A Reactive Force Field Based Molecular Dynamics ... - ACS Publications

Article Cite This: J. Phys. Chem. C 2019, 123, 16823−16835

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Formation of AlFx Gaseous Phases during High Temperature Etching: A Reactive Force Field Based Molecular Dynamics Study Yongli Liu,†,‡ Yang Qi,*,†,‡ Xianwei Hu,§ and Adri C. T. van Duin*,∥ †

Institute of Materials Physics and Chemistry, College of Material Science and Engineering, ‡Key Laboratory for Anisotropy and Texture of Materials, and §School of Metallurgy, Northeastern University, Shenyang 110819, China ∥ Department of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States

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S Supporting Information *

ABSTRACT: The progress of research focused upon the etching of metal films or substrates using fluorine gases has been restricted by limited information regarding etching reactants and byproducts. Indeed, aspects of the etching mechanism itself remain unclear. In this study, a new reactive force field (ReaxFF) for Al−F was developed to describe the interaction and reactions in Al−F materials. The ReaxFF accurately reproduces the quantum mechanics derived training set for structures and energies of gaseous AlFx molecules and Al−F crystals. Based on this Al−F ReaxFF, the effects of chemical source (F/Al = 1−6) and temperature (1000−1500 K) on the etching product and rate were studied. The formation of gaseous AlFx was revealed in five steps with the fluorine concentration being the prime factor affecting the etching products. Below the critical concentration ratio of F/Al = 3, where the chemical driving force is insufficient, only four of the five steps occur and a AlFx cluster is formed without significant gaseous species; above this critical concentration, a fifth step happens, and isolated AlFx gaseous phases with much more negative formation energies, such as AlF4, AlF5, and AlF6, can be formed. Besides this concentration ratio, external parameters such as elevated temperature or higher voltage dischage may be an important energetic factor affecting the product quantity. These results may provide insights into controlling the formation kinetics of specific AlFx compounds or gaseous phases for the preparative chemistry of Al−F porous catalyst, and the Al−F ReaxFF provides a useful tool for studying the interaction and reaction of Al−F materials at the atomic scale. semiconductor application,8−10 and catalytic area.11−15 Furthermore, AlF3 readily decomposes upon irradiation with lowenergy or midenergy electrons,16−18 releasing molecular fluorine and leaving a deposit of metallic Al on the substrate. This feature makes AlF3 an attractive inorganic resist for electron-beam nanopatterning techniques.19,20 In addition to this, fluorine-rich cleaning discharges can transform chamber interior/mask components made from aluminum into aluminum fluoride,21,22 and that enables application for fabrication of complementary metal oxide semiconductor devices. However, along with the significant study of the decomposition and formation of solid Al−F compounds,23−30 formation of Al−F complex molecules is another common phenomenon, and very little information on this topic is available now.31 Metal fluorides are traditionally prepared by fluorination or other chemical synthesis, such as the plasma chemistry of dry etching method, which involves much more complicated processes exceeding the way that isolated atom or

1. INTRODUCTION Aluminum is the most abundant metal in the earth’s crust (8.3% m/m) and a major component of many minerals. Of more than 60 metal ion species, Al3+ binds F− the most strongly, and its chemical binding in fluoride complexes, AlFx, is much stronger than those with other halides. Since the initial finding that adenylate cyclase is activated by fluorides with proteins,1 and further consideration of aluminum fluoride (AlF4−) as an active stimulatory agent rather than AlF3,2−4 the usefulness of aluminum fluoride is highlighted in more complex biological problems5,6 and therefore was regarded as the biological molecule of the year 1997.7 With the development of more advanced methods and wide applications, more AlFx in different states were observed and proposed either in experiment or in a theoretical way, and the corresponding formation, structures, and properties and the inherent transition mechanism are further becoming highly focused issues in materials study today. To date, AlF3 is one of the most widely used AlF x compounds, which is a good passivating agent with a wide band gap (10.8 eV) and good insulating characteristics. Solid AlF3 has been applied in the solar cell technology, 8 © 2019 American Chemical Society

Received: April 27, 2019 Revised: June 8, 2019 Published: June 11, 2019 16823

DOI: 10.1021/acs.jpcc.9b03957 J. Phys. Chem. C 2019, 123, 16823−16835

Article

The Journal of Physical Chemistry C

and further to provide a better understanding of the etching condition facilitating the formation of specific AlFx phase for the preparative chemistry of Al−F materials.

molecule diffuses over a metal surface. Even the behaviors of the isolated AlF3 molecules and bimolecule were found closely related to the large diffusion coefficient, sticking at both sides of steps, and island atomistic arrangement during the growth process of AlF3 film.10 To realize the above-mentioned applications of AlF3, an accurate control of the preparation conditions needs to be reached, and the existence of the Al−F complex molecules is a crucial point, either for the homogeneous and compact films with low porosity or for the AlF3 catalyst with high surface (HS) area. Further studies for the formation of Al−F complex molecules over different surfaces during the etching process are justified. The formation of five- and four-coordinated AlFx compounds or molecules at the AlF3 surface is confirmed in several studies of the reactivity of α-AlF3 nanoparticles,11 surface defects, fluorine mobility, and HF and HCl adsorption on βAlF3(100) surfaces.12−15 These undercoordinated Al ions can generate catalytic activity during the growth of AlF3 with high surface (HS) area. Therefore, a challenge for the preparative chemistry of HS-AlF3 is to explore the formation mechanism of undercoordinated AlFx compounds or molecules on the surface, and to create the right kind of undercoordinated sites. With the development of the experimental methods, more Al−F ions have been confirmed in water and soil, such as AlF2+, AlF2+, AlF30, and AlF4− (AlFx(3−x), x ≤ 4).32−35 Further, high temperature Raman and NMR36−39 spectra provide an alternative experimental window allowing insight into the evolution of [AlFx](3−x) groups with different compositions and temperatures of Na3[AlFx] molten salt because of its key roles in the electrodeposition of Al metal from alumina in the industrial Hall−Heroult process.36−43 The existence of tetrahedral [AlF4]− groups in NaAlF4 molten salt38 and the dominant roles of five-coordinated [AlF5]2− and six-coordinated [AlF6]3− groups in cryolite32,41,42 are proposed, and the latter study is consistent with the NMR data. The specification of above-mentioned versatile ionic AlFx species leads us to study the possible formation of similar AlFx gaseous phases over the metal surface. To date, only Acker et al. studied the impact of the chemical form of different fluorine sources on the formation of AlF, and found that the AlF molecules are formed by the reaction between the fluorine and aluminum atoms, which are transported into the flame presumably via oxidic and/or carbidic species.44 Due to significant cost in the development of processors and devices for the gas reaction condition, and great difficulty to identify the elementary processes and to measure the composition of plasma and reaction products, the study of the AlFx vapor phases in microscopic detail or at a molecular level is extremely limited. Major frontiers still exist in formation mechanisms of AlFx complexes over the metal surface during the metal and metal dioxide dry etching process12−15,45,46 and some other fields.47−49 Further theoretical studies are greatly demanded to explore the formation, stabilities, and structures of AlFx compounds or gas phases and the main factors influencing the etching process. In this paper, an Al−F reactive force field (ReaxFF) was initially developed and discussed. Subsequently, we studied the etching process of Al substrate with fluorine under different chemical and temperature conditions using the Al−F ReaxFF based molecular dynamics method. The average energy, radicals, and numbers of the etching product as a function of molar ratios of F/Al and plasma temperature were discussed to reveal the formation mechanism of AlFx clusters or molecules,

