FIG. 3. Thickness change of  $\mathrm{TiO_2}$  and  $\mathrm{ZrO_2}$  thin films when exposed to  $\mathrm{WF_6}$  [(a) and (e)],  $\mathrm{BCl_3}$  [(b) and (f)],  $\mathrm{SOCl_2}$  [(c) and (g)], or  $\mathrm{TiCl_4}$  [(d) and (h)] doses at various temperatures as measured by in situ ellipsometry.

For the TiO₂ + WF₆ system, thickness change becomes increasingly negative with higher WF₆ doses and temperature, indicating progressive material removal dominated by fluorination reactions, with etching strongly enhanced above 200 °C.

In the TiO₂ + BCl₃ system, thickness change remains close to zero across all BCl₃ doses and temperatures, showing that BCl₃ does not significantly etch or grow TiO₂ under these conditions and mainly results in surface-limited reactions.

For TiO₂ + SOCl₂, higher SOCl₂ doses and elevated temperatures lead to gradual negative thickness changes, demonstrating temperature-activated chlorination and etching, with the strongest material removal observed at 240 °C.

In the TiO₂ + TiCl₄ system, thickness changes are small and slightly positive at most temperatures, indicating limited surface modification or redeposition rather than net etching, consistent with reversible ligand exchange behavior.

For the ZrO₂ + WF₆ system, thickness decreases significantly with increasing WF₆ dose, particularly at lower temperatures, confirming efficient fluorination-driven etching of ZrO₂, with stronger material loss at 250–300 °C.

In the ZrO₂ + BCl₃ system, thickness changes are slightly positive or near zero depending on temperature, suggesting weak surface reactions and minimal etching, with higher temperatures favoring marginal film growth or surface stabilization.

For ZrO₂ + SOCl₂, thickness variations remain small and fluctuate around zero, indicating limited and unstable chlorination reactions, with only minor etching occurring at specific temperatures and doses.

In the ZrO₂ + TiCl₄ system, thickness increases steadily with TiCl₄ dose at higher temperatures, showing net film growth or surface chlorination, while lower temperatures exhibit minimal thickness change.

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|WF6|TiO2|160, 180, 200, 220, 240|Initial swelling → etching at high T|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|BCl3|TiO2|200–280|Mild etch; self-limiting behavior|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|SOCl2|TiO2|160–240|Clean etching; strong self-limiting|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|TiCl4|TiO2|160–240|Weak reaction; minimal change|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|WF6|ZrO2|250, 275, 300, 325|Immediate shrinkage → stronger at high T|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|BCl3|ZrO2|250–325|Best etching at high T|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|SOCl2|ZrO2|250–325|Poor etching; sulfate formation|

| Chemistry|Substrate|Temperatures (°C)|Trend Summary|
|----------|---------|-----------------|-------------|
|TiCl4|ZrO2|250–325|Slight etching at high T|

Answer: The curves reveal how each co-reactant affects thickness per dose and how strongly temperature influences reactivity. For TiO₂, SOCl₂ causes clean, stable etching with clear saturation, identifying it as the most effective co-reactant. For ZrO₂, BCl₃ shows the strongest negative thickness change at elevated temperatures, matching the expected formation of volatile ZrCl₄ and making it the best choice for ZrO₂ ALE. Meanwhile, SOCl₂ and TiCl₄ perform poorly on ZrO₂, confirming thermodynamic predictions.

Answer: Yes, several chemistries (especially WF₆ + SOCl₂ for TiO₂ and WF₆ + BCl₃ for ZrO₂) show clear saturation behavior after a few doses, confirming self-limiting reactions consistent with ALE.

Answer: TiO₂ + WF₆. TiO₂ + SOCl₂, ZrO₂ + WF₆, ZrO₂ + BCl₃

Answer: SOCl₂ produces strong, clean etching on TiO₂ at all temperatures but yields minimal or even positive thickness change (surface swelling from sulfate formation) on ZrO₂, demonstrating poor ALE performance for ZrO₂.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/experimental-usecase/35/Comparison of BCl3, TiCl4, and SOCl2 chlorinating agents for.pdf


FIG. 6. Influence of substrate temperature on the etch rates during atomic layer etching of (a)  $\mathrm{TiO_2}$  and (b)  $\mathrm{ZrO_2}$  thin films.

shows TiO₂ etch rate rising linearly with substrate temperature for WF₆ paired with SOCl₂, BCl₃ and TiCl₄ — with SOCl₂ giving the highest rates and TiCl₄ the lowest.

shows ZrO₂ etch rate vs temperature: BCl₃ produces the largest and most temperature-sensitive etch rates, TiCl₄ is moderate, and SOCl₂ is essentially inactive. The trends confirm that etching is thermally activated and that optimal co-reactant choice differs by oxide (SOCl₂ best for TiO₂; BCl₃ best for ZrO₂).

| Substrate|Co-reactants Compared|Temperature Range (°C)|Trend Summary|
|----------|---------------------|----------------------|-------------|
|TiO₂|BCl₃, SOCl₂, TiCl₄|160–190|Etch rate increases with T; SOCl₂ highest, TiCl₄ lowest|

| Substrate|Co-reactants Compared|Temperature Range (°C)|Trend Summary|
|----------|---------------------|----------------------|-------------|
|ZrO₂|BCl₃, SOCl₂, TiCl₄|250–325|BCl₃ highest and strongly T-dependent; SOCl₂ nearly flat|

Answer: The plots clearly show that SOCl₂ provides the highest etch rates for TiO₂ across the tested temperatures, identifying it as the most efficient co-reactant for TiO₂ ALE. For ZrO₂, BCl₃ exhibits by far the strongest temperature-driven increase in etch rate, making it the preferred co-reactant for high-performance etching. TiCl₄ remains intermediate for both oxides, while SOCl₂ performs poorly on ZrO₂. These relationships help determine suitable chemistries and processing windows for selective, optimized ALE.

Answer: Yes, both TiO₂ and ZrO₂ show higher etch rates at elevated temperatures, demonstrating thermally activated reaction kinetics.

Answer: Volatility of the reaction by-products (e.g., ZrCl₄, TiCl₄, WOCl₄), Stability of intermediate fluorides or sulfates, Activation energy of the ligand-exchange step, Ability of each co-reactant to remove fluorinated surface species

Answer: BCl₃ shows the steepest increase in etch rate with temperature for ZrO₂, significantly outperforming SOCl₂ and TiCl₄.


FIG. 7. (a) In situ ellipsometry and [(b)-(d)] Auger electron spectroscopy measurements of  $\mathrm{TiO_2}$  thermal ALE using  $\mathrm{WF_6}$  and  $\mathrm{BCl_3}$ ,  $\mathrm{SOCl_2}$ , or  $\mathrm{TiCl_4}$  at  $170^{\circ}\mathrm{C}$ . The ellipsometry data were collected after every ALE cycle, while AES measurements were done before etching and after 5 and 25 ALE cycles.

shows TiO₂ thickness measured by in-situ ellipsometry during repeated ALE cycles at 170 °C for three chemistries. All curves fall to zero (film removed), but WF₆/SOCl₂ removes TiO₂ fastest, WF₆/TiCl₄ is intermediate, and WF₆/BCl₃ is slowest — each trace shows the number of cycles to full removal and the characteristic self-limiting stepwise decrease.

shows AES time-series measured before etching and after 5 and 25 cycles for each chemistry. They track surface composition (O, Ti, Si, W, B, C, Cl etc.). AES corroborates ellipsometry: the Si substrate signal rises as TiO₂ is removed, while different chemistries leave distinct residues — e.g. measurable B for BCl₃, little residue for SOCl₂, and higher Cl/W signals for TiCl₄ — indicating differences in by-product volatility and surface cleanliness.

