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Surface properties of film deposition using molecular dynamics simulation
Surface & Coatings Technology 201 (2006) 1796 – 1804 www.elsevier.com/locate/surfcoat
Surface properties of film deposition using molecular dynamics simulation Ching-Jiung Chu, Tei-Chen Chen ⁎ Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan Received 13 August 2005; accepted in revised form 7 March 2006 Available online 19 April 2006
Abstract The morphology of growing film by the sputtering process is studied with molecular dynamics (MD) simulation. We focus on the roughness and layer coverage for diverse deposition process parameters including substrate temperature, deposition rate, incident energy and incident angle. This paper presents the effect of different substrate sizes. The results of simulation show smaller roughness and better layer coverage at low substrate temperature of 500 K and high incident energy of 10–15 eV. The film–substrate system becomes rapidly stabilized at the end of deposition. Our simulation shows that thin films can also grow with two-dimensional layer-by-layer-like way for larger size of substrate at room temperature. These simulated results are consistent with both earlier MD simulations and experimental observation. © 2006 Elsevier B.V. All rights reserved. Keywords: Molecular dynamics; Roughness; Layer coverage; Deposition process parameters; Substrate sizes
1. Introduction The growth of thin films on substrate has become a field of much current research, because of the fabrication of many modern devices. A large variety of techniques can be used to grow thin films. The morphology and coverage of thin films grown by the sputtering process was investigated with the twodimensional molecular dynamics (MD) simulation in the study of Ju et al. [1]. They found that there exists an optimal deposition rate region at specific incident energy for the best film quality. Nevertheless, two-dimensional simulation is not enough to model the three-dimensional atomic motions in the real deposition process. There are other ways to grow thin films, such as pulsed laser deposition (PLD) [2], ionized cluster beam deposition (ICBD) [3–6], cluster deposition [7–9] and chemistry vapor deposition (CVD) for non-conductor film [10,11]. The growing mechanisms of thin films are difficult to understand only from experiments because they are not
⁎ Corresponding author. Tel.: +886 6 275 7575 62168; fax: +886 6 235 2973. E-mail addresses: [email protected] (C.-J. Chu), [email protected] (T.-C. Chen). 0257-8972/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2006.03.014
sufficient to analyze thin-film morphology in detail. Therefore, some numerical methods have been developed to investigate the growing mechanisms of thin films. The method of MD simulation is a powerful tool to investigate the growth of thin films and has been presented in a number of excellent books [12,13]. In previous research, Schneider, Rahman and Schuller [14] studied the epitaxial growth of thin films as a function of substrate temperature and deposition rate, and found that the growth of films is well-ordered for all substrate temperatures. Gilmer et al. [15] investigated the morphologies of the deposited films with MD simulation in different vapor temperature, substrate temperature, incident energy and incident angle at a constant deposition flux. Gilmore and Sprague [16] studied the influence of incident energy on surface coverage and defect formation at room temperature of 300 K and a constant deposition rate, but only three deposited layers were included in their model. The effects of substrate temperature and incident energies on the growth of Cu atoms onto a Cu substrate by pulsed laser deposition were studied by Yue et al. [2]. They found that these two factors can promote the mobility of surface atoms and lead to smooth growth of films at lower substrate temperature. In order to obtain films of high quality, we need to understand the relation between the configurations of the
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growing films and various parameters of the film process, especially the effect of incident energy and substrate temperature on the growth of films. Smooth surface and perfect structure, generally, are basic requirement for the film technology of fabrication of many modern micro-devices such as optic thin films, microsensors/micro-actuators, superconductors, very large-scale integrated (VLSI) circuits, etc. Therefore, it is important to know how to obtain smooth layer-by-layer growth of thin films. Kelchner and DePristo [17] calculated the interface width to measure the roughness of the surface for various deposition rates of Pd/Pd (001) and Cu/Cu (001), and discussed the effect of varying the size of the system. The configurations of the growing films for different substrate sizes, however, were not presented. Evans [18] studied the layer coverage of the growing films as a function of time steps and the relative coverage of the adjacent layers by random deposition, and indicated that growth of successive layers becomes increasingly less layer-by-layer-like. Trushin et al. [19] investigated the total coverage for the growth of the first five Ag layers (1–5) on Cu substrate as a function of time steps at incident energy of 7 eV by MD simulations and observed a well-ordered growth of an Ag film on the Cu substrate, close to layer-by-layer mode. Robbemond and Thijsse [20] evaluated the topography of the deposited film in evaporation process with low incident energy by using MD. Kelchner and DePristo [21] investigated the surface
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topographies of thin films with low energy cluster deposition at a substrate temperature of 0 K. Iizuka and Hoshide [22] simulated the morphologies of the growing films at different substrate temperature using MD with Morse potential. Zhang et al. [23] studied film stress as a function of incident ion energy and mechanisms of diverse ion energy in carbon thin films grown by ion-beam deposition using MD simulations. In the work of Zhang et al. [24], the growing structures of hydrogenated carbon films were simulated by MD and experimental studies showed that the film surface is smooth and its root-mean-square roughness is ranged within 0.13–0.17 nm by using atomic force microscopy. From the results of above literature, we are interested to gain an insight into the mechanism of film deposition and then investigate how to deposit thin film structure with smaller surface roughness and higher layer coverage. In this article, we investigate the morphologies, surface roughness in three different definitions and layer coverage of the growing films under different deposition conditions in the system of Cu on Cu (001) substrate using MD simulations. We obtain a physical morphology of the growing mechanism by the observation of the atomic movement during film deposition. Consequently, we know how to achieve a smooth film with high quality by selecting suitable process parameters. In the next section, the method of MD simulations is briefly introduced. Some important results of numerical simulations are presented
