence of the etching depth on the opening size.

<table><caption>**Table 2.** Parameters of the saturating exponential function fitted to the data.</caption><thead><tr><th></th><th>A (µm<sup>-1</sup>)</th><th>r<sup>2</sup></th></tr></thead><tbody><tr><td>DRIE</td><td>0.1382</td><td>0.9073</td></tr><tr><td>XeF<sub>2</sub></td><td>0.1798</td><td>0.9745</td></tr><tr><td>RIE</td><td>0.2055</td><td>0.9358</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Comparison of etching depth for different opening mask sizes with added curve fitting of saturating exponential function.</figcaption></figure>

**4. Conclusion**

The current study detailed the phenomenon of ARDE in silicon etching, with a specific focus on comparing the XeF$_{2}$ etching technique to others. The objective was to explore the understanding of this phenomenon across various etching methods through experimental observations. With meticulous experimentation and analysis, it was first observed that RIE parameters can influence ARDE due to the chemical dependence inherent in this phenomenon. Then it was demonstrated that XeF$_{2}$ etching and RIE, with specific parameters, can exhibit strikingly similar ARDE profiles. In contrast, the DRIE profile displayed a distinct trend, characterized by slower growth of ARDE compared to RIE or XeF$_{2}$. The precise understanding of these discrepancies however stills requires further investigation and analysis. Nonetheless, the main outcome of this study is that ARDE can properly be applied in etching processes without plasma, such as XeF$_{2}$, and can be used to achieve etching profiles qualitatively similar to the ones obtained with plasma etching.

By examining different etching profiles and their saturation, the authors suggest that ARDE can be modeled using a saturating exponential function, and may
then be approximately modeled as a first-order system response. By performing a curve fitting analysis, it was shown that this type of function captures satisfactorily the profile for opening diameters greater than 1.5 µm by adjusting the function parameter. This approach provides a valuable tool for estimating ARDE from a database and can be used to easily design photo-masks for micro-machine silicon.

## Acknowledgments

The authors acknowledge the support of the staff at the Centrale de Technologie en Micro et Nanoélectronique (CTM), Université of Montpellier, France, during the etching process. They also particularly thanks A.Lecestre from LAAS Toulouse for the realisation of DRIE process. This research was partly funded by Région Occitanie, France with the funding program ALTDOC.

For the purpose of Open Access, a CC-BY public copyright license has been applied by the authors to the present document and will be applied to all subsequent versions up to the author-accepted manuscript arising from this submission.

## References

[1] Elwenspoek M and Jansen H V 2004 *Silicon Micromachining* first paperback ed ed (*Cambridge studies in semiconductor physics and microelectronic engineering* no 7) (Cambridge: Cambridge University Press) ISBN 978-0-521-60767-4

[2] Wu B, Kumar A and Pamarthy S 2010 *Journal of Applied Physics* **108** 051101 ISSN 0021-8979, 1089-7550 URL https://pubs.aip.org/jap/article/108/5/051101/345960/High-aspect-ratio-silicon-etch-A-review

[3] Guo H, Cao S, Li L and Zhang X 2022 *Materials Science in Semiconductor Processing* **137** 106182 ISSN 13698001 URL https://linkinghub.elsevier.com/retrieve/pii/S1369800121005205

[4] Huff M 2021 *Micromachines* **12** 991 ISSN 2072-666X URL https://www.mdpi.com/2072-666X/12/8/991

[5] Jansen H, Gardeniers H, Boer M d, Elwenspoek M and Fluitman J 1996 *Journal of Micromechanics and Microengineering* **6** 14-28 ISSN 0960-1317, 1361-6439 URL https://iopscience.iop.org/article/10.1088/0960-1317/6/1/002

[6] Jansen H, de Boer M, Wiegerink R, Tas N, Smulders E, Neagu C and Elwenspoek M 1997 *Microelectronic Engineering* **35** 45-50 ISSN 01679317 URL https://linkinghub.elsevier.com/retrieve/pii/S0167931796001426

