The influence of hydrogen concentration in amorphous carbon films on mechanical properties and fluorine penetration: a density functional theory and ab initio molecular dynamics study

Abstract

Amorphous carbon (a-C) films have attracted significant attention due to their reliable structures and superior mechanical, chemical and electronic properties, making them a strong candidate as an etch hard mask material for the fabrication of future integrated semiconductor devices. Density functional theory (DFT) calculations and ab initio molecular dynamics (AIMD) simulations were performed to investigate the energetics, structure, and mechanical properties of the a-C films with an increasing sp³ content by adjusting the atomic density or hydrogen content. A drastic increase in the bulk modulus is observed by increasing the atomic density of the a-C films, which suggests that it would be difficult for the films hardened by high atomic density to relieve the stress of the individual layers within the overall stack in integrated semiconductor devices. However, the addition of hydrogen into the a-C films has little effect on increasing the bulk modulus even though the sp³ content increases. For the F blocking nature, the change in the sp³ content by both atomic density and H concentration makes the diffusion barrier against the F atom even higher and suppresses the F diffusion, indicating that the F atom would follow the diffusion path passing through the sp² carbon and not the sp³ carbon due to the significantly high barrier. For the material design of a-C films with adequate doped characteristics, our results can provide a new straightforward strategy to tailor the a-C films with excellent mechanical and other novel physical and chemical properties.

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1. Introduction

Amorphous carbon (a-C) films have attracted significant attention due to their reliable structures and superior mechanical, chemical and electronic properties,^1–3 making them a strong candidate as an etch hard mask material for the fabrication of future integrated semiconductor devices. However, for wider applications, it is still necessary to overcome the current limitations such as high internal stresses, low blocking nature of fluorine attack to sub-layers, and low temperature stability.⁴ In order to eliminate the aforementioned drawbacks and enhance the properties of the a-C films, the influence of hydrogen to modify their structure during the deposition process was studied.

The a-C films are mainly deposited on large areas at relatively low temperatures by plasma-enhanced chemical vapor deposition (PECVD) using hydro-carbon mixed precursor gases such as CH₄ or C₂H₂ diluted in H₂.^5,6 However, it is well known that the F atoms, which originate from the injection of etchant gases such as CF_x during the device fabrication process, generally attack the sub-layers and significantly degrade the device performance due to the extremely high reactive nature of F atoms with other atoms that have an electron-donating nature such as B, Al, and Ga; this results in the bond breaking of sub-layer materials to form F-containing alloys. This problem is a primary obstacle in the development of future integrated semiconductor devices.^7,8 To address this problem, a theoretical comprehension of the a-C films is required for the device fabrication process due to the experimentally limited observations on the atomistic scale.

The properties of the a-C films depend on the sp³-to-sp² hybridization ratio and the H content.^9,10 Depending on the composition, these films exhibit different characteristics such as hardness, electrical resistivity, optical transparency, and chemical inertness. The a-C films with high hardness, high sp² content, and low optical band gaps are referred to as hard graphitic a-C.¹¹ On the other hand, the a-C films with hardness and resistivity similar to that of a diamond are referred to as diamond-like carbon (DLC).¹²

Briefly, in previous studies, Mikami et al.¹³ found that an increase in the H₂ flow rate leads to an increase in the sp³ fraction and disorder during the deposition of the DLC films by radiofrequency (RF) magnetron sputtering. Vietzke et al.¹⁴ investigated the hydrogen-induced chemical erosion of C atoms from the a-C films using mass spectrometry. They reported the formation of CH₃ radicals along with a wide range of high hydrocarbons due to the reaction of the thermal H atoms within the a-C films. Other researchers reported that the growth rate, film structure, mechanical properties, optical gaps and field emission were all considerably affected by hydrogen.^15,16

Although several experimental studies on the influence of the hydrogen content in an a-C film have been investigated, no guidelines exist for improving the a-C film as an etch hard mask because the relationship between the structure of the a-C film and its etching characteristics remains unclear. Ab initio calculations provide a powerful tool to determine the atomic and electronic details and provide a deeper insight into the stress reduction mechanism of the a-C films.^17–19

In this paper, we examine the energetics, structure, and mechanical properties of a-C films with increasing sp³ content by adjusting the atomic density or hydrogen content using density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations. In our simulation, we generated amorphous carbon structures containing 64 C atoms to focus on studying the influence of the increase in the sp³ content by adjusting the atomic density or hydrogen content on the mechanical properties during the device fabrication processes.

