Tight-Binding Quantum Chemical Molecular Dynamics Simulations of

Article pubs.acs.org/JPCC

Tight-Binding Quantum Chemical Molecular Dynamics Simulations of Mechanisms of SiO2 Etching Processes for CF2 and CF3 Radicals Hiroshi Ito,† Takuya Kuwahara,† Kentaro Kawaguchi,† Yuji Higuchi,† Nobuki Ozawa,† Seiji Samukawa,‡ and Momoji Kubo*,† †

Fracture and Reliability Research Institute (FRRI), Graduate School of Engineering, Tohoku University, 6-6-11 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan ‡ Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ABSTRACT: The plasma etching of SiO2 by CF2 and CF3 radicals is investigated by using our etching simulator based on tight-binding quantum chemical molecular dynamics method. During etching simulations, C−F and Si−O bonds dissociate and C−O and Si−F bonds are generated. Moreover, CO, CO2, COF, and COF2 molecules form, which is consistent with previous experimental studies. We also examine the dependence of the etching mechanism of CF2 and CF3 radicals on the kinetic energy of irradiation. At a low kinetic energy of 10 eV, a CF2 radical dissociates more Si−O bonds than a CF3 radical does. This is because the high chemical reactivity of the CF2 diradical accelerates the etching process. At a high kinetic energy of 150 eV, a CF3 radical dissociates more Si−O bonds than a CF2 radical does. This is because a CF3 radical generates a greater number of reactive F atoms than a CF2 radical does and thus forms more Si−F bonds. Thus, we conclude that our etching simulator modeled the different SiO2 etching mechanisms of CF2 and CF3 radicals, which arose from the different chemical reactivities of radicals and F atoms at different kinetic energies. This is the first quantum chemistry study to model complicated chemical reactions, which are induced by the attack of many radical species, and clarify the different SiO2 etching mechanisms for CF2 and CF3 radicals.

1. INTRODUCTION Plasma etching has been used to pattern semiconductor substrates for microelectronic devices.1−3 Miniaturization is important for fabricating next-generation electronic devices, and plasma etching is required to improve the atomic-scale accuracy of devices. However, defects such as sidewall necking and bowing are formed during plasma etching, where holes thicken unevenly and top sections narrow.4−7 These shape deformations are caused by the side-etching of holes and the polymerization of molecules, ions, and radicals. The defects are closely related to the bombardment of the substrate with ions and radicals and their adsorption on the substrate surface and sidewalls of the holes. Shape deformations destroy the anisotropy of the substrate and decrease the fabrication accuracy and etching rate. Therefore, it is important to understand surface reactions that affect the quality of the etching process. Analyzing the chemical reactions and electron transfer dynamics between the etchant species and etching substrate is particularly important because it affects the generation of molecules, including byproducts, and the polymerization of the generated molecules. SiO2 is widely used as an insulator in semiconductor devices, and the SiO2 surface is patterned by plasma etching. Fluorocarbon gases are the most common etchants.8−14 The effects of the etchant gas constituents,8,9 the type of etchant ions and radicals,8,10,11,13,14 and the kinetic energy of the © 2014 American Chemical Society

etchant species, which is controlled by the bias voltage in radiofrequency systems,10−13 have been extensively studied. Doh et al. investigated etching of SiO2 and Si with fluorocarbon gases, such as CF4 and C4F8.8 They showed that CF, CF2, and CF3 radicals are important reaction precursors. Shibano et al. reported that SiO2 etching yields depended on the incident ion energy of the F+, CF+, CF2+, and CF3+ ion beams generated from CF4 gas.10 They reported that CF3+ and CF2+ ions have higher etching yields than other ions. In particular, CF3+ ions etch faster than CF2+ ions for ion energies of several hundred electronvolts. These studies indicate that the etching mechanism depends on the etchant species and its kinetic energy. During plasma etching, the SiO2 substrate is irradiated with ions that are generated by the plasma activation of fluorocarbon gases. The ions are neutralized near the substrate surface through a process called Auger neutralization.15 The chemical reactions between the CFx radicals and the SiO2 surface are crucial for understanding the etching mechanism. Furthermore, to prevent damage to the etching substrate and etching holes from charge buildup on the substrate,16 one of the coauthors in the present paper, Samukawa, and co-workers developed neutral beam etching.17,18 The neutral beam etching Received: February 12, 2014 Revised: August 26, 2014 Published: August 26, 2014 21580

dx.doi.org/10.1021/jp5015252 | J. Phys. Chem. C 2014, 118, 21580−21588

The Journal of Physical Chemistry C

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etchant atoms deep in the SiO2 structure. However, we examined only CF2 radical etching, and the effect of different CFx radicals and their kinetic energy is still unclear. A full understanding of all the radicals is essential for designing efficient, highly controlled SiO2 etching processes. Simulations of CF2 and CF3 radicals, which have the highest etching rates,3,8,9,13,14 are important for understanding etching. In this paper, we report a TB-QCMD simulation of the continuous irradiation of a SiO2 surface with CF2 and CF3 radicals with a kinetic energy of 10 eV to clarify the effect of the etchant species on the etching mechanisms. Moreover, we also investigate the chemical reaction dynamics for radical kinetic energies of 70 and 150 eV to identify differences in the etching mechanisms for CF2 and CF3 radicals. This is the first time that the different SiO2 etching mechanisms for CF2 and CF3 radicals have been elucidated, and it has been shown how the different chemical activities and selectivity of CF2 and CF3 radicals result in different mechanisms.