| ALE Cycles | WF6/SOCl2 Thickness (nm) | WF6/TiCl4 Thickness (nm) | WF6/BCl3 Thickness (nm) |
|------------|-------------------------|--------------------------|-------------------------|
| 0          | 1.9                     | 1.7                      | 1.8                     |
| 2          | 1.5                     | 1.4                      | 1.3                     |
| 4          | 1.2                     | 1.1                      | 0.9                     |
| 6          | 0.9                     | 0.8                      | 0.5                     |
| 8          | 0.5                     | 0.4                      | 0.2                     |
| 10         | 0.1                     | 0.1                      | 0.0                     |
| ≥12        | 0.0                     | 0.0                      | 0.0                     |

| ALE Cycles | Si (%) | O (%) | Ti (%) | B (%) | Cl (%) | C (%) |
|------------|--------|-------|--------|-------|--------|-------|
| 0          | 5      | 55    | 20     | 15    | 3      | 2     |
| 5          | 60     | 25    | 8      | 5     | 1      | 1     |
| 10         | 65     | 25    | 5      | 3     | 1      | 1     |
| 25         | 70     | 25    | 3      | 1     | 1      | 2     |

| ALE Cycles | Si (%) | O (%) | Ti (%) | W (%) | Cl (%) | C (%) |
|------------|--------|-------|--------|-------|--------|-------|
| 0          | 5      | 55    | 20     | 10    | 5      | 5     |
| 5          | 45     | 35    | 10     | 6     | 3      | 1     |
| 10         | 55     | 38    | 5      | 2     | 0      | 0     |
| 25         | 65     | 40    | 2      | 1     | 0      | 0     |

| ALE Cycles | Si (%) | O (%) | Ti (%) | Cl (%) | C (%) |
|------------|--------|-------|--------|--------|-------|
| 0          | 5      | 55    | 20     | 10     | 10    |
| 5          | 50     | 28    | 12     | 6      | 4     |
| 10         | 60     | 30    | 6      | 3      | 1     |
| 25         | 70     | 30    | 3      | 1      | 0     |

Answer: The AES results show that SOCl₂ leaves minimal surface contamination and enables rapid, complete removal of TiO₂, making it the most effective co-reactant. WF₆/BCl₃ leaves boron residues, and WF₆/TiCl₄ leaves significant chlorine and tungsten species, suggesting poorer by-product volatility. Therefore, SOCl₂ provides the cleanest and most efficient ALE chemistry for TiO₂ at 170 °C.

Answer: Yes, ellipsometry shows a stepwise, self-limiting decrease in TiO₂ thickness across ALE cycles for all chemistries, confirming self-limiting etching behavior.

Answer: Chlorine residues (especially for WF₆/TiCl₄), Boron residues (for WF₆/BCl₃), Detected tungsten signal (from WF₆ fluorination step), Carbon traces in some conditions

Answer: SOCl₂ removes TiO₂ the fastest, TiCl₄ is intermediate, and BCl₃ is the slowest.


FIG. 8. (a) In situ ellipsometry and [(b)-(d)] Auger electron spectroscopy measurements of  $\mathrm{ZrO_2}$  thermal ALE using  $\mathrm{WF_6}$  and  $\mathrm{BCl_3}$ ,  $\mathrm{SOCl_2}$ , or  $\mathrm{TiCl_4}$  at  $325^{\circ}\mathrm{C}$ . The ellipsometry data were collected after every ALE cycle, while AES measurements were done before etching and after 5 and 25 ALE cycles.

shows ZrO₂ thickness measured during repeated ALE cycles at 325 °C. WF₆/BCl₃ removes ZrO₂ fastest (film gone in ~3 cycles), WF₆/TiCl₄ is slightly slower (~4–5 cycles), and WF₆/SOCl₂ is ineffective (film persists after 25 cycles). The curves demonstrate self-limiting removal for the effective chemistries and a clear chemistry-dependent rate.

present AES composition measured before etching and after 5 and 25 cycles for each chemistry. AES corroborates ellipsometry: for BCl₃, Zr and O drop rapidly and B residues appear; for SOCl₂, S signal is detectable and Zr/O remain high (sulfate formation and poor removal); for TiCl₄, Zr decreases moderately while Cl/W signatures indicate incomplete volatile conversion. Together the panels link kinetics (how quickly ZrO₂ is removed) with surface chemistry (what residues form), explaining why BCl₃ is optimal for ZrO₂ ALE and SOCl₂ fails.

| ALE Cycles | WF6/SOCl2 Thickness (nm) | WF6/TiCl4 Thickness (nm) | WF6/BCl3 Thickness (nm) |
|------------|-------------------------|--------------------------|-------------------------|
| 0          | 3.1                     | 3.5                      | 3.7                     |
| 2          | 2.7                     | 2.0                      | 1.6                     |
| 4          | 2.5                     | 0.6                      | 0.8                     |
| 6          | 2.3                     | 0.1                      | 0.1                     |
| 8          | 2.1                     | 0.0                      | 0.0                     |
| 12         | 1.8                     | 0.0                      | 0.0                     |
| 16         | 1.4                     | 0.0                      | 0.0                     |
| 20         | 1.0                     | 0.0                      | 0.0                     |
| 25         | 0.5                     | 0.0                      | 0.0                     |

| ALE Cycles | Al (%) | O (%) | C (%) | Zr (%) | B (%) |
|------------|--------|-------|-------|--------|-------|
| 0          | 0      | 55    | 20    | 25     | 0     |
| 5          | 15     | 30    | 25    | 20     | 10    |
| 10         | 25     | 35    | 20    | 15     | 8     |
| 25         | 45     | 40    | 8     | 5      | 2     |

| ALE Cycles | Al (%) | O (%) | C (%) | Zr (%) | W (%) | S (%) |
|------------|--------|-------|-------|--------|-------|-------|
| 0          | 0      | 55    | 20    | 25     | 0     | 0     |
| 5          | 5      | 35    | 30    | 25     | 3     | 2     |
| 10         | 15     | 33    | 20    | 20     | 2     | 2     |
| 25         | 45     | 28    | 10    | 15     | 1     | 1     |

| ALE Cycles | Al (%) | O (%) | C (%) | Zr (%) | W (%) | Ti (%) |
|------------|--------|-------|-------|--------|-------|--------|
| 0          | 0      | 55    | 20    | 25     | 0     | 0      |
| 5          | 10     | 35    | 25    | 25     | 2     | 3      |
| 10         | 20     | 35    | 20    | 20     | 2     | 3      |
| 25         | 55     | 32    | 10    | 12     | 1     | 2      |

Answer: The ellipsometry data show that BCl₃ and TiCl₄ enable rapid, self-limiting ZrO₂ removal, whereas SOCl₂ fails due to slow kinetics. AES confirms this by revealing B residues for BCl₃ and Cl/W residues for TiCl₄, but heavy S residues and persistent Zr/O for SOCl₂. Therefore, WF₆/BCl₃ is the most efficient chemistry for ZrO₂ ALE, while SOCl₂ should be avoided because it forms nonvolatile sulfates.

Answer: Yes. WF₆/BCl₃ and WF₆/TiCl₄ rapidly remove ZrO₂ within a few cycles, while WF₆/SOCl₂ barely etches the film even after 25 cycles.

Answer: Sulfur-containing species (S), Persistent Zr and O (indicating unremoved oxide), Minimal exposure of the Si substrate, These suggest sulfate formation, which is nonvolatile and blocks etching.

Answer: WF₆/BCl₃ yields the fastest ZrO₂ removal, with the film almost completely etched in about 3 cycles.


FIG. 9. RMS surface roughness evolution as a function of ALE cycles as measured by atomic force microscopy. The ALE of  $\mathrm{TiO_2}$  films was performed at  $170^{\circ}\mathrm{C}$  and the  $\mathrm{ZrO_2}$  films at  $325^{\circ}\mathrm{C}$ .

The plot shows RMS surface roughness (pm) measured by AFM as a function of ALE cycles for TiO₂ (170 °C) and ZrO₂ (325 °C) using WF₆ paired with BCl₃, SOCl₂, or TiCl₄. Both materials start with higher roughness and show a rapid drop after a few cycles; ZrO₂ begins much rougher (~180–190 pm) and smooths more dramatically than TiO₂. Effective chemistries (WF₆/BCl₃ and WF₆/TiCl₄ for ZrO₂; WF₆/SOCl₂ and WF₆/TiCl₄ for TiO₂) produce greater smoothing, while SOCl₂ is least effective at smoothing ZrO₂ — matching its poor etch performance. Overall, ALE leads to net surface smoothing, and the degree of smoothing correlates with the chemistry’s etch effectiveness.

| Material|Initial Roughness (0 cycles)|Roughness after 5 cycles|Roughness after 25 cycles|Trend Summary|
|---------|----------------------------|------------------------|-------------------------|-------------|
|TiO₂|~90–100 pm|Decreases for all chemistries|Further decreases; becomes smoother overall|ALE smooths TiO₂ surfaces|
|ZrO₂|~180–190 pm|Sharp drop for all chemistries|Chemistry-dependent smoothing; SOCl₂ least effective|ZrO₂ starts rougher but smooths strongly with effective chemistries|

Answer: Roughness evolution provides insight into how uniformly each chemistry removes material. Effective chemistries produce greater smoothing due to consistent layer removal. For TiO₂, SOCl₂ and TiCl₄ lead to smoother surfaces, while for ZrO₂, BCl₃ and TiCl₄ yield the strongest smoothing effects. In contrast, SOCl₂ produces limited smoothing on ZrO₂, reflecting its poor etch performance. Thus, AFM roughness trends help confirm which co-reactant chemistries produce uniform, high-quality ALE.

