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The previously developed high-performance method of the atomistic simulation of thin film deposition is applied to the investigation of effects connected with SiO2 films annealing. It is found that the film density is reduced for about 0.15 g/cm3 under annealing with the temperature of 1300 K. This corresponds to the reduction of the refractive index for approximately 0.03. Concentrations of the non-bridging and threefold coordinated oxygen atoms are reduced up to four times after annealing. The stress value essentially reduces after annealing at 1300 K and the film thickness increases for 3 nm.
© 2016 Optical Society of America
1. Introduction
It was experimentally demonstrated that post-deposition thermal annealing influences properties of deposited films resulting in the decrease of their refractive index and optical thickness [1]. Annealing effects in SiO2 films deposited on different substrates using ion beam sputtering (IBS) method was investigated in [2]. It was revealed that the interface layer properties can be improved using annealing with an optimal temperature. Thickness of the transition layer between SiO2 film and Si substrate was essentially reduced under the annealing with temperature of 900 K [2]. Reduction of the refractive index of SiO2 films under annealing with temperatures in the interval 1200-1400 K was reported in [3]. The increase of film thickness up to 4 nm was found for the film with initial thickness of 100 nm [3]. The influence of annealing on electrical properties was investigated in [4].
Atomistic simulation provides the understanding of film growth process on the microscopic level and can be a useful tool for the improvement of deposition technologies. The high-performance parallel molecular dynamic (MD) simulation method with the original DESIL force field was applied for the simulation of deposition of SiO2 films with the thicknesses up to 100 nm [5, 6]. In the present work this method is applied for the investigation of the post-deposited thermal annealing of SiO2 films. The atomistic MD simulation with duration 200 ps was used earlier to obtain the annealed structure of the SiO2 atomistic cluster consisting of only ~103 – 10−4 atoms [7,8]. In the present paper the MD simulation of annealing of IBS deposited SiO2 films for the first time is performed for the films with more than one million of atoms and thicknesses of 50 nm. The influence of annealing with different temperatures on film density, structural parameters (covalent bonds and valence angles), concentration of point defects, surface roughness, rings statistic and stresses is investigated.
2. Simulation method
Simulation of thin film growth is organized as a step-by-step MD procedure described in details in [5,6]. In the present work the following deposition parameters are used. The deposition temperature is T = 300 K, the duration of one injection cycle is t1 = 6 ps, the time step of MD modeling is 1 fs, the number of injected SiO2 groups per one injection cycle is 50. The NVT ensemble (constant number of atoms, volume and temperature) with Berendsen thermostat [9] and DESIL force field [5,6] are used. Atomistic structure of the simulation box, horizontal sizes of the substrate and an approximate value of film thickness are shown in Fig. 1a. Structure of the glassy substrate is obtained from the crystalline structure under the melting-cooling procedure as described in [5]. Density and thickness of the substrate are 2.14 g/cm3 and 2.5 nm, respectively.
Fig. 1 To the description of the simulation of film growth a), and calculation of stresses in the film-substrate atomistic clusters b). See the text for the details.
Two series of simulation experiments are performed with the energies 1 eV and 10 eV of vertically injected deposited Si atoms. Initial velocities of oxygen atoms are oriented normally to the substrate and correspond to the kinetic energy of 0.1 eV. The number of the injection cycles at the end of SiO2 film growth simulation achieves 5000, the total duration of growth simulation is close to 3 ns. For calculating the electrostatic component of interatomic energy the Particle Mesh Ewald [10,11] method is used. The main structural characteristics of deposited films are listed in the Results and discussion section. Densities of deposited films exceed the experimental silica glass density for 0.1-0.2 g/cm3.
The annealing simulation is performed using the standard GROMACS facilities [11,12]. The next values of the annealing temperature Ta are taken: 500 K, 900 K and 1300 K. These values correspond to experimental values in Refs [1–3]. The volume of simulation box is kept equal to the value, obtained at the last injection cycle of the deposition procedure.
The annealing simulation procedure consists of the next steps:
- 1. Heating of the deposited film from the initial temperature Ti = 300 K to the chosen value of annealing temperature Ta with heating rate 1 K/ps at constant volume.