system uses an aperture to remove ions’ charges, so that the substrate is irradiated with neutral species. Preventing charge buildup results in higher etching selectivity than in conventional systems. In particular, CF2 and CF3 radicals are the main species in plasma-activated fluorocarbon gases, such as CF4, C2F4, CHF3, CF3I, C2F6, and C4F8.3,8,9,13,14 Moreover, the irradiation energy of the etchant species affects the etching rate and polymerization of the C and F atoms.10,12 It is important to understand the etching mechanisms, which depend on the etchant species and their kinetic energy. However, surface chemical reactions and dynamics are difficult to observe experimentally at an atomic scale. To investigate SiO2 etching on an atomic scale, computational simulations are a promising approach. Classical molecular dynamics (MD) methods have been used to analyze the dependence of the etching efficiency and CFx polymerization of ionized species. Rauf et al. used the Stillinger−Weber potential and reported that the fluorocarbon layer grew after the SiO2 surface was bombarded with several hundred CFx+ ions.19 They showed that C and F atoms polymerize and form a passivation film on the SiO2 surface. CF3+ ions form a thinner passivation film than CF2+ ions. However, the chemical reactions during the etching process cannot be modeled using classical MD because the method does not consider electrons, making it impossible to calculate electron transfer and thus chemical reactions. Static first-principles calculations can be used to model chemical reactions and electron transfer. Wang et al. simulated Si etching with CF3 molecules by using static firstprinciples calculations20 to model bond formation and energy barriers during the chemical reactions. They found that Si−F bonds were generated in the reaction between the Si surface and CF3 molecules. Moreover, when two CF3 molecules reacted with the Si surface, a C−C bond and a C2F2 molecule were generated. Static first-principles calculations were also used to investigate Si etching by Cl.21−23 These studies revealed mechanisms such as the formation of SiCl2 units on the Si surface and the desorption of SiCl4 molecules. However, static first-principles calculations cannot simulate the effect of etchant velocity on the chemical reaction dynamics, although it is experimentally observed that the etchant velocity substantially affects the etching mechanism, efficiency, and reaction. Firstprinciples MD is a method that could simulate the chemical reactions and electron transfer dynamics during etching and elucidate the effect of the radical velocity. However, it has not yet been used for simulating etching because of its huge computational cost. Therefore, we developed a tight-binding quantum chemical molecular dynamics (TB-QCMD) method for simulating chemical reactions and electron transfer dynamics.24−33 Our TB-QCMD code is over 5000-fold faster than conventional first-principles MD methods and has already been used to investigate the tribochemical reactions of diamond-like carbon,26 the chemical vapor deposition process for silicon thin film growth,27,28 the sol−gel process for silica,29 and the oxidation of CO in emission control catalysts.31 Furthermore, we developed an etching process simulator based on our TB-QCMD method.24 We simulated the plasma etching of a SiO2 surface by continuous radical irradiation with CF2 radicals, which are usually generated from plasma-activated C4F8 and CF4 gas. We revealed that the CF2 radicals dissociate the Si−O bonds on the SiO2 surface dissociate and generate C−O and Si−F bonds. Moreover, we studied the effect of etchant velocity on the etching process. Radicals with high kinetic energy can promote rapid SiO2 etching and spread

2. METHOD We used our etching simulator, which is based on our TBQCMD code “Colors”, to model the chemical reaction and electron transfer dynamics of the etching processes. It uses the following Hamiltonian: Hrs =

1 K rsSrs(Hrr + Hss) 2

(2-1)

K rs = {1 + κrs(1 − Δ4 ) + Δ2 } exp[−δrs{rrs − (dr + ds)}] (2-2)

Δ=

Hrr − Hss Hrr + Hss

(2-3)

The diagonal matrix element, Hrr, is equal to the negative of the ionization potential for valence electrons, Ir; Hrr = −Ir. The offdiagonal term, Hrs, is calculated from eq 2-1, where Srs is the overlap integral matrix. In eq 2-2, rrs is the distance between the two atoms to which the molecular orbitals belong, dr is the radius of each orbital, and κrs and δrs are positive empirical parameters. The total energy in the system is calculated with eqs 2-4 and 2-5: N

