Influence of Small-Size Contaminations on Thin Film Structural Properties

F. V. Grigoriev$^{1\hyperlink{s}{**}}$, V. B. Sulimov$^{1}$, Jinlong Zhang(张锦龙)$^{2,3,4}$, Xinbin Cheng(程鑫彬)$^{2,3,4}$, \\ Zhanshan Wang(王占山)$^{2,3,4}$, A. V. Tikhonravov$^{1}$

doi:10.1088/0256-307X/36/3/038101

⇦Chinese Physics Letters, 2019, Vol. 36, No. 3, Article code 038101⇨ Influence of Small-Size Contaminations on Thin Film Structural Properties * F. V. Grigoriev1**, V. B. Sulimov1, Jinlong Zhang (张锦龙)2,3,4, Xinbin Cheng (程鑫彬)2,3,4, Zhanshan Wang (王占山)2,3,4, A. V. Tikhonravov1 Affiliations 1Research Computing Center, M.V. Lomonosov Moscow State University, Moscow 119991, Russia 2MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai 200092 3Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai 200092 4IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240 Received 23 October 2018, online 23 February 2019 ^*Supported by the RFBR under Grant No 17-57-53091, and the National Natural Science Foundation of China under Grant No 11611530687.
^**Corresponding author. Email: fedor.grigoriev@gmail.com Citation Text: Grigoriev F V, Sulimov V B, Zhang J L, Cheng X B and Wang Z S et al 2019 Chin. Phys. Lett. 36 038101 Abstract An approach for studying the influence of nano-particles on the structural properties of deposited thin films is proposed. It is based on the molecular dynamic modeling of the deposition process in the presence of contaminating nano-particles. The nano-particle is assumed to be immobile and its interaction with film atoms is described by a spherically symmetric potential. The approach is applied to the investigation of properties of silicon dioxide films. Visualization tools are used to investigate the porosity associated with nano-particles. The structure of the film near the nano-particle is studied using the radial distribution function. It is found that fluctuations of film density near the nano-particles are essentially different in the cases of low-energy and high-energy deposition processes. DOI:10.1088/0256-307X/36/3/038101 PACS:81.15.Aa © 2019 Chinese Physics Society Article Text Even small contaminations in thin films may be a limiting factor for achieving superior optical characteristics of optical coatings that are required for such challenging applications as gravitational wave detection systems, laser gyroscopes, etc. Using energetic deposition processes, one can obtain high-quality thin films with negligible scattering losses caused by surface roughness and bulk inhomogeneity.[1-3] Thus the presence of contamination defects is currently the main factor that should be taken into account for achieving further progress in the production of coatings with extremely low losses. Contamination defects in thin films may vary in size by several orders of magnitude. In recent years considerable efforts have been taken to study phenomena connected with the defects whose sizes are close to the wavelength of incident light. Investigations of the light losses by scattering connected with such defects were performed theoretically and experimentally.[4-8] Since the sizes of polluting particles can vary by several orders of magnitude, it is also important to investigate phenomena connected with nano-defects with dimensions being on the order of a few nanometers. Such small defects cannot directly cause light losses by scattering but they can influence structural properties of thin films on a much wider scale. Studying the related variations in structural properties is also important for the production of thin films with superior optical properties. In this Letter, we apply molecular dynamics (MD) simulation for the investigation of the influence of small nano-particles on the local structural properties of thin films. The main advantage of the classical MD simulation compared with early approaches like hard-spheres models (see, for example, Ref. [9]) is a more accurate description of the interatomic interactions including formation of chemical bonds. The potential energy of the interacting particles is calculated using the force field describing the dependence of the interaction energy on the interatomic distance. This allows one to investigate the influence of various parameters such as substrate temperature, energy of deposition atoms, and external and internal stresses on thin film fabrication. The relaxation processes including temperature annealing can also be studied using the MD approach. The model for the MD simulation of SiO$_{2}$ thin film growth was developed earlier and has proven to be suitable for the description of various properties of amorphous SiO$_{2}$ films.[10-14] It was shown that the developed model reproduces different structural and mechanical parameters of SiO$_{2}$ glassy films with a very good accuracy. These parameters include film density, peak positions of the radial distribution functions (RDFs), geometry of the chemical bonds, roughness, values of bulk modulus, values of mechanical stresses in films, and dependence of density and porosity on the energy and incident angle of deposition atoms. We model the film growth in the neighborhood of a contaminating particle for the cases of low-energetic and high-energetic deposition processes. The local structural properties are studied by constructing RDFs centered on nano-particles. We also perform a visual analysis based on the construction of constant-density surfaces in plane-parallel film layers passing through the centers of nano-particles. We perform the MD simulation of the silicon dioxide thin film growth using the force field DESIL proposed in our previous publications.[10-14] This force field is used for calculating interatomic interactions. The simulation procedure starts with the preparation of a fused silica substrate on which the film is later deposited. For this preparation we use the initial crystalline structure with the total number of atoms equaling 36000. This cluster has lateral dimensions of $10.46\times9.06$ nm$^{2}$ and its thickness is equal to 5.75 nm. To obtain a glassy amorphous substrate, the initial structure is subjected to the annealing procedure at a temperature of 2500$^{\circ}\!$C. The details of this procedure are described in Refs. [11,12]. The cluster density at the end of the annealing procedure is 2.14 g/cm$^{3}$, which is close to the experimental value of the fused silica density. The simulation of silicon dioxide film growth is organized as a step-by-step procedure. At every deposition step the MD simulation is performed using periodic boundary conditions with the $NVT$ ensemble, which means that the number of atoms, volume, and temperature inside the deposition box are kept constant. The Berendsen thermostat[15] is used to maintain a constant temperature in the modeling box. The duration of one deposition step is 10 ps, and the number of steps is 1000. The number of injected SiO$_{2}$ groups of atoms at each deposition step is equal to 25, which ensures the same flux density of the deposited atoms as used in the previous works.[10-14] A glassy substrate is prepared as described in Ref. [12]. The heating rate is equal to 2 K/ps, which is a typical value in MD simulation.[16] The interaction of the nano-particle with the deposited atoms and with the atoms of the substrate is described by the Lennard–Jones potential $$ U_{ij} =\frac{C_{12 ij}}{r_{ij}^{12}}-\frac{C_{6 ij}}{r_{ij}^{6}},~~ \tag {1} $$ where $r_{ij}$ is the distance between the $i$th and $j$th atoms. The parameters of this potential for the nano-particles with two different radii are provided in the first and second rows of Table 1. The value of the parameter $C_{12 ij}$ is chosen in such a way that the repulsive part of the Lennard–Jones potential is 10 kJ/mol at a distance from the center of the nano-particle equaling $R$. Under such a condition, the penetration of the film atoms into the nano-particle is insignificant, thus the value of $R$ can be considered to be the radius of the nano-particle. The electrostatic component of the interaction potential is not specified in our simulation procedure, which corresponds to the case of the electrically neutral nano-particle.