2. COMPUTATIONAL DETAILS 2.1. The ReaxFF Method. The ReaxFF method is able to simulate the breaking and re-forming phenomena of bonds during a dynamic evolution process. It can also reproduce the structures and mechanical properties of condensed phases.50−52 The total interaction energy expression of the ReaxFF is Esystem = E bond + Eover + Eunder + E lp + Eval + Epen + Etors + Econj + EvdW + ECoulomb

(1)

The terms included in eq 1 refer to the bond energy Ebond, undercoordination penalty energy Eunder, lone-pair energy Elp, overcoordination penalty energy Eover, valence angle energy Eval, penalty energy for handling atoms with two double bonds Epen, torsion angle energy Etors, conjugated bond energy Econj, and energy terms to handle nonbonded interactions, namely van der Waals interaction EvdW and Coulomb interaction ECoulomb, respectively. All terms except the last two are bondorder dependent; i.e. they will contribute more or less depending on the local environment of each atom. The Coulomb energy (ECoulomb) of the system is calculated using a geometry dependent charge distribution determined using the electronegativity equalization method (EEM).51 All other nonbonded interactions (short-range Pauli repulsion and long-range dispersion) are included in the van der Waals term (EvdW). The nonbonded terms (ECoulomb and EvdW) are screened by a seventh-order Taper function and shielded to avoid excessive repulsion at short distances and proper behavior at the nonbonded cutoff (10 Å). The forces are derived from above-mentioned general energy expression (1). For a more detailed description of the ReaxFF method, please see the recent review by Senftle and co-workers.53 2.2. Al−F Parameters. The force field parameters were optimized against quantum mechanics (QM) data present in the training set using a single parameter based parabolic extrapolation method54 based on the ReaxFF literature on Al metal.52 The optimized parameters are the bond parameters for Al−F and F−F and the valence angle parameters for Al− F−Al and F−Al−F. This development was performed against a substantial density functional theory (DFT) based training set, including bulk systems Al and AlF3, and molecular systems F2, AlF, AlF2+ cation, AlF2, AlF2+ cation, AlF3, Al2F6, AlF4−, AlF52−, and AlF63−. Most of the fluorine molecules are set based on the experimental detection of corresponding ions. 2.3. Al−F Model. 2.3.1. Al−F Crystal Structures. The R3̅cAlF3 crystal28 (Figure 1a) and fcc-Al crystal (Figure 1b) were adopted for the optimization of ReaxFF parameters. 2.3.2. Al−F Molecular Structures. Based on the consideration of possible Al−F bonding and angles of F−Al−F and Al−F−Al, all of the possible existing molecular structures of F2, AlF, AlF2+, AlF2, AlF2+, AlF3, Al2F6, AlF4−, AlF52−, and AlF63− are considered for further parameter optimization. In Figure 2, the neutral F2, AlF, AlF2, AlF3, and Al2F6 and ionic AlF4−, AlF52−, and AlF63− are shown, since these structures are considered as the stable configurations in both the present calculation and literature results. 16824


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The Journal of Physical Chemistry C E HF = E AlFx − (EAl + x /2E F2)

(2)

Here, EAlFx, EAl, and EF2 refer to the energies of AlFx, Al, and F2, respectively. Generally, negative heat formation energy implies the formation of new compounds involving a heat release process, while a positive value indicates the compound cannot exist stably at the equilibrium state because formation of the compounds needs more energy from surroundings. The structure in this work involves the crystal and gaseous phases, which was obtained respectively by the package CASTEP and Gaussian 09, leading to potential discrepancies. Therefore, the experimental results for F2, AlF (AlF2+ cation), AlF2 (AlF2+ cation), AlF3, Al2F6, AlF4− anion, and AlF63− anion were taken as the present training data. For AlF52− anion, no available information was found in the literature, and the evaluated value is proposed as follows. First, we obtained the energies of the AlFx and F2 molecules from Gaussian calculations and EHF from the experimental work; then the value of EAl was calculated according to eq 2, and the average EAl was also obtained (Table 1). Based on the value of EAl, the EHF of AlF52− was further calculated according to eq 2. Results of the detailed calculations of EAl and EHF for AlF52− are shown in Table 1. The optimizations for the molecular systems of F2, AlF, AlF2+ cation, AlF2, AlF2+ cation, AlF3, Al2F6, AlF4− anion, AlF52− anion, and AlF63− anion are shown in Table 2. It is found that, for the EHF values of F2, AlF3 crystal, and gaseous phase AlFx, the present calculations are in good accordance with those of the experimental work.62 For the AlF52− anion, no available experimental work is available. Both the experiment and present calculation show that AlF2+ and AlF2+ possess positive EHF values, and that may imply their preferential electroneutral existence in nature rather than the cation state. For the Al2F6 molecule, its EHf (−322.8274 kcal/ mol) is much more negative than that of the AlF3 molecule (−287.2642 kcal/mol), indicating that the bimolecule is energetically more stable than isolated AlF3 molecules, consistent with calculations documented in the literature.10 3.1.2. Structure of AlFx. Both bonding length and angle are important parameters describing the molecular structure. However, much less information is available because of the limit of the structure characterization technology. The present work took the structural information obtained from QM work as training data. The bond lengths, valence angles, and torsion angles for the present AlFx molecular structures (Figures 1 and 2) are presented in Tables 3 and 4 together with the data from

Figure 1. Al−F related crystal structures for the present reactive force field potential.