We also theoretically investigated the influence of the increase in the sp³ content by adjusting the atomic density or hydrogen content on the diffusion of F atoms during the dry etch process, generating important findings in the field of materials science.

2. Computational methods

2.1. Generation of the model structure

Ab initio molecular dynamics (AIMD) simulations were carried out to obtain amorphous carbon structures. The cubic supercell of 64 atoms with a fixed lattice constant of 7.61 Å was used, which corresponded to the density of the reference amorphous carbon with 2.9 g cm⁻³.

The melt-quench simulations^20,21 were performed by pre-melting for 2 ps at 12 000 K, melting for 10 ps at 5000 K, and quenching to 0 K with a constant cooling rate of −250 K ps⁻¹. In the designed doped amorphous structures, the densities of dense a-C structures were selected as 3.2, 3.5, and 4.0 g cm⁻³, which corresponded to the lattice constants of 7.36, 7.14, and 6.83 Å. Hydrogen concentrations in H-added a-C structures were selected as 15.6, 23.4, and 31.2 at%, corresponding to 10, 15, and 20 atoms in 64-atom models. The final amorphous carbon structure was obtained by full relaxation of the atomic positions. Finally, the amorphous carbon structure comprised a tetra-coordinated C fraction of 56.3% with a radius of 1.8 Å to define the distances between the nearest neighbours for all amorphous carbon structures. This cut-off radius was obtained by calculating the first minimum value in the radial distribution function (RDF).²²

2.2. DFT calculations

In our theoretical results, all DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP) program with the Perdew–Burke–Ernzerhof (PBE) functional in the generalized gradient approximation (GGA).^23,24 We used the PBE-D2 functional²⁵ based on the projector augmented wave (PAW) method²⁶ with a conventional Kohn–Sham DFT energy correction to treat the van der Waals interactions for all DFT calculations (see the ESI†²⁷).

Valence orbitals were described by a plane-wave basis set with the cut-off energy of 400 eV. Ultrasoft Vanderbilt-type pseudopotentials²⁸ were used to describe the interactions between ions and electrons. The Brillouin zone for all amorphous structures was sampled with a 3 × 3 × 3 Monkhorst–Pack k-point mesh. Geometry optimization was performed by minimizing the forces of all atoms to less than 0.02 eV Å⁻¹ with the total energy of the system converged within 10⁻⁴ eV during self-consistent iterations. We determined the energy barriers (activation energies) through the climbing-image nudged elastic band (CINEB) method²⁹ using a force tolerance of 0.02 eV Å⁻¹. For an accurate calculation of the barriers, the CINEB method with a more precise transition-state search algorithm than the NEB method was used.^30,31 This method was made to search one of the various states near the transition-state along the reaction path, converging at the highest saddle point.^32–35

3. Results and discussion

3.1. Influence of atomic density and hydrogen concentration on mechanical properties

Fig. 1 shows the final atomic structures of 64 C atom-containing a-C films with an increase in the atomic density (3.2 to 4.0 g cm⁻³) and hydrogen concentrations (15.6 to 31.2 at%). The dependence of the calculated bulk modulus on the atomic density is illustrated in Fig. 2(a). In the case of the reference a-C film (Ref. a-C), a bulk modulus of about 212 GPa was estimated. With the increase in atomic density, the bulk modulus drastically increased; when the atomic density was 4.0 g cm⁻³, a maximal bulk modulus of about 617 GPa was obtained, which was around three-fold larger than that of the reference a-C film. On the other hand, on introducing H atoms in the a-C films, as shown in Fig. 2(b), the bulk modulus as a function of the H concentration increased and then slightly increased. When the H concentration was 31.2 at%, a maximal bulk modulus of about 248 GPa was obtained, which slightly increased by 17% compared to that for the reference a-C film.

Fig. 1 Optimized atomic structures of 64 C atom-containing amorphous carbon structures with increasing atomic density (3.2 to 4.0 g cm⁻³) and hydrogen concentrations (15.6 to 31.2 at%). Blue, sky-blue, yellow, and pink colors indicate sp³, sp², sp hybridized C and H atoms, respectively.

Fig. 2 Dependency of the calculated bulk modulus on (a) atomic density from 3.2 to 4.0 g cm⁻³ and (b) hydrogen concentrations from 15.6 to 31.2 at%, corresponding to 10 H, 15 H, and 20 H-added a-C.