**Table 1.** Parameters of the Lennard–Jones potential used in the simulation procedure.
	O	O
	$R_{n}=1.0$ nm	$R_{n}=1.5$ nm
$C_{12}$ (kJ$\cdot$nm$^{12}$/mol)	10	1.3$\times10^{3}$
$C_{6}$ (kJ$\cdot$nm$^{6}$/mol)	1.0

The radii of nano-particles are equal to 1.0 nm and 1.5 nm (Table 1). The chosen radii correspond to the values that have been mentioned in a number of experimental works. Metallic nano-particles having dimensions of about several nanometers and embedded in silicon dioxide films were considered in Refs. [17,18]. Another study[19] clearly showed that laser-induced damage in thin films is driven by localized nanoscale absorbers, and in coatings containing metal-oxide components these absorbers are suspected to be metal clusters. To visualize the simulation results, we use the visual molecular dynamics (VMD) software,[20] which allows one to quickly draw a constant density surface. Using the MD simulation procedure, we performed experiments with various energies of deposited Si atoms. To study the influence of contaminating nano-particles on the local structural properties of thin films, experiments with nano-particles were accompanied by experiments with analogous deposition conditions in the absence of such nano-particles. The thicknesses of deposited films reached 25 nm, which is enough for studying variations in the film structure near the nano-particles. The results of three such experiments are presented in Fig. 1. In two of these simulation experiments there are contaminating nano-particles with a radius equaling 1.5 nm. In Fig. 1 the atomic structures are represented by constant density surfaces, which are calculated as the sums of exponentially decreasing atomic contributions with the centers corresponding to the centers of the atoms.