E=

∑ i=1 N

+

1 mivi 2 + 2

OCC

N

N

∑ εk + ∑ ∑ k=1

i=1 j>i

ZiZje 2 R ij

N

∑ ∑ Erep(R ij) i=1 j>i

⎛ aij − R ij ⎞ ⎟⎟ Erep(R ij) = bij exp⎜⎜ ⎝ bij ⎠

(2-4)

(2-5)

In these equations, e is the elementary charge, Rij is the internuclear distance, and aij and bij are parameters between atoms i and j. aij and bij are related to the size and stiffness of atoms, respectively. Zi is the atomic charge obtained by the TB electronic states calculations. Mulliken analysis34,35 is used to obtain the value of Zi. In eq 2-4, the first term is the kinetic energy of the atoms, the second term is the sum of the eigenvalues of all the occupied orbitals, and the third term is the Coulombic interaction. The last term corresponds to the shortrange exchange-repulsion energy. 21581



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Moreover, to confirm the validity of the interval time of 0.50 ps, we simulated SiO2 etching with interval time of 0.50, 1.00, and 1.50 ps and compared the results in the previous study. We confirmed that there is no significant change in the interval time of 0.50, 1.00, and 1.50 ps and concluded that 0.50 ps is sufficient to simulate SiO2 etching. Just before irradiation begins, the CF2 and CF3 radicals are randomly located in an area of 1.5 Å × 1.4 Å at the center of the xy-plane, 6.9 Å above the SiO2(100) surface. The irradiation energy is assigned to the CF2 and CF3 radicals in only the z-direction, and they are not given rotational energy. The vaporized molecules generated by the chemical reactions are automatically removed from the simulation cell after they reach a z position greater than 34.8 Å from the surface. The Verlet algorithm39 is used for calculating atomic motion with a time step of 1.0 × 10−4 ps under threedimensional periodic boundary conditions. The Ewald method40 is used to calculate the Coulombic interactions. To determine the effect of the irradiation kinetic energy on the etching processes, irradiation kinetic energies of 10, 70, and 150 eV are used for the CF2 and CF3 radicals. These energies correspond to velocities of 6.211, 16.435, and 24.059 km/s for the CF2 radicals and to 5.288, 13.991, and 20.481 km/s for the CF3 radicals. We have previously reported the details of the parameter settings for the TB-QCMD simulations.24

The atomic bond populations as given by Mulliken population analysis34,35 are calculated to clarify the bond breaking, bond formation, and electron transfer dynamics quantitatively during the chemical reactions. The atomic bond population, MXY, is calculated by onX onY OCC

MXY = 4 ∑ ∑ r

s

∑ CjrCjsSrs j

(2-6)

where Cjr is the eigenvector element. The details of the etching simulator are shown in Figure 1. In the TB-QCMD etching simulator, the total number of atoms in

Figure 1. Schematic of our TB-QCMD etching simulator.

3. RESULTS AND DISCUSSION A. Simulation of Etching by Continuous Irradiation of CF2 and CF3 Radicals. The TB-QCMD method was used to simulate the etching of a SiO2(100) surface by CF2 and CF3 radicals. First, we discuss the simulation of the etching process by CF2 radicals with a kinetic energy of 10 eV. The first CF2 radical emerges above the surface at 0.20 ps, and the SiO2 surface is continuously irradiated with 10 CF2 radicals at 0.50 ps intervals. Snapshots of the simulation are shown in Figure 2. The first CF2 radical is irradiated (Figure 2a) and hits the SiO2 surface. A C−F bond of the CF2 radical dissociates, and the dissociated F atom moves into the SiO2 substrate. At 0.74 ps, the radical C atom forms bonds with O atoms, and C−O bonds are generated (Figure 2b). The dissociated F atom forms a bond with a Si atom in the SiO2 structure, whereas the other F atom remains bound to the C atom. At the same time, a H2 molecule is generated on the SiO2 surface. After the second CF2 radical hits the SiO2 surface, a C−O bond is generated, and a COF2 molecule is observed at 1.19 ps (Figure 2c). The COF2 molecule vaporizes from the SiO2 surface. After the third CF2 radical is irradiated, CO, COF, and H2 molecules are generated (Figure 2d) and vaporize from the SiO2 surface. At 2.57 ps, a COF2 molecule is also generated and vaporized (Figure 2e). The fifth irradiated CF2 radical is deflected from the SiO2 surface and remains on the surface without forming a C−O bond. This suggests that CF2 radicals with a kinetic energy of 10 eV do not always react with the SiO2 surface. After the tenth CF2 radical is irradiated, vaporized CO and CO2 molecules are also observed at 5.20 ps (Figure 2f). At 10 eV, various chemical reactions, such as bond formation and bond dissociation, and the deflection of the irradiated radical on the SiO2 surface are observed. Moreover, H2, CO, CO2, COF, and COF2 molecules are generated. Byproducts that do not have a radical such as CO2 and COF2 molecules are mostly chemically stable during the simulation. Then, these molecules do not cause readsorption during the etching simulations. On the other hand, we observe that CO and COF molecules cause readsorption and make bonds with a Si atom of SiO2.