I. N. Remediakis et al.,³⁶ revealed that the bulk modulus of a-C films was enhanced as the film density increased (335 GPa at 2.7 g cm⁻³, 375 GPa at 3.05 g cm⁻³, and 465 GPa at 3.55 g cm⁻³). This experimental result showed a similar trend with our DFT results (212 GPa at 2.6 g cm⁻³, 351 GPa at 3.2 g cm⁻³, and 450 GPa at 3.5 g cm⁻³); however, there is some discrepancy since the amorphous phase is characterized by a short-range order and the atoms are bonded in randomly disordered positions due to a phenomenon that does not allow the formation of a regular arrangement.

Nevertheless, taking advantage of the benefits of the simulation, it is noted that the drastic increase in the bulk modulus is observed by increasing the atomic density of the a-C films, which suggests that it would be difficult for the films hardened by high atomic density to relieve the stress of the individual layers within the overall stack in integrated semiconductor devices. However, the addition of hydrogen in the a-C films has little effect on increasing the bulk modulus even though the sp³ content increases. These findings suggest that the process design for high-sp³-content a-C films should be carried out by adding hydrogen rather than increasing the atomic density. These requirements become more important and increasingly challenging to meet as the device integrity increases.^37,38 To elucidate the mechanism of the increase in bulk modulus caused by atomic density and hydrogen concentrations, more direct evidence for the atomic bond structure including bond length distributions was collected first.

Fig. 3 shows the calculated results of the bond length and bond angle distributions for the dense a-C film with the highest atomic density of 4.0 g cm⁻³ and those for the H-added a-C film with the highest H concentration of 31.2 at%, in which the highest bulk modulus is observed, as shown in Fig. 2. For comparison, the case for the Ref. a-C film was also considered. The total bond length and bond angle distributions shown in Fig. 3 mainly consist of a C–C bond. Li et al.³⁹ revealed that the distortion of bond lengths (<1.42 Å) and bond angles (>120°) in the carbon network was the key factor for the low level of the bulk modulus. Therefore, the bond lengths and bond angles in these three a-C films were particularly studied in order to gain the fractions of distorted bonds, which are illustrated in Table 1. The equilibrium bond lengths of stable sp² and sp³ C–C bonds are 1.42 and 1.54 Å, respectively (the black vertical dotted lines in Fig. 3). The fractions of the distorted bond lengths (<1.42 Å) for the dense a-C film with the highest atomic density (4.0 g cm⁻³, sp³ content = 95.3%) and the H-added a-C film at maximum at% (31.2%, sp³ content = 76.6%) were deduced separately, as shown in Table 1. The calculations for the Ref. a-C film were also obtained for comparison.

Fig. 3 (a) Bond length distributions and (b) bond angle distributions for Ref. a-C, dense a-C, and H-added a-C films, respectively.

Table 1 Comparison of sp³ content, fractions of the distorted bond, and bulk modulus in Ref. a-C, dense a-C, and H-added a-C films

	Ref. a-C	Dense a-C	H-added a-C
sp^3 content (%)	54.7	95.3	76.6
Fraction of distorted bond length (%)	17.2	1.0	14.3
Fraction of distorted bond angle (%)	35.8	15.6	33.1
Bulk modulus (GPa)	212	617	248

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For the Ref. a-C film (Fig. 3), the fractions of the distorted bond length and bond angle are 17.2%, and 35.8%, respectively. For the dense a-C film, the fractions are 1.0% and 15.6%. However, after adding H into the a-C film, the fractions are 14.3% and 33.1%, showing similar values to both the bulk modulus and the fraction of the distorted bond length of the Ref. a-C film. This indicates that even the smaller bulk modulus than that of the dense a-C film is attributed to the high fraction of the distorted C–C bond relaxed by lattice vibrations during stress calculations using VASP.

So-Yeon Lee et al.,⁴⁰ reported that the RDF of the a-C films can be extracted from diffraction pattern measurements (mean bond length = 1.50 Å for the dense a-C film with sp³ content = 78.5%; mean bond length = 1.45 Å for the normal a-C film with sp³ content = 52.6%). These experimental RDF values show a similar trend with our DFT calculation results (mean bond length = 1.53 Å for the dense a-C film with sp³ content = 95.3%; mean bond length = 1.50 Å for the Ref. a-C film with sp³ content = 54.7%); however, there is slight discrepancy because the atoms in amorphous materials are bonded in randomly disordered positions due to the tendency that does not allow the formation of a regular atomic arrangement.