Fig. 1. The growing film morphology of substrate size of (10 × 10 × 5) unit cells at substrate temperature of 500 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms/ps at 300 ps. The color of atoms represents incidence in sequence while the blue denotes substrate atoms and each color has the number of one-layer atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 1 The number of deposited atoms in the growing thin films for different deposition time, in the case of substrate size of (10 × 10 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV and 15 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms per 1 ps Deposition time (ps)
Incident energy 5 eV/15 eV Total
1st ML
2nd ML
3rd ML
4th ML
5th ML
6th ML
50.00 100.00 150.00 200.00 250.00 300.00
195/196 395/397 595/597 791/797 994/997 998/1000
170/176 200/200 200/200 200/200 200/201 200/200
25/20 158/175 199/200 200/200 200/199 200/200
0/0 37/22 163/170 198/200 200/202 200/200
0/0 0/0 33/27 155/172 199/202 199/200
0/0 0/0 0/0 38/25 160/172 162/174
0/0 0/0 0/0 0/0 35/21 37/26
and discussed in Section 3. Finally, conclusions are given in Section 4. 2. Simulation model In this study, three-dimensional MD simulations and classical NVT ensemble (constant particle number N, constant volume V and constant temperature T) are adopted to investigate the atomistic behavior during film deposition. The substrate consists of 10 atomic layers and the lowermost one is fixed, while the upper two layers of substrate are entirely free to transmit energy freely with the deposited atoms. The other layers are assigned as the thermal control layers where the velocities of all atoms are rescaled at each time step according to the prescribed substrate temperature. Periodic boundary conditions are imposed on the surface plane along the directions of x and y, respectively. Moreover, non-periodic boundary conditions are applied to the direction z perpendicular to the surface plane. Molecular dynamics simulation with a many-body potential is one of powerful methods to investigate the mechanism of the growing films. In our MD simulations, the equations of motion are solved through the Gear's five-order predictorcorrector algorithm [13] with a constant time step of t = 5 fs and the interaction potential between atoms in the system is described with embedded-atom method (EAM) [25,26], the functional dependencies proposed by Johnson [27] in 1988 are employed. The EAM potential is a many-body potential based on density function theory (DFT) and especially suitable for metals. Initial velocities of substrate particles are randomly selected from a Maxwell's velocity distribution [13]. A new incident atom is placed at the height of 10-fold lattice length above the substrate surface plane with random x- and ycoordinates. The incident atom possesses an incident kinetic energy of 5 or 10 or 15 eV with random incident angle within the maximum value, ranged from 0° to 36°. Three different substrate temperatures of 300 K, 500 K and 800 K are used in simulation. The “main system” of simulation is defined as the condition of substrate size of (10 × 10 × 5) unit cells, substrate temperature of 300 K, incident energy of 5 eV per atom, maximum random incident angle of 18° and deposition rate of 4 atoms/ps. The other simulation models can be established by changing only one of deposition parameters of the main system, or the substrate size: (5 × 5 × 5) unit cells, (10 × 10 × 5) unit cells and (20 × 20 × 5) unit cells, while the
other parameters remain unchanged. All of MD simulation models are deposited totally five layers. The largest models are composed of 20 × 20 × 2 × (10 + 5) = 12,000 atoms and take 1000 ps at least to finish the deposition process. 3. Results and discussion 3.1. Morphology of thin films The morphologies and the growing mechanisms of deposited films under different conditions are evaluated and discussed as follows. Fig. 1 shows the final film configuration of substrate size of (10 × 10 × 5) unit cells at constant-temperature of 500 K at 300 ps. In Fig. 1, 1000 atoms are deposited in six film layers on substrate with two-dimensional layer-by-layer-like growth. The coverage in the first five film layers is about 4.83 ML and only 0.17 ML coverage in the sixth layer. This result is well consistent with Thornton's study [28], which showed that higher substrate temperature will promote layer-by-layer-like growth of film structure. Moreover, it is seen that only one atom of substrate moves to the first film layer. Therefore, some
Fig. 2. The growing film morphology of substrate size of (20 × 20 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms/ps at 1050 ps. The color of atoms represents incidence in sequence while the blue denotes substrate atoms and each color has the number of one-layer atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
C.-J. Chu, T.-C. Chen / Surface & Coatings Technology 201 (2006) 1796–1804 Table 2 The number of deposited atoms in the growing thin films for different deposition time, in the case of substrate size of (20 × 20 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms per 1 ps Deposition Total 1st ML 2nd ML 3rd ML 4th ML 5th ML 6th ML time (ps) 200.00 400.00 600.00 800.00 1000.00 1050.00
793 1589 2381 3175 3984 3988
666 794 800 800 800 800
127 640 792 800 800 800
0 155 617 790 800 800
0 0 172 610 798 799
0 0 0 175 620 622
0 0 0 0 166 167
substrate atoms will probably move to film layers at temperature higher than 500 K. The detailed exchange of film–substrate atoms will be presented and discussed in the future work. Table 1 shows that higher incident energy of sputtering atom is more beneficial for layer-by-layer growth of film structure. Qiang's study [29] also indicated that larger incident energy can produce smoother film surface. Two atoms are deposited in the seventh film layer at incident energy of 5 eV and substrate temperature of 300 K (see Table 1). There is 4.87 ML coverage in the first five film
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layers at incident energy of 15 eV from Table 1 and it shows higher layer coverage in comparison with Fig. 1. Consequently, to improve layer coverage, selection of larger incident energy is more effective than higher substrate temperature. From above results, a film structure of high quality may be obtained by properly enhancing incident energy and substrate temperature. Fig. 2 and Table 2 show the morphology of deposited film at larger substrate and the number of deposited atoms in each film layer after some specific deposition time. The results indicate that thin films can also grow with two-dimensional layer-bylayer-like way at larger size of substrate. From Table 2, the coverage in the first five layers is about 4.776 ML and 12 atoms are not well deposited in the first six film layers, where six atoms of them are adsorbed in the seventh layer while six atoms are desorbed. The average kinetic energy of exposed atoms on the film surface represents the temperature of film surface. In other words, higher average kinetic energy corresponds to better thermal diffusion or mobility, which is helpful to produce the smoother film surface. Fig. 3a shows the exposed atoms on the film surface have better ability of migration at higher substrate temperature. The average kinetic energy increases when
Fig. 3. Average kinetic energy of exposed atoms versus monolayer of evolution (time dependence) in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other process parameters of all cases are the parameters of main system defined in Section 2.