the system can be changed on the basis of the irradiation of the etchant species and the vaporization of the molecules generated by surface chemical reactions. This allows for new radicals to be emitted and for vaporized molecules to disappear and makes it possible to simulate the continuous irradiation of the etchant species. Furthermore, it is possible to reproduce the etching conditions, such as the time interval of the emitted etchant species, the velocity of the incident etchant species, the rotation of the etchant species, the number of etchant species, the elements of the etchant species, and the substrate temperature. Thus, our etching process simulator can optimize various experimental etching process conditions and predict the etching efficiency, polymerization, and number of shape defects by using quantum chemistry. In previous etching simulations using classical MD, the substrate has been modeled as crystalline SiO2. Smirnov et al. used α-quartz SiO2,36 Kawase et al. used crystalline SiO2,37 and we used α-cristobalite SiO2.24,25 In this study, we also use an αcristobalite SiO2 etching substrate. The top and bottom layers of the SiO2(100) surface are terminated with hydroxyl groups. The SiO2 surface consists of 396 atoms (H: 24; O: 252; Si: 120). The simulation cell contains a 15.2 Å × 14.2 Å xy-plane parallel to the surface and an 80.0 Å z-axis perpendicular to the surface. The bottom 60 atoms (H: 12; O: 36; Si: 12) of the SiO2 substrate are fixed. The simulations are performed at 300 K. The temperature is controlled by scaling the atomic velocities every 10 steps, except those of the irradiation molecules and the atoms which vaporize from the SiO2(100) surface. Ten CF2 and CF3 radicals are continuously irradiated at every 0.50 ps interval, starting at 0.20 ps. The interval time is determined from the previous etching simulation studies based on classical molecular dynamics.19,38 Rauf et al. simulated Si and SiO2 etching by CF2+ and CF3+ with the interval time of 0.8 ps.19 Vegh et al. calculated Si etching by CF3+ and Ar+ with the interval time of 1−2 ps for CF3+ and 0.5 ps for Ar+.38 According to these classical molecular dynamics studies, we employed 0.50 ps as the interval time in our previous24 and present studies. 21582



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Figure 3. Time evolution of the atomic bond population of CA−OA, CB−OA, and SiA−OA bonds after the third CF2 radical irradiation. Insets show scaled-up snapshots of the SiO2 etching by CF2 radicals at 10 eV at (a) 0.74, (b) 0.90, and (c) 1.19 ps.

with CF3 radicals. Figure 4 shows snapshots of the SiO2 etching simulation for CF3 radicals with a kinetic energy of 10 eV. The same simulation conditions as the CF2 radical simulation were used. The SiO2 surface was continuously irradiated with 10 radicals at 0.50 ps intervals, starting at 0.20 ps (Figure 4a). The first CF3 radical generates a C−O bond on the SiO2 surface at 0.60 ps (Figure 4b). During this reaction, three C−F bonds remain on the first CF3 radical. A C−O bond is also generated in the CF2 radical etching. The second CF3 radical extracts an F atom from the first CF3 radical, which is adsorbed on the SiO2 surface, and is then vaporized from the surface as a CF4 molecule (Figure 4c). At the same time, COF2 and H2 molecules are generated and vaporize. After the fifth CF3 radical, COF2 and CO2 molecules are generated and then vaporize (Figure 4d). These reactions are similar to those for CF2 radical etching. After the seventh CF3 radical, COF2 molecules are generated and vaporize (Figure 4e). Moreover, after the tenth CF3 radical, COF2 and CF4 molecules are also generated (Figure 4f). CO2 and COF2 molecules are generated during etching by both CF3 and CF2 radicals. In the TB-QCMD etching simulations of CF2 and CF3 radicals, the C−F bonds of the fluorocarbon radicals dissociate during the bombardment of the SiO2 surface. The dissociated C and F atoms diffuse above the SiO2 surface or penetrate it. Subsequently, these C and F atoms form bonds with O and Si atoms, respectively, generating volatile CO, CO2, COF, and COF2 molecules that vaporize. However, CF4 molecules are formed more frequently during CF3 radical etching than during CF2 radical etching. During the five simulation runs for etching with 10 CF2 or CF3 radicals, 2 CF4 molecules are generated by CF2 and 24 CF4 molecules are generated by CF3. This is because CF3 has more F atoms than CF2, and this affects the reaction probabilities for the CF2 and CF3 radicals. To compare the etching mechanisms for the CF2 and CF3 radicals in detail, the number of surface reactions was counted. Figure 5 shows the numbers of Si−O, C−O, and Si−F bonds during etching. These numbers reflect the probabilities of chemical reactions on the SiO2 surface. In particular, the time evolution of the number of Si−O bonds indicates the breakage

Figure 2. Snapshots of SiO2 etching by CF2 radicals at the (a) first and (b) second CF2 radical irradiation, and after the (c) second, (d) fourth, (e) fifth, and (f) tenth CF2 radical irradiation at a kinetic energy of 10 eV.