3.2. Influence of the atomic density and hydrogen concentration on diffusion profile of F atom in the point of energetics

During the dry etch process, the injection of etchant molecules such as CF_x leads to the penetration of F atoms through the a-C film up to the sub-layers. To enhance the performance of the a-C film as an etch hard mask, the a-C film has to block the F atoms on the top surface to diffuse downward up to the sub-layers, which are very important layers in highly integrated devices. For F diffusion to proceed, the F atom can pass though the dopant atom in the a-C films.

The optimized structures of the first, second, third, and fourth states for F penetration in the a-C films are shown in Fig. 4: (a) Ref. a-C film, (b) dense a-C film (at the highest density), (c) H-added a-C film (at the highest H concentration). Fig. 5 shows the minimum energy path of F diffusion, corresponding to the 1^st to 4^th state in Fig. 4. The 1^st state shows the energy profile of the downward diffusion of F atoms initially adsorbed on the top layer of the a-C films. In Fig. 4(a–c), Ref. and H-added a-C films show that the F atom diffuses downward and is bound to the sp² carbon atom.

Fig. 4 The optimized structures of the first, second, third, and fourth states for the F penetration into the a-C films; (a) Ref. a-C, (b) dense a-C, and (c) H-added a-C films.

Fig. 5 Minimum energy path of F diffusion, corresponding to the initial, transition, and final states; Ref. a-C (black), dense a-C (blue), and H-added a-C (red) films. E_a means activation energy obtained from NEB calculations.

Within the dense a-C film, the F atom diffuses downward and is bound to the surrounding carbon atom by breaking the C–C bond. The interesting point is that the F atom surrounded by sp³ C atoms has much higher barriers compared to that for the Ref. a-C and H-added a-C films. This implies that the sp² C atoms play an important role in determining the diffusion path of the F atom because of the higher reactive nature of sp² C than that of sp³ C.¹⁹ Furthermore, in our previous study, we reported that the energy barrier for the diffusion of an F atom through the sp³ bonding path is much higher than that for an F atom through the sp² boding path in a-C films.⁴⁰

The energy diagram in Fig. 5 clearly shows that the dense a-C film has the highest energy barrier, which can be explained in two perspectives, that is, sp³ content and atomic density. In the perspective of the sp³ content, an increase in the sp³ content causes the penetration of the F atom to weaken due to the decrease in the sp² carbon sites, enabling the formation of the C–F bonds and strengthening the blocking nature for F penetration. From the perspective of atomic density, an increase in the density leads to an increase in the sp³ content and then hinders the diffusion of F atoms due to the surrounding dense sp³ C atoms. Thus, the change in the sp³ content by both atomic density and H concentration significantly impacts the blocking characteristic against the F atom.

3.3. Dynamic behaviors at finite temperatures

AIMD simulations were performed to examine the dynamic behavior of these three a-C structures. A simulation temperature of 1000 K was chosen. To better understand the dynamic properties, AIMD simulations were also performed to estimate the F mobility within these three a-C structures at 1000 K. The MD duration of 10 ps was used to calculate the mean-square displacements (MSD). Fig. 6 shows the variations in MSD as the simulation time progresses. The diffusion coefficients of F atoms can be calculated based on the Einstein relation:
here, R_i is the atomic position; broken brackets denote thermal averages and t is the time.

Fig. 6 Variations in the diffusivities of the F atom within the a-C films; Ref. a-C (black), dense a-C (blue), and H-added a-C (red) films.

For the Ref. a-C structure, the diffusion coefficient of F was predicted to be D_F = 9.66 × 10⁻⁴ cm² s⁻¹. The diffusivities of the dense and H-added a-C structures were estimated to be 2.22 × 10⁻⁴ and 4.83 × 10⁻⁴ cm² s⁻¹, respectively. These calculations clearly show that F mobility tends to be hindered by both the atomic density and H concentration. The drastic reduction in F diffusivities within the dense and H-added a-C structures can be explained by the enhancement in the characteristic barrier of F diffusion, as aforementioned in Section 3.2.

Table 2 shows the comparison of the sp³ contents, activation energies (E_a, eV), and diffusion coefficients (D_F, cm² s⁻¹) for F diffusion for the Ref., dense, and H-added a-C films. This table clearly shows that the change in the sp³ content by both atomic density and H concentration makes the diffusion barrier of the F atom even higher and suppresses the F diffusion, meaning that the F atom would follow the diffusion path passing through the sp² carbon and not the sp³ carbon due to the significantly high barriers of 3.88 eV and 7.04 eV, respectively.