2.4. QM Calculation Setup. QM data for fcc-Al and R3̅cAlF3 crystals was obtained with the package CASTEP.55 The generalized gradient approximation (GGA) with the Perdew− Burke−Ernzerhof (PBE) exchange correlation potential was adopted.56 The Al 3s2 3p1 electrons and F 2s2 2p5 electrons were taken as valence electrons. The ultrasoft pseudopotentials (USPPs) were employed for all the ion−electron interactions.57 Energy cutoffs of 160 eV for Al and 370 eV for AlF3 eV and a 6 × 6 × 6 k-point mesh were chosen for use in this QM calculation. The ionic cores were represented by USPPs for Al and F atoms. During the geometry optimization process, the maximum force was set to 0.01 eV/Å, the maximum stress was set to 0.02 GPa, and the maximum displacement was set to 5.0 × 10−4 Å. QM data for AlFx molecules was obtained using the DFT/ B3LYP58,59 method and a split valence 6-311G basis set.60 Gaussian 09 was used for all the energy and geometry calculations.61

3. RESULTS AND DISCUSSION In this section, to show the validity of the present force field, we first compare the ReaxFF and experimental results for the heat of formation energies, the lattice parameters of the abovementioned Al−F crystal, and molecular structures with respect to bond length and valence angle. Equations of state (EOSs) for R3̅c-AlF3 crystal, AlF3 and Al2F6 molecules, and the reaction energies were optimized. Further, based on the present Al−F ReaxFF parameters, the effect of the molar ratio of F/Al and temperature on the formation of the different AlFx molecules was investigated through etching study to reveal the etching mechanism of Al metal substrate in fluorine gas. 3.1. Al−F Force Field Optimization. 3.1.1. Heat of Formation Energy. The heat of formation energy (EHF) of the compound inherently reflects the stability of the phase. For AlFx, the EHF was calculated as follows:

Figure 2. Molecular structures of AlFx. 16825


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Table 1. Present Calculation Results of EAl and EHF for AlF52− Based on EAlFx and EF2 from Gaussian Calculations and EHF from Experimental Work (kcal/mol) AlFx molecule

EAlFx(calc)

EHF(expt)

EF2

EAl

AlF AlF2 AlF3 AlF4− AlF63− AlF52−

−214 837.336 3 −277 302.388 7 −340 156.191 7 −403 033.804 0 −528 148.746 8 −465 647.112 2

−63 −166 −289.825 2 −476 −440.39 −541.326 77

−62 609.730 4 −62 609.730 3 −62 609.730 3 −62 609.730 3 −62 609.730 3 −62 609.730 3

−152 164.605 9 −151 916.928 0 −152 037.175 5 −152 118.882 6 −152 049.974 7 −152 057.513 3

with both the Al−F distance in gas62 and ionic states30,70 in experiment and the HF interaction with the Al surface or catalyst.67,68 For molecules of AlF, AlF2, AlF4−, AlF52−, and AlF63−, the corresponding bonding length from ReaxFF slowly increases with the addition of more F atoms, showing a similar trend with the data predicted from QM calculation. The F−Al−F and Al−F−Al related valence and torsion angle values of the AlFx molecules obtained from ReaxFF are in good accordance with those obtained from QM work (Table 4). For Al2F6, we found that there is a little discrepancy between the ReaxFF and QM calculations for the valence angles 3F−1Al−2F (∼ −1.6245°), 1Al−2F−5Al (∼1.7137°), 5Al−1Al−4F (∼1.1776°), 6F−5Al−1Al (∼1.7226°), and 7F− 1Al−5Al (∼2.1195°). This may imply that the structure predicted by ReaxFF is a little more stretched along the 1Al− 5Al axis than that predicted by Gaussian calculation. The structural parameters of Al2F6 are comparable with thos of Al2F6 absorbed on the Al2O3 surface,10 and the detailed information still needs to be verified in the future. 3.1.3. Equation of State (EOS) Curve. The EOS curve is extremely important in evaluating the state of matter under certain conditions. For the well-known Al−F structures such as R3̅c-AlF3 crystal, F2 gas, AlF3 and AlF3 bimolecule (Al2F6), the corresponding EOS curves were calculated and are presented in Figures 3−5. The equations of state of the R3̅c AlF3 crystal in Figure 3a show that ReaxFF predicts the same equilibrium volume as the DFT method does. However, as the cell deviates from the

Table 2. Present Calculated Heat of Formation Energies of Al−F Crystal and AlFx Molecules in Comparison with Experimental Work (kcal/mol) product

reactant

reactant

Reax (present work)

expta

F2 AlF3 (R3̅c) AlF AlF2+ AlF2 AlF2+ AlF3 Al2F6 AlF4− AlF52− AlF63−

F Al Al Al Al Al Al 2Al Al Al Al

F F2 0.5F2 0.5F2 1F2 1F2 1.5F2 3F2 2F2 2.5F2 3F2

−37.1643 −355.9135 −71.3029 563.6690 −177.7208 66.8548 −287.26422 −322.8274 −492.1661 −521.1428 −453.3141

−37.0000 −360.9856 −63.0000 165.4000 −166.0 22 −289.3000 −314.7000 −476.00 −541.3300 −440.39

a

Reference 62.

