Origin of Enhanced Thermal Atomic Layer Etching of Amorphous HfO2 Running title: Origin of Enhanced Thermal Atomic Layer Etching of Amorphous HfO2 Running Authors: Mullins et al

HfO2 is a high-k material that is used in semiconductor devices. Atomic-level control of material processing is required for the fabrication of thin films of high-k materials at nanoscale device sizes. Thermal atomic layer etching (ALE) of metal oxides, in which up to one monolayer of material can be removed, can be achieved by sequential self-limiting (SL) fluorination and ligand-exchange reactions at elevated temperatures. First-principles based atomic-level simulations using density functional theory (DFT) can give deep insights into the precursor chemistry and the reactions that drive the etch of metal oxides. A previous study examined the hydrogen fluoride (HF) pulse in the first step in the thermal ALE process of crystalline HfO2 and ZrO2. This study examines the HF pulse on amorphous HfO2 using first-principles simulations. The Natarajan-Elliott analysis, a thermodynamic methodology is used to compare reaction models representing the selflimiting and spontaneous etch processes taking place during an ALE pulse. For the HF pulse on amorphous HfO2, we found that thermodynamic barriers impeding spontaneous etching are present at ALE relevant temperatures. HF adsorption calculations on the amorphous oxide surface is studied to understand the mechanistic details of the HF pulse. A HF molecule adsorbs dissociatively by forming Hf-F and O-H bonds. HF coverages ranging from 1.1 ± 0.3 to 18.0 ± 0.3 HF/nm2 are investigated and a mixture of molecularly and dissociatively adsorbed HF molecules is present at higher coverages. A theoretical etch rate of -0.82 ± 0.02 Å/cycle for amorphous HfO2 was calculated using a maximum coverage

of 9.0 ± 0.3 Hf-F/nm 2 . This theoretical etch rate is greater than the theoretical etch rate for crystalline HfO2 that we previously calculated at -0.61 ± 0.02 Å/cycle. Undercoordinated atoms and void regions in amorphous HfO2 allows for more binding sites during fluorination whereas crystalline HfO2 has a limited number of adsorption sites.