Fig. 1. Slices of the films deposited at different energies of Si atoms.

Slices of the deposited films are taken at 4.5 nm$ < x < 5.5$ nm in the coordinate system shown in the right bottom part of the figure. The nano-particles are shown as grayed circles. The right figure corresponds to the deposition in the absence of contaminating nano-particle. It can be seen that the film structures, especially their porosity, differ significantly in the cases of high-energy ($E_{\rm Si}$ = 10 eV) and low-energy ($E_{\rm Si}$ = 0.1 eV) deposition processes. At a low energy of deposited Si atoms an irregular cavity is formed near the nano-particle. This cavity extends almost to the upper boundary of the film. High porosity is also characteristic for a film deposited at $E_{\rm Si}$ = 0.1 eV in the absence of a nano-particle (see the right part of Fig. 1). However, in the case of contaminating nano-particles, the dimensions of pores are essentially higher than those in the case of their absence. This is clearly demonstrated in Fig. 2. In Fig. 2 the viewpoint is inside the film cluster. In this figure the substance of the film is transparent, and the three-dimensional figures of complex shape are areas in which the substance is absent, that is, pores. It is clearly seen that the largest pore is formed near the nano-particle.

Fig. 2. Pores in the film deposited at low energy of Si atoms.

The detailed analysis of density distribution around the nano-particles is performed using the RDFs. This function is defined as $$ g(r)=\frac{A[N(r+dr)-N(r)]}{\langle n\rangle4\pi r^{2}dr},~~ \tag {2} $$ where $\langle n\rangle$ is the average concentration of film atoms, and $N(r+dr)$ and $N(r)$ are the numbers of atoms inside spheres having radii $r+dr$ and $r$, respectively. The centers of spheres coincide with the center of the nano-particle, and $A$ is the normalizing coefficient. The value of $A$ is chosen so as to satisfy the condition $\lim_{r \to \infty }g(r)=N_{\rm c}$, where $N_{\rm c}=3$ is the average coordinate number of atoms in SiO$_{2}$ films. The RDFs of the deposited films are shown in Fig. 3. It is seen that in the case of high-energy deposition, the RDF starts to increase at smaller values of the distance from the center of the nano-particle than in the case of low-energy deposition. For both values of deposition energy, RDFs fluctuate near the nano-particles. In contrary to it, the RDFs of pure SiO$_{2}$ films have no such fluctuations and their peaks correspond to the averaged distances between atoms in different coordination spheres.[10] We guess that non-regular positions of RDF peaks indicate a disorder in the film structure near the nano-particles. Additional information about the film density near the boundary with the nano-particle is provided by the cumulative number function, $N(r)$.[21] This function is proportional to the integral of $g(r)$ in the range from 0 to $r$ and for this reason has a smoother behavior than $g(r)$. Figure 4 presents the cumulative number functions corresponding to the RDFs shown in Fig. 3.

Fig. 3. Dependence of RDFs on the distance to the nano-particle center. Black line corresponds to $E_{\rm Si}$ = 0.1 eV, blue line corresponds to $E_{\rm Si}$ = 10 eV. Vertical dotted lines indicate the boundaries of nano-particles: $R_{n}=1.0$ nm for the plots in (a), and $R_{n}=1.5$ nm for the plots in (b).

Fig. 4. Cumulative number function $N(r)$ corresponding to the RDFs from Fig. 3: black curves $E_{\rm Si}$ = 0.1 eV, blue curves $E_{\rm Si}$ = 10 eV, and vertical dotted lines indicate the boundaries of nano-particles with $R_{n}=1.0$ nm for (a) and $R_{n}=1.5$ nm for (b).