the present QM and other data in the literature for comparison. From Table 3, it can be found that the lattice parameters of fcc-Al and R3̅c-AlF3 obtained from ReaxFF are in good accordance with those data taken from other documented calculations (QM and molecular dynamics methods) and experimental work. For the AlF3 molecule, the bonding length 1Al−2F (1.7367 Å) is close to the data from other calculations10 and experimental results.71 For the Al−F bonding in gaseous phases, the present value is comparable

Table 3. Bonding Distance (BD) and Lattice Length (LL) for Al−F Crystal and Molecules in Figures 1 and 2 formula

parameters

Reax(present) (Å)

QM(present) (Å)

Al (fcc) AlF3 (R3̅c)

BD: Al−Al LL: a LL: c BD: 1Al−2F BD: 1Al−2F BD: 1Al−2F BD: 1Al−2F BD:1Al−2F BD:1Al−4F BD: 1Al−4F BD: 1Al−2F BD: 1Al−2F BD: 1Al−4F BD: 1Al−5F

2.8161 5.1233 12.6148 1.4923 1.7356 1.7367 1.8219 1.9524 1.9129 1.9877 1.7367 1.9747 1.7477 3.1647

2.8666 5.1233 12.6148 1.4689 1.7347 1.7318 1.7357 1.8400 1.8100 1.9042 1.6886 1.8574 1.8574 2.9210

F2 AlF AlF2 AlF4− AlF52− 3−

AlF6 AlF3 Al2F6

expt (Å)

other calculations (Å)

2.863a 4.9305c 12.4462c 1.45g 1.65l (gas)

2.863b 5.11,d 4.55,e 5.15,e 4.99f 12.504,d 6.97,e 6.3161,e 12.61f − 1.93h (H···F−Al)

1.793c (ionic)

1.79g,i (H···F−Al)

1.768−1.830k (ionic)

1.85j (ionic)

1.654l

1.642m 2.04m 3.16m

a

Reference 63. Experiment. bReference 64. Molecular dynamics (MD) method. cReference 30. At 300 K, determined by X-ray powder profile refinement. dReference 28. GRINSP, Geometrically Restrained IN organic Structure Prediction. eReference 43. MD simulations with the Buckingham potential model, dispersion-corrected DFT-D2 method provided by the program package CASTEP. fReference 65. First-principles method. gReference 66. Experiment. hReference 67. Semiempirical methods. iReference 68. Density functional theory. jReference 69. MD simulation. kReference 70. High-resolution synchrotron diffraction method (25−600 °C). lReference 71. Experiment. mReference 10. Metropolis Monte Carlo free energy minimization and density functional theory calculations. 16826


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DFT) are stable when the angle is around 120°, and ReaxFF fits well with DFT overall. Figure 5a presents the energy difference from the minimum with a bond distance of 1Al−4F between 1.111 and 2.488 Å for the Al2F6 molecules. The ReaxFF fits well with DFT overall. The minimum energy exists when the Al−F bond is 1.7477 Å, close to the minimum Al−F bond of the AlF3 molecule. Figure 5b presents the energy difference from the minimum with the valence angle of 2F−1Al−4F changing from 92.1330 to 131.6522°. As is indicated, the Al2F6 molecule possesses the same symmetry for both ReaxFF and QM calculations. However, the energy has a minimum at 111.7551° for DFT, while ReaxFF has a minimum at 112.9057°. To date, no comparative experimental or calculation data is available for Al2F6. As the valence angle deviates further from the lowest point, good agreement between ReaxFF and QM still exists. 3.1.4. Charge Distribution. For the radicals and the ionic molecules with negative heats of formation, the corresponding charge distributions are further evaluated by our present ReaxFF description and compared with Mulliken/QC results as shown in Table 5. It can be seen that the present ReaxFF predicts charge distribution quite well for most of the molecules; however, discrepancies are observed for some of the anionic species. 3.2. Effect of F/Al Molar Ratio on the Formation of AlFx Gaseous Phases. In section 3.1, we can see that the present Al−F ReaxFF is reliable in evaluating the formation and structure of AlFx molecules. Based on the present force field, the formation of AlFx gaseous phases with different F/Al molar ratios was further studied to investigate the effect of the origin chemical source on the etching product, reaction time, and energy, and to explore the etching mechanism. 3.2.1. Model and Calculation Setup. A slab model with the dimensions of 30 Å × 30 Å × 80 Å, a three-layered Al crystal plate with 288 atoms, and F2 molecules in the number of 1−3 times Al to ensure F/Al varying from 1 to 6, respectively, were used for the simulations. The NVT ensemble was used. The etching temperature was set as 1250 K according to the general etching condition (1000−3000 K) and the melting point of cryolite (1283 K). The total time duration was 250 ps, and the time step was 0.25 fs. Considering that our aim is to study the concentration and temperature effects on the formation of AlFx gaseous phases rather than the polarization effect, the anions of AlF4−, AlF52−, and AlF63− are shown as radical ones for simplification. 3.2.2. Formation of AlFx Gaseous Phases with Different F/ Al Molar Ratios. The etching of Al in different concentrations

Table 4. Calculated Valence Angle (VA) and Torsion Angle (TA) Values for Al−F Crystal and AlFx Molecules in Figure 2 formula

parameters

ReaxFF (°)

QM (°)

AlF2 R3̅c-AlF3

VA: 3F−1Al−2F VA: 3F−1Al−2F VA: 4F−1Al−3F TA: 4F−1Al−3F−2F VA: 3F−1Al−2F (4F ,5F) TA: 4F−1Al−3F−2F VA: 3F−1Al−2F VA: 4F−1Al−2F VA: 5F−1Al−4F TA: 5F−1Al−4F−2F TA: 6F−1Al−5F TA: 6F−1Al−5F−3F VA: 3F−1Al−2F VA:4F−1Al−2F VA: 6F−1Al−4F TA: 5F−1Al−2F−4F TA: 6F−1Al−5F−2F VA: 3F−1Al−2F VA: 4F−1Al−2F VA: 1Al−2F−5Al TA: 4F−1Al−2F−3F VA: 5Al−1Al−4F TA: 5Al−1Al−4F−3F VA: 6F−5Al−1Al TA: 6F−5Al−1Al−4F VA: 7F−1Al−5Al TA: 7F−1Al−5Al−6F