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Fig. 4. Average kinetic energy of exposed atoms versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
incident atoms are adsorbed on the film–substrate surface and then decreases gradually due to the energy exchange. This leads to the phenomenon of energy oscillation (see Fig. 3). The oscillation of the average kinetic energy increases after 3 ML deposition. The average kinetic energy then reduces rapidly and film–substrate system becomes stabilized when all
of incident atoms have finished sputtering and are adsorbed on the film surface. In Fig. 3d, the average kinetic energy is smaller without significant oscillation (surface atoms move stably at any time step) at lower deposition rate of 0.5 atom per 1 ps during film deposition. The exposed atoms of film surface possess better ability of migration at higher deposition rate of 4 atoms per 1 ps. Fig. 3b indicates that the curve does not show acute oscillation at incident energy of 15 eV during film deposition. The average kinetic energy at 15 eV, however, is not larger than 10 eV after 2 ML deposition. The variation of average kinetic energy is insignificant for different value of maximum incident angle and the oscillation of curve becomes smaller at vertical incidence (Fig. 3c). The influence of substrate size on the average kinetic energy is shown in Fig. 4. The mobility of surface atoms is better at smaller substrate scale, but it becomes smaller and more uniform at larger substrate size of (20 × 20 × 5) unit cells during film deposition. 3.2. Coverage of the growing film In this section, the characteristics of film growth are investigated and discussed by evaluating the variation of
Fig. 5. Number of deposited atoms at 4–6 layers versus time of evolution in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other process parameters of all cases are the parameters of main system defined in Section 2.
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Fig. 6. Coverage of film layers versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
coverage rate. We are interested in the coverage of each film layer under different deposition conditions because the defects in materials will affect the conductivity, optical properties and mechanical properties significantly. Liang and Shi [30] indicated that thermal conductivity of materials decreases with the reduction of the number of atomic layers, which has been confirmed by many experiments. Fig. 5 shows the number of adatoms at 4–6 layers varies with time while first 1–3 layers have completely filled with 200 atoms in each layer. From Fig. 5a, it is seen that the layer coverage is better at substrate temperature of 500 K. The number of atoms in the sixth layer reaches its maximum at substrate temperature of 800 K due to the higher average kinetic energy. In other words, the roughness of surface becomes larger. In the experimental work of Wang et al. [31], it was reported that increasing temperature of the deposition will cause the smooth Fe film to break up and nano-scale Fe islands are sequentially formed. Therefore, the film deposition under higher temperature more than 500/600 K may be
disadvantageous to the smoothness of the film layers. Fig. 5b indicates that the layer coverage becomes better at higher incident energy of 15 eV. However, the layer coverages are very close for incident energy of 10 eV and 15 eV. Therefore, higher layer coverage may be accomplished by adopting temperature of 500 K and incident energy of 10 eV per atom. Fig. 5c shows that the layer coverage is insensitive to the maximum incident angles. The fourth layer exhibits coverage of 100% only for vertical incidence. In fact, columnar structural growth of film will be easily formed in case the incident angle is more than 45 degree. As shown in Figs. 3d and 5d, the layer coverage becomes better at higher deposition rate due to the higher average kinetic energy. The coverage in each layer and total coverage of all layers as a function of time steps for different substrate sizes are shown in Fig. 6. The steeper curve of layer coverage represents more well-layered growth. The layer coverage becomes better for smaller substrate size by observing the film growth of 4–6 layers.
Fig. 7. (a) Relative coverage of two adjacent film layers at constant substrate temperature of 500 K. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
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Fig. 8. (a) Relative coverage of two adjacent film layers at incident energy of 10 eV per atom. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
A different representation of the layer coverage is provided through Figs. 7–9, which shows the relation of coverage at two adjacent layers. Fig. 7b indicates that the coverage in the first layer already reaches to 60% when the second layer just starts to grow at substrate temperature of 500 K. Fig. 8b shows that 0.7 ML coverage in the first layer has been attained when the second layer begins to grow at incident energy of 10 eV. Moreover, the coverage in layer i + 1 is only 0.1 ML to 0.2 ML when 0.9 ML coverage in layer i has already been attained, where 1 ≤ i ≤ 4. We can obtain a well-ordered growth of films in near layer-by-layer way at substrate temperature of 500 K and incident energy of 10 eV. Compare Fig. 9 with Fig. 7 or 8, it can be seen that, although the sound layer coverage can be obtained at the end of deposition, the helpfulness of well-layered growth is not significant for vertical incidence. These results indicate that the growth of successive layers is gradually less welllayered because the atoms easily troop together in successively higher layers. This is in agreement with the simulation results evaluated by Evans [18].
3.3. Surface roughness Three different definitions are used to quantify the surface roughness on the growing films as a function of time. They are respectively calculated as follows: Rmax ¼ Zimax −Zimin ; n X jZi −Z¯ j Ra ¼
Rq ¼
ð1Þ
i¼1
; n vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX n 2 u u Zi −Z¯ t i¼1
n
ð2Þ
;
ð3Þ
where Rmax is the maximum roughness, Ra is the center-line average roughness, Rq is the root-mean-square roughness, Zi represents the height of the exposed atoms on the film surface,
Fig. 9. (a) Relative coverage of two adjacent film layers with vertical incidence for all sputtering atoms. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
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Fig. 10. Time evolution of three different roughness of surface at the process parameters of main system defined in Section 2.