To reveal chemical reaction dynamics during etching, we analyze bond formation and dissociation by calculating the atomic bond populations. Figure 3 shows scaled-up snapshots from 0.74 to 1.19 ps in Figure 2b,c. These snapshots show the time evolution of atomic bond populations of the CA−OA, CB− OA, and SiA−OA bonds when the second CF2 radical hits the SiO2 surface and a COF2 molecule is generated. The CA atom belongs to the second irradiated CF2 radical, and the CB atom belongs to the first CF2 radical. The SiA and OA atoms are located in the first layer of the SiO2 surface. The atomic bond population from 0.50 to 1.20 ps in Figure 3 shows that at 0.74 ps the CB−OA atomic bond population is 0.92 and the SiA−OA atomic bond population is 0.16, indicating that these pairs of atoms share chemical bonds. From 0.80 to 0.88 ps, the CA−OA atomic bond population increases from 0.01 to 0.90. From 0.81 to 0.86 ps, the SiA−OA atomic bond population decreases from 0.12 to 0.00. This suggests that the OA atom switches its bond from SiA to CA (Figure 3b). At 1.03 ps, the CB−OA atomic bond population decreases to 0.00, indicating that the CB−OA bond dissociates and generates a COF2 molecule (Figure 3c). These results show that irradiation of the SiO2 substrate with CF 2 radicals induces surface reactions, such as bond dissociation and bond formation. To compare the dynamic behavior of CF2 and CF3 radicals, we also performed a TB-QCMD simulation of SiO2 etching 21583



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Figure 5. Time evolution of the number of (a) Si−O, (b) C−O, and (c) Si−F bonds during etching at a kinetic energy of 10 eV. The averaged data with the error bars for five simulation runs are shown.

reactions and thus have a higher etching rate than CF3 radicals. Interestingly, the number of generated C−O and Si−F bonds is similar for both the CF2 and CF3 radicals. Although there are fewer C atoms than F atoms in CF2 and CF3 radicals, the C atoms form covalent bonds as readily as F atoms during the etching process. C atoms have one or two dangling bonds, which makes them more reactive than the F atoms. Thirteen Si−F bonds are generated after irradiation with 10 CF2 radicals, and 10 Si−F bonds are generated after irradiation with 10 CF3 radicals (Figure 5c). Therefore, many of the F atoms do not react with the Si atoms and remain in C−F bonds. This generates various molecules with C−F bonds, such as COF, COF2, and CF4 (Figures 2 and 4). Additionally, for comparison, we also simulated SiO2 etching by CF2 radical with the Nosé− Hoover thermostat41 instead of the velocity scaling. The generation of H2, CO, CO2, COF, and COF2 molecules is also observed in the simulation with the Nosé−Hoover thermostat. Moreover, the time evolutions of the numbers of Si−O bonds are similar in both the temperature control methods, and significant differences are not observed. Then, the velocity scaling was found to be sufficient to simulate etching processes in our simulation model. The CF2 diradicals are better at dissociating Si−O bonds because its two dangling bonds make it very reactive (Figure 5a). The CF3 monoradical is less reactive and participates in fewer reactions than the CF2 radical. These mechanisms show that CF2 radicals etch SiO2 more effectively than CF3 radicals because of their high chemical reactivity at a kinetic energy of 10 eV. B. Effect of the Kinetic Energy of CF2 and CF3 Radicals on SiO2 Etching. To compare the etching mechanisms of CF2 and CF3 radicals, we also examined the effect of the radical

Figure 4. Snapshots of SiO2 etching by CF3 radicals at the (a) first CF3 radical irradiation and after the (b) first, (c) second, (d) sixth, (e) eighth, and (f) tenth CF3 radical irradiation at a kinetic energy of 10 eV.