177.4379 119.6556 120.5254 178.8286 109.4969 −119.9656 179.7598 89.9307 120.0769 89.9165 119.9880 −90.0209 179.8469 90.1027 120.0868 −179.9992 −90.1435 73.4804 112.9057 106.5285 −107.8934 119.0314 40.3439 119.6404 0.5141 120.0592 −179.6525

177.4243 119.9771 120.0204 179.9863 109.4729 −120.0099 179.9016 89.9777 120.1348 89.9584 120.0000 −90.0379 179.9902 90.0112 120.1348 −179.9988 −90.0012 75.1049 111.7551 104.8148 −107.8404 117.8538 41.0042 117.9174 0.0438 117.9397 −179.9580

AlF4− AlF52−

AlF63−

Al2F6

equilibrium position much more, ReaxFF slows down the rate of energy increase. As for F2 gas, the present ReaxFF predicts a longer F−F bonding distance than the DFT data does, with a difference of about 0.0234 Å at the lowest energy position, and the ReaxFF value fits well with the QM calculation when the bonding distance diverts from the equilibrium state (Figure 3b). Figure 4a presents the energy difference from the minimum with bond distance of 1Al−2F between 1.1118 and 2.4800 Å for the AlF3 molecule. The minimum energy exists when the Al−F bond is 1.7366 Å, which is close to the experimental measurement (1.6540 Å)69 and the present calculation (1.6886 Å). Figure 4b presents the energy difference from the minimum with the valence angle of 2F−1Al−3F changing from 100.0 to 140.0°. As is indicated, both data (ReaxFF and

Figure 3. Energy difference from the minimum with respect to crystal volume of R3̅c AlF3 (a) and F−F bonding length of F2 (b). 16827


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Figure 4. Energy difference from the minimum with respect to 1Al−2F bonding distance (a) and 2F−1Al−3F valence angle of AlF3 molecule (b).

Figure 5. Energy difference from the minimum with respect to bonding length of 1Al−4F (a) and 2F−1Al−4F valence angle (b) of Al2F6 molecule.

Table 5. ReaxFF and QC/Mulliken Charges of Several Neutral and Anionic Al−F Molecules charge molecule AlF AlF2

AlF3

AlF4−

charge

atom

ReaxFF

QC

molecule

atom

ReaxFF

QC

1Al 2F 1Al 2F 3F 1Al 2F 3F 4F 1Al 2F 3F 4F 5F

0.6372 −0.6372 0.956 −0.4779 −0.478 1.0957 −0.3648 −0.3654 −0.3655 1.0915 −0.5227 −0.5231 −0.5229 −0.5228

0.59 −0.59 1.057 −0.529 −0.529 1.7130 −0.5710 −0.5710 −0.5710 1.616 −0.654 −0.654 −0.654 −0.654

AlF52−

1Al 2F 3F 4F 5F 6F 1Al 2F 3F 4F 5F 6F 7F

1.1403 −0.6218 −0.6216 −0.632 −0.6326 −0.6326 1.2305 −0.7061 −0.7041 −0.7046 −0.7055 −0.7051 −0.7052

1.538 −0.698 −0.698 −0.714 −0.714 −0.714 1.446 −0.741 −0.741 −0.741 −0.741 −0.741 −0.741

AlF63−

mol). The Al−F reactions result in rapid surface extension. The Al amorphous cluster loses coherence, which further promotes the penetration of the F or F2 into the Al cluster (Figure 6b,c). When the reaction continues, the F atom can fully diffuse and penetrate into the Al cluster, and break the Al−Al bonding, finally forming the Al288Fx cluster (Figure 6d,e). During the etching process, several isolated AlFx molecules can be temporarily observed to dissociate from the cluster. It seems that, even for the condition of F/Al at 3, although some isolated AlFx molecules are temporarily observed, the final etching product is an AlF3 cluster rather than a gaseous phase. Therefore, the etching is not completed for the present chemical and temperature condition, and a substantially excess number of fluorine atoms are required.

of F2 gas presents abundant information. It is found that the Al−F reactant is strongly related to the concentration, or molar ratio of F/Al. The instant snapshots during the etching process with the F/Al molar ratios at 3 and 5 are presented in Figures 6 and 7 to show the reaction details. When the molar ratio of F/Al is smaller than 3, the etching initially involves the adherence of F2 molecule to Al metal (Figure 6a), the quick transformation of initial ordered Al crystal to amorphous Al clusters due to the disorder induced by high temperature, the size effect, and the Al−F chemical potential (Figure 6a,b). With the adherence of F2 to Al cluster, Al and F bind quickly and the F2 molecules dissociate into F atoms because the former reaction possesses higher reaction energy (−71.3029 kcal/mol) than the latter (−37.1643 kcal/ 16828


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Figure 6. Etching process of Al in F2 at 1250 K when the F/Al molar ratio is 3. The big (small) pink (blue) balls represent the Al (F) atoms.

Figure 7. Etching process of Al in F2 at 1250 K when the molar ratio of F/Al is 5. The big (small) pink (blue) balls represent the Al (F) atoms.

dissociation of Al−F cluster into isolated AlFx molecules, accompanied by the dissociation and rebinding among the isolated AlF x molecules until the reaction meets the equilibrium state (Figure 7e). Our results agree with the etching processes described by Coburn and Winters;72,73 in particular, we observed the transformation of crystal to cluster. Comparison of the etching of F/Al = 3 and 5 shows that the increase of F2 can accelerate the dissociation of AlnFx cluster, and promote the production of more AlFx molecules, such as AlF3, AlF4, AlF5, and AlF6. If we fix the number of Al crystals, the etching product is strongly related to the F2 concentration. Besides the isolated molecules of AlF3, AlF4, AlF5, and AlF6, molecular clusters of AlnFx are also observed. We consider AlnFx as the simplified chemical formula nAlFx/n. If x/n equals an integer, then n is added to the number of isolated AlFx/n ones; if x/n is a fractional number, we counted them separately, exampled as AlF3−4, AlF4−5, and AlF5−6, which also refers to the full or partial bonding of AlF4, AlF5, and AlF6 respectively. The detailed result of reaction product changing with different F2 concentrations (F/Al = 3.5, 4, 4.5, 5, 5.5, 6) as a function of etching time is shown in Figure 8. It can be observed that, when the F/Al ratio ≤ 4, the gas phase is dominated by AlF4 (Figure 8a,b), followed by AlF3−4. Between 10 and 20 molecules of AlF5 are initially formed, but these are

