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Morphology evolution of glancing angle deposition Ag films on nanosphere-array substrates: Kinetic Monte Carlo simulation
Computational Materials Science 79 (2013) 31–35
Contents lists available at SciVerse ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Morphology evolution of glancing angle deposition Ag films on nanosphere-array substrates: Kinetic Monte Carlo simulation Jing-Shu Liang, Shu-Han Chen, En-Yu Lin, Di-Fan Luo, Shao-Ji Jiang ⇑ State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 24 March 2013 Received in revised form 3 June 2013 Accepted 8 June 2013
Keywords: Glancing angle deposition Ag film growth Sphere-array substrate Kinetic Monte Carlo simulation
a b s t r a c t The mechanism of Ag film growing processes by glancing angle deposition on various substrates is investigated via a three-dimensional kinetic Monte Carlo technique. From the morphology evolution of the film structures, three stages of the columnar growth on a close-packed spherical seed layer are demonstrated. At the initial stage, the Ag film is enforced to grow in periodically aligned columns instead of random distribution. As film height increases, the growth competition among columns becomes more drastic, leading to column broadening and extinction. At the later stage, the modulation of seed layers vanishes and random multiple Ag rods are formed on the broadened transection, which is similar to the columnar growth on the bare substrate. The variation of the growth exponent with film height increasing suggests the same three stages. In addition, different spherical periods play a significant role in duration of the height in each stage. Simulation conclusions are in agreement with the corresponding experiments. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Glancing angle deposition (GLAD) has been a fashionable technique for fabrication of porous and controllable nanostructured thin films in recent years [1]. Generally, GLAD is a physical vapor deposition technique, which atoms of a vapor stream are deposited at a large oblique angle from the substrate normal, combining with rapid substrate rotation in an unusual configuration, instead of striking the immobile substrate perpendicularly. The various structures and rough surface of thin-film materials produced through GLAD have attracted much attention, for the potential applications in magnetic-storage media, flat-panel displays, optoelectronics, and biomedical sensing trace [2–7]. For example, aligned Ag nanorods prepared by GLAD are good substrates for surface-enhanced Raman scattering, utilized as a powerful tool in detection of trace level of pollutants and biochemical molecules [8–10]. It is well known that the major factors affecting the morphologies of GLAD films are the deposition angle of flux, the deposition rate, the rotation of substrate and the substrate temperature. However, the subtle interactions at the atomic level, which should be taken into account to explicitly illustrate the formation of nanoclusters and nanorods, still cannot be precisely studied in experimental conditions. A particularly effective alternative is to use the atomistic lattice-gas models with stochastic dynamics via Kinetic Monte Carlo (KMC) computational simulations. It has been ⇑ Corresponding author. Tel./fax: +86 20 84113306. E-mail address: [email protected] (S.-J. Jiang). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.06.014
proved to be a powerful approach to understanding growth processes and growth mechanism of thin films on a microscopic level [11–15]. In Toh-Ming Lu’s work [16], the most significant growth effects of thin films are caused by step barrier diffusion, shadowing and reemission. During the deposition, shadowing contributes to roughening of the surface, while surface diffusion and reemission tend to smooth the surface. By introducing pre-patterned substrates with finite size seeds, regular structures with periodical and well-separated arrays of nanorods could be more effectively fabricated through GLAD in experiments [17,18]. A tetragonal or hexagonal seed layer with square, circular or pyramidal shaped seeds were used to enforce controlled film nucleation of silicon in GLAD growth, and excellent periodic arrays of different structures were fabricated in Michael J. Brett’s article [19]. Recently, silver nanorods were organized into a hexangular lattice with a pattern size of 400 nm [20], but the Ag nanorods were joined to each other in a single seed. In addition, the interplay between the mechanisms involved in the growth processes of nanorods was not expressly discussed. The evolution of nanorods on seed layers has not been fully studied, though it may be crucial to understand the exploitation of the periodical nanostructure fabrication through GLAD. In this work, we study the growth mechanism of GLAD silver films on non-patterned substrate and spherical seed layers through KMC simulations, associating with corresponding experiments. The morphology evolution of Ag films of the simulated and experimental results indicates a three-stage columnar growth. The variation of the growth exponent in the film height also suggests
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Fig. 1. Tetragonal spherical seed layer on the bare substrate, where atoms obliquely deposit in our KMC model.