Zimax represents the maximum value of Zi, Zimin represents the minimum value of Zi, Z¯ represents the mean height of all the exposed atoms and n is the total number of exposed atoms at a specific time step. Fig. 10 shows three different roughness of surface in the MD simulation of main system defined in previous section.
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The maximum roughness represents the distance between the highest and the lowest position of surface atoms along the vertical direction. The value of peak is about one lattice length in the curve of maximum roughness. And the value of trough i, which implies that layer i has been already filled with particles, is about half of lattice length for 1 ≤ i ≤ 3. Since the fourth trough cannot be seen through the curve of maximum roughness, it means the fourth film layer is not filled, which is consistent with the condition of 5 eV shown in Table 2. The meaning of troughs is the same as the maximum roughness for two kinds of average roughness (Ra and Rq), and we find that the shorter the distance between peak and trough the more the film layer not filled yet. The oscillated aspect of surface roughness in Fig. 10 is in agreement with the experimental observation by Giergiel et al. [32], which showed that surface roughness tends to oscillate around the average value for ultrathin Fe films on Cu substrate and the films were found to grow in a good layer-by-layer mode at room temperature. The surface roughness rapidly reaches to a constant value at the end of deposition. The discrepancy between Ra and Rq is very small, but Ra < Rq. Moreover, Rmax is about fourfold of Ra or Rq, in agreement with the experimental work. Consequently, only the behaviors of Rq are shown hereafter.
Fig. 11. Time evolution of root-mean-square roughness in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other parameters of all cases are the parameters of main system defined in Section 2.
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reduce surface roughness. Regarding the effect of substrate size, if we wish to obtain a better quality of film structure at larger substrate, a suitable enhancement on incident energy or temperature shall be provided. Moreover, all the simulation results, presented in this article, are qualitatively consistent with both earlier MD and experimental work. It is believed that the results may provide a solid guide for the selection of process parameters in the deposition of thin film structure. Acknowledgments
Fig. 12. Root-mean-square roughness versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
Fig. 11 shows the root-mean-square roughness as a function of time. The roughness is smaller at substrate temperature of 500 K (Fig. 11a) as well as at incident energy of 15 eV (Fig. 11b). The discrepancy in roughness, however, is very small for energy of 10 eV and 15 eV. Therefore, smoother surface may be obtained by adopting low temperature of 500 K and high energy of 10–15 eV. Fig. 11c indicates that the influence of maximum incident angle on the surface roughness is very small during film deposition. The roughness tends to be smaller at higher deposition rate (see Fig. 11d). The effect of the substrate size is shown in Fig. 12. It is seen that during film deposition the smaller the size the smaller the roughness. In general, the root-mean-square roughness is about 0.1–0.12 nm after the film deposition for different conditions and this quantity is equivalent to experimental results of Ref. [24]. 4. Conclusion This paper investigates the morphologies, surface roughness and layer coverage of thin film structure under different deposition conditions in the epitaxial growth of Cu-single crystals using MD simulation with EAM potential. The simulation results show that films may grow with twodimensional quasi-layer-by-layer mode under appropriate deposition conditions even for larger size of substrate. If the temperature of substrate becomes too high in our MD simulations, it will be less helpful for layer coverage and surface roughness due to the limited enhancement of surface diffusion. Moreover, larger incident energy may be more effective to produce smoother surface rather than higher substrate temperature in the results of simulations. Better layer coverage and smaller surface roughness may thus be obtained at low substrate temperature of 500 K and high incident energy of 10–15 eV. On the other hand, the effect of maximum random incident angle, which is not in excess of 45 degree, is not significant. It is clear that higher deposition rate is helpful to increase layer coverage and
The authors gratefully acknowledge the support of the National Science Council of Taiwan, ROC (Grant No, NSC 922212-E-006-020). References [1] S.P. Ju, C.I. Weng, J.G. Chang, C.C. Hwang, Surf. Coat. Technol. 149 (2002) 135. [2] Y. Yue, Y.K. Ho, Z.Y. Pan, R.W. Lee, Z.Y. Man, J. Xie, Phys. Lett., A 235 (1997) 267. [3] K. Yorizane, Y. Yamamuia, Comput. Mater. Sci. 14 (1999) 241. [4] Z. Insepov, I. Yamada, Nucl. Instrum. Methods Phys., B 153 (1999) 199. [5] H. Usui, I. Yamada, T. Takagi, J. Vac. Sci. Technol., A 4 (1986) 52. [6] T. Takagi, Ionized Cluster Beam Deposition and Epitaxy, Noyes, Park Ridge, New Jersey, 1988. [7] J.Q. Xie, J.Y. Feng, H.W. Lu, Model. Simul. Mater. Sci. Eng. 7 (1999) 289. [8] L. He, Z. Xia, H. Zhang, J. Feng, Y. Lu, Model. Simul. Mater. Sci. Eng. 6 (1998) 709. [9] R. Lee, Z. Pan, Y. Ho, Phys. Rev., B 53 (1996) 4156. [10] W.N.G. Hitchon, Plasma Processes for Semiconductor Fabrication, Cambridge University Press, London, 1999. [11] A.A.R. Elshabini, F.D. Barlow, Thin Film Technology Handbook, McrawHill, New York, 1998. [12] D. Frenkel, B. Smit, Understanding Molecular Simulations, Academic, New York, 1996. [13] J.M. Haile, Molecular Dynamics Simulation, John Wiley and Sons, Inc., New York, 1992. [14] M. Schneider, A. Rahman, I.K. Schuller, Phys. Rev. Lett. 55 (1985) 604. [15] G.H. Gilmer, M.H. Grabow, A.F. Bakker, Mater. Sci. Eng., B 6 (1990) 101. [16] C.M. Gilmore, J.A. Sprague, Phys. Rev., B 44 (1991) 8950. [17] C.L. Kelchner, A.E. DePristo, Surf. Sci. 393 (1997) 72. [18] J.W. Evans, Phys. Rev., B 39 (1989) 5655. [19] O.S. Trushin, K. Kokko, P.T. Salo, Surf. Sci. 442 (1999) 420. [20] A. Robbemond, B.J. Thijsse, Nucl. Instrum. Methods Phys. Res., B 127– 128 (1997) 273. [21] C.L. Kelchner, A.E. DePristo, Nanostruct. Mater. 8 (1997) 253. [22] T. Iizuka, T. Hoshide, JSME Ser., A 42 (1999) 334. [23] S. Zhang, H.T. Johnson, G.J. Wagner, W.K. Liu, K.J. Hsia, Acta Mater. 51 (2003) 5211. [24] S. Zhang, G. Wagner, S.N. Medyanik, W.K. Liu, Y.H. Yu, Y.W. Chung, Surf. Coat. Technol. 177–178 (2004) 818. [25] M.S. Daw, M.I. Baskes, Phys. Rev. Lett. 50 (1983) 1285. [26] M.S. Daw, M.I. Baskes, Phys. Rev., B 29 (1984) 6443. [27] R.A. Johnson, Phys. Rev., B 37 (1988) 3924. [28] J.A. Thornton, J. Vac. Sci. Technol. 11 (1974) 666. [29] Y. Qiang, Y. Thurner, T. Reiners, O. Rattunde, H. Haberland, Surf. Coat. Technol. 100 (1998) 27. [30] X.G. Liang, B. Shi, Mater. Sci. Eng., A 292 (2000) 198. [31] W.T. Wang, D.Y. Guan, G. Yang, G.Z. Yang, Y.L. Zhou, H.B. Lu, Z.H. Chen, Thin Solid Films 471 (2005) 86. [32] J. Giergiel, J. Shen, J. Woltersdorf, A. Kirilyuk, J. Kirschner, Phys. Rev., B 52 (1995) 8528.