- 2. MD simulation of the film in NVT ensemble (constant number of the atoms, volume and temperature, T = Ta). Time of annealing varies from 1 ns to 4 ns.
- 3. Cooling of the deposited film from Ta to the initial temperature Ti = 300 K with cooling rate 1 K/ps.
- 4. Relaxation of the annealed structure at the temperature Ti = 300 K during 100 ps.
Rates of heating and cooling correspond to the values that was used earlier in the MD procedure of preparation of SiO2 glassy structures from the crystalline ones [5,6].
Differences in structural and mechanical properties of the substrate and deposited film result in stresses in the transition layer between them. There are two types of stresses: tensile and compressive (see Fig. 1b). Compressive stress has negative sign while tensile stress has positive sign. In the frame of our simulation scheme stresses are calculated as horizontal components of the pressure tensor pxx(yy): σxx(yy) = - pxx(yy). Negative sign before the pressure ensures the correct sign of stress value. Since the pressure is calculated for the simulation box as a whole, the correction to the empty volume in the upper part of the box is performed in the way described in Ref [13].
Components of the pressure tensor are averaged over MD trajectory after finishing of the deposition process (for deposited films) or annealing procedure (for annealed films). Length of the MD trajectory for the averaging is taken equal to100 ps. This value is enough for the convergence of pxx(yy) values with time of modeling. Simulation is carried out in NVT ensemble with T = 300 K.
The distribution of n-membered rings (n – number of the Si atoms in the ring) is investigated using the shortest-path analysis (SPA) [14,15]. The corresponding numerical procedure is time-consuming for the large atomistic clusters since it is based on the analysis of all links (chemical bonds) of all atoms. For this reason in present work an empirical scheme is used for the evaluation of rings distribution. This scheme is based on the Monte-Carlo random sampling of atoms of the investigated cluster. For every chosen atom search for all rings including this atom is carried out and relative numbers of n-membered rings for all n are calculated.
Surface roughness is calculated in accordance with a standard definition of a root mean square deviation of vertical coordinates of surface atoms [16]. It is assumed that the deposited film grows in the vertical direction.
All calculations were performed on the supercomputer ‘Lomonosov’ of the Supercomputing Center of Lomonosov Moscow State University [17]. The maximum number of used computational cores was 1024.
3. Results and discussion
Thicknesses of deposited films at the end of deposition process simulations are 50 nm. Structural properties of deposited and annealed films are listed in Table 1. To exclude the influence of transition zones substrate-film and film-air all values are averaged over the internal part of the film located between vertical coordinates hmin = 10 nm and hmax = 40 nm . Zero value of the vertical coordinate corresponds to the bottom of the substrate (Fig. 1 a). The maximum Si-O distance defining existence of the Si-O bond is taken equal to 0.2 nm. This value is used for calculations of defect concentrations.
Table 1. Structural properties of the deposited and annealed films. E (eV) – energy of the deposited Si atoms, ρ (g/cm3) – density, T- deposition temperature, Ta - annealing temperature (K), RSi-O is the length of the Si-O bonds, RO-O is the distance between nearest oxygen atoms (nm), α1 and α2 are O-Si-O and Si-O-Si angles (grad.), c – concentration (%), lower index indicates the coordination number of atom, τ - time of the deposition and annealing (ns).
The films density, concentrations of one- and three-coordinated oxygen atoms O1 and O3, concentration of the five-coordinated Si5 atoms vary most significantly under annealing. Respective values are marked as bold. The density reduces for 0.15 g/cm3 (Ta = 1300 K, τ = 4 ns). Based on the linear relation between density and refractive index [18], variation of the refractive index can be estimated as ≈0.03, which corresponds to the experimental value [19]. Values of concentrations c(O1) and c(O3) reduce nearly four times for E = 1 eV and three times for E = 10 eV. Concentration of the Si5 defects also reduces essentially. Noticeable variations of structural parameters are observed for the annealing temperatures 900 K and 1300 K.
Values of the Si-O bonds lengths do not change under annealing in the investigated interval of Ta and τ. Concentrations of Si5 defects are small both in deposited and annealed films. The average Si-O-Si angle increase results in the density decrease.