the same three stages, which implies the competing effects of shadowing and surface diffusion during the three diverse growth stages. 2. Simulation model of KMC Our 3D simulation model is performed in a (1 0 0) fcc lattice structure of a finite volume V = Lx Ly Lz, with periodic boundary conditions, and Lx = Ly = 512, whilst Lz can be adjusted according to the surface coverage. As the nearest neighbor distance of Ag in diagonal is 0.288 nm, the lattice period is about 0.204 nm. The tetragonal spherical seed layer on the bare substrate is displayed in Fig. 1. The diameters of spheres can be arranged in different lattice units. The main possible events are simplified as two procedures, deposition event and diffusion event. First, a silver atom deposits from a random position at a given deposition rate and deposition angle. The arrival of the incident Ag atom on the substrate follows the Monte Carlo ballistic deposition (BD) process [21]. During the deposition, the self-shadowing effect is taken into account. In the traditional ballistic deposition (BD) process, the atoms are assumed to stick onto the first position, where they initially touch the surface [22,23]. In the downward funneling (DF) process [24], the depositing atoms ‘‘cascade’’, when they meet block atoms on the surface, until they reach a fourfold hollow site. The assumption of our model is that we allow the system to form voids and overhangs during growth rather than the DF model. The schematic of 3D Monte Carlo simulation of ballistic deposition at glancing incidence has been described in detail in our previous work [25]. Then atoms deposited on the surface diffuse to nucleation or columnar growth depending on their diffusion rates. They can only jump into the nearest-neighbor positions. The diffusion rate D is defined by the Arrhenius rate equation as D (i j ? i0 j0 ) = D0 exp(E/kBT), where (i, j) is the occupied site and (i0 , j0 ) is the potential
jump site, D0 is the attempt rate (1013s1), kB is the Boltzmann’s constant, T is the substrate temperature. E is the activation energy of an adatom diffusion from (i, j) to (i0 , j0 ), which is confirmed by the diffusion processes [26]. The terrace diffusion barrier Et is counted when a single atom diffuses on the flat Ag surface. The bonding energy Eb of a cluster of two atoms is an additional barrier for monomer diffusing on the terrace. EES is an extra step-edge barrier, named Ehrlich–Schwoebel (ES) diffusion barrier, added in E, when the interlayer diffusion takes place. In addition, edge diffusion and corner/kink rounding diffusion are also considered, in which the diffusion barrier is Ee and Ekr correspondingly. The diffusion probability pi of an atom hopping to the direction i can be calculated by P the formula pi = Di/ Di. Here for simplicity, we do not involve the bare substrate patterning prior to GLAD and set that the Ag atoms deposited on the first surface layer of the spherical seeded substrates adhere immediately. Reemission [27] is not considered in this model due to the fast GLAD process and its little impact on our results. We assume Et = 0.4 eV, Eb = 0.29 eV, EES = 0.07 eV [28]. The adopted edge diffusion barrier is Ee = 0.25 eV [29], and kink rounding barrier is Ekr = 0.41 eV [30]. The film growth rate r is determined by L2F [31,32], where F is the flux of incoming particles (deposition rate) in ML/s, and L2 is the number of total atoms contained in the surface monolayer, in our model L2 = 0.5 Lx Ly. The value of surface diffusion strength D/F depends on the energetic parameters of the film material, the film temperature, the deposition rate, and the concentration of residual gases in the deposition chamber in a complicated manner [33,34]. In the simulation, we set D/F = 105 with T = 300 K and F = 2.5 ML/s reasonably approximating with the adopted value from J. G. Amar’s work [14]. 3. Results and discussions We set the deposition angle a = 80°, the rotation rate R = 0.7 rev/ML, the substrate temperature T = 300 K, and simulated a fixed coverage of 32 ML of deposited atoms on a bare substrate and a periodic spherical seed layer with a period of 64 lattice units respectively (Fig. 2). Fig. 2a shows a porous film structure of randomly distributed columns formed on a smooth substrate while Fig. 2b shows a rather uniform periodic columnar film grown on the seeded layer. During the evolution of GLAD films, the initial 3D mounded surface is very crucial for the later nanocolumnar growth. Under the condition of a shadowing effect by the high inclined angle of a depositing flux and a sufficient low adatom surface diffusion, the mounds can act as nucleation centers [35] and adsorb more and more atoms from the vapor flux to form a columnar morphology with deep grooves and large vacancy. A high value of the substrate rotation rate makes the shadowing distribute isotropic to the substrate normal and leads to vertically aligned columns [36]. When atoms of materials were obliquely deposited on the bare substrate initially, they aggregated into islands at random locations. Then a rough surface consisting of 3D irregular mounds was formed as
Fig. 2. Simulated morphologies of Ag films deposited at 80° on (a) a bare substrate and (b) a spherical seed layer with a lattice period of 64. Here, the substrate temperature is 300 K, the deposition rate is 2.5 ML/s and the rotation rate is 0.7 rev/ML.