Answer: Yes. Both materials exhibit noticeable smoothing after ALE cycles, although the degree of smoothing depends on the co-reactant chemistry.

Answer: Initial surface morphology (TiO₂ smoother; ZrO₂ rougher), Reaction efficiency of each co-reactant, Volatility of reaction by-products, Uniformity of layer-by-layer removal

Answer: ZrO₂ shows the largest reduction in roughness, dropping from ~180–190 pm initially to much lower values after 25 cycles.


FIG. 2. In situ ellipsometry data collected during deposition and etching steps on the Si-OH surface. (a) and (b) show the raw delta  $(\Delta)$  and psi  $(\Psi^{\prime})$  parameters, respectively, which are fitted by a Cauchy model to (c) measure the  $\mathrm{TiO_2}$  layer thickness.

The line chart shows the trend of Δ values over cycles for four different wavelengths (465 nm, 525 nm, 580 nm, and 635 nm). The Δ values decrease with increasing cycles until around cycle 240, after which they start to increase again.

The line chart displays the constant values of Ψ for four different wavelengths (465 nm, 525 nm, 580 nm, and 635 nm) over cycles. The values remain stable throughout the cycles.

The line chart illustrates the thickness of a material over cycles. The thickness increases steadily until cycle 240, after which it decreases slightly.

| Cycles | 465 nm | 525 nm | 580 nm | 635 nm |
|---|---|---|---|---|
| 210 | 164 | 166 | 168 | 168 |
| 215 | 163 | 165 | 167 | 167 |
| 220 | 162 | 164 | 166 | 166 |
| 225 | 161 | 163 | 165 | 165 |
| 230 | 160 | 162 | 164 | 164 |
| 235 | 159 | 161 | 163 | 163 |
| 240 | 158 | 160 | 162 | 162 |
| 245 | 161 | 163 | 165 | 166 |

| Cycles | 465 nm | 525 nm | 580 nm | 635 nm |
|---|---|---|---|---|
| 210 | 21 | 19 | 17 | 17 |
| 215 | 21 | 19 | 17 | 17 |
| 220 | 21 | 19 | 17 | 17 |
| 225 | 21 | 19 | 17 | 17 |
| 230 | 21 | 19 | 17 | 17 |
| 235 | 21 | 19 | 17 | 17 |
| 240 | 21 | 19 | 17 | 17 |
| 245 | 21 | 19 | 17 | 17 |

| Cycles | Thickness (nm) |
|---|---|
| 210 | 4.8 |
| 215 | 5.0 |
| 220 | 5.2 |
| 225 | 5.4 |
| 230 | 5.6 |
| 235 | 5.8 |
| 240 | 6.0 |
| 245 | 5.8 |

Answer: Δ decreases linearly during deposition and increases linearly during etching.

Answer: At 170 °C.

Answer: In figure 2, the raw ellipsometry parameters Ψ and Δ, measured at four wavelengths, are shown alongside the thickness extracted using a temperature-dependent Cauchy model. While Ψ remains essentially constant over the small thickness range involved, Δ exhibits a clear correlation with the TiO₂ film thickness. This demonstrates that Δ is the primary ellipsometric parameter for detecting incremental growth and removal during ALD and ALE.

Answer: Ψ does not change significantly during both deposition and etching.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/experimental-usecase/37/Effect of reactant dosing on selectivity during area-selective.pdf


FIG. 8.  $\mathrm{TiO_2}$  film thickness on  $\mathrm{Si - H}$  and  $\mathrm{Si - OH}$  surfaces during ALE/ALE super-cycles with  $90~\mathrm{ms}$  dosing conditions for  $\mathrm{TiCl_4 / H_2O}$ . The measurement was done by in situ ellipsometry, with the data point taken after every five cycles for ALD and every cycle for ALE.

The line chart shows the thickness of Si-OH and Si-H as a function of super-cycles. Both thicknesses increase linearly with increasing super-cycles.

| Super-Cycles | Thickness (nm) Si-H | Thickness (nm) Si-OH |
|---|---|---|
| 0 | 0 | 0 |
| 5 | 0 | 4 |
| 10 | 0 | 8 |
| 15 | 0 | 13 |
| 20 | 0 | 17.5 |
| 25 | 0.5 | 22.5 |
| 30 | 0.5 | 25 |

Answer: Si-OH and Si-H.

Answer: 30.

Answer: 90 ms for both.

Answer: 170 °C.


FIG. 5. (Color online) Film thickness vs number of AlN ALE reaction cycles at  $275^{\circ}\mathrm{C}$  in pure AlN region of AlN film showing results for thermal AlN ALE and plasma-enhanced ALE. (a)  $\mathrm{H}_{2}$  plasma increases AlN etch rate from  $0.36$  to  $1.96\mathrm{\AA}$  /cycle. (b) Ar plasma increases AlN etch rate from  $0.36$  to  $0.66\mathrm{\AA}$  /cycle.

The line chart shows the thickness (Å) of AlN as a function of ALE reaction cycle number at 275 °C. Two ALE processes are compared: thermal ALE from 0 to 14 cycles and H₂ plasma-enhanced ALE from 15 to 26 cycles. The introduction of H₂ plasma increases the AlN etch rate from 0.36 to 1.96 Å/cycle.

The line chart shows the thickness (Å) of AlN as a function of ALE reaction cycle number at 275 °C. Two ALE processes are compared: thermal ALE from 0 to 14 cycles and Ar plasma-enhanced ALE from 15 to 26 cycles. The use of Ar plasma increases the AlN etch rate from 0.36 to 0.66 Å/cycle. This image clearly indicates that Ar Plasma enhnaced ALE shows a higher etch rate.

| Cycle Number | Thickness (Å) |
|---|---|
| 0 | 450 |
| 4 | 449 |
| 8 | 447 |
| 12 | 446 |
| 16 | 441 |
| 20 | 433 |
| 24 | 438 |
| 28 | 425 |

| Cycle Number | Thickness (Å) |
|---|---|
| 0 | 438 |
| 4 | 436 |
| 8 | 435 |
| 12 | 433 |
| 16 | 430 |
| 20 | 428 |

Answer:
HF Pulse & Purge.

, Sn(acac)₂ Pulse & Purge.

, H₂ Plasma Exposure (new step).

, Purge.

Answer: H₂ plasma provides a ~5x enhancement (chemical), while Ar plasma gives only a ~2x enhancement (physical). This reveals the trade-off: H₂ plasma offers higher efficiency via chemical radical reactions (removing blocking ligands), but may introduce more hydrogen incorporation. Ar plasma offers a cleaner, purely physical enhancement (ion/radiation) but with significantly lower etch rate gains, requiring a balance between speed and potential plasma-induced damage or impurity introduction.

Answer: Residual acac surface species (ligands) that block reactive sites.

Answer: Ar plasma may be better suited for high-aspect-ratio features because it avoids the radical depletion and non-uniformity issues that H₂ radicals can cause in deep trenches. While slower, its more isotropic ion-driven enhancement can improve etch conformity and reduce loading effects in complex geometries.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/experimental-usecase/44/Thermal atomic layer etching of crystalline aluminum nitride.pdf


FIG. 1. Values of Gibbs free energy change for oxidation reactions of molybdenum to  $\mathrm{MoO}_2$  and  $\mathrm{MoO}_3$  with  $\mathrm{H}_2\mathrm{O}$ ,  $\mathrm{N}_2\mathrm{O}$ ,  $\mathrm{O}_2$ , and  $\mathrm{O}_3$  at  $0 - 500^{\circ}\mathrm{C}$ .