The reaction time is considered from the beginning until only several F atoms were left (Table 6). It is clear that increase of F2 concentration can increase the reaction time. When the molar ratio of F/Al is 5, the adherence of F2 to the Al crystal and the transformation of Al crystal to cluster are similar to the condition in which the F2 is insufficient (Figure 7a,b). With the increase of adsorbed F2 molecules, some AlFx molecules desorb from the Al surface and become the isolated gas phase (Figure 7c,d), and then comes the complete Table 6. Reaction Product, Energy, and Time for the Chemical Source Condition of F/Al = 1−3 molar ratio of F/Al

reaction product

state

energy (kcal/atom)

1

F288Al288

cluster

−122.33938

1.5

F432Al288

cluster

−126.31648

2

F576Al288

cluster

−128.17957

2.5

F720Al288

cluster

−126.74036

3

F864Al288

cluster

−123.00075

reaction time (ps) 25.8 (5 atoms 38.875 (5 atoms 41.000 (5 atoms 52.750 (5 atoms 116.375 (5 atoms

left) left) left) left) left) 16829


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Figure 8. Number of AlFx as a function of time step with different F/Al molar ratios.

information in Table 6. When the molar ratio of F/Al > 3, the reaction potential energy increases obviously with the increase of the F2 concentration, while the reaction time decreases quickly. Coburn and Winters72,73 also state that, by increasing the F/C ratio within the plasma, the etch rate of the substrate is enhanced. Conversely, if the F/C ratio in the plasma is decreased, the etch rate of the substrate is reduced. 3.3. Etching of Al−F with Different Temperatures. Temperature is a critical parameter in determining the rate of the aluminum etching process and must be well-controlled. Based on consideration of the melting point of cryolite, the etching system of molar ratios F/Al = 3 and 5 at 1000, 1250, and 1500 K were further respectively studied to explore the corresponding temperature effect for the etching process and product as shown in Figure 10. For etching of F/Al = 3, when the temperature increases, more Al−F molecules temporarily occurred during the etching process, while no isolated AlFx molecules remained after the full reaction. For etching of F/Al = 5, the molecule numbers of AlF3, AlF4, AlF5, and AlF6 were taken into account as a function of temperature, and the results are presented in Figure 10. It can be seen that the number of AlF4 and of AlF5 is about 35 at 1000 K (Figure 10a), and both quickly increase to 55 at 1250 K (Figure 10b) and then increase to 75 and 65 respectively at 1500 K (Figure 10c). The numbers of AlF6 and AlF3 are weakly affected by the temperature. This result can be reasonably correlated with the involved energy variation. With the unvaried F/Al molar ratio, the kinetic energy of each atom is greatly increased with the increasing temperature, and the dissociation and bonding probability of Al−F is enhanced. Therefore, with the increase of the temperature, more and more Al−F bonding in AlF3 and AlF6 molecules may be dissociated to facilitate the formation of AlF4 and AlF5, because the latter possesses much more negative heat of formation energy. With the increase of the temperature, the system energy is reasonably increased, less time was required for the

reduced to similar amounts of AlF4−5. When the F/Al ratio = 4.5 (Figure 8c), the amount of AlF5 and AlF4−5 increases quickly. With further increase of F2 concentration (Figure 8d− f), the amount of AlF5, AlF4−5, and AlF6 continues to increase, while the number of AlF4 slowly decreases. We observe, in that case, that the AlF5 related molecules (clusters) become the dominant products, followed by the AlF4 related molecules (clusters) and AlF6 related ones. Besides the effect of the F2 concentration, the dominant formation of AlF4 and AlF5 molecules (clusters) under the present etching condition (4 ≤ F/Al ratio ≤ 6) is mainly due to their lower heat of formation energy compared to that of AlF6. Figure 9 presents the average energy as a function of etching time with different F2 concentrations (F/Al = 1−6). When the molar ratio of F/Al ≤ 3, the reaction potential energy increases slowly with the increase of the F2 concentration, and the reaction time shows a similar trend, in agreement with the

Figure 9. Energy variation as a function of time step with different F/ Al molar ratios. 16830


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Figure 10. Number of AlFx as a function of time step at different temperatures with ratio of F/Al at 5.

Figure 11. Diagram of the etching mechanism for the Al substrate in the fluorine gas.

ratio is below a critical value, the plasma may cease the etching of Si or Si oxides in the fluorine related gas. The present study of etching of Al in different F2 concentrations shows that there is a critical concentration of F/Al = 3. Below this ratio, the etching is not complete, since the etching gas is required to form a volatile compound with the film or substrate that is being etched.8 Based on the above conclusion, further study of the mechanism by which chemical sources influence the reaction product is merited. The present study further shows that, when the concentration is in the range 6 ≥ F/Al > 3, the formation of AlFx gaseous phase is not in direct proportion to the F/Al molar ratio. The AlF4 and AlF5 is the dominant phase, followed by the AlF6 and AlF3. This result transcends the general understanding of AlF3 formation during the Al−F etching process. Through studying the etching of the Si(100) surface by F and Cl atoms, Walch et al. thought that fluorine etching proceeds through formation of SiFx species in the fluorosilyl layer with SiF4 as the main gaseous product, with no barrier to

reaction system to reach equilibrium (Figure 10d), and the reaction rate was obviously improved. This result shows an important role of temperature in preparing the HS-AlF3 which contains undercoordinated Al ions that facilitate Lewis acid reactions. Also, significant amounts of OH groups and water absorbed on the HS-AlF3 need to be removed by treatment at higher temperature before HS-AlF3 reagents can fully develop their Lewis acidity.13 The relation of the reaction rate and temperature in the present work is similar to that found in the study of Si−F etching.74 3.4. Discussion of the Etching Mechanism. Both calculation and experimental study show that the concentration of etching gas is very important in governing the species and rate of the etching process. Experimentally, the Al fluoride layer formation can be prevented if NF3/noble gas mixtures containing a high noble gas proportion are employed instead. An increasingly thicker Al fluoride layer is produced with a greater proportion of NF3 in He/NF3, Ne/NF3, and Ar/NF3.28 Coburn and Winters72,73 also observed that, when the F/C 16831


