Lei Wang*
College of Mathematics and Physics, Qingdao University of Science and Technology, Shandong Advanced Optoelectronic Materials and Technologies Engineering Laboratory, Qingdao 266061, China. E-mail: Phdwangl@163.com
First published on 16th September 2022
The spinodal instability and thermal nucleation mechanisms successfully describe the dewetting of metallic thin films. The previous research mainly focuses on homogeneous and continuous films. However, less attention is paid to the effect of random vacancy defects that frequently appear in actual situations on the film dewetting. In this work, the thermally-induced dewetting of a 0.4 nm thick ultrathin Ag film with different vacancy rate (f) ranging from 0.01 to 0.5 on a SiO2 substrate is investigated by the molecular dynamics (MD) simulation. Thermal nucleation and growth of holes appear in the dewetting process. The characteristic dewetting time (t) decreases dramatically with the increase of vacancy rate (f) of the Ag film. This is possibly because the presence of vacancy defects effectively reduce the incubation period of the initial holes, which is significant even for a very small vacancy rate less than 0.05.
In previous studies, the author noted that the as-deposited Ag, Ni, and In metallic films on SiO2 substrates with thickness below several nanometers generally contain random vacancy defects, such as nano-sized holes and nano-islands,13,14 which is fairly common due to the well-known island growth mode.15 The vacancy defects in the film have nonnegligible effects on the dewetting process. On the one hand, the van der Waals potential between interfaces in spinodal instability is difficult to be described by a concise analytic expression in the presence of vast vacancy defects. On the other hand, the vacancy defects in the film might affect the thermal nucleation process and change the triggering condition of dewetting. Therefore, it is necessary to detailedly study the dewetting behaviour of a thin metallic film with vacancy defects on a nonwetting substrate.
In this work, dewetting of an ultrathin Ag film with random vacancy defects on a SiO2 substrate is investigated by the molecular dynamics (MD) simulation. The number of vacancy defects appearing in the film is defined and regulated by the vacancy rate (f) that is in the range of 0.01–0.5 herein. The characteristic dewetting time (t) is systematacially analysed for different f by using a Minkowski measurement. It is found that, the characteristic dewetting time (t) of the Ag film decreases dramatically with the increase of vacancy rate (f). This is possibly because the presence of vacancy defects effectively reduce the incubation period of the initial holes and thus accelerate the dewetting. This kind of dewetting acceleration effect is significant even for a very small vacancy rate less than 0.05.
The initial temperature of the simulation is 300 K. The whole system was firstly heated from 300 K to 1500 K within 10 ps in NVT ensemble. Then, the heat preservation was implemented for 1 ns at 1500 K in NVT ensemble. The time step in simulation is 1 fs. The Nose–Hoover thermostat was adopted and the temperature damping parameter (Δt) was 0.1 ps (namely 100 timesteps) that was recommended by LAMMPS. Besides, the effect of temperature damping parameters (0.01 ps, 0.1 ps, and 1 ps) on the film dewetting time was inapparent (Fig. S1†). The film-substrate system with no atomic vacancy contains 37906 atoms, where the SiO2 substrate contains 27
540 atoms. The dewetting patterns over time were displayed with OVITO. By using the image processing software ImageJ, the top-view dewetting patterns were transformed into 8 bit greyscale images. Then, the area ratio (St) of the dewetted Ag to the initial Ag film was calculated at each moment using ImageJ to quantificationally estimate the dewetting evolution, which is a simplified Minkowski measure method.21 As for the final stable dewetted patterns at 300 ps, the area ratio is S′. Herein, the characteristic dewetting time (t) was defined as the earliest moment when∣(St − S′)/S′| < 10% is satisfied.
Fig. 2a–i show the time-dependent dewetting evolution of the Ag thin film without vacancy defects within 300 ps. The Ag thin film is rapidly liquefied and becomes disordered through heating. In this process, some atomic vacancy defects arise (circle A in Fig. 2b) and also disappear randomly, and a few vacancy defects can form small initial holes (circle B in Fig. 2c). Such an initial hole will rapidly grow (circle C in Fig. 2d) and finally rupture the film. Thermal nucleation and growth of holes are clearly shown in the above film dewetting process. In order to quantitatively describe this process, 8 bit greyscale images at each moments were obtained as shown in Fig. 2j as an example, and then the area ratio (St) of the dewetted Ag to the initial Ag film was calculated from 0 ps to 300 ps (Fig. 2k). As shown in Fig. 2k, St firstly presents a plateau and secondly shows a dramatic decrease, and finally achieves a stable value. In fact, the variation of St completely describe the film dewetting. The plateau of St corresponds to the incubation period (τ0) of an initial hole, which is about 100 ps (Fig. 2k) for the perfect Ag film (Fig. 2a). The dramatic decrease stage of St corresponds to the hole growth and film rupture process from 110 ps (Fig. 2d) to 240 ps (Fig. 2h). After t = 240 ps, the variation of dewetting patterns is unconspicuous and the stable pattern is achieved at 300 ps, namely S′ = 19.0 (Fig. 2k). Because the error between St (240 ps) and S′ is less than 10%, the characteristic dewetting time (t) of the Ag film without vacancy defects is 240 s according to the definition stated in the section of Simulation method.