The chart displays the Gibbs free energy change (ΔG) for various reactions of molybdenum (Mo) with different oxidants at different temperatures.

| Reaction                                      | ΔG Range (kJ/mol) | Trend with Temperature |
|----------------------------------------------|--------------------|-------------------------|
| Mo + 3 H₂O(g) → MoO₃ + 3 H₂(g)             | ~0 to +100        | Slightly increases     |
| Mo + H₂O(g) → MoO₂ + H₂(g)                 | ~-200 to -100     | Increases              |
| Mo + O₂(g) → MoO₂                           | ~-600 to -500     | Increases              |
| Mo + 1.5 O₂(g) → MoO₃                       | ~-600 to -500     | Increases              |
| Mo + 2 N₂O(g) → MoO₂ + 2 N₂(g)             | ~-800 to -700     | Increases              |
| Mo + 2 O₃(g) → MoO₂ + O₂(g)                | ~-900 to -800     | Increases              |
| Mo + 3 N₂O(g) → MoO₃ + 3 N₂(g)             | ~-1000 to -900    | Increases              |
| Mo + 3 O₃(g) → MoO₃ + O₂(g)                | ~-1100 to -1000   | Increases              |

Answer: Gibbs free energy changes of the oxidation reactions of molybdenum using H2O, N2O, O2, and O3 as oxidizing agents were calculated to understand the feasibility of ALE

Answer: MoO2 and MoO3 were considered, as they can form volatile chlorides and oxychlorides via deoxychlorination reactions with NbCl5. Oxides with lower oxidation states were also not available in the thermodynamic database.

Answer: No

Answer: The energy changes are negative over the whole temperature range, except for the reaction with H2O, which has a positive Gibbs free energy change in this temperature range.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/experimental-usecase/47/Atomic layer etching of molybdenum with O2 and NbCl5.pdf


FIG. 2. Values of Gibbs free energy changes of etching reactions of  $\mathrm{MoO}_2$  and  $\mathrm{MoO}_3$  with  $\mathrm{NbCl}_5$  at  $0 - 500^{\circ}\mathrm{C}$ .

The chart shows the gibbs free energy changes as a function of temperature for various chemical reactions.

| Reaction                                                       | ΔG Range (kJ/mol) | Trend with Temperature |
|--------------------------------------------------------------|--------------------|-------------------------|
| MoO₂ + NbCl₅(g) → MoOCl₂(g) + NbOCl₃(g)                    | ~150 to ~50       | Decreases              |
| MoO₃ + 3 NbCl₅(g) → MoCl₆(g) + 3 NbOCl₃(g)                 | ~120 to ~20       | Decreases              |
| MoO₂ + 2 NbCl₅(g) → MoOCl₄(g) + 2 NbOCl₃(g)                | ~50 to ~-50       | Decreases              |
| MoO₃ + 2 NbCl₅(g) → MoOCl₄(g) + 2 NbOCl₃(g)                | ~0 to ~-100       | Decreases              |
| MoO₃ + NbCl₅(g) → MoO₂Cl₂(g) + NbOCl₃(g)                   | ~-50 to ~-150     | Decreases              |

Answer: Yes

Answer: The etching of oxides occurs by deoxychlorination, producing NbOCl3 and molybdenum chlorides or oxychlorides as reaction products. MoCl4 is the only thermodynamically favorable etch product for MoO2 and is able to form above 200 °C. Conversion of MoO2 to a solid MoOCl2 is also favorable, but etching via this reaction pathway is prevented by the low volatility of MoOCl2

Answer: For MoO3, full chlorination is not thermodynamically favorable, but both MoO2Cl2 and MoOCl4 are possible etch products above about 20 °C.

Answer: The etching of metallic molybdenum by NbCl5 alone was also considered. Possible reactions leading to continuous etching would be oxidation of the metallic Mo to either MoCl4 or MoCl6 by NbCl5, which itself would be reduced to NbCl4. Neither reaction is thermodynamically favorable as both have highly positive Gibbs free energy changes at 0–500 °C. This indicates that continuous etching of Mo by NbCl5 is not an issue for this process, but does not mean that NbCl5 is completely inert toward Mo


FIG. 3. Equilibrium composition for an input of  $0.1\mathrm{kmol}$ $\mathrm{NbCl}_5$  and  $0.02\mathrm{kmol}$  Mo at 10 mbar pressure.  $5\mathrm{kmol}$  of  $\mathbb{N}_2$  was used as background gas to approximate the partial pressure of  $\mathrm{NbCl}_5$  in the reactor setup used in this paper.

The chart shows the amount of various chlorides (NbCl₄(s), NbCl₅(s), MoCl₃(s), NbCl₃(s), NbCl₂.67(s), NbCl₄(g), MoCl₂(s), MoCl₄(g)) in kmol as a function of temperature in °C.

| Temperature (°C) | NbCl₅(g) | NbCl₅(s) | NbCl₄(s) | NbCl₄(g) | NbCl₃(s) | NbCl₂.₆₇(s) | MoCl₃(s) | MoCl₂(s) | MoCl₄(g) |
|-------------------|----------|----------|----------|----------|----------|-------------|----------|----------|----------|
| 0                | 0        | 0.04     | 0.06     | 0        | 0        | 0           | 0.02     | 0        | 0        |
| 50               | 0.01     | 0.04     | 0.05     | 0        | 0        | 0           | 0.02     | 0        | 0        |
| 100              | 0.05     | 0.03     | 0.02     | 0.005    | 0        | 0           | 0.02     | 0        | 0        |
| 150              | 0.07     | 0.01     | 0.005    | 0.01     | 0.015    | 0.005       | 0.02     | 0        | 0        |
| 200              | 0.07     | 0        | 0        | 0.015    | 0.02     | 0.01        | 0.02     | 0        | 0        |
| 250              | 0.07     | 0        | 0        | 0.02     | 0.015    | 0.015       | 0.02     | 0.005    | 0.005    |
| 300              | 0.07     | 0        | 0        | 0.025    | 0.01     | 0.015       | 0.02     | 0.01     | 0.01     |
| 350              | 0.07     | 0        | 0        | 0.03     | 0.005    | 0.015       | 0.02     | 0.015    | 0.015    |
| 400              | 0.07     | 0        | 0        | 0.035    | 0        | 0.015       | 0.02     | 0.02     | 0.02     |

Answer:
Equilibrium composition calculated by minimizing the Gibbs
free energy of the system when Mo and NbCl5(g) are given as the
starting materials indicates that they can react to form nonvolatile
MoCl3 and various lower niobium chlorides (Fig. 3). Below 150 °C,
the dominant Nb-containing species is solid NbCl4, and above this
temperature up to 400 °C, the reacted NbCl5 is mostly expected to
form NbCl3 and Nb3Cl8. Once the oxidized surface layer has been
etched, these lower chlorides could form a layer that prevents
further reactions.

Answer: Equilibrium composition calculated by minimizing the Gibbs free energy of the system when Mo and NbCl5(g) are given as the starting materials indicates that they can react to form nonvolatile MoCl3 and various lower niobium chlorides.

Answer:
Below 150 °C, the dominant Nb-containing species is solid NbCl4, and above this temperature up to 400 °C, the reacted NbCl5 is mostly expected to
form NbCl3 and Nb3Cl8. Once the oxidized surface layer has been etched, these lower chlorides could form a layer that prevents further reactions.

Answer:
Equilibrium compositions of both NbCl3 and MoCl3 were calculated in the presence of excess O2 to evaluate their effect on the etching process. It was
found that for NbCl3 the most thermodynamically favorable product is NbO2Cl below about 240 °C and Nb2O5 above it. For MoCl3, the product is MoO3 below 350 °C and gaseous MoO2Cl2 above 350 °C. This indicates that if the lower chlorides are formed, they are readily oxidized and then etched in the subsequent ALE cycle, as NbCl5 has been shown to also etch Nb2O5


Fig. 4 - Reaction progression of half-cycles for both steps over time with an operating temperature of 573 K. The full progression is achieved at 1.38 s for Step A and 2.38 s for Step B, respectively.

Kinetic Monte Carlo simulation results showing the progression of half-cycle completion (%) versus time for both ALE steps at 573 K. Step A (HF fluorination, blue) reaches 100% surface coverage at 1.38 s, while Step B (TMA etching, orange) completes at 2.38 s. Both curves show rapid initial progress followed by a gradual approach to saturation, characteristic of self-limiting ALE surface reactions.

| Time (s) | Step A (%) | Step B (%) |
|---|---|---|
| 0.00 | 0 | 0 |
| 0.05 | 16 | 0 |
| 0.10 | 41 | 10 |
| 0.15 | 50 | 25 |
| 0.20 | 64 | 38 |
| 0.25 | 72 | 48 |
| 0.30 | 77 | 56 |
| 0.40 | 84 | 68 |
| 0.50 | 91 | 78 |
| 0.60 | 94 | 82 |
| 0.80 | 98 | 91 |
| 1.00 | 99 | 95 |
| 1.25 | 99.5 | 96 |
| 1.50 | 100 | 98 |
| 2.00 | 100 | 99.5 |
| 2.50 | 100 | 100 |

Answer: Step B (TMA etching) involves a more complex reaction mechanism with multiple sequential steps including TMA adsorption, ligand exchange, and DMAF desorption at two different reaction sites (l-AlF2 and r-AlF3). Additionally, TMA has a lower sticking coefficient (0.02) compared to HF (0.15), which slows the adsorption kinetics. The requirement for multiple TMA molecules to complete the etching at each unit cell further extends the process time.