I. INTRODUCTION
Atomic layer processing has become increasingly important due to the continued downscaling of semiconductor devices, which necessitates deposition of thinner materials films in complex structures. The control of film etch offered by thermal atomic layer etching (ALE) is necessary for state-of-the-art semiconductor devices. 1 Thermal ALE is a technique that removes thin layers of material using sequential, self-limiting surface reactions and can be viewed as the reverse of atomic layer deposition (ALD). 2 Thermal ALE is based on surface modification and volatilization reactions, where the modification step alters the surface layer into a non-volatile later followed by the release of volatile etch products from the surface layer in the second reaction. 2 For metal oxides, thermal ALE has been performed using fluorination and ligand exchange reactions as shown in Figure 1. 3 Fluorination converts the surface of the metal oxide to a surface fluoride layer and ligand exchange can volatilize the metal fluoride layer to produce stable etch products. Thermal ALE relies on temperature and thermochemically favourable reactions to remove surface species 4 and etches at the same rate in all directions. 5 Many technologically important metal oxides have been etched using thermal ALE including HfO2, [6][7][8][9] ZrO2, 6,9 SiO2,10 Al2O3, 9,[11][12][13][14][15][16][17] TiO2, 18 VO2, 19 WO3, 20 ZnO, 21 Ga2O3, 22 as well as metal nitrides such as Si3N4, 23 AlN, 24 TiN, 25,26 and GaN. 27,28 Thermal ALE of amorphous Al2O3 has also been reported using NbF5 to replace HF as the fluorination agent and CCl4 for the halideexchange reaction. 29 As well as fluorination and ligand-exchange, thermal ALE can also be performed by other processes such as conversion, 21 oxidation 25 oxidation/chlorination 30 and chlorine-fluorine ligand exchange. 31 Advantages of ALE include high uniformity, the ability to etch high-aspect-ratio features, selectivity, and smoothing. 32 Semiconductor devices have features at the nanometer scale due to Moore's Law scaling. SiO2 gate dielectrics are so thin that electron tunnelling through the dielectric layer, which leads to high leakage currents, is impossible to avoid. 33,34 HfO2 is a high-k material with a dielectric constant of 22; it allows a high drive current to be maintained, while minimized leakage current meaning that a low equivalent oxide thickness can be used. 35 HfO2 is thermodynamically stable when interfaced with silicon in semiconductor devices. 36,37 Amorphous HfO2 has a dielectric constant of ~ 16 to 19. 38 In terms of mechanisms, thermal ALE processes generally use HF for the fluorination step 25 for metal oxides as it is a useful nucleophilic fluorination reactant 19 in which the fluoride anion serves as the active reaction species. For the ligand-exchange step examples of metal precursors used are Sn(acac)2, 6 Al(CH3)3, 6,39 Al(CH3)2Cl, 6 SiCl4, 6 BCl3, 31 TiCl4 8 and WF6 40 . The surface fluorination step in thermal ALE using HF is the focus of our work and the focus of this paper.
Experimental studies have shown that crystalline films have lower etch rates than amorphous films for thermal ALE of metal oxides HfO2, ZrO2, HfZrO4 at 250 °C and Al2O3 at 300 °C. 41,42 Using HF as the fluorinating agent and TiCl4 as the ligand-exchange agent, the etch rate for amorphous HfO2 was 18 times higher than the etch rate for crystalline HfO2. 41 Using the same reagents, the etch rate for amorphous ZrO2 was 2.3 times higher than the etch rate for crystalline ZrO2. 41 Similarly using HF and dimethyl aluminium chloride (DMAC, Al(CH3)2Cl) the etch rate on amorphous HfO2 was 8.5 times higher than the etch rate on crystalline HfO2, whereas for ZrO2 the amorphous etch rate was 1.4 times higher than the crystalline etch rate. 41 This shows for HfO2 that the etch rates is strongly dependent on whether a crystalline or amorphous film is etched. 41 Amorphous materials have a lower density than their crystalline form, which may facilitate the fluorination that leads to an expansion of the metal oxide. 41 In wet HF etching, crystalline HfO2 is also etched more slowly than amorphous HfO2. 43 The differences in etch rates show potential for selective ALE where two different materials have different etch rates under the same conditions. 41 Given that it is difficult to investigate thermal ALE reactions directly using experimental techniques, first-principles based atomic-level simulations using density functional theory (DFT) can give deep insights into the precursor chemistry and the reactions that drive the etch of metal oxides. Our previous study examined the difference in thermal ALE for the fluorination step for crystalline HfO2 and ZrO2 using HF. 44 In the present paper, the HF pulse in the first step in thermal ALE of amorphous HfO2 is examined in detail with first-principles DFT calculations of the fluorination mechanism. HF molecules adsorb at the surfaces of metal oxides by forming metal-F bonds and they may remain intact or dissociate. 45 If HF dissociates it may form Hf-F and O-H bonds, and release water, similar to previous studies on etch modelling for crystalline HfO2, ZrO2 and Al2O3. 44,45 The amount etched (etch rate) is determined by how much of the oxide surface is fluorinated; a larger fluoride film thickness after fluorination can lead to more fluoride removed during the ligand-exchange step and high etch rates. 41 The Natarajan-Elliott analysis 44 (N-E) is used to predict the conditions at which a self-limiting (SL) or spontaneous etching (SE) reaction becomes thermodynamically favourable and can therefore be used to direct experimental studies of thermal ALE. Selflimiting reactions are a necessary part of thermal ALE and allow the degree of etching to be well controlled and defined. In this study, it is found that SL reactions are more favourable than the competing SE reaction for the HF pulse on amorphous HfO2 at 0 and 520 K; the latter corresponds to the temperature used in experimental studies of thermal ALE for HfO2 using HF as the fluorination agent 46 . The temperatures above which spontaneous etching is favoured range from 718 to 1302 K at typical thermal ALE reactant pressures, depending on the degree of fluorination; these are significantly higher than on crystalline HfO2. Introducing HF molecules to the amorphous HfO2 surface results in dissociative HF adsorption. The maximum coverage of Hf-F bonds on the surface is used to calculate a theoretical etch rate. The spontaneous formation of water and hydrogen peroxide is also discussed. Combining the thermodynamic and mechanistic investigation using first-principles simulation demonstrates the origin of the large difference in etch rates for crystalline and amorphous HfO2 allowing the design of novel ALE processes for other technologically relevant materials.