Surface properties of film deposition using molecular dynamics simulation Ching-Jiung Chu, Tei-Chen Chen ⁎ Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan Received 13 August 2005; accepted in revised form 7 March 2006 Available online 19 April 2006
Abstract The morphology of growing film by the sputtering process is studied with molecular dynamics (MD) simulation. We focus on the roughness and layer coverage for diverse deposition process parameters including substrate temperature, deposition rate, incident energy and incident angle. This paper presents the effect of different substrate sizes. The results of simulation show smaller roughness and better layer coverage at low substrate temperature of 500 K and high incident energy of 10–15 eV. The film–substrate system becomes rapidly stabilized at the end of deposition. Our simulation shows that thin films can also grow with two-dimensional layer-by-layer-like way for larger size of substrate at room temperature. These simulated results are consistent with both earlier MD simulations and experimental observation. © 2006 Elsevier B.V. All rights reserved. Keywords: Molecular dynamics; Roughness; Layer coverage; Deposition process parameters; Substrate sizes
1. Introduction The growth of thin films on substrate has become a field of much current research, because of the fabrication of many modern devices. A large variety of techniques can be used to grow thin films. The morphology and coverage of thin films grown by the sputtering process was investigated with the twodimensional molecular dynamics (MD) simulation in the study of Ju et al. [1]. They found that there exists an optimal deposition rate region at specific incident energy for the best film quality. Nevertheless, two-dimensional simulation is not enough to model the three-dimensional atomic motions in the real deposition process. There are other ways to grow thin films, such as pulsed laser deposition (PLD) [2], ionized cluster beam deposition (ICBD) [3–6], cluster deposition [7–9] and chemistry vapor deposition (CVD) for non-conductor film [10,11]. The growing mechanisms of thin films are difficult to understand only from experiments because they are not
⁎ Corresponding author. Tel.: +886 6 275 7575 62168; fax: +886 6 235 2973. E-mail addresses: [email protected] (C.-J. Chu), [email protected] (T.-C. Chen). 0257-8972/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2006.03.014
sufficient to analyze thin-film morphology in detail. Therefore, some numerical methods have been developed to investigate the growing mechanisms of thin films. The method of MD simulation is a powerful tool to investigate the growth of thin films and has been presented in a number of excellent books [12,13]. In previous research, Schneider, Rahman and Schuller [14] studied the epitaxial growth of thin films as a function of substrate temperature and deposition rate, and found that the growth of films is well-ordered for all substrate temperatures. Gilmer et al. [15] investigated the morphologies of the deposited films with MD simulation in different vapor temperature, substrate temperature, incident energy and incident angle at a constant deposition flux. Gilmore and Sprague [16] studied the influence of incident energy on surface coverage and defect formation at room temperature of 300 K and a constant deposition rate, but only three deposited layers were included in their model. The effects of substrate temperature and incident energies on the growth of Cu atoms onto a Cu substrate by pulsed laser deposition were studied by Yue et al. [2]. They found that these two factors can promote the mobility of surface atoms and lead to smooth growth of films at lower substrate temperature. In order to obtain films of high quality, we need to understand the relation between the configurations of the
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growing films and various parameters of the film process, especially the effect of incident energy and substrate temperature on the growth of films. Smooth surface and perfect structure, generally, are basic requirement for the film technology of fabrication of many modern micro-devices such as optic thin films, microsensors/micro-actuators, superconductors, very large-scale integrated (VLSI) circuits, etc. Therefore, it is important to know how to obtain smooth layer-by-layer growth of thin films. Kelchner and DePristo [17] calculated the interface width to measure the roughness of the surface for various deposition rates of Pd/Pd (001) and Cu/Cu (001), and discussed the effect of varying the size of the system. The configurations of the growing films for different substrate sizes, however, were not presented. Evans [18] studied the layer coverage of the growing films as a function of time steps and the relative coverage of the adjacent layers by random deposition, and indicated that growth of successive layers becomes increasingly less layer-by-layer-like. Trushin et al. [19] investigated the total coverage for the growth of the first five Ag layers (1–5) on Cu substrate as a function of time steps at incident energy of 7 eV by MD simulations and observed a well-ordered growth of an Ag film on the Cu substrate, close to layer-by-layer mode. Robbemond and Thijsse [20] evaluated the topography of the deposited film in evaporation process with low incident energy by using MD. Kelchner and DePristo [21] investigated the surface