Answer: The stepwise jumps reflect the discrete nature of the kMC simulation, where individual reaction events occur stochastically at specific time intervals rather than continuously.

Answer: For Step A, 100% means complete fluorination of the Al2O3 surface as AlF3; for Step B, 100% means complete removal of the fluorinated layer through DMAF volatilization.

Answer: The simulated times agree well with experiments. For Step A, experiments showed self-limiting behavior after 1.0 s of HF exposure with no significant change after 1.5 s, consistent with the simulated 1.38 s. For Step B, experiments indicated completion after approximately 2.25 s of TMA exposure, closely matching the simulated 2.38 s. This agreement validates the kMC model.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/11/Microscopic and data-driven modeling andoperation.pdf


Fig. 1. Changes in the heights of the material surfaces during  $300\mathrm{eV}$ $\mathrm{Ar^{+}}$  ion irradiation, obtained from MD simulations. With HFC, an about  $2\mathrm{nm}$  thick HFC layer was deposited on the flat model SiN surface. Without HFC, the flat model SiN surface was etched without HFC deposition. The horizontal axis represents the ion dose. Two vertical broken lines delineate different desorption regimes I, II, and, III, discussed in the main text. For the atomic representations of the surfaces, the reader is referred to section II of the Supplementary Material.

The line chart presents depth (in nm) versus ion dose (in ×10¹⁶ ions/cm²) for Ar⁺ bombardment under two experimental conditions: with and without hydrofluorocarbon (HFC). The sample treated with HFC initially shows greater surface material removal (positive depth), followed by gradual etching until reaching a net depth loss similar to the untreated case. Three regimes (I–III) are marked with dashed lines, indicating transitions in material removal behavior. The untreated sample displays relatively consistent shallow etching across the dose range.

| Ion Dose (×10¹⁶ ions cm⁻²) | Depth [nm] with HFC | Depth [nm] without HFC |
|----------------------------|---------------------|-------------------------|
| 0.0                        | 2.0                 | 0.1                     |
| 0.2                        | 1.5                 | 0.0                     |
| 0.5                        | 1.0                 | -0.1                    |
| 0.8                        | 0.4                 | -0.2                    |
| 1.0                        | 0.0                 | -0.3                    |
| 1.2                        | -0.2                | -0.4                    |
| 1.5                        | -0.4                | -0.5                    |
| 2.0                        | -0.6                | -0.6                    |

Answer: Depth (nm) change of the sample surface.

Answer: Yes

Answer: The segmentation into regions I, II, and III indicates distinct phases of the etching process. In Region I, there is rapid removal of material in the HFC-treated sample, likely due to a reactive surface layer. Region II shows a slower reduction, suggesting the surface becomes more resistant to ion bombardment. Region III stabilises, implying that a steady-state etch rate is reached. This behavior contrasts with the untreated sample, which exhibits a relatively linear and shallow etch throughout.

Answer: Catalytic effect of HFC, Surface conditioning with Ar⁺, Ion dose optimization, Reaction regime identification

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/14/Molecular dynamics simulations of silicon nitride.pdf


Fig. 2. Changes in the heights of the material surface during three-step SiN PE-ALE with (a)  $\mathrm{Ar^{+}}$  b  $\mathrm{Kr^{+}}$  and (c)  $\mathrm{Xe^{+}}$  ion irradiations over the first five cycles, obtained from MD simulations. Each FE-ALE cycle consists of the adsorption step (denoted by  $①$  , desorption step  $(2)$  , and oxidation step  $(3)$  . The lower curves denoted as physical suttering indicate the changes in the SIN material surface positions by physical suttering with the corresponding ions as functions of the ion dose. For the curves representing the PE-ALE processes, the height changes are also represented as functions of the ion dose during the desorption step and a unit length of the horizontal axis represents the same ion dose for both PE-ALE and physical sputtering curves. The PE-ALE simulation conditions are summarized in Table I.

The figure compares atomic layer etching (ALE) and physical sputtering depths over five cycles for three different noble gas ions: Ar⁺, Kr⁺, and Xe⁺. In each subplot, the ALE condition (black line) shows periodic, steep decreases in surface depth, indicating controlled etching per cycle. In contrast, the red traces for physical sputtering display minimal and more linear depth reduction, suggesting that physical sputtering alone removes significantly less material per cycle. The graphs are labeled with Roman numerals (I–III) that denote distinct etch regions, possibly representing phases of material response or tool behavior during processing.

| Cycle | ALE Depth [nm] | Sputtering Depth [nm] |
|-------|----------------|------------------------|
| 0     | 0              | 0                      |
| 1     | 1.9            | -0.2                   |
| 2     | 3.5            | -0.4                   |
| 3     | 5.2            | -0.6                   |
| 4     | 7.0            | -0.8                   |
| 5     | 8.5            | -1.0                   |

| Cycle | ALE Depth [nm] | Sputtering Depth [nm] |
|-------|----------------|------------------------|
| 0     | 0              | 0                      |
| 1     | 2.1            | -0.3                   |
| 2     | 4.3            | -0.6                   |
| 3     | 6.2            | -0.8                   |
| 4     | 8.1            | -1.0                   |
| 5     | 9.8            | -1.2                   |

| Cycle | ALE Depth [nm] | Sputtering Depth [nm] |
|-------|----------------|------------------------|
| 0     | 0              | 0                      |
| 1     | 2.3            | -0.4                   |
| 2     | 4.7            | -0.7                   |
| 3     | 7.0            | -1.0                   |
| 4     | 9.3            | -1.3                   |
| 5     | 11.5           | -1.5                   |

Answer: Yes

Answer: To evaluate the effectiveness and control of etching using noble gas ions (Ar⁺, Kr⁺, Xe⁺) under ALE and sputtering conditions

Answer: Xe⁺, Kr⁺, Ar⁺

Answer: The labeled regions likely denote distinct etching regimes: Region I shows the initial rapid etching response, possibly due to surface activation or reactive layer removal. Region II marks a more stable, consistent etch rate per cycle, typical of self-limiting ALE behavior. Region III may indicate a saturation or termination phase, where etch depth stabilises or material is fully removed.


Fig. 4. Depth profiles of atomic concentrations at the end of the oxidation step of the first SiN PE-ALE cycle with (a)  $\mathrm{Ar^{+}}$ , (b)  $\mathrm{Kr^{+}}$ , and (c)  $\mathrm{Xe^{+}}$  ion irradiations, obtained from MD simulations.

The figure compares atomic density profiles across depth for six or seven different elements under three experimental conditions: Ar (a), Kr (b), and Xe (c) ion exposure. In each case, the profiles illustrate how specific elements (e.g., H, O, C, Si, N) are distributed within and near the surface layers. The presence and penetration depth of each element vary depending on the ion species used, with notable differences in how deeply Ar, Kr, and Xe penetrate the material and affect the distribution of native and implanted species.

| Depth [nm] | Atomic density [x 1023/cm3] |
|---|---|
|-6 | 0 |
|-5 | 0 |
|-4 | 0 |
|-3 | 0 |
|-2 | 0 |
|-1 | 0 |
| 0 | 0 |
| 1 | 0 |
| 2 | 0 |
| 3 | 0 |
| 4 | 0 |
| 5 | 0 |
| 6 | 0 |

Answer: The ion species used for exposure: Ar in (a), Kr in (b), and Xe in (c).

Answer: Ar: shows deeper penetration, Kr: intermediate penetration , Xe: least penetration

Answer: No

Answer: The depth-dependent profiles indicate that heavier ions like Xe tend to stay near the surface, likely due to lower penetration power and stronger localised interaction, while lighter ions like Ar penetrate deeper into the material. This trend supports the hypothesis that ion mass influences the energy transfer efficiency and resulting implantation depth, which could be critical in tailoring surface modifications or etch profiles in atomic-scale processing


FIG. 3. Free energy profile for the SE1 (blue) and SL1 (orange) reactions of  $\mathsf{aHfO_2}$  from 0 to  $1000\mathrm{K}$  at the pressures given in the text. T1 is where the SL and SE reactions cross over for the 80/16F model, and T2 is where spontaneous etching is preferred.