Table 2 Comparison of sp³ content, activation energies (E_a, eV), and diffusion coefficients (D_F, cm² s⁻¹) for F diffusion on Ref., dense, and H-added a-C films

	Ref. a-C	Dense a-C	H-added a-C
sp^3 content (%)	54.7	95.3	76.6
Ea,min (eV)	1.57	3.39	6.28
Ea,max (eV)	2.42	5.98	9.37
DF (cm^2 s^−1)	9.66	2.22	4.83

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3.4. Discussion

According to several studies on the etch process,^41–43 during the initial etch process (within 10 s), etching is very fast because it has an unstable atomistic structure by dangling bonds of the top-surface atoms. However, after the initial etch of on the surface, the bulk part of the thin film starts to get slowly etched due to its characteristics of stable atomic bonds and condensed atomic arrangement. Due to this slow etching, the bulk etch process determines the overall etch reaction rate. Therefore, the reason we only considered the “bulk” part is that during the real etch process, the “surface” part takes place in a very short time and most of the time is required for the “bulk” part. In fact, many other researchers in the fields of etch processes^44–46 have controlled the etch profile by tuning the “density” of thin films, which is a very important “bulk” property that can be easily tuned by the etch chemistry ratio, temperature, and plasma power.

Our DFT calculation shows that increasing the atomic density of the a-C films dramatically increases the bulk modulus. Similarly, several researchers reported experimentally that the bulk modulus of a-C is proportional to density.^12,47–49 Ito A. M. et al.⁴⁹ explained the dependence of the bulk modulus on density by counting the covalent bonds in a-C materials. They revealed that the number of covalent bonds increased in proportion to the film density as well as the bulk modulus. Other researchers^50,51 stated that an increase in the modulus is attributed to the change from sp² to sp³ bonds with an increase in the density. The combination of their results and our DFT calculated results for the relation between density and bulk modulus in actual thin films provides deep insights for analyzing the thin film chemistry and physics from this approach.

All our DFT calculated results suggest that the dense a-C film would be difficult to apply for highly integrated devices due to the high bulk modulus even though this film has a superior F blocking nature. On the other hand, the H-added a-C film would have an advantage for highly integrated devices due to the excellent F blocking nature by keeping the bulk modulus from rising steeply.

Even though a-C films with increasing atomic density and H concentration have not been reported as an etch hard mask, our DFT calculated results suggest that the H-added a-C films would have outstanding characteristics such as mechanical properties and blocking nature of F atoms for an etch hard mask in ultra-high integrated semiconductor devices. In our DFT calculated results, the combinational study of atomic density and H concentration in the a-C films would provide a deep insight into improving the mechanical properties and etch selectivity of the films, enhancing the performance of the future memory devices.

4. Conclusions

We investigated the energetics, structure, and mechanical properties of a-C films with an increase in the sp³ content by adjusting the atomic density or hydrogen content based on DFT and AIMD calculations. Drastic increase in bulk modulus was observed by increasing the atomic density of the a-C films, which suggested that it would be difficult for the films hardened by high atomic density to relieve the stress of the individual layers within the overall stack in integrated semiconductor devices. However, the addition of hydrogen into the a-C films had little effect on increasing the bulk modulus even though the sp³ content increased. These findings suggest that the process design for high-sp³-content a-C films should be carried out by adding hydrogen rather than increasing atomic density. These requirements become more important and increasingly challenging to meet as the device integrity increases. In the perspective of the F blocking nature, a change in the sp³ content by both atomic density and H concentration makes the diffusion barrier of the F atom even higher and suppresses the F diffusion, meaning that the F atom would follow the diffusion path that passes the sp² carbon and not the sp³ carbon due to the significantly high barrier. For the material design of a-C films with adequate doped characteristics, our results can provide a new straightforward strategy to tailor the a-C films with excellent mechanical and other novel physical and chemical properties.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Euijoon Yoon and Gun-Do Lee acknowledge support from the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources (KSC-2017-C3-0020), from the joint program for Samsung Electronics Co., Ltd. (SEC), from BK21PLUS SNU Materials Division for Educating Creative Global Leaders (21A20131912052), and from the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. RIAM 2019R1A2C2005098) and the Ministry of Science, ICT and Future Planning (2017M3D1A1040688). Hwanyeol Park acknowledge support from the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources (KSC-2019-CRE-0148). The computation data to support the findings of this paper is available from the corresponding author on reasonable request. The code to analyze ab initio molecular dynamics simulation is available at: https://github.com/mogroupumd/aimd.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra09328a

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