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Fig. 3. SEM images of Ag films at deposition angle 80° on (a) a bare substrate and (b) a colloid self-assembly spherical monolayer with a lattice period of 450 nm. Here, the substrate temperature is 300 K, the deposition rate is 0.5 nm/s and the rotation rate is 10 rev/min.
Fig. 4. Simulation results on a bare substrate and different spherical seed layers with different lattice periods at a = 80°, T = 300 K and R = 0.7 rev/ML. Side-view images of film growth on a bare substrate (a), and different lattice periods (c) 16, (e) 32 and (g) 64. Corresponding top-view images on a bare substrate (b), and different lattice periods (d) 16, (f) 32 and (h) 64. It distinctly shows the different stages of columnar growth at specific height h (ML). The top-view images illustrate that they reach a similar growth at the random stage free from the confinement of the seed layer.
the film thickness increased. The strong growth competition between the shadowing and the surface diffusion among the mounds of non-uniformed sizes resulted in randomly standing columns as shown in Fig. 2a. However, by introducing nucleation centers of periodical seeds in advance, it powerfully enhanced the growth on those periodical nucleation centers at the early stage and stimulated well-organized columnar growth as shown in Fig. 2b. We deposited Ag thin films on a bare substrate and a colloid self-assembly spherical monolayer with a lattice period of 450 nm respectively. The deposition was carried out at room temperature (T = 300 K) in a high-vacuum chamber with a base pressure of 3 103 Pa. For both experiments, the deposition angle of flux was 80°, the deposition rate was kept constant at nominal 0.5 nm s1, and the rotation rate was 10 r/min. Film structures were investigated by using scanning electron microscope (SEM). From Figs. 2 and 3, it is revealed that the growth morphologies of simulations in both cases agree well with the experiments. Interestingly, both in simulations and experiments, we find that the columns on the spheres are broadening and multiple 3D mounds start growing on the top surface of some columns. To acquire insight into the later morphology evolution during columnar growth on varied substrates, we simulated a fixed coverage of 160 ML atoms at 80° on the bare substrate and spherical seed layers with lattice periods (P) of 16, 32 and 64 respectively (Fig. 4). The rotation rate and substrate temperature was the same as above. From the side-view morphologies of columnar growth in Fig. 4c, e and g, we observe a non-monotonic variation of column
structures as thin films grow thicker. We supposedly divide it into stage A, B, C. As mentioned above, the sphere seeds acting as nucleation centers capture more and more incident atoms in the ballistic direction of incoming vapor flux and grow up into sharp uniform columns at stage A. As films continue proceeding, the strong
Fig. 5. The growth exponent evolution as a function of film height on a bare substrate and spherical seed layers with different lattice periods at a = 80°. Here, the substrate temperature is 300 K, the deposition rate is 2.5 ML/s and the rotation rate is 0.7 rev/ML.
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Fig. 6. SEM images of Ag films at deposition angle 80° on a colloid self-assembly spherical monolayer with a lattice period of 450 nm. (a) Side-view image of evolution and (b) top-view image of columnar growth. Here, the substrate temperature is 300 K, the deposition rate is 0.5 nm/s and the rotation rate is 10 rev/min.