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The Journal of Physical Chemistry C adding a third F atom to a monofluorinated dimer.75 However, the mechanism whereby F2 etches the metal substrate and the corresponding reactants remains unclear. We can analyze the detailed etching mechanism by exploring the detailed etching process (Figures 6 and 7) and the energy variation involved. The present etching can be summarized as follows: Step 1. Nondissociative adsorption: F2(gas) + Al(crystal) → F2(ads) + Al(crystal) Step 2. Crystal transformation: Al(crystal) → Al(cluster) Step 3. Dissociative adsorption: F2(ads) + Aln(cluster) → F(ads) + F(ads) + Aln(cluster) Step 4. Formation of products (cluster): xF(ads) + Aln(cluster) → AlnFx(cluster) Step 5. Desorption of products (molecule): AlnFx(cluster) → AlFx(gas) For the above steps, the minimal involved energy may be the adhesion energy of F2 on the Al substrates (step 1), the surface energy and the formation energy of the cluster (step 2), the dissociative energy of F2 into F atoms, the adhesion energy of F atoms on the Al cluster (step 3), the formation energy of AlFx cluster (step 4), and the formation energy of AlFx gaseous phase (step 5). Generally, the former four steps can happen spontaneously under certain energetic driving forces, such as high temperature, rc bias power, and discharge. In step 4, the AlFx (cluster) is formed with Al bonding to F atom, and F bonding to Al atoms. Step 5 can happen only when further driving force is provided to segregate or break the Al−F bonding in the cluster, and subsequently form more stable AlFx molecules, as shown in Figure 11. Comparison of the reaction products in different etching chemical conditions (F/Al ratios and temperatures) shows that the F2 concentration should be the primary factor which may affect the resulting reaction product. Below the critical line of F/Al = 3, chemical driving force is insufficient to induce the reaction of step 5; exceeding the critical line, the chemical driving force can be provided by formation of new gaseous phases with much more negative formation energies, such as AlF4, AlF5, and AlF6. Besides the chemical factor, the high kinetic energy induced by the higher temperature, the strong ion bombardment with higher rate, and the large discharge with higher voltage may also be important energetic factors affecting the product quantities, rather than the product type, as shown in Figure 10. This can adequately explain the cessation of etching when the F2 density is obviously decreased by noble gases, and the Al fluoride layer grows with a greater proportion of F in the NF3, He/NF3, Ne/NF3, Ar/NF3, and C/F systems.28,72,73 As for the formation of the reaction products in the present work, based on the heat of formation energy calculation (Table 2), the gaseous phases AlFx (x ≥ 3) possess much lower formation energy than that of AlF3. They are all much more stable than AlF3 and can form AlFx (x ≥ 3) spontaneously with increasing addition of F2 source. Therefore, only when the ratio of F/Al ≥ 3, the etching is really happening with the formation of gaseous AlFx (x ≥ 3) based on step 4. In the initial F2-rich conditions, AlF4 is the most productive gaseous phase in the way of AlF4/AlF3−4 molecules (clusters). With more addition of F2, the AlF5/AlF4−5 molecules (clusters) are the dominant gaseous phase, while the number of AlF4 dropped somewhat since its heat of formation energy is less negative than that of AlF5. Similarly, the number of AlF6 is reasonably increased with more addition of F2; however, the

corresponding number is still less than those of AlF4 and AlF5 considering the heat of formation energy and the F/Al concentration. Exceeding the present chemical source, if the F/ Al is larger than 6, the AlF4, AlF5, and AlF6 reactants may reasonably be the main etching products, as predicted by theoretical investigation on local structure and transport properties of NaF−AlF3 when the molecular ratio of NaF/ AlF3 ≥ 2.6.43 Based on these results, the preparative chemistry of HS-AlF3 tends to create more undercoordinated Lewis acidity sites under F2/F−-rich condition, while the compact AlF3 film tends to be obtained under F2/F−-insufficient condition. The present heat of formation energy calculation also shows that, similar to F−Si systems,74,75 no barrier exists for adding an F atom to an existing AlF, AlF2, AlF3, or AlF4 molecule. We know that it is advantageous if the etching gas is able to form a volatile compound with the film or silicon/aluminum substrate that is being etched. Based on these results, aluminum may be a suitable etch stop and etch mask material. Although we did not consider structure of AlFx (x > 6), we still found seldom AlF7, AlF8, and such within the present force field scheme. This nonsaturation property has been observed in the experimental literature.21 For etching of Al in the NF3rich system, the thickness of the Al fluoride layer continues to grow as a function of time, without saturation.21

4. CONCLUSIONS We have developed ReaxFF Al−F parameters by training against a QM training set consisting of various small AlFx clusters and Al−F condensed phases, and then studied the etching of Al metal in F2 using ReaxFF based molecular dynamics simulations. Our results show the following: (i) The Al−F structural and heat formation energy calculation within the present ReaxFF scheme is in good accordance with the literature data. (ii) The present etching can be summarized as five steps: step 1, the nondissociative adsorption of F2(gas) on Al crystal; step 2, the transformation of Al crystal to Al cluster; step 3, the dissociation of F2 molecules into F atoms and adsorption of F atoms on the Al cluster; step 4, the formation of AlFx cluster; and step 5, the desorption of AlFx cluster into isolated AlFx gaseous phase. (iii) F2 concentration appears to be the primary factor which may affect the etching process and products. Below the critical line of F/Al = 3, the chemical driving force is insufficient, only the former four steps occur, and the AlnFx cluster is formed; above the critical line, the fifth step happens and new gaseous phases with much more negative formation energies such as AlF4, AlF5, and AlF6 can be formed. (iv) Besides the chemical source, the high energy induced by higher temperature, strong ion bombardment with higher rate, and discharge with higher voltage may be the important energetic factors affecting the qualities of the etching, rather than the product type. Both the chemical and energetic driving forces can obviously affect the etching rate. The present results provide insight on the formation of AlFx cluster/gaseous phases during the etching of metal films and substrate in fluorine gases, and provide guidance for controlling kinetics of the formation of specific AlF x compounds or gaseous phases for the preparative chemistry of AlF3 materials. 16832