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topographies of thin films with low energy cluster deposition at a substrate temperature of 0 K. Iizuka and Hoshide [22] simulated the morphologies of the growing films at different substrate temperature using MD with Morse potential. Zhang et al. [23] studied film stress as a function of incident ion energy and mechanisms of diverse ion energy in carbon thin films grown by ion-beam deposition using MD simulations. In the work of Zhang et al. [24], the growing structures of hydrogenated carbon films were simulated by MD and experimental studies showed that the film surface is smooth and its root-mean-square roughness is ranged within 0.13–0.17 nm by using atomic force microscopy. From the results of above literature, we are interested to gain an insight into the mechanism of film deposition and then investigate how to deposit thin film structure with smaller surface roughness and higher layer coverage. In this article, we investigate the morphologies, surface roughness in three different definitions and layer coverage of the growing films under different deposition conditions in the system of Cu on Cu (001) substrate using MD simulations. We obtain a physical morphology of the growing mechanism by the observation of the atomic movement during film deposition. Consequently, we know how to achieve a smooth film with high quality by selecting suitable process parameters. In the next section, the method of MD simulations is briefly introduced. Some important results of numerical simulations are presented
Fig. 1. The growing film morphology of substrate size of (10 × 10 × 5) unit cells at substrate temperature of 500 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms/ps at 300 ps. The color of atoms represents incidence in sequence while the blue denotes substrate atoms and each color has the number of one-layer atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Table 1 The number of deposited atoms in the growing thin films for different deposition time, in the case of substrate size of (10 × 10 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV and 15 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms per 1 ps Deposition time (ps)
Incident energy 5 eV/15 eV Total
1st ML
2nd ML
3rd ML
4th ML
5th ML
6th ML
50.00 100.00 150.00 200.00 250.00 300.00
195/196 395/397 595/597 791/797 994/997 998/1000
170/176 200/200 200/200 200/200 200/201 200/200
25/20 158/175 199/200 200/200 200/199 200/200
0/0 37/22 163/170 198/200 200/202 200/200
0/0 0/0 33/27 155/172 199/202 199/200
0/0 0/0 0/0 38/25 160/172 162/174
0/0 0/0 0/0 0/0 35/21 37/26
and discussed in Section 3. Finally, conclusions are given in Section 4. 2. Simulation model In this study, three-dimensional MD simulations and classical NVT ensemble (constant particle number N, constant volume V and constant temperature T) are adopted to investigate the atomistic behavior during film deposition. The substrate consists of 10 atomic layers and the lowermost one is fixed, while the upper two layers of substrate are entirely free to transmit energy freely with the deposited atoms. The other layers are assigned as the thermal control layers where the velocities of all atoms are rescaled at each time step according to the prescribed substrate temperature. Periodic boundary conditions are imposed on the surface plane along the directions of x and y, respectively. Moreover, non-periodic boundary conditions are applied to the direction z perpendicular to the surface plane. Molecular dynamics simulation with a many-body potential is one of powerful methods to investigate the mechanism of the growing films. In our MD simulations, the equations of motion are solved through the Gear's five-order predictorcorrector algorithm [13] with a constant time step of t = 5 fs and the interaction potential between atoms in the system is described with embedded-atom method (EAM) [25,26], the functional dependencies proposed by Johnson [27] in 1988 are employed. The EAM potential is a many-body potential based on density function theory (DFT) and especially suitable for metals. Initial velocities of substrate particles are randomly selected from a Maxwell's velocity distribution [13]. A new incident atom is placed at the height of 10-fold lattice length above the substrate surface plane with random x- and ycoordinates. The incident atom possesses an incident kinetic energy of 5 or 10 or 15 eV with random incident angle within the maximum value, ranged from 0° to 36°. Three different substrate temperatures of 300 K, 500 K and 800 K are used in simulation. The “main system” of simulation is defined as the condition of substrate size of (10 × 10 × 5) unit cells, substrate temperature of 300 K, incident energy of 5 eV per atom, maximum random incident angle of 18° and deposition rate of 4 atoms/ps. The other simulation models can be established by changing only one of deposition parameters of the main system, or the substrate size: (5 × 5 × 5) unit cells, (10 × 10 × 5) unit cells and (20 × 20 × 5) unit cells, while the
other parameters remain unchanged. All of MD simulation models are deposited totally five layers. The largest models are composed of 20 × 20 × 2 × (10 + 5) = 12,000 atoms and take 1000 ps at least to finish the deposition process. 3. Results and discussion 3.1. Morphology of thin films The morphologies and the growing mechanisms of deposited films under different conditions are evaluated and discussed as follows. Fig. 1 shows the final film configuration of substrate size of (10 × 10 × 5) unit cells at constant-temperature of 500 K at 300 ps. In Fig. 1, 1000 atoms are deposited in six film layers on substrate with two-dimensional layer-by-layer-like growth. The coverage in the first five film layers is about 4.83 ML and only 0.17 ML coverage in the sixth layer. This result is well consistent with Thornton's study [28], which showed that higher substrate temperature will promote layer-by-layer-like growth of film structure. Moreover, it is seen that only one atom of substrate moves to the first film layer. Therefore, some
Fig. 2. The growing film morphology of substrate size of (20 × 20 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms/ps at 1050 ps. The color of atoms represents incidence in sequence while the blue denotes substrate atoms and each color has the number of one-layer atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
C.-J. Chu, T.-C. Chen / Surface & Coatings Technology 201 (2006) 1796–1804 Table 2 The number of deposited atoms in the growing thin films for different deposition time, in the case of substrate size of (20 × 20 × 5) unit cells at substrate temperature of 300 K, incident energy of 5 eV, maximum random incident angle of π/10 and deposition rate of 4 atoms per 1 ps Deposition Total 1st ML 2nd ML 3rd ML 4th ML 5th ML 6th ML time (ps) 200.00 400.00 600.00 800.00 1000.00 1050.00
793 1589 2381 3175 3984 3988
666 794 800 800 800 800