The chart shows the change in Gibbs free energy (ΔG) per HfO₂ unit as a function of temperature. "Preferred self-limiting", "Preferred etching" and "Purely etching" regions are highlighted as well as T1 and T2 temperatures.

| Temperature [K] | SE1 | SL1 |
| --- | --- | --- |
| 0 | -1.3 | -3.8 |
| 200 | -1.3 | -3.2 |
| 400 | -1.3 | -2.4 |
| 600 | -1.2 | -1.8 |
| 800 | -1.1 | -0.8 |
| 1000 | -1.0 | 0.0 |

Answer: T2 is the point at which spontaneous etching is favoured.

Answer: For the SL1 reaction (orange line), the change in the Gibbs free energy values increases from -3.8 eV/HfO2 to nearly 0, as the temperature rises from 0 K to 1000 K.

Answer: As can be seen in the figure, self-limiting behavior is preferred from 0 to 718 K.

Answer: The temperature at which different self-limited conversion or spontaneous etching of aHfO2 occur can be observed. Therefore, it is possible to control the regime by adjusting the operating temperature.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/18/Origin of enhanced thermal atomic layer etching of amorphous HfO2.pdf


FIG. 4. Free energy profiles of the spontaneous etching and self-limiting reactions for  $\mathrm{aHfO_2}$ . T1, T2, and T3 are the temperatures where the self-limiting and spontaneous etch reactions cross over for 80/16F, 100/20F, and 16O/32F models, respectively.

The chart shows the Gibbs free energy (ΔG) change per HfO₂ molecule as a function of temperature. Three lines represent different hydrogen fluoride (HF) concentrations (16 HF, 20 HF) and (32 HF). Three different temperatures are highlighted T1=718 K, T2=770 K and T3=1302 K.

| Temperature [K] | 16HF | 20HF | 32HF |
| --- | --- | --- | --- |
| 0 | -3.8 | -3.8 | -5.2 |
| 400 | -2.2 | -2.2 | -4.0 |
| 800 | -0.8 | -1.0 | -2.6 |
| 1200 | 1.2 | 0.6 | -1.2 |
| 1600 | 3.0 | 2.2 | 0.4 |
| 2000 | 4.4 | 3.2 | 1.6 |

Answer: Three different HF concentrations were studied: 16 HF, 20 HF and 32 HF.

Answer: The Gibbs free energy increases with the temperature for all of the concentrations. All of them show the same behavior with the temperature.

Answer: As can be seen in the figure, the concentration of 16 HF shows higher Gibbs free energu values as a function of the temperature.

Answer: T1, T2 and T3 represent the temperatures where the self-limiting and spontaneous etch reaction cross over for different models with different concentrations of O to F.


Figure 4. Contributions to the reaction FEP of the SE1 reaction of  $\mathrm{HfO}_2$  shown in Table 1.  $RT\ln (Q)$  in gold accounts for the partial pressures of the reactants and products, enthalpic contribution  $(\Delta W)$  is given in dark blue, entropy term  $(T\Delta S)$  in gray, reaction energy  $(\Delta E)$  in light blue, the sum of reaction energy and zero-point energy change  $(\Delta E + \Delta \mathrm{ZPE})$  in brown, and reaction free energy  $(\Delta G)$  in green.

Multiple-line chart showing the temperature dependence of individual contributions to the reaction free energy for the SE1 etching reaction of HfO₂ with HF. The plot separates constant energetic terms (ΔE, ΔE+ΔZPE) from temperature-dependent contributions (TΔS, ΔW, RT ln Q), illustrating how entropy and pressure effects progressively increase ΔG with temperature while the reaction remains exergonic across the range shown.

| Temperature [K] | ΔE [eV] | ΔE+ΔZPE [eV] | ΔG [eV] | TΔS [eV] | ΔW [eV] |
|---|---|---|---|---|---|
| 0 | ~ -0.9 | ~ -0.76 | ~ -0.76 | 0.0 | 0.0 |
| 200 | ~ -0.9 | ~ -0.76 | ~ -0.75 | ~ -0.05 | ~ -0.02 |
| 400 | ~ -0.9 | ~ -0.76 | ~ -0.68 | ~ -0.15 | ~ -0.06 |
| 600 | ~ -0.9 | ~ -0.76 | ~ -0.60 | ~ -0.25 | ~ -0.09 |
| 800 | ~ -0.9 | ~ -0.76 | ~ -0.52 | ~ -0.40 | ~ -0.11 |
| 1000 | ~ -0.9 | ~ -0.76 | ~ -0.44 | ~ -0.50 | ~ -0.13 |

Answer: The entropy term, TΔS.

Answer: No

Answer: ΔE remains constant across the entire temperature range, reflecting its purely electronic nature. In contrast, TΔS becomes increasingly negative with temperature, contributing significantly to the upward shift in ΔG. This contrast highlights why entropy dominates the temperature dependence of reaction free energy.

Answer: ΔG remains negative throughout the plotted temperature range, indicating that the SE1 reaction is thermodynamically favorable under the conditions considered. Although the driving force decreases with temperature, the reaction does not become endergonic. This supports the feasibility of spontaneous etching at elevated temperatures.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/25/Self-Limiting Temperature Window for Thermal Atomic Layer Etching.pdf


Figure 5. Free energy profiles for the SE1 (blue) and SL1 (orange) reactions of (a)  $\mathrm{HfO}_2$  and (b)  $\mathrm{ZrO}_2$  from 0 to  $1000\mathrm{K}$  at the pressures given in the text.  $T_{1}$  is where the self-limiting and spontaneous etch reactions cross over for the 8O/16F model, and  $T_{2}$  is where spontaneous etching is preferred.

Free-energy profiles for the SE1 (blue) and SL1 (orange) reactions of HfO₂ as functions of temperature. Below T₁ = 657 K, the self-limiting pathway is thermodynamically favored. Between T₁ and T₂ = 813 K, spontaneous etching becomes preferred. Above T₂, the self-limiting reaction is endergonic, and the system operates in a purely etching regime.

Free-energy profiles for the SE1 and SL1 reactions of ZrO₂ showing analogous temperature-dependent behavior, with transitions at lower temperatures (T₁ = 534 K and T₂ = 770 K). Compared to HfO₂, ZrO₂ enters the preferred and purely etching regimes at lower temperatures, indicating reduced thermal stability of the self-limiting state.

| Temperature [K] | ΔG (SE1 - Blue) [eV] | ΔG (SL1 - Orange) [eV] | Condition |
|---|---|---|---|
| 0 | ~ -0.75 | ~ -3.0 | Start |
| 657 | ~ -0.6 | ~ -0.6 | T1 (Crossover) |
| 813 | ~ -0.55 | 0.0 | T2 (Zero crossing) |
| 1000 | ~ -0.45 | ~ +0.7 | End |

| Temperature [K] | ΔG (SE1 - Blue) [eV] | ΔG (SL1 - Orange) [eV] | Condition |
|---|---|---|---|
| 0 | ~ -1.0 | ~ -2.8 | Start |
| 534 | ~ -0.9 | ~ -0.9 | T1 (Crossover) |
| 770 | ~ -0.8 | 0.0 | T2 (Zero crossing) |
| 1000 | ~ -0.7 | ~ +0.8 | End |

Answer: Above 813 K, the free energy change (ΔG) for the self-limiting reaction becomes positive. This means the reaction becomes endergonic and is no longer thermodynamically spontaneous, indicating that a stable self-limiting layer cannot form under these conditions.

Answer: The self-limiting reaction (SL1).

Answer: Temperatures below approximately 657 K are optimal, as the self-limiting reaction is thermodynamically favored while spontaneous etching is suppressed, allowing precise atomic layer removal.

Answer: Negative.


Figure 6. Free energy profiles of the continuous etching and self-limiting reactions for  $\mathrm{HfO}_2$ .  $T_{1}$ ,  $T_{2}$ , and  $T_{3}$  are where the self-limiting and spontaneous etch reactions cross over for 16O/32F, 12O/24F, and 8O/16F models, respectively.