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study of disorder and reactivity of a-AlF3 nanoparticles. Phys. Chem. Chem. Phys. 2006, 8, 5045−5055. (12) Wander, A.; Bailey, C. L.; Searle, B. G.; Mukhopadhyay, S.; Harrison, N. M. Identification of possible Lewis acid sites on the βAlF3(100)surface: An ab initio total energy study. Phys. Chem. Chem. Phys. 2005, 7, 3989−3993. (13) Bailey, C. L.; Mukhopadhyay, S.; Wander, A.; Searle, B. G.; Carr, J. M.; Harrison, N. M. Reactivity of the b-AlF3(100) surface: Defects, fluorine mobility and catalysis of the CCl2F2 dismutation reaction. Phys. Chem. Chem. Phys. 2010, 12, 6124−6134. (14) Makarowicz, A. C.; Bailey, L.; Weiher, N.; Kemnitz, E.; Schroeder, S. L. M.; Mukhopadhyay, S.; Wander, A.; Searle, B. G.; Harrison, N. M. Electronic structure of Lewis acid sites on high surface area aluminium fluorides: A combined XPS and ab initio investigation. Phys. Chem. Chem. Phys. 2009, 11, 5664−5673. (15) Bailey, C. L.; Wander, A.; Mukhopadhyay, S.; Searle, B. G.; Harrison, N. M. Adsorption of HF and HCl on the b-AlF3 (100) surface. Phys. Chem. Chem. Phys. 2008, 10, 2918−2924. (16) Muray, A.; Scheinfein, M.; Isaacson, M.; Adesida, I. Radiolysis and resolution limits of inorganic halide resists. J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 1985, 3, 367−372. (17) Langheinrich, W.; Spangenberg, B.; Beneking, H. Nanostructure fabrication using lithium fluoride films as an electron beam resist. J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 1992, 10, 2868− 2872. (18) Vergara, L. I.; Vidal, R. A.; Ferrón, J. Electron induced reduction on AlF3 thin films. Appl. Surf. Sci. 2004, 229, 301−310. (19) Chen, G. S.; Boothroyd, C. B.; Humphreys, C. J. Electron-beam induced crystallization transition in self-developing amorphous AlF3 resists. Appl. Phys. Lett. 1996, 69, 170−172. (20) Kratschmer, E.; Isaacson, M. Progress in self-developing metal fluoride resists. J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 1987, 5, 369−373. (21) Li, X.; Hua, X. F.; Ling, L.; Oehrlein, G. S.; Karwacki, E.; Ji, B. Surface chemical changes of aluminum during NF3-based plasma processing used for in situ chamber cleaning. J. Vac. Sci. Technol., A 2004, 22, 158−164. (22) Donnelly, V. M.; Kornblit, A. Plasma etching: Yesterday, today, and tomorrow. J. Vac. Sci. Technol., A 2013, 31, 050825−050872. (23) Profijt, H. B.; Potts, S. E.; van de Sanden, M. C. M.; Kessels, W. M. M. Plasma-assisted atomic layer deposition: Basics, opportunities, and challenges. J. Vac. Sci. Technol., A 2011, 29, 050801−050826. (24) Tago, K.; Kazumi, H.; Kobayashi, K. A plasma kinetics model: Analysis of wall loss reactions in dry etching of silicon dioxide. J. Alloys Compd. 1998, 279, 60−65. (25) Kim, J. W.; Kim, Y. C.; Lee, W. J. Reactive ion etching mechanism of plasma enhanced chemically vapour deposited aluminum oxide film in CF4/O2 plasma. J. Appl. Phys. 1995, 78, 2045−2049. (26) Dictus, D.; Shamiryan, D.; Paraschiv, V.; Boullart, W.; De Gendt, S. De; Vinckier, C. Impact of metal etch residues on etch species density and uniformity. J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 2010, 28, 789−794. (27) Limcharoen, A.; Pakpum, C.; Limsuwan, P. A polymer-rich redeposition technique for non-volatile etching by-products in reactive ion etching systems. Chin. Phys. Lett. 2013, 30, 075202−075205. (28) Le Bail, A.; Calvayrac, F. Hypothetical AlF3 crystal structures. J. Solid State Chem. 2006, 179, 3159−3166. (29) Morelock, C. R.; Hancock, J. C.; Wilkinson, A. P. Thermal expansion and phase transitions of α-AlF3. J. Solid State Chem. 2014, 219, 143−147. (30) Daniel, P.; Bulou, A.; Rousseau, M.; Nouet, J.; Fourquet, J. L.; Leblanc, M.; Burriel, R. A study of the structural phase transitions in AlF3: X-ray powder diffraction, differential scanning calorimetry (DSC) and Raman scattering investigations of the lattice dynamics and phonon spectrum. J. Phys.: Condens. Matter 1990, 2, 5663−5679. (31) Earnshaw, A.; Greenwood, N. Chemistry of the Elements, 2nd ed.; Butterworth-Heinemann: Oxford, U.K., 1997.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b03957.

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ReaxFF file describing the interactions of Al−Al, Al−F, and F−F in the etching process (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 814-863-6277. ORCID

Yongli Liu: 0000-0002-8594-702X Yang Qi: 0000-0003-1915-474X Xianwei Hu: 0000-0002-8722-276X Adri C. T. van Duin: 0000-0002-3478-4945 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computational support was provided by the high performance computing center of Northeastern University and the Research Computation and Cyber infrastructure group at The Pennsylvania State University. ACTvD acknowledges support from funding from the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences for developing methodology for simulating MAX-materials etching, which is related to MXene synthesis.

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