127 640 792 800 800 800
0 155 617 790 800 800
0 0 172 610 798 799
0 0 0 175 620 622
0 0 0 0 166 167
substrate atoms will probably move to film layers at temperature higher than 500 K. The detailed exchange of film–substrate atoms will be presented and discussed in the future work. Table 1 shows that higher incident energy of sputtering atom is more beneficial for layer-by-layer growth of film structure. Qiang's study [29] also indicated that larger incident energy can produce smoother film surface. Two atoms are deposited in the seventh film layer at incident energy of 5 eV and substrate temperature of 300 K (see Table 1). There is 4.87 ML coverage in the first five film
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layers at incident energy of 15 eV from Table 1 and it shows higher layer coverage in comparison with Fig. 1. Consequently, to improve layer coverage, selection of larger incident energy is more effective than higher substrate temperature. From above results, a film structure of high quality may be obtained by properly enhancing incident energy and substrate temperature. Fig. 2 and Table 2 show the morphology of deposited film at larger substrate and the number of deposited atoms in each film layer after some specific deposition time. The results indicate that thin films can also grow with two-dimensional layer-bylayer-like way at larger size of substrate. From Table 2, the coverage in the first five layers is about 4.776 ML and 12 atoms are not well deposited in the first six film layers, where six atoms of them are adsorbed in the seventh layer while six atoms are desorbed. The average kinetic energy of exposed atoms on the film surface represents the temperature of film surface. In other words, higher average kinetic energy corresponds to better thermal diffusion or mobility, which is helpful to produce the smoother film surface. Fig. 3a shows the exposed atoms on the film surface have better ability of migration at higher substrate temperature. The average kinetic energy increases when
Fig. 3. Average kinetic energy of exposed atoms versus monolayer of evolution (time dependence) in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other process parameters of all cases are the parameters of main system defined in Section 2.
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Fig. 4. Average kinetic energy of exposed atoms versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
incident atoms are adsorbed on the film–substrate surface and then decreases gradually due to the energy exchange. This leads to the phenomenon of energy oscillation (see Fig. 3). The oscillation of the average kinetic energy increases after 3 ML deposition. The average kinetic energy then reduces rapidly and film–substrate system becomes stabilized when all
of incident atoms have finished sputtering and are adsorbed on the film surface. In Fig. 3d, the average kinetic energy is smaller without significant oscillation (surface atoms move stably at any time step) at lower deposition rate of 0.5 atom per 1 ps during film deposition. The exposed atoms of film surface possess better ability of migration at higher deposition rate of 4 atoms per 1 ps. Fig. 3b indicates that the curve does not show acute oscillation at incident energy of 15 eV during film deposition. The average kinetic energy at 15 eV, however, is not larger than 10 eV after 2 ML deposition. The variation of average kinetic energy is insignificant for different value of maximum incident angle and the oscillation of curve becomes smaller at vertical incidence (Fig. 3c). The influence of substrate size on the average kinetic energy is shown in Fig. 4. The mobility of surface atoms is better at smaller substrate scale, but it becomes smaller and more uniform at larger substrate size of (20 × 20 × 5) unit cells during film deposition. 3.2. Coverage of the growing film In this section, the characteristics of film growth are investigated and discussed by evaluating the variation of
Fig. 5. Number of deposited atoms at 4–6 layers versus time of evolution in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other process parameters of all cases are the parameters of main system defined in Section 2.
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Fig. 6. Coverage of film layers versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
coverage rate. We are interested in the coverage of each film layer under different deposition conditions because the defects in materials will affect the conductivity, optical properties and mechanical properties significantly. Liang and Shi [30] indicated that thermal conductivity of materials decreases with the reduction of the number of atomic layers, which has been confirmed by many experiments. Fig. 5 shows the number of adatoms at 4–6 layers varies with time while first 1–3 layers have completely filled with 200 atoms in each layer. From Fig. 5a, it is seen that the layer coverage is better at substrate temperature of 500 K. The number of atoms in the sixth layer reaches its maximum at substrate temperature of 800 K due to the higher average kinetic energy. In other words, the roughness of surface becomes larger. In the experimental work of Wang et al. [31], it was reported that increasing temperature of the deposition will cause the smooth Fe film to break up and nano-scale Fe islands are sequentially formed. Therefore, the film deposition under higher temperature more than 500/600 K may be
disadvantageous to the smoothness of the film layers. Fig. 5b indicates that the layer coverage becomes better at higher incident energy of 15 eV. However, the layer coverages are very close for incident energy of 10 eV and 15 eV. Therefore, higher layer coverage may be accomplished by adopting temperature of 500 K and incident energy of 10 eV per atom. Fig. 5c shows that the layer coverage is insensitive to the maximum incident angles. The fourth layer exhibits coverage of 100% only for vertical incidence. In fact, columnar structural growth of film will be easily formed in case the incident angle is more than 45 degree. As shown in Figs. 3d and 5d, the layer coverage becomes better at higher deposition rate due to the higher average kinetic energy. The coverage in each layer and total coverage of all layers as a function of time steps for different substrate sizes are shown in Fig. 6. The steeper curve of layer coverage represents more well-layered growth. The layer coverage becomes better for smaller substrate size by observing the film growth of 4–6 layers.