growth competition among the neighbor columns leads to column broadening and extinction as noticed at stage B. During stage B, the columnar growth is still modulated periodically though some small branched rods are growing separately on the top of a single column. This phenomenon is mainly due to the shadowing effect. On the transection of the large column formed at stage A, small islands are randomly distributed on the surface and grow into 3D mounds. These mounds play as new nucleation centers in later deposition and gradually form small separated rods due to the shadowing effect. At stage C, we could not distinguish the periodic columns anymore and the columnar growth on seeded layers appears similar to the bare substrate (Fig. 4a). The effective modulation of periodical seeds vanishes while growing multiple rods become dominant. It is worth to mention that the growth of multiple rods is also strengthened by the uneven opportunity to receive flux for the rods of different positions. The rods at the edge of the column section received more flux than those in the center, so that the rods close to the edge are fanning out, while the growth of rods in the center is suppressed. From the top-view images in Fig. 4b, d, f and h, the morphologies on different periodical seed layers are obviously analogous as the topography on the bare substrate at a sufficient height. Furthermore, to quantitatively examine the morphology evolution, we calculate the growth exponent b as a function of film height (Fig. 5). According to the dynamic scaling hypothesis, the growth exponent b has the scaling form w tb, where w is called the root-mean-square (rms) roughness, given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 P w¼ N i ðhi hÞ [37], and t is the mean film thickness. Here, N is the total number of surface sites, hi is the height of ith site, is the average height of the surface. The b can be used to clasand h sify the underlying physical phenomena controlling a given growth process and describe the growth mode, where a smaller value of b indicates a smoother surface [38,39] and a more diffuse-dominant mechanism at low temperatures (<600 K) [37]. Fig. 5 shows the growth exponent b as functions of the film height under deposition on various substrates. The b was obtained from the roughness data influenced by the surface height profile. We can find that growth on the bare substrate begins with a small growth exponent, suggesting strong surface diffusion and a low porosity layer. Then the growth exponent ascends sharply until h 40 ML and peaks at h 100 ML, after where b saturates at 0.63 (b > 0.5), implying the strong shadowing effect and a much more porous film [36]. In the case of growth on the 16-lattice periodic seed layer, the b increases more dynamically until h 20 ML, then decreases dramatically until h 40 ML and increases slightly until h 70 ML. In terms of growth on the 32- and 64-lattice periodic seed layer, they both have a similar tendency as the case of 16-lattice periodic seed layer. The difference is that the peaking value of b is at h 40 ML where P = 32 and h 80 ML where P = 64. Correspondingly, the saturated value of b is at h 120 ML and h 260 ML respectively.
As well known in GLAD preparation, the competition between surface diffusion and nonlocal shadowing effect plays an important role in the surface roughness of thin films [40], which directly affects the value of b. The variation of b with film height h during the growth on the periodic spherical seed layers showed a non-unique behavior and can be divided into the same three different stages as described above. The ascending stage (stage A) with larger value than the case of bare substrate suggests a more porous film, resulting from the strengthened shadowing effect by the columnar growth on the preexisting seeds, where atoms could only diffuse on the confined area of the separated seeds. The descending stage (stage B) is generated by the enhancement of surface diffusion which leads to column expansion as the film heightens, and reduces the interspace between the columns as well. The modulation of seed layer is weakened but still works. At last, the saturate stage (stage C), as all the cases follow, indicates a similar random growth of multiple rods on the broadened cross section where the modulation of seed layers totally vanishes. The values of b all reach the steady trend near the value of 0.6, indicating that the competing effect of shadowing and surface diffusion reaches a stable level as on the bare substrate. It is revealed that the growth exponent of deposition on the 16-lattice periodic seed layer is smaller than the one on the bare substrate after h 20 ML. This is due to that the spherical seeds of small diameter (16 lattices) on the substrate act as dense uniform nuclei, which enhance more intensively surface aggregation of the deposited atoms for the subsequent growth. Experimentally, we deposited Ag thin films on a colloid selfassembly spherical monolayer with a lattice period of 450 nm. The conditions during the experiment were identical as reference above. The evolution of film structures investigated by using scanning electron microscope (SEM) in Fig. 6 first experienced a uniform columnar growth, then a broadened columnar growth and last a multiple nanorod growth, reaching a good agreement with mimic results and the analysis above.