II. Computational Methods
All calculations reported in this paper were carried out using spin-polarized density functional theory implemented in VASP 47  The Gibbs free energy, ΔG, at a temperature, T, is computed as follows: The ΔH and ΔS terms in Eq. (1) are the changes in reaction enthalpy and reaction entropy respectively, with term RTln(Q) included since the partial pressures of the reactants and products are variable in the reaction chamber. In Eq. It is however, lower than the reactant pressure, so a value of 0.01 Torr for our calculations is consistent with this and previous work of DFT investigation in thermal etching of TiN. 50

A. Bulk and Slab Models
Bulk amorphous HfO2 (henceforth aHfO2) was prepared using classical molecular dynamics (MD) simulations with the LAMMPS package. 51 Atomic pair interactions were adopted from the Morse type potential developed by Broglia et al. 52 This potential is accurate for the simulation of glasses at high temperature and pressure and has been previously used for the study of aHfO2. 52 The Nosé-Hoover thermostat in its isothermalisobaric form (NPT) was used to set the constant pressure at 1 atm and the temperatures during the simulation. The integration time step was set to 0.1 fs. The amorphous structure was produced using the melt-quenching method. Initially, a total of 216 atoms with a stoichiometric HfO2 composition (72 Hf and 144 O atoms) are randomly placed in a periodic cubic box. After an initial equilibration, the system is warmed up to 4000 K at a rate of 10 K/ps. The temperature was set well above the experimental melting point and equilibrated for 2 ns to assure the initially random distribution of the atomic species in our model. The melted structure is then quenched to 300 K in consecutive steps of 10 K/ps (i.e. every 10 4 time-steps) and finally equilibrated for 1 ns at room conditions. The quenching rate was chosen to be quick enough to produce an amorphous structure at equilibrium; a pair distribution function is shown in Section 1 of the supplementary material. This procedure leads to an equilibrated cubic box with side dimensions of 13.72 Å. The density of the resulting simulation box is 9.62 g/cm 3 , which is in good agreement with other aHfO2 models generated by MD. [53][54][55] The surface model is cleaved from the bulk at a plane parallel to one of the box sides, where a large vacuum layer is introduced. To moderate the likely abundance of uncoordinated species at the surface formed from a random cleavage of the amorphous bulk, a rapid melt-quenching was run for the slab model keeping constant volume and temperature (NVT ensemble). The surface model was warmed to 4000 K at 20 K/ps rate, relaxed for 50 ps, quenched to 300 K at 10 K/ps rate, and finally equilibrated for 1 ns. The slab model is then relaxed using DFT. is smaller than the crystalline HfO2 (monoclinic, cHfO2) density from our previous study which was 10.01 g/cm 3 . 44 The surface slab of aHfO2 with 16 Å of vacuum separating the slabs is used for the surface models with a stoichiometry of Hf72O144 per supercell. A kpoint sampling mesh of (2 x 2 x 1) is used for geometry optimization. Experimental studies have shown that the chemical composition of aHfO2 is essentially stoichiometric. 61 Theoretical studies of aHfO2 reported that the coordination numbers for the Hf atoms were five, six, seven and eight with a preference for six and seven. For oxygen two, three and four coordination are found, with a preference for three and four coordination. 53 The distribution of the coordination numbers for the Hf and O atoms of the bulk aHfO2 model used in this study is shown in Figure 2.