It is seen from the Table 1 that c(O1)≈c(O3), while c(Si3(5)) << c(O1(3)).A possible scheme of point defects formation that can explain these relations is shown in Fig. 2. Broking of the Si-O bond results in the formation of Si3 and O1 centers (Fig. 2(b)). The center Si3 forms covalent bond with the O2 center which results in the formation of the Si4 and O3 centers (Fig. 2 c).
Structural properties of the three internal film layers with the thickness of 10 nm are listed in Table 2.Noticeable variations of structural properties are observed only in the cases of Ta = 900 K and Ta = 1300 K as it is observed in the case of films as a whole (see Table 1). Structural parameters of the first layer (H = 10-20 nm) vary most significantly. The density of this layer reduces for ≈0.15 g/cm3at both energies of deposited Si atoms under the annealing with parameters Ta= 1300 K, τ = 4 ns.
Table 2. Structural properties of the sub-layers of deposited and annealed films, H (nm) is the vertical coordinate of sub-layer. Annealing time is τ = 4 ns. Other notations are as in the Table 1.
Concentrations of defects in deposited films reduce with H for both values of the Si atoms energy. In the annealed films similar dependence is observed only for E = 10 eV, while for the case of E = 1 eV the concentration of defects varies only slightly with H. For the case of 1 eV and Ta = 1300 K the concentrations of O1 and O3 defects reduce four times in the annealed film compared with the deposited one.
Results of calculation of the rings statistic are listed in Table 3. Numbers of rings with n = 2 and n>9 are small and respective results are not presented. Relative weights fn of n-membered rings are normalized to the total number of rings N: fn = Nn/N, where Nn is the number of n-membered rings. Duration of the annealing procedure for all Ta values is taken equal to 4 ns. The obtained distribution is in agreement with the earlier known results for silica glass [20].
Table 3. Rings statistic of n-membered rings for deposited and annealed films
For understanding of structural relaxation of deposited film, the variations of f3,4 values are the most essential ones. The geometry of chemical bonds is strained in the 3,4 – membered rings. The double reduction of the f3 values for the case of Ta = 1300 K indicates an essential relaxation of film structure for the both values of E. This result is in agreement with the increase of average Si-O-Si angle from 145° to 147° (Table 1). Note that 147° corresponds to the fused silica in the frame of DESIL force field.
The surface roughness varies only slightly under annealing procedure for all values of the Ta and 1 eV and 10 eV energies of deposited Si atoms (Table 4).
Table 4. Surface roughness of deposited and annealed films.
The density profiles of films are shown in Fig. 3. For both values of energies of deposited Si atoms the deposited film density reduces for ≈0.1 - 0.2 g/cm3.It can be seen from the density profiles (Fig. 3) that the deposited film thickness increases for ≈3 nm after annealing. This result is in agreement with the experimental observation [3,19]. Density of the deposited film for the case of E = 10 eV reduces with film thickness. This dependence almost disappears after the annealing procedure (Fig. 3, right part). Shape and thickness of the transition layer between film and gas phase do not vary after annealing.
Fig. 3 Density profiles of deposited and annealed films. Annealing temperature Ta = 1300 K, deposition temperature 300 K, annealing time τ = 4 ns, ρ(g/cm3), H (nm) is the distance from the substrate.
Results of the stress calculations are listed in Table 5. The obtained values of σxx and σyy are in the interval of experimental values [21]. Duration of the annealing procedure is taken equal to 4 ns. It is seen that annealing results in reducing of absolute values of σxx and σyy. This corresponds to the experimental data [19].
Table 5. Diagonal components of the stress tensor σxx(yy) (MPa) for deposited and annealed films.
4. Conclusion
The impact of thermal annealing on properties of IBS deposited SiO2 thin films is investigated using high-performance simulation based on the molecular dynamic approach with novel DESIL force field [5, 6].
It is found that the film density and concentrations of main types of point defects vary significantly under annealing with temperature 1300 K. Density of the films reduces for ≈0.15 g/cm3 which corresponds to the reduction of refractive index for Δn ≈0.03. Concentrations of point defects in deposited films decrease three or four times after annealing. Concentrations of the strained three- and four-membered rings are halved after annealing with the temperature of 1300 K. Components of the compressive stress tensor of deposited film decreases significantly.
Funding
Russian Science Foundation (grant number 14-11-00409).
References and links
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