4. Conclusion The morphology evolution of Ag columnar films through initial and later growth through GLAD on various substrates is studied both by atomic KMC simulations and experiments. We first demonstrate that a periodic spherical seed layer rather than a bare substrate can enforce controlled uniform columns within certain film thickness. Then the morphology evolution of the Ag films indicates that as Ag films continue to deposit, the uniform columnar growth translates to the stage of column broadening and extinction, and finally multiple Ag rods are separated by the effect of shadowing and tend to a random growth, which is similar to the competing growth on the smooth substrate. The variation of the growth exponent with film height increasing also suggests the same three stages
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in the columnar growth. We can find the critical values of film height at different stages from the exponent-height curve, and larger spherical period contributes to longer durations of each stage, which may facilitate the design of periodic seed layers. Additionally, the experimental morphologies reach an agreement with the simulations and the analysis. These results provide insight into the growth mechanism in the integrated depositing process behind the experiments and offer a constructive understanding to designing nanostructures with well-defined surface morphologies on the close-packed seed layers experimentally. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant Nos. 61275159, 60977042 and 11074 311). References [1] M.J. Brett, M.M. Hawkeye, Science 319 (2008) 1192–1193. [2] Y.P. Zhao, D.X. Ye, P.I. Wang, G.-C. Wang, T.-M. Lu, Int. J. Nanosci. 1 (2002) 87– 97. [3] S.R. Kennedy, M.J. Brett, Nano Lett. 2 (2002) 59–62. [4] K.D. Harris, J.R. McBride, K.E. Nietering, M.J. Brett, Sens. Mater. 13 (2001) 225– 234. [5] A.T. Wu, M.J. Brett, D.J. Broer, Sens. Mater. 13 (2001) 399–431. [6] K. Robbie, D.J. Broer, M.J. Brett, Nature (London) 399 (1999) 764–766. [7] Y. He, J. Fu, Y. Zhang, Y. Zhao, L. Zhang, A. Xia, J. Cai, Small 3 (2007) 153–160. [8] M. Moskovits, Rev. Mod. Phys. 57 (1985) 783–826. [9] S.B. Chaney, S. Shanmukh, R.A. Dluhy, Y.P. Zhao, Appl. Phys. Lett. 87 (2005) 031908. [10] H.Y. Chu, Y.J. Liu, Y.W. Huang, Y.P. Zhao, Opt. Express 15 (2007) 12230–12239. [11] T. Karabacak, G.-C. Wang, T.-M. Lu, J. Vac. Sci. Technol. A 22 (2004) 1778–1784. [12] N. Fazouan, E. Atmani, M. Djafari-Rouhani, A. Estève, Comput. Mater. Sci. 33 (2005) 382–387. [13] Andrzej Sikorski, Comput. Mater. Sci. 43 (2008) 132–136. [14] Y. Shim, J.G. Amar, Phys. Rev. Lett. 98 (2007) 046103.
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Contents lists available at SciVerse ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Morphology evolution of glancing angle deposition Ag films on nanosphere-array substrates: Kinetic Monte Carlo simulation Jing-Shu Liang, Shu-Han Chen, En-Yu Lin, Di-Fan Luo, Shao-Ji Jiang ⇑ State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 24 March 2013 Received in revised form 3 June 2013 Accepted 8 June 2013
Keywords: Glancing angle deposition Ag film growth Sphere-array substrate Kinetic Monte Carlo simulation
a b s t r a c t The mechanism of Ag film growing processes by glancing angle deposition on various substrates is investigated via a three-dimensional kinetic Monte Carlo technique. From the morphology evolution of the film structures, three stages of the columnar growth on a close-packed spherical seed layer are demonstrated. At the initial stage, the Ag film is enforced to grow in periodically aligned columns instead of random distribution. As film height increases, the growth competition among columns becomes more drastic, leading to column broadening and extinction. At the later stage, the modulation of seed layers vanishes and random multiple Ag rods are formed on the broadened transection, which is similar to the columnar growth on the bare substrate. The variation of the growth exponent with film height increasing suggests the same three stages. In addition, different spherical periods play a significant role in duration of the height in each stage. Simulation conclusions are in agreement with the corresponding experiments. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Glancing angle deposition (GLAD) has been a fashionable technique for fabrication of porous and controllable nanostructured thin films in recent years [1]. Generally, GLAD is a physical vapor deposition technique, which atoms of a vapor stream are deposited at a large oblique angle from the substrate normal, combining with rapid substrate rotation in an unusual configuration, instead of striking the immobile substrate perpendicularly. The various structures and rough surface of thin-film materials produced through GLAD have attracted much attention, for the potential applications in magnetic-storage media, flat-panel displays, optoelectronics, and biomedical sensing trace [2–7]. For example, aligned Ag nanorods prepared by GLAD are good substrates for surface-enhanced Raman scattering, utilized as a powerful tool in detection of trace level of pollutants and biochemical molecules [8–10]. It is well known that the major factors affecting the morphologies of GLAD films are the deposition angle of flux, the deposition rate, the rotation of substrate and the substrate temperature. However, the subtle interactions at the atomic level, which should be taken into account to explicitly illustrate the formation of nanoclusters and nanorods, still cannot be precisely studied in experimental conditions. A particularly effective alternative is to use the atomistic lattice-gas models with stochastic dynamics via Kinetic Monte Carlo (KMC) computational simulations. It has been ⇑ Corresponding author. Tel./fax: +86 20 84113306. E-mail address: [email protected] (S.-J. Jiang). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.06.014
proved to be a powerful approach to understanding growth processes and growth mechanism of thin films on a microscopic level [11–15]. In Toh-Ming Lu’s work [16], the most significant growth effects of thin films are caused by step barrier diffusion, shadowing and reemission. During the deposition, shadowing contributes to roughening of the surface, while surface diffusion and reemission tend to smooth the surface. By introducing pre-patterned substrates with finite size seeds, regular structures with periodical and well-separated arrays of nanorods could be more effectively fabricated through GLAD in experiments [17,18]. A tetragonal or hexagonal seed layer with square, circular or pyramidal shaped seeds were used to enforce controlled film nucleation of silicon in GLAD growth, and excellent periodic arrays of different structures were fabricated in Michael J. Brett’s article [19]. Recently, silver nanorods were organized into a hexangular lattice with a pattern size of 400 nm [20], but the Ag nanorods were joined to each other in a single seed. In addition, the interplay between the mechanisms involved in the growth processes of nanorods was not expressly discussed. The evolution of nanorods on seed layers has not been fully studied, though it may be crucial to understand the exploitation of the periodical nanostructure fabrication through GLAD. In this work, we study the growth mechanism of GLAD silver films on non-patterned substrate and spherical seed layers through KMC simulations, associating with corresponding experiments. The morphology evolution of Ag films of the simulated and experimental results indicates a three-stage columnar growth. The variation of the growth exponent in the film height also suggests
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J.-S. Liang et al. / Computational Materials Science 79 (2013) 31–35
Fig. 1. Tetragonal spherical seed layer on the bare substrate, where atoms obliquely deposit in our KMC model.