Fig. 7. (a) Relative coverage of two adjacent film layers at constant substrate temperature of 500 K. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
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Fig. 8. (a) Relative coverage of two adjacent film layers at incident energy of 10 eV per atom. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
A different representation of the layer coverage is provided through Figs. 7–9, which shows the relation of coverage at two adjacent layers. Fig. 7b indicates that the coverage in the first layer already reaches to 60% when the second layer just starts to grow at substrate temperature of 500 K. Fig. 8b shows that 0.7 ML coverage in the first layer has been attained when the second layer begins to grow at incident energy of 10 eV. Moreover, the coverage in layer i + 1 is only 0.1 ML to 0.2 ML when 0.9 ML coverage in layer i has already been attained, where 1 ≤ i ≤ 4. We can obtain a well-ordered growth of films in near layer-by-layer way at substrate temperature of 500 K and incident energy of 10 eV. Compare Fig. 9 with Fig. 7 or 8, it can be seen that, although the sound layer coverage can be obtained at the end of deposition, the helpfulness of well-layered growth is not significant for vertical incidence. These results indicate that the growth of successive layers is gradually less welllayered because the atoms easily troop together in successively higher layers. This is in agreement with the simulation results evaluated by Evans [18].
3.3. Surface roughness Three different definitions are used to quantify the surface roughness on the growing films as a function of time. They are respectively calculated as follows: Rmax ¼ Zimax −Zimin ; n X jZi −Z¯ j Ra ¼
Rq ¼
ð1Þ
i¼1
; n vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX n 2 u u Zi −Z¯ t i¼1
n
ð2Þ
;
ð3Þ
where Rmax is the maximum roughness, Ra is the center-line average roughness, Rq is the root-mean-square roughness, Zi represents the height of the exposed atoms on the film surface,
Fig. 9. (a) Relative coverage of two adjacent film layers with vertical incidence for all sputtering atoms. The other parameters are the parameters of main system defined in Section 2. (b) Specific local plot of (a).
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Fig. 10. Time evolution of three different roughness of surface at the process parameters of main system defined in Section 2.
Zimax represents the maximum value of Zi, Zimin represents the minimum value of Zi, Z¯ represents the mean height of all the exposed atoms and n is the total number of exposed atoms at a specific time step. Fig. 10 shows three different roughness of surface in the MD simulation of main system defined in previous section.
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The maximum roughness represents the distance between the highest and the lowest position of surface atoms along the vertical direction. The value of peak is about one lattice length in the curve of maximum roughness. And the value of trough i, which implies that layer i has been already filled with particles, is about half of lattice length for 1 ≤ i ≤ 3. Since the fourth trough cannot be seen through the curve of maximum roughness, it means the fourth film layer is not filled, which is consistent with the condition of 5 eV shown in Table 2. The meaning of troughs is the same as the maximum roughness for two kinds of average roughness (Ra and Rq), and we find that the shorter the distance between peak and trough the more the film layer not filled yet. The oscillated aspect of surface roughness in Fig. 10 is in agreement with the experimental observation by Giergiel et al. [32], which showed that surface roughness tends to oscillate around the average value for ultrathin Fe films on Cu substrate and the films were found to grow in a good layer-by-layer mode at room temperature. The surface roughness rapidly reaches to a constant value at the end of deposition. The discrepancy between Ra and Rq is very small, but Ra < Rq. Moreover, Rmax is about fourfold of Ra or Rq, in agreement with the experimental work. Consequently, only the behaviors of Rq are shown hereafter.
Fig. 11. Time evolution of root-mean-square roughness in the case of substrate size of (10 × 10 × 5) unit cells for (a) different substrate temperature, (b) different incident energy, (c) different incident angle and (d) different deposition rate. The other parameters of all cases are the parameters of main system defined in Section 2.
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reduce surface roughness. Regarding the effect of substrate size, if we wish to obtain a better quality of film structure at larger substrate, a suitable enhancement on incident energy or temperature shall be provided. Moreover, all the simulation results, presented in this article, are qualitatively consistent with both earlier MD and experimental work. It is believed that the results may provide a solid guide for the selection of process parameters in the deposition of thin film structure. Acknowledgments
Fig. 12. Root-mean-square roughness versus monolayer of evolution (time dependence) for different substrate sizes and process parameters of main system defined in Section 2.
Fig. 11 shows the root-mean-square roughness as a function of time. The roughness is smaller at substrate temperature of 500 K (Fig. 11a) as well as at incident energy of 15 eV (Fig. 11b). The discrepancy in roughness, however, is very small for energy of 10 eV and 15 eV. Therefore, smoother surface may be obtained by adopting low temperature of 500 K and high energy of 10–15 eV. Fig. 11c indicates that the influence of maximum incident angle on the surface roughness is very small during film deposition. The roughness tends to be smaller at higher deposition rate (see Fig. 11d). The effect of the substrate size is shown in Fig. 12. It is seen that during film deposition the smaller the size the smaller the roughness. In general, the root-mean-square roughness is about 0.1–0.12 nm after the film deposition for different conditions and this quantity is equivalent to experimental results of Ref. [24]. 4. Conclusion This paper investigates the morphologies, surface roughness and layer coverage of thin film structure under different deposition conditions in the epitaxial growth of Cu-single crystals using MD simulation with EAM potential. The simulation results show that films may grow with twodimensional quasi-layer-by-layer mode under appropriate deposition conditions even for larger size of substrate. If the temperature of substrate becomes too high in our MD simulations, it will be less helpful for layer coverage and surface roughness due to the limited enhancement of surface diffusion. Moreover, larger incident energy may be more effective to produce smoother surface rather than higher substrate temperature in the results of simulations. Better layer coverage and smaller surface roughness may thus be obtained at low substrate temperature of 500 K and high incident energy of 10–15 eV. On the other hand, the effect of maximum random incident angle, which is not in excess of 45 degree, is not significant. It is clear that higher deposition rate is helpful to increase layer coverage and
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