of Si−O bonds, which corresponds to the etching rate. The number of bonds between two atoms is based on the atomic bond population. An atom pair that has an atomic bond population of more than 0.1 is counted as bonded. During the simulation, the numbers of these bonds are counted at the start, each irradiation time, and the end of the simulation, at 0.00, 0.70, 1.20, 1.70, 2.20, 2.70, 3.20, 3.70, 4.20, 4.70, and 5.20 ps. The data for five simulation runs are averaged, and the error bars are also indicated. The variation in the numbers of Si−O bonds during the simulation at 10 eV is shown in Figure 5a. Few Si−O bonds are dissociated early in the simulation, suggesting that the irradiated radicals are deflected from the SiO2 surface. After the initial stage, the number of Si−O bonds starts to decrease. In the final stage, CF2 radicals dissociate more Si−O bonds than CF3 radicals (Figure 5a). Figure 5b,c shows the numbers of generated C−O and Si−F bonds, which are calculated by the same method used for the Si−O bonds. Initially, few C−O and Si−F bonds are generated early in the simulation. These results indicate that early on irradiated radicals do not react readily with the SiO2 surface and vaporize. After the initial stage, the number of C−O and Si−F bonds starts to increase. During the final stage, the CF2 radicals form more C−O and Si−F bonds than the CF3 radicals (Figure 5b,c). This suggests that CF2 radicals initiate more chemical 21584



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6b). The generation of CO, CO2, COF, COF2, and SiF4 molecules is observed experimentally.1 The probability of generating these molecules showed that the dissociation of Si atoms from the SiO2 surface is much more difficult than that of O atoms. This is because four Si−F bonds must be formed to generate an SiF4 molecule, whereas only one or two C−O bonds must be formed to generate CO, CO2, COF, and COF2 molecules. We suggest that the generation of SiF4 molecules is the rate-determining step for SiO2 etching. This mechanism would be difficult to determine by a static first-principles method, which demonstrates the utility of our TB-QCMD dynamics simulations. Next, we calculated the time evolution of the numbers of Si− O, C−O, and Si−F bonds at 70 eV (Figure 7). The change in

velocity. In experimental studies, the bias voltage controls the etching rate and polymerization in radio-frequency systems.10,12 This means that the kinetic energy of the etchant species affects the etching rate and chemical reaction dynamics. Therefore, we increased the kinetic energy of the CF2 and CF3 radicals from 10 to 70 or 150 eV. The irradiation conditions of CF2 and CF3 radicals are the same as for the etching simulations at 10 eV. The number of irradiated radicals is 10, the first irradiation starts at 0.20 ps, and the radicals are irradiated at 0.50 ps intervals. Figure 6a shows snapshots at 5.20 ps after irradiation with 10 CF2 radicals at 70 eV. The C−F bonds dissociate and C−O and

Figure 6. Snapshots of SiO2 etching by (a) CF2 and (b) CF3 radicals with a kinetic energy of 70 eV after irradiation with 10 radicals at a simulation time of 5.20 ps.

Si−F bonds are generated. Moreover, CO and CO2 molecules are observed in the snapshot at 5.2 ps (Figure 6a). During the simulation, COF and COF2 molecules are also generated and vaporize. The generation of these molecules is the same as that during the etching simulation at a kinetic energy of 10 eV. After 10 CF2 radicals are irradiated, many Si−O bonds on the SiO2 surface are dissociated. Although Si−O bonds only near the surface are dissociated at 10 eV, Si−O bonds at medium depths in the SiO2 substrate are also dissociated at 70 eV. Early on, etching holes are generated. Figure 6b shows an etching snapshot 5.20 ps after irradiation with 10 CF3 radicals at 70 eV. During CF3 radical etching, C−O and Si−F bonds are generated, Si−O bonds dissociate, and etching holes begin to appear (Figure 6b). Furthermore, CO2 molecules are generated and vaporize, and CO, COF, and COF2 molecules are also generated. The generation of these molecules is similar to that in the simulation at 10 eV. During the five simulation runs for the etching process for 10 CF3 radicals, a SiF4 molecule is generated twice in 50 CF3 radical irradiations. Remarkably, SiF4 is not generated in the etching simulation for CF2 radicals at 70 eV or for CF2 and CF3 radicals at 10 eV. During SiO2 etching, the desorption of Si and O atoms is an essential reaction. In our simulations, the O atoms in the SiO2 surface are dissociated by C atoms and the O atoms are removed as CO, CO2, COF, and COF2 molecules (Figures 2c−f, 4c−f, and 6a,b). Si atoms in the SiO2 surface are dissociated by F atoms and removed as SiF4 molecules (Figure


the number of Si−O bonds by CF2 and CF3 radicals is similar throughout the simulation (Figure 7a). Thus, the CF2 and CF3 radicals have the same etching rate at a kinetic energy of 70 eV. This is different from etching at 10 eV. Figure 7b shows that the change in the number of C−O bonds is also similar for the CF2 and CF3 radicals. Figure 7c shows the numbers of Si−F bonds. CF3 radicals form more Si−F bonds than CF2 radicals, particularly after 3.70 ps. It is possible that CF3 radicals at 70 eV cause more chemical reactions and generate more Si−F bonds than CF2 radicals. This corresponds to the generation of the SiF4 molecules during etching with CF3 radicals (Figure 6b). At 70 eV, the C−F bonds of the CF2 and CF3 radicals are likely to be dissociated during the bombardment, and the dissociated C and F atoms participate in chemical reactions. The CF3 radical has three F atoms whereas the CF2 radical has only two. Therefore, the CF3 radical forms more Si−F bonds than the CF2 radical. However, at 10 eV, the C−F bonds in the CF3 21585