the same three stages, which implies the competing effects of shadowing and surface diffusion during the three diverse growth stages. 2. Simulation model of KMC Our 3D simulation model is performed in a (1 0 0) fcc lattice structure of a finite volume V = Lx Ly Lz, with periodic boundary conditions, and Lx = Ly = 512, whilst Lz can be adjusted according to the surface coverage. As the nearest neighbor distance of Ag in diagonal is 0.288 nm, the lattice period is about 0.204 nm. The tetragonal spherical seed layer on the bare substrate is displayed in Fig. 1. The diameters of spheres can be arranged in different lattice units. The main possible events are simplified as two procedures, deposition event and diffusion event. First, a silver atom deposits from a random position at a given deposition rate and deposition angle. The arrival of the incident Ag atom on the substrate follows the Monte Carlo ballistic deposition (BD) process [21]. During the deposition, the self-shadowing effect is taken into account. In the traditional ballistic deposition (BD) process, the atoms are assumed to stick onto the first position, where they initially touch the surface [22,23]. In the downward funneling (DF) process [24], the depositing atoms ‘‘cascade’’, when they meet block atoms on the surface, until they reach a fourfold hollow site. The assumption of our model is that we allow the system to form voids and overhangs during growth rather than the DF model. The schematic of 3D Monte Carlo simulation of ballistic deposition at glancing incidence has been described in detail in our previous work [25]. Then atoms deposited on the surface diffuse to nucleation or columnar growth depending on their diffusion rates. They can only jump into the nearest-neighbor positions. The diffusion rate D is defined by the Arrhenius rate equation as D (i j ? i0 j0 ) = D0 exp(E/kBT), where (i, j) is the occupied site and (i0 , j0 ) is the potential
jump site, D0 is the attempt rate (1013s1), kB is the Boltzmann’s constant, T is the substrate temperature. E is the activation energy of an adatom diffusion from (i, j) to (i0 , j0 ), which is confirmed by the diffusion processes [26]. The terrace diffusion barrier Et is counted when a single atom diffuses on the flat Ag surface. The bonding energy Eb of a cluster of two atoms is an additional barrier for monomer diffusing on the terrace. EES is an extra step-edge barrier, named Ehrlich–Schwoebel (ES) diffusion barrier, added in E, when the interlayer diffusion takes place. In addition, edge diffusion and corner/kink rounding diffusion are also considered, in which the diffusion barrier is Ee and Ekr correspondingly. The diffusion probability pi of an atom hopping to the direction i can be calculated by P the formula pi = Di/ Di. Here for simplicity, we do not involve the bare substrate patterning prior to GLAD and set that the Ag atoms deposited on the first surface layer of the spherical seeded substrates adhere immediately. Reemission [27] is not considered in this model due to the fast GLAD process and its little impact on our results. We assume Et = 0.4 eV, Eb = 0.29 eV, EES = 0.07 eV [28]. The adopted edge diffusion barrier is Ee = 0.25 eV [29], and kink rounding barrier is Ekr = 0.41 eV [30]. The film growth rate r is determined by L2F [31,32], where F is the flux of incoming particles (deposition rate) in ML/s, and L2 is the number of total atoms contained in the surface monolayer, in our model L2 = 0.5 Lx Ly. The value of surface diffusion strength D/F depends on the energetic parameters of the film material, the film temperature, the deposition rate, and the concentration of residual gases in the deposition chamber in a complicated manner [33,34]. In the simulation, we set D/F = 105 with T = 300 K and F = 2.5 ML/s reasonably approximating with the adopted value from J. G. Amar’s work [14]. 