A. Self-Limiting vs Spontaneous Etch
To predict if the HF pulse will promote spontaneous etch (SE) or a self-limiting (SL) reaction on aHfO2, the energetics and thermodynamics at given conditions are compared. Table I shows two possible SE and two possible SL reactions for the HF pulse on aHfO2 as well as the reaction (free) energies at 0 K and at a typical thermal ALE temperature of 520 K and the computed minimum barrier to spontaneous etching. A negative minimum barrier would indicate that spontaneous etching is thermodynamically favourable and is prevented only by potential kinetic barriers. The SE1 and SE2 reactions convert the bulk aHfO2 into a volatile metal fluoride or metal oxyfluoride, respectively, and water. In reaction SE1, four HF molecules are required to etch one unit of bulk HfO2 forming HfF4 and water. In reaction SE2, two HF molecules are needed to etch one unit of HfO2 to form HfOF2 and H2O. In both SE reactions, the surface of the material before and after each precursor pulse is identical and therefore their contributions are not required in these models.
The SL1 and SL2 reactions involve the conversion of the outermost surface layer of aHfO2 into the nonvolatile metal fluoride and nonvolatile metal oxyfluoride respectively with the release of water molecules. The SL product state of the surface is 8O/16F where eight oxygen were removed and replaced by sixteen fluorine. For both SL reactions, the surfaces are not identical before and after the pulse and their contributions have to be included. A negative free energy means that the corresponding reaction is exergonic (favourable), while a positive free energy means that the corresponding reaction is endergonic (unfavourable). At 0 and 520 K, the SE1 reaction is favourable whereas the SE2 reaction is unfavorable. Table I shows that the barrier to spontaneous etch is positive for all the SE and SL reactions at 0 K, indicating that the self-limiting reaction is most favourable energetically and at 520 K this barrier to spontaneous etching, although reduced, remains positive. Therefore, up to 520 K, the reactions with HF in the first step will be preferentially self-limiting on aHfO2, similar to crystalline HfO2.
Only the SE1 reaction is considered for further analysis, as the SE2 reaction is unfavorable at 0 and 520 K and the SL2 reaction is less favorable than the SL1 reaction at 0 and 520 K. In addition, the high barrier to etch for the SL2 and SE2 reactions suggests that spontaneous formation of the metal oxyfluoride is not likely at ALE-relevant temperatures around 520 K. The reaction free energy profiles (FEPs) of the SE1 and SL1 reactions are shown in Figure 3 and  In Figure 3 the self-limiting reaction is preferred up to 717 K, at 718 K the minimum barrier to etch is zero with SE1 and SL1 being isoenergetic and at temperatures higher than 718 K spontaneous etching becomes more favourable. At 973 K, the self-limiting reaction becomes unfavourable while spontaneous etching remains favourable. Surface hafnium atoms are easier to remove in the ligand-exchange step when more oxygen atoms are removed due to the reduced hafnium-oxygen bonds interaction. The surface of aHfO2 has 19 oxygen atoms in the supercell that could react with the HF molecules, therefore we study the FEPs for two other SL product models, 10O/20F (SL2) and 16O/32F (SL3) as shown in Table II  to replace them. All three SL product states are more favourable than the SE reaction at 0 and 520 K with positive minimum barriers as shown in Table II. Experimental work showed that the HF reaction is self-limiting on amorphous HfO2 at 250 °C (523 K). 41 Figure   4 shows that the self-limiting product state models are more favourable than the spontaneous etch reaction at 523 K with the 16O/32F (SL3) being favourable up to 1302 K.    Colour coding is the same as in Figure 5.
The binding energies per HF and per unit surface area of the material were computed as shown in Table III. As the number of Hf-F bonds increases on the bare aHfO2 surface with higher HF coverages, the binding energy per surface area becomes more favourable as shown in Table III    Hf-F coverage versus adsorbed HF coverage is shown in plot (a) in Figure 7 with the HF coverages that resulted in complete dissociation lying along the correlation line.
This corresponds to coverages of 1.1, 1.6, 2.1 and 2.7 HF/nm 2 . The remaining data points are HF coverages that correspond to geometries where partially dissociated HF and molecular adsorbed HF molecules are present and therefore lie below the correlation line.
The Hf-F coverage starts to plateau at higher HF coverages suggesting a maximum coverage of 9.0 ± 0.3 Hf-F/nm 2 . Also note that the number of Hf-F/nm 2 is the same for HF coverages 32 and 34 HF. It is also shown that a saturation in the binding energy is not reached at high HF coverages and Hf-F coverages respectively as shown in plots (b) and (c) in Figure 7. We use the highest adsorbed HF coverage of 34 HF with Hf-F coverage of 9.0 ± 0.3 Hf-F/nm 2 as the maximum coverage for the aHfO2 etch rate prediction.