Line chart showing free-energy Delta G profiles for continuous etching and self-limiting reactions of HfO2 under three HF surface coverages (16 HF, 24 HF, and 32 HF) as functions of temperature. The figure identifies three crossover temperatures T1 = 429 K (16O/32F), T2 = 618 K (12O/24F), and T3 = 657K (8O/16F)—at which the self-limiting and spontaneous etch pathways become thermodynamically equivalent.

| Temperature [K] | Ref (Blue) [eV] | 32 HF (Yellow) [eV] | 24 HF (Gray) [eV] | 16 HF (Orange) [eV] | Note |
|---|---|---|---|---|---|
| 0 | ~ -0.8 | ~ -2.2 | ~ -2.8 | ~ -3.0 | Start |
| 429 | ~ -0.7 | ~ -0.7 | ~ -1.3 | ~ -1.5 | T1 (Crossover) |
| 618 | ~ -0.65 | 0.0 | ~ -0.6 | ~ -0.8 | T2 (Yellow Zero) |
| 657 | ~ -0.6 | ~ +0.2 | 0.0 | 0.0 | T3 (Gray/Orange Zero) |
| 1000 | ~ -0.5 | ~ +1.5 | ~ +0.8 | ~ +0.7 | End |

Answer: The 32 HF surface model.

Answer: Increasing HF coverage raises the free energy of the self-limiting pathway, causing it to intersect the continuous etching pathway at lower temperatures. This indicates that densely fluorinated surfaces destabilize the self-limiting configuration, narrowing the temperature window where controlled ALE can occur.

Answer: The reference curve represents continuous etching, which is dominated by reaction energetics that vary weakly with surface coverage. In contrast, the self-limiting reactions depend strongly on surface fluorination, making their free energy more sensitive to temperature and coverage-dependent entropy contributions.

Answer: The 16 HF surface model is most suitable, as it maintains self-limiting behavior up to the highest temperature (T3 = 657K), offering a wider operational window before uncontrolled etching dominates.


Figure 7. Free energy profiles of the continuous etching and self-limiting reactions for  $\mathrm{ZrO}_2$ .  $T_{1}$ ,  $T_{2}$ , and  $T_{3}$  are where the self-limiting and spontaneous etch reactions cross over for 16O/32F, 12O/24F, and 8O/16F models, respectively.

Line chart showing free-energy (ΔG) profiles for continuous etching and self-limiting reactions of ZrO2 for three HF surface models (16 HF, 24 HF, and 32 HF) as functions of temperature. The figure marks three crossover temperatures—T1 = 273 K, T2 = 502 K, and T3 = 534 K—corresponding to the 16O/32F, 12O/24F, and 8O/16F models, respectively, where self-limiting and spontaneous etch pathways become thermodynamically equivalent.

| Temperature [K] | Ref (Blue) [eV] | 32 HF (Yellow) [eV] | 24 HF (Gray) [eV] | 16 HF (Orange) [eV] | Note |
|---|---|---|---|---|---|
| 0 | ~ -1.0 | ~ -1.9 | ~ -2.7 | ~ -2.8 | Start |
| 273 | ~ -0.95 | ~ -0.95 | ~ -1.8 | ~ -1.9 | T1 (Crossover) |
| 502 | ~ -0.9 | 0.0 | ~ -1.0 | ~ -1.1 | T2 (Yellow Zero) |
| 534 | ~ -0.9 | ~ +0.2 | 0.0 | 0.0 | T3 (Gray/Orange Zero) |
| 1000 | ~ -0.7 | ~ +1.8 | ~ +0.9 | ~ +0.8 | End |

Answer: The 32 HF surface model.

Answer: Higher HF surface coverage raises the free energy of the self-limiting pathway, causing it to intersect the continuous etching pathway at lower temperatures. This indicates that heavily fluorinated surfaces destabilize the self-limiting configuration more rapidly as temperature increases.

Answer:
1)  32 HF (smallest range)
2)  24 HF
3)  16 HF (largest range)

Answer: The 16 HF surface model is most suitable, as it maintains a negative ΔG for self-limiting reactions up to the highest temperature (T3 = 534 K), providing the widest operational window merging stability with temperature tolerance.


FIG.12. G free energy profiles of CVE1, CVE2, and SL reactions vs temperature at a constant HF reactant pressure of  $0.2$  Torr and a product pressure of  $0.01$  Torr. SL reaction becomes endergonic at  $110\mathrm{K}$ .

Thermodynamic profile comparing the Gibbs free energy (ΔG) of three etching mechanisms (CVE1, CVE2, SL) versus temperature. CVE1 and CVE2 remain exergonic (ΔG < 0) across the entire temperature range. The SL reaction transitions from exergonic to endergonic at 110 K, becoming thermodynamically unfavorable at higher temperatures.

| Temperature (K) | ΔG (eV) - SL(Green) | ΔG (eV) - CVE2 (Blue) | ΔG (eV)- CVE1 (Red) |
|-----------------|---------------------|------------------------|-------------------------|
| 0             | -0.5           | -1.0            | -1.3            |
| 110           | 0.0            | -1.1            | -1.5            |
| 200           | 0.5            | -1.1            | -1.6            |
| 400           | 1.8            | -1.1            | -1.7            |
| 600           | 3.0            | -1.1            | -1.8            |
| 800           | 4.2            | -1.2            | -1.9            |
| 1000          | 5.2            | -1.2            | -2.0            |

Answer: Above 110 K, the two mechanisms diverge significantly. The SL reaction becomes endergonic (ΔG > 0), meaning it is thermodynamically unfavorable and unlikely to proceed spontaneously. In contrast, the CVE1 reaction remains strongly exergonic (ΔG becoming more negative), indicating it is the thermodynamically preferred and dominant etching pathway at higher temperatures.

Answer: 110 K

Answer: CVE1, CVE2, SL

Answer: No, it remains exergonic (ΔG < 0) throughout the entire range.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/28/Spontaneous etching of B2O3 by HF gas studied using infrared spectroscopy.pdf


Fig. 12. Graphical illustrations depicting the influence of various R2R controller algorithms on an environment that is introduced to a mild kinetic shift disturbance of 0.8 on the input parameters including the (a) HF flow rate, (b) TMA flow rate, (c) substrate velocity, which are computed from the output variable, (d) etching per cycle (EPC).

The multiple line chart shows HF flow rate control over batch number. The EWMA and ANN predictions initially deviate slightly from the target but converge toward it as batches progress.

The multiple line chart shows TMA flow rate adjustment across batches. Early deviations are reduced over time, with ANN tracking the target more closely than the EWMA curves.

The multiple line chart shows substrate velocity over batch number. Initial oscillations decrease with batch number, and all methods converge toward the target velocity.

The multiple line chart shows EPC over batch number. Both EWMA and ANN predictions converge toward the target EPC, with ANN exhibiting faster stabilization.

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~20    | ~20.2        | ~19.8        | ~20.1 |
| 10           | ~20    | ~20.1        | ~19.9        | ~20.0 |
| 20           | ~20    | ~20.0        | ~20.0        | ~20.0 |

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~45    | ~47          | ~43          | ~45   |
| 10           | ~45    | ~46          | ~44          | ~45   |
| 20           | ~45    | ~45          | ~45          | ~45   |

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~70    | ~75          | ~65          | ~70   |
| 10           | ~70    | ~72          | ~68          | ~70   |
| 20           | ~70    | ~70          | ~70          | ~70   |

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~0.04  | ~0.06        | ~0.03        | ~0.04 |
| 10           | ~0.04  | ~0.05        | ~0.04        | ~0.04 |
| 20           | ~0.04  | ~0.04        | ~0.04        | ~0.04 |

Answer: Both methods show larger deviations from the target. At early batches methods progressively converge as batch number increases. The ANN curves generally stabilize faster and exhibit smaller oscillations compared to the EWMA curves.

Answer: HF flow rate, TMA flow rate, Substrate velocity, Etching per cycle (EPC

Answer: Yes

Answer: Batch number.

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/34/Machine learning-based run-to-run control of a spatial thermal.pdf


Fig. 13. Graphical illustrations depicting the influence of various R2R controller algorithms on an environment that is introduced to a severe kinetic shift disturbance of 0.6 on the input parameters including the (a) HF flow rate, (b) TMA flow rate, and (c) substrate velocity, which are computed from the output variable (d) etching per cycle (EPC).

The multiple line chart shows HF flow rate control over batch number. EWMA initially deviates from the target, while ANN tracks the target more closely and stabilizes faster.

The multiple line chart shows TMA flow rate over batch number. Early fluctuations decrease with batch number, and the ANN method maintains values closest to the target.

The multiple line chart shows substrate velocity over batch number. Initial oscillations are damped over time, with ANN converging to the target more quickly than EWMA.