3. Results and discussions We set the deposition angle a = 80°, the rotation rate R = 0.7 rev/ML, the substrate temperature T = 300 K, and simulated a fixed coverage of 32 ML of deposited atoms on a bare substrate and a periodic spherical seed layer with a period of 64 lattice units respectively (Fig. 2). Fig. 2a shows a porous film structure of randomly distributed columns formed on a smooth substrate while Fig. 2b shows a rather uniform periodic columnar film grown on the seeded layer. During the evolution of GLAD films, the initial 3D mounded surface is very crucial for the later nanocolumnar growth. Under the condition of a shadowing effect by the high inclined angle of a depositing flux and a sufficient low adatom surface diffusion, the mounds can act as nucleation centers [35] and adsorb more and more atoms from the vapor flux to form a columnar morphology with deep grooves and large vacancy. A high value of the substrate rotation rate makes the shadowing distribute isotropic to the substrate normal and leads to vertically aligned columns [36]. When atoms of materials were obliquely deposited on the bare substrate initially, they aggregated into islands at random locations. Then a rough surface consisting of 3D irregular mounds was formed as
Fig. 2. Simulated morphologies of Ag films deposited at 80° on (a) a bare substrate and (b) a spherical seed layer with a lattice period of 64. Here, the substrate temperature is 300 K, the deposition rate is 2.5 ML/s and the rotation rate is 0.7 rev/ML.
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Fig. 3. SEM images of Ag films at deposition angle 80° on (a) a bare substrate and (b) a colloid self-assembly spherical monolayer with a lattice period of 450 nm. Here, the substrate temperature is 300 K, the deposition rate is 0.5 nm/s and the rotation rate is 10 rev/min.
Fig. 4. Simulation results on a bare substrate and different spherical seed layers with different lattice periods at a = 80°, T = 300 K and R = 0.7 rev/ML. Side-view images of film growth on a bare substrate (a), and different lattice periods (c) 16, (e) 32 and (g) 64. Corresponding top-view images on a bare substrate (b), and different lattice periods (d) 16, (f) 32 and (h) 64. It distinctly shows the different stages of columnar growth at specific height h (ML). The top-view images illustrate that they reach a similar growth at the random stage free from the confinement of the seed layer.
the film thickness increased. The strong growth competition between the shadowing and the surface diffusion among the mounds of non-uniformed sizes resulted in randomly standing columns as shown in Fig. 2a. However, by introducing nucleation centers of periodical seeds in advance, it powerfully enhanced the growth on those periodical nucleation centers at the early stage and stimulated well-organized columnar growth as shown in Fig. 2b. We deposited Ag thin films on a bare substrate and a colloid self-assembly spherical monolayer with a lattice period of 450 nm respectively. The deposition was carried out at room temperature (T = 300 K) in a high-vacuum chamber with a base pressure of 3 103 Pa. For both experiments, the deposition angle of flux was 80°, the deposition rate was kept constant at nominal 0.5 nm s1, and the rotation rate was 10 r/min. Film structures were investigated by using scanning electron microscope (SEM). From Figs. 2 and 3, it is revealed that the growth morphologies of simulations in both cases agree well with the experiments. Interestingly, both in simulations and experiments, we find that the columns on the spheres are broadening and multiple 3D mounds start growing on the top surface of some columns. To acquire insight into the later morphology evolution during columnar growth on varied substrates, we simulated a fixed coverage of 160 ML atoms at 80° on the bare substrate and spherical seed layers with lattice periods (P) of 16, 32 and 64 respectively (Fig. 4). The rotation rate and substrate temperature was the same as above. From the side-view morphologies of columnar growth in Fig. 4c, e and g, we observe a non-monotonic variation of column
structures as thin films grow thicker. We supposedly divide it into stage A, B, C. As mentioned above, the sphere seeds acting as nucleation centers capture more and more incident atoms in the ballistic direction of incoming vapor flux and grow up into sharp uniform columns at stage A. As films continue proceeding, the strong
Fig. 5. The growth exponent evolution as a function of film height on a bare substrate and spherical seed layers with different lattice periods at a = 80°. Here, the substrate temperature is 300 K, the deposition rate is 2.5 ML/s and the rotation rate is 0.7 rev/ML.