D. Spontaneous Formation of H2O and H2O2
H2O spontaneously formed in some of the relaxed geometries such as 5HF C, 8HF C and 16 HF A as shown in Figure 8.  formed spontaneously. Colour coding is the same as in Figure 5.
The spontaneous formation of H2O2 was also observed at higher HF coverages such as 28HF as shown in Figure 9. Similar to H2O, the dissociation of at least two HF molecules provides the hydrogen atoms required to form H2O2 as a reaction product which removes oxygen from aHfO2. The H2O2 formed in Figure 9 had

E. Discussion
Comparing the spontaneous etch reaction to the self-limiting reaction for the 8O/16F SL product state model, at all temperatures less than 520 K using reactant and product pressures of 0.2 and 0.01 Torr respectively, the HF pulse on aHfO2 is self-limiting in nature as the reaction energies for the self-limiting reaction were more favourable than the spontaneous etch reaction. From this, it is suggested that the first precursor pulse using HF will produce a stable and non-volatile layer of metal fluorides and H2O or H2O2 as byproducts. The reaction energies for the SL product state models 8O/16F and 10O/20F were similar up to 400 K due to the small difference in the degree of fluorination between the models. The 16O/32F SL product state model reaction energies were more favourable than the 8O/16F and 10O/20F reactions up to 1302 K. Comparing to our previous study examining the fluorination step of crystalline HfO2, the reaction energies for the 16O/32F product state model were less favourable than the partially fluorinated SL product state models. 44 The greater the degree of fluorination on aHfO2, the more favourable the reaction energies are, showing aHfO2 favours higher fluorine content SL product states than less fluorinated SL product states, which will promote the self-limiting surface modification step. The replacement of oxygen with fluorine during fluorination may be easier due to the lower density of amorphous materials compared to crystalline materials. 41 HF coverages on aHfO2 ranging from 1.

IV. SUMMARY AND CONCLUSIONS
In this paper, we present DFT calculations to understand the nature of the HF pulse on amorphous HfO2 for thermal ALE. A thermodynamic analysis of the self-limiting and spontaneous etch reactions representing the fluorination on amorphous HfO2 allowed us to predict whether the SE or SL reaction is favourable at a given temperature and a given pressure. At temperatures less than 520 K, the HF reaction is found to be in the preferred self-limiting state. This is a relatively inexpensive way to screen the reactant molecules for ALE of any given substrate. The adsorption of HF molecules on amorphous HfO2 for HF coverages ranging from 1.1 ± 0.3 to 18.0 ± 0.3 HF/nm 2 along with analysis of H2O and H2O2 formation was studied. From this analysis, we predict a theoretical etch rate based on the maximum possible coverage of surface-bound HF for amorphous HfO2 which was calculated to be -0.82 ± 0.02 Å/cycle. This computed etch rate for amorphous HfO2 is greater than the etch rate computed for crystalline HfO2 from our previous study. We can use the presented methodology for the first pulse on crystalline and amorphous metal oxides to examine other reagents such as SF4 and XeF2 with a similar analysis.

SUPPLEMENTAL MATERIAL
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