[7] Gottscho R A, Jurgensen C W and Vitkavage D J 1992 *Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement,*
and Phenomena 10 2133-2147 ISSN 1071-1023, 1520-8567 URL https://pubs.aip.org/jvb/article/10/5/2133/470714/Microscopic-uniformity-in-plasma

[8] Bates R L, Goeckner M J and Overzet L J 2014 *Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films* **32** 051302 ISSN 0734-2101, 1520-8559 URL https://pubs.aip.org/jva/article/32/5/051302/244763/Correction-of-aspect-ratio-dependent-etch

[9] Vanraes P, Parayil Venugopalan S, Besemer M and Bogaerts A 2023 *Plasma Sources Science and Technology* **32** 064004 ISSN 0963-0252, 1361-6595 URL https://iopscience.iop.org/article/10.1088/1361-6595/acdc4f

[10] Yoshie T, Ishikawa K, Nguyen T T N, Hsiao S N, Tsutsumi T, Sekine M and Hori M 2023 *Applied Surface Science* **638** 157981 ISSN 01694332 URL https://linkinghub.elsevier.com/retrieve/pii/S0169433223016604

[11] Winters H F and Coburn J W 1979 *Applied Physics Letters* **34** 70-73 ISSN 0003-6951, 1077-3118 URL http://aip.scitation.org/doi/10.1063/1.90562

[12] Sarkar D, Baboly M G, Elahi M M, Abbas K, Butner J, Piñon D, Ward T L, Hieber T, Schuberth A and Leseman Z C 2018 *Journal of Micromechanics and Microengineering* **28** 045007 ISSN 0960-1317, 1361-6439 URL https://iopscience.iop.org/article/10.1088/1361-6439/aaa74e

[13] Chan I, Brown K, Lawson R, Robinson A, Yuan Ma and Strembicke D 1999 Gas phase pulse etching of silicon for MEMS with xenon difluoride *Engineering Solutions for the Next Millennium. 1999 IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.99TH8411)* vol 3 (Edmonton, Alta., Canada: IEEE) pp 1637-1642 ISBN 978-0-7803-5579-8 URL http://ieeexplore.ieee.org/document/804962/

[14] Kim S, Yeo H G, Ryu J and Choi H 2023 *Sensors and Actuators A: Physical* **351** 114159 ISSN 09244247 URL https://linkinghub.elsevier.com/retrieve/pii/S0924424723000080

[15] Matsutani A, Sato M, Hasebe K and Takada A 2019 *Sensors and Materials* **31** 1325 ISSN 0914-4935 URL http://myukk.org/SM2017/article.php?ss=2235

[16] Williams K, Gupta K and Wasilik M 2003 *Journal of Microelectromechanical Systems* **12** 761-778 ISSN 1057-7157 URL http://ieeexplore.ieee.org/document/1257354/

[17] Legtenberg R, Jansen H, De Boer M and Elwenspoek M 1995 *Journal of The Electrochemical Society* **142** 2020-2028 ISSN 0013-4651, 1945-7111 URL https://iopscience.iop.org/article/10.1149/1.2044234

[18] Lai S L, Johnson D and Westerman R 2006 *Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films* **24** 1283-1288 ISSN 0734-2101, 1520-8559 URL https://pubs.aip.org/jva/article/24/4/1283/103422/Aspect-ratio-dependent-etching-lag-reduction-in

[19] Dey R K, Ekinci H and Cui B 2020 *Journal of Vacuum Science & Technology B* **38** 012207 ISSN 2166-2746, 2166-2754 URL http://avs.scitation.org/doi/10.1116/1.5123601

[20] Zhang Y, Hou Z, Si C, Han G, Zhao Y, Lu X, Liu J, Ning J and Yang F 2023 *Micromachines* **14** 306 ISSN 2072-666X URL https://www.mdpi.com/2072-666X/14/2/306
[21] Jansen H, De Boer M, Burger J, Legtenberg R and Elwenspoek M 1995 *Microelectronic Engineering* **27** 475–480 ISSN 01679317 URL https://linkinghub.elsevier.com/retrieve/pii/0167931794001490