As shown in Fig. 3a, the vacancy defects were introduced into the initial Ag thin film by randomly removing small cylinders with 0.2 nm in radius from the film, where the distances between adjacent removed cylinders are totally random. The vacancy rate (f) is defined as the number ratio of the surviving Ag atoms to the initial Ag atoms. It should be noted that the heights of the film and the cylinder are both 0.4 nm containing 3 layers of Ag atoms, which can be proved by the film morphologies as shown in panel I of Fig. 3b–e before the procedure of energy minimization. After the energy minimization in LAMMPS, stable film structures with different f are obtained, where some vacancy defects vanish and some grow in volume. As shown in panel II of Fig. 3b–d with f ≤ 0.5, the stable Ag film is connected inside. This kind of film structure is very common in real metallic nano-films prepared by magnetron sputtering, electronic beam evaporation and other techniques, which will rupture in film dewetting. This kind of film is the focus of this paper. Besides, when f > 0.5, as shown in panel II of Fig. 3e, the film gradually becomes island shaped. This kind of island-shaped film generally presents also an aggregation behaviour in addition to rupture in film dewetting, thus it is not the focus of this paper. As for the Ag film with f ≤ 0.5 after energy minimization, the atom number density along the thickness direction is calculated (Fig. 3f). The decrease of atom number density for 0.01 ≤ f ≤ 0.5 is mainly due to the existence of vacancy defects. The height of top layer is about 5.5 nm and its atom number density shows a monotone decrease with an increase in f. By comparing the three peaks of the atom density, the atoms on top layer are more easily to migrate from their initial positions. In this work, the film after energy minimization with LAMMPS shown in panel II of Fig. 3 was considered as the initial stage in film dewetting. It should be noted that, this initial pattern may not be universal since the distribution of vacancies may have some spatial bias during the real fabrication by different techniques although the actual process leads to the same overall vacancy rate of the random distribution in panel I, which the author defines as the number ratio of the surviving Ag atoms to the initial Ag atoms.
Fig. 4 detailedly display the time-dependent film dewetting evolution for different f. The case of f = 0 has been analysed above. As shown in Fig. 4b, for f = 0.01, the vacancy defects disappear within 40 ps (Fig. 4b(II)) rather than directly form a hole. As shown in Fig. 4b(IV), the incubation period (τ0) of its initial hole is less than 100 ps that is shorter than the case of f = 0 by comparing Fig. 4a(IV) and b(IV). For f = 0.02, the vacancy defects also disappear within 40 ps, but the incubation period (τ0) of its initial hole further reduces to less than 80 ps. For f > 0.04, the area of vacancy defects is large, in which case, the initial hole is directly formed with a negligible τ0 and fast film rupture happens. Obviously, the characteristic dewetting time (t) shows a significant decrease when f increases from 0 to 0.5 (Fig. 4a–g).
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Fig. 4 The dewetting pattern evolution over time of the Ag film with different f of 0 (a), 0.01 (b), 0.02 (c), 0.04 (d), 0.1 (e), 0.3 (f) and 0.5 (g). |
Similar to Fig. 2k, the functions of area ratio (St) versus time are also obtained for different f ranging from 0 to 0.5. As shown in Fig. 5a, when f increases from 0 to 0.1, the plateau of the plot becomes shorter and in other words the incubation period (τ0) of its initial hole gradually shortens. The decrease of τ0 dramatically accelerate the film dewetting process, which is also clearly revealed in Fig. 4. As shown in Fig. 5b, the characteristic dewetting time (t) rapidly decreases from 240 ps down to 120 ps for 0 < f< 0.1. For f = 0.4 and f = 0.5, the characteristic dewetting time (t) is only about 80 ps.
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Fig. 5 (a) The function of area ratio St versus time with different f; (b) the characteristic dewetting time (t) of the 0.4 nm thick Ag film with different f. |
In this simulation work, the spatially-correlated particle array was not observed in the film dewetting process. The interaction between the Ag film and the SiO2 substrate is relatively weak compared with the surface tension within the Ag film, in which case, the characteristic length (or the particle distance) in film dewetting tends to be a large value. This might be able to explain the formation of final single drop for all cases in the simulation using a small model with a transverse size of 15 nm. The author speculates that a spatially-correlated particle array will be observed if a larger model is adopted in the simulation. Previous experimental and theoretical researches indicate that the characteristic dewetting time (t) depends on the film thickness. This work further shows that vacancy defects contained in the film also have significant effect on τ, even if the vacancy rate (f) is less than 0.05. Actually, vacancy defects exist widely in a real thin metallic film system and this effect might describe a more realistic dewetting process thus has practical significances. The simulation indicates that the incubation period of an initial hole reduces dramatically with an increase in f, which might be a key point that speeds up the film dewetting. This result also confirms the importance of thermal nucleation of holes in a film dewetting process. Besides, the nanosecond laser pulse is generally regarded as a necessity to trigger metallic film dewetting.2,22 However, this simulation indicates that a picosecond laser pulse might be also an possible heating tool to achieve thin film dewetting in the presence of vast vacancy effects.
Footnote |
† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ra03137j |
This journal is © The Royal Society of Chemistry 2022 |