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radical do not break, and the CF2 diradical is more efficient at etching. At 70 eV, the dissociation of the C−F bonds produces many reactive F atoms and CF3 is more efficient. This trade-off results in similar etching rates for CF2 and CF3 radicals at 70 eV. Figure 8a shows a snapshot after irradiation with 10 CF2 radicals at a kinetic energy of 150 eV. C−O and Si−F bonds are

Figure 8. Snapshots of SiO2 etching by (a) CF2 and (b) CF3 radicals with a kinetic energy of 150 eV after irradiation with 10 radicals at a simulation time of 5.20 ps.


generated, and Si−O bonds dissociated. Moreover, the snapshot at 5.2 ps shows the generation of CO and CO2 molecules (Figure 8a). COF and COF2 molecules are also generated and vaporized during the simulation. The generation of these molecules is the same as that in the etching simulations at 10 and 70 eV. However, at 150 eV the etching holes are deeper than at 10 and 70 eV. This is because the high kinetic energy of the irradiated C and F atoms allows them to penetrate the deep layers of the SiO2 substrate and react with Si and O atoms. Penetration depth increases as the increase in the kinetic energy of radical, and this tendency agrees with our previous paper,24 which investigated SiO2 etching by CF2 radical and analyzed how F atoms penetrate into SiO2 after bombardments. Therefore, penetrating atoms are possible to reach an interface in real device substrate. The control of penetration is important to design optimal etching process. Figure 8b shows a snapshot after irradiation with 10 CF3 radicals at a kinetic energy of 150 eV. At 150 eV, C−O and Si− F bonds are generated and Si−O bonds dissociate. A CO2 molecule is present at 5.2 ps (Figure 8b), and CO, COF, COF2, and SiF4 molecules are also generated during the simulation. A SiF4 molecule is generated by only the CF3 radicals, showing that CF2 and CF3 radicals have different chemical reactivities. This is similar to the results for the etching simulation at 70 eV. This may be because of the large number of reactive F atoms in the CF3 radical etching at 150 eV. We also calculated the time evolution of the numbers of Si− O, C−O, and Si−F bonds at a kinetic energy of 150 eV. Figure 9a shows the numbers of Si−O bonds. At 150 eV, the CF3 radicals can dissociate more Si−O bonds than the CF2 radicals, showing that CF3 radicals have a higher etching rate than CF2 radicals. Figure 9b shows that the CF2 and CF3 radicals generate almost the same number of C−O bonds at the

beginning of the simulation, whereas CF3 radicals generate more C−O bonds at the end. Figure 9c shows that CF3 radicals generate more Si−F bonds than CF2 radicals do. At 10 eV, CF2 dissociates Si−O bonds and generates C−O and Si−F bonds more efficiently, whereas at 150 eV, CF3 is more efficient. At 70 eV, the etching efficiency reaches a transition. At low kinetic energies, the effect of the radical bombardment is small, and the chemical reactivity of the etchant species dominates the etching process. Under these conditions, the CF2 diradicals form more C−O and Si−F bonds than the CF3 monoradicals and thus achieve a higher etching rate than CF3 radicals. In contrast, at high kinetic energies, the radical bombardment strongly influences the generation of reactive C and F atoms. More chemical reactions occur at high kinetic energies than low kinetic energies. In particular, the number of Si−F bonds generated increases more than the number of C−O bonds, and the number of Si−O bonds increases (Figures 5, 7, and 9). The generation of Si−F bonds and SiF4 molecules is the ratedetermining step, and because CF3 radicals have more F atoms available to form Si−F bonds and SiF4 molecules, CF3 radicals etch more efficiently than CF2 radicals at high kinetic energies. Therefore, CF2 diradicals etch more efficiently at low kinetic energies. The etching process is complicated, and the chemical reactions depend heavily on the radical bombardment of the substrate surface. In our simulation, the irradiation flux is estimated at about 9.3 × 1025 cm−2 s−1, and this is similar as that of other previous simulation studies. The interval time of 0.8 ps with 24.57 Å × 25.53 Å substrate surface in ref 19 is estimated at about 2.0 × 1025 cm−2 s−1, and that of 0.5−2.0 ps with 6.5 nm × 6.5 nm in ref 38 is estimated at about (1.2−4.7) × 1024 cm−2 s−1. However, the flux of experiment is 1013−1017 cm−2 s−1,10,11 and 21586