It is seen that in the case of low-energy deposition, $N(r)$ reaches an asymptotic value slower than in the case of high-energy deposition. This means that the volume of a film with reduced film density in the case of $E_{\rm Si}$ = 0.1 eV is much higher than in the case of $E_{\rm Si}$ = 10 eV. Figure 3 shows that the presence of a nano-particle with a diameter $D$ leads to significant fluctuations in the film density at distances up to several $D$ from the center of the nano-particle. Such fluctuations can result in the increase of the concentration of point defects in the film, which in its turn can increase the absorption coefficient of the film. It should be noted that the relative influence of regions with reduced film density near the nano-particles can be essential even in the case of high-energy deposition, despite the fact that there is no noticeable porosity connected with these nano-particles. The influence of the substrate temperature $T$ on the RDF dependences was also studied (Fig. 5). The RDFs will not noticeably depend on $T$ if the distance from the nano-particle boundary does not exceed approximately 0.5 nm. With further growth of $r$, RDFs fluctuate for both considered substrate temperature values, which indicates a disorder in the film structure. The amplitudes of these fluctuations are close for both values of $T$. It is found that the variation of the atomic flow incident angle within 30$^{\circ}\!$ from the normal to the substrate does not significantly influence the RDF dependences. The considered incidence angles correspond to typical deposition conditions. At the same time the deposition at high incidence angles (glancing angle deposition) results in the formation of separated sculptured structures having thicknesses of tens of nanometers.[22] This case requires a special separate investigation.

Fig. 5. Dependence of RDF on the distance from the nano-particle center for the two values of substrate temperatures (a) to $E_{\rm Si}$ = 0.1 eV, and (b) to $E_{\rm Si}$ = 10 eV. Solid and dashed curves correspond to the substrate temperature of 300 K and 500 K, respectively. Vertical dotted lines indicate the boundary of the nano-particle, $R_{n}=1.5$ nm.

Typical thin film deposition processes result in the formation of non-crystalline amorphous structures and the presented investigation relates to this case. We assume that in the case of crystalline structures the insertion of nano-particles to the crystal results in the formation of disordered shells surrounding these nano-particles. In principle the thicknesses of these shells can be found using the RDFs in the same way as it is described in the presented study. A detailed investigation of such structures would be an interesting topic for future work. In summary, we have proposed a model that allows one to estimate the effect of nano-particles on the structural properties of deposited thin films. The deposition process is modeled using the classical MD approach and a nano-particle is considered as a fixed elastic neutral sphere interacting with the film atoms by the Lennard–Jones potential. We model the deposition of silicon dioxide films at various energies of Si atoms. The influence of nano-particles on the porosity of thin films is studied by comparison of results obtained in the course of simulation experiments with nano-particles with the results of simulation experiments without nano-particles. Fluctuations of the film density near the nano-particles are investigated using RDFs. It is found that significant fluctuations in the film density are observed at distances up to several particle diameters from the particle center. In the case of high-energy deposition no noticeable porosity is observed. However, even in this case nano-particles can influence thin film properties due to noticeable fluctuations in the film density near the nano-particles and possible increase in the concentration of point defects in these areas of the film. The research was carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University. References Reducing light scattering in high-reflection coatings through destructive interference at fully correlated interfacesEffects of wet etch processing on laser-induced damage of fused silica surfacesAnalysis and fabrication of antireflection coating with ultralow residual reflectance for single wavelengthBroadband negative refraction in stacked fishnet metamaterialSimulation of structural anisotropy and void formation in amorphous thin filmsHigh-performance atomistic modeling of optical thin films deposited by energetic processesFull-atomistic nanoscale modeling of the ion beam sputtering deposition of SiO 2 thin filmsAnnealing of deposited SiO_2 thin films: full-atomistic simulation resultsMolecular dynamics with coupling to an external bathViscosity of Aluminum during the Glass Transition Process, According to Molecular DynamicsSPIE ProceedingsOptical Absorptivity Enhancement of SiO2 Thin Film by Ti and Ag AdditiveGROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputersChiral sculptured thin films

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