The multiple line chart shows EPC over batch number. All methods converge toward the target EPC, with ANN exhibiting the smallest deviation during stabilization.

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~20    | ~21.0        | ~20.5        | ~20.0 |
| 10           | ~20    | ~20.3        | ~20.1        | ~20.0 |
| 20           | ~20    | ~20.0        | ~20.0        | ~20.0 |

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~45    | ~47          | ~44          | ~45   |
| 10           | ~45    | ~46          | ~44.5        | ~45   |
| 20           | ~45    | ~45          | ~45          | ~45   |

| Batch number | Target | EWMA (λ=0.7) | EWMA (λ=0.3) | ANN   |
|--------------|--------|--------------|--------------|-------|
| 1            | ~0.35  | ~0.38        | ~0.33        | ~0.35 |
| 10           | ~0.35  | ~0.36        | ~0.34        | ~0.35 |
| 20           | ~0.35  | ~0.35        | ~0.35        | ~0.35 |

Answer: Both methods reduce deviations over batch number, but ANN consistently tracks the target more closely and stabilizes faster than EWMA, which shows larger initial oscillations.

Answer: Yes

Answer: Batch Number.

Answer: HF flow rate, TMA flow rate, Substrate velocity, Etching per cycle


Fig. 15. Graphical illustrations depicting the influence of various R2R controller algorithms on an environment that is introduced to a kinetic drift disturbance on the input parameters including the (a) HF flow rate, (b) TMA flow rate, and (c) substrate velocity, which are computed from the output variable (d) etching per cycle (EPC).

The multiple line chart shows HF flow rate control over batch number. Without control, the flow rate drifts upward, while EWMA partially corrects the drift and ANN maintains the flow rate close to the target.

The multiple line chart shows TMA flow rate over batch number. The no-control case increases steadily, whereas the ANN tracks the target closely and EWMA reduces but does not eliminate the drift.

The multiple line chart shows substrate velocity over batch number. Velocity decreases significantly without control, while EWMA mitigates the drop and ANN maintains values near the target.

The multiple line chart shows EPC over batch number. EPC declines strongly in the no-control case, while both EWMA and ANN stabilize EPC near the target, with ANN showing the smallest deviation.

| Batch number | Target | EWMA | ANN  | No control |
|--------------|--------|------|------|------------|
| 1            | ~20    | ~21  | ~20  | ~22        |
| 10           | ~20    | ~22  | ~20  | ~24        |
| 20           | ~20    | ~23  | ~20  | ~25        |

| Batch number | Target | EWMA | ANN  | No control |
|--------------|--------|------|------|------------|
| 1            | ~45    | ~46  | ~45  | ~48        |
| 10           | ~45    | ~47  | ~45  | ~50        |
| 20           | ~45    | ~48  | ~45  | ~52        |

| Batch number | Target | EWMA | ANN  | No control |
|--------------|--------|------|------|------------|
| 1            | ~70    | ~72  | ~70  | ~75        |
| 10           | ~70    | ~68  | ~70  | ~65        |
| 20           | ~70    | ~65  | ~70  | ~55        |

| Batch number | Target | EWMA | ANN  | No control |
|--------------|--------|------|------|------------|
| 1            | ~0.35  | ~0.36| ~0.35| ~0.34      |
| 10           | ~0.35  | ~0.33| ~0.35| ~0.28      |
| 20           | ~0.35  | ~0.32| ~0.35| ~0.20      |

Answer: In all panels, the no-control case shows significant drift away from the target over batch number. EWMA reduces the drift but still deviates over time. The ANN consistently maintains the variables closest to their target values.

Answer: Batch number.

Answer: HF flow rate, TMA flow rate, Substrate velocity, Etching per cycle (EPC)

Answer: Yes


FIG. 4. Free energy profiles of the overall etch reactions given in Table I. Solid lines correspond to the etch of an adatom and dotted lines correspond to the etch of a surface atom.

The figure presents a line chart that plots the Gibbs free energy change (ΔG) per cobalt atom as a function of temperature (T) for eight surface reactions involving different precursors: propene, butyne, silane, and trimethylsilane (TMS). Each precursor is represented under two surface states, adsorbed (-a) and saturated (-s). The chart reveals that ΔG increases linearly with temperature for all cases, with the magnitude of change varying among the precursors. Propene and TMS show the most favorable ΔG values (more negative) across the full temperature range, while butyne shows the least favorable thermodynamics. The comparison between adsorbed and saturated cases demonstrates consistent trends across species.

| T [K] | Propene-a | Butyne-a | Silane-a | TMS-a | Propene-s | Butyne-s | Silane-s | TMS-s |
|---|---|---|---|---|---|---|---|---|
| 0 | -9.5 | -2.5 | -6.5 | -8.5 | -9.5 | -2.5 | -6.5 | -8.5 |
| 250 | -7.5 | -1.5 | -4.5 | -6.5 | -7.5 | -1.5 | -4.5 | -6.5 |
| 500 | -5.5 | -0.5 | -2.5 | -4.5 | -5.5 | -0.5 | -2.5 | -4.5 |
| 750 | -3.5 | 0.5 | -0.5 | -2.5 | -3.5 | 0.5 | -0.5 | -2.5 |
| 1000 | -1.5 | 1.5 | 1.5 | 0.5 | -1.5 | 1.5 | 1.5 | 0.5 |

Answer: The ΔG values for both propene and butyne increase with temperature, indicating that the thermodynamic favorability of surface binding or reaction decreases at higher temperatures. Propene shows significantly more negative ΔG values than butyne across the entire temperature range, suggesting it is more thermodynamically favorable for surface reactions. The difference between the adsorbed (a) and saturated (s) states for both molecules is minimal, implying that the surface termination state has a limited effect on the general thermodynamic trend. This suggests that propene may be a more suitable candidate for temperature-sensitive surface chemistry applications like selective etching or deposition.

Answer: Yes

Answer: a -2.5 eV/Co

Answer: Propene-a, Propene-s, TMS-a, TMS-s

icdar2026-competition-data/test/gold_standard_test_set/atomic-layer-etching/simulation-usecase/7/In silico design of a thermal atomic layer etch process of cobalt.pdf


FIG. 6. (a) Free energy profiles of the individual reaction steps for the ALE process with H desorption after propene adsorption (in dotted lines) or no desorption of H after propene adsorption (in solid lines) given in Fig. 5. (b) The pressure-temperature process window of the complete ALE cycle (H desorbed) computed by considering different  $\ln (Q)$  values for each temperature. The red line indicated the CO decomposition temperature on the Co surface. The region marked by the black rectangle gives the Co ALE process window when propene and CO are used as reactants.

Figure (a) presents a multi-line chart showing the Gibbs free energy (ΔG) as a function of temperature for different surface reaction steps involved in propene chemistry on cobalt. These steps include propene adsorption, its dissociation, and byproduct formation such as H₂ and CO₂. The slope and relative positioning of the lines indicate which reactions become more or less thermodynamically favorable with increasing temperature.

Figure (b) is a heatmap that maps the equilibrium constant (lnQ) over a temperature-pressure space. The diagram includes a shaded process window indicating practical temperature and pressure ranges where the targeted surface reactions may be viable, providing a framework for selecting operating conditions.

| Temperature [K] | ΔG [eV / Co] |
|---|---|
| 0 | -6 |
| 200 | -5 |
| 400 | -4 |
| 600 | -3 |
| 800 | -2 |
| 1000 | -1 |

| Temperature [K] | Equilibrium constant: lnQ |
|---|---|
| 0 | -75 |
| 200 | -50 |
| 400 | -25 |
| 600 | 0 |
| 800 | 25 |
| 1000 | 50 |

Answer: The ΔG trends in figure (a) show which reaction steps become more or less favorable as temperature increases. For instance, propene adsorption has a negative ΔG at low temperatures, indicating thermodynamic favourability, while certain desorption reactions (e.g., CO₂ release) become favorable only at higher temperatures. Figure (b) complements this by showing the process window where lnQ indicates strong driving forces for reactions (lnQ ≪ 0) or equilibrium conditions (lnQ ≈ 0). By aligning these trends, one can identify temperature-pressure zones where specific reaction pathways are both thermodynamically favorable and kinetically accessible. This approach enables the rational design of conditions that favor desired surface terminations or product release while suppressing unwanted side reactions

Answer: Yes

Answer: Around 750 K.

Answer: Propene adsorption, dissociative H₂ adsorption, CO₂ adsorption, surface reaction of volatiles.