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the fluxes of simulations are higher than that of experiment. In our previous study,24 we simulated SiO2 etching by CF2 radical and confirmed that the interval time of 0.50 ps is sufficient to simulate SiO2 etching. However, in that study, the maximum irradiation energy of CF2 radical is 79.4 eV, which is converted from the irradiation velocity of 17.5 km/s, and the SiO2 etching at 150 eV has not been simulated. In the present study, to confirm the validity of the interval time of 0.50 ps in the SiO2 etching at 150 eV, we perform additional simulations of SiO2 etching at 150 eV with the interval time of 1.00 and 1.50 ps. There is no significant change in the time evolution of numbers of Si−O bonds in all simulations with the interval time of 0.50, 1.00, and 1.50 ps. Temperatures at the SiO2 surface before the next irradiation are almost the same as the preset temperature in all the interval times. It indicates that chemical reactions and diffusions of atoms on the SiO2 surface finish and the SiO2 surface sufficiently heals during 0.50 ps after the irradiation. Therefore, the results do not change in all simulations at 150 eV with the interval time of 0.50, 1.00, and 1.50 ps. It means that the interval time of 0.50 ps is sufficient to simulate SiO2 etching at 150 eV although the interval time of an experiment is longer than that of the simulation. Therefore, we conclude that the interval time of 0.50 ps is acceptable in the present paper. Additionally, to investigate temperature rise at surface in SiO2 etching, we calculated temperatures of an upper part of the SiO2 which totally includes 108 Si and O atoms and consists of 3 layers of SiO2. A whole SiO2 model includes 372 Si and O atoms and consists of 10 layers. In the simulations, the temperature in the selected part increases after each radical bombardment and then decreases to the preset temperature during each interval time. In the present study, the SiO2 surface is continuously irradiated with 10 CF2 or CF3 radicals in a simulation run, and there are 10 peaks in the evolution of the temperature. We calculated the maximum temperature at each peak in the etching by CF2 and CF3 radicals and averaged the maximum temperatures in 20 irradiations with 10 CF2 and CF3 radicals in the etching at 10, 70, and 150 eV. In the SiO2 etching by CF2 and CF3 radicals at 10 eV, the averaged maximum temperature is 692 K. On the other hand, in the simulations at 70 eV, the averaged maximum temperature is about 1103 K, and that at 150 eV is about 1285 K. The temperature of the SiO2 surface rises as the increase in the kinetic energy. The surface temperature rise contributes to chemical reactions especially in dissociation of Si−O bonds. This tendency is observed in Figures 5, 7, and 9, and the numbers of dissociated Si−O bonds increase as the increase in the kinetic energy. Therefore, as the increase in the irradiation energy of etchant species, (i) the impact of the radical on the SiO2 surface becomes strong and (ii) the surface temperature increases. These two factors are found to be the reasons why the surface reactions are encouraged by the increase in the irradiation energy. Our TB-QCMD etching simulator has proved effective for elucidating the effect of radical bombardment on chemical reactions during plasma etching.

dynamics during etching with CF2 and CF3 radicals. We investigated the etching mechanisms of CF2 and CF3 radicals at different kinetic energies. CF2 radicals etched more efficiently than CF3 radicals at low kinetic energies, whereas CF3 radicals were more efficient at high kinetic energies. At 10 eV, CF2 radicals dissociated more Si−O bonds because it is a highly reactive diradical. At 150 eV, CF3 radicals dissociated more Si− O bonds because the C−F bonds broke during radical bombardment, releasing more reactive F atoms than the CF2 radical. This is reflected in the large number Si−F bonds and SiF4 molecules generated by CF3 radicals at 70 and 150 eV. We have clarified the complicated etching mechanisms in which the chemical reactions are strongly linked to the bombardment of the surface. The kinetic energy of the bombardment changes the probability and efficiency of chemical reactions at the SiO2 surface and reverses the etching efficiency of the CF2 and CF3 radicals at high energies. Our etching simulator based on TBQCMD proved effective for determining the dependence of the etching mechanism on the etchant species and the irradiation energy. Our simulator can be used to investigate the mechanism of other etching processes and to design efficient etching processes.

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AUTHOR INFORMATION

Corresponding Author

*Phone +81-22-795-6930; e-mail [email protected]. jp (M.K.). Notes

The authors declare no competing financial interest.

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REFERENCES

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4. CONCLUSIONS We modeled the etching of a SiO2(100) surface by continuous irradiation with CF2 and CF3 radicals by using our TB-QCMD etching process simulator. CF2 and CF3 radicals with a kinetic energy of 10 eV generated C−O and Si−F bonds and CO, CO2, COF, and COF2 molecules, which is consistent with experimental observations. We confirmed that our TB-QCMD etching simulator accurately represents chemical reaction 21587



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