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Fig. 6. SEM images of Ag films at deposition angle 80° on a colloid self-assembly spherical monolayer with a lattice period of 450 nm. (a) Side-view image of evolution and (b) top-view image of columnar growth. Here, the substrate temperature is 300 K, the deposition rate is 0.5 nm/s and the rotation rate is 10 rev/min.
growth competition among the neighbor columns leads to column broadening and extinction as noticed at stage B. During stage B, the columnar growth is still modulated periodically though some small branched rods are growing separately on the top of a single column. This phenomenon is mainly due to the shadowing effect. On the transection of the large column formed at stage A, small islands are randomly distributed on the surface and grow into 3D mounds. These mounds play as new nucleation centers in later deposition and gradually form small separated rods due to the shadowing effect. At stage C, we could not distinguish the periodic columns anymore and the columnar growth on seeded layers appears similar to the bare substrate (Fig. 4a). The effective modulation of periodical seeds vanishes while growing multiple rods become dominant. It is worth to mention that the growth of multiple rods is also strengthened by the uneven opportunity to receive flux for the rods of different positions. The rods at the edge of the column section received more flux than those in the center, so that the rods close to the edge are fanning out, while the growth of rods in the center is suppressed. From the top-view images in Fig. 4b, d, f and h, the morphologies on different periodical seed layers are obviously analogous as the topography on the bare substrate at a sufficient height. Furthermore, to quantitatively examine the morphology evolution, we calculate the growth exponent b as a function of film height (Fig. 5). According to the dynamic scaling hypothesis, the growth exponent b has the scaling form w tb, where w is called the root-mean-square (rms) roughness, given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 P w¼ N i ðhi hÞ [37], and t is the mean film thickness. Here, N is the total number of surface sites, hi is the height of ith site, is the average height of the surface. The b can be used to clasand h sify the underlying physical phenomena controlling a given growth process and describe the growth mode, where a smaller value of b indicates a smoother surface [38,39] and a more diffuse-dominant mechanism at low temperatures (<600 K) [37]. Fig. 5 shows the growth exponent b as functions of the film height under deposition on various substrates. The b was obtained from the roughness data influenced by the surface height profile. We can find that growth on the bare substrate begins with a small growth exponent, suggesting strong surface diffusion and a low porosity layer. Then the growth exponent ascends sharply until h 40 ML and peaks at h 100 ML, after where b saturates at 0.63 (b > 0.5), implying the strong shadowing effect and a much more porous film [36]. In the case of growth on the 16-lattice periodic seed layer, the b increases more dynamically until h 20 ML, then decreases dramatically until h 40 ML and increases slightly until h 70 ML. In terms of growth on the 32- and 64-lattice periodic seed layer, they both have a similar tendency as the case of 16-lattice periodic seed layer. The difference is that the peaking value of b is at h 40 ML where P = 32 and h 80 ML where P = 64. Correspondingly, the saturated value of b is at h 120 ML and h 260 ML respectively.
As well known in GLAD preparation, the competition between surface diffusion and nonlocal shadowing effect plays an important role in the surface roughness of thin films [40], which directly affects the value of b. The variation of b with film height h during the growth on the periodic spherical seed layers showed a non-unique behavior and can be divided into the same three different stages as described above. The ascending stage (stage A) with larger value than the case of bare substrate suggests a more porous film, resulting from the strengthened shadowing effect by the columnar growth on the preexisting seeds, where atoms could only diffuse on the confined area of the separated seeds. The descending stage (stage B) is generated by the enhancement of surface diffusion which leads to column expansion as the film heightens, and reduces the interspace between the columns as well. The modulation of seed layer is weakened but still works. At last, the saturate stage (stage C), as all the cases follow, indicates a similar random growth of multiple rods on the broadened cross section where the modulation of seed layers totally vanishes. The values of b all reach the steady trend near the value of 0.6, indicating that the competing effect of shadowing and surface diffusion reaches a stable level as on the bare substrate. It is revealed that the growth exponent of deposition on the 16-lattice periodic seed layer is smaller than the one on the bare substrate after h 20 ML. This is due to that the spherical seeds of small diameter (16 lattices) on the substrate act as dense uniform nuclei, which enhance more intensively surface aggregation of the deposited atoms for the subsequent growth. Experimentally, we deposited Ag thin films on a colloid selfassembly spherical monolayer with a lattice period of 450 nm. The conditions during the experiment were identical as reference above. The evolution of film structures investigated by using scanning electron microscope (SEM) in Fig. 6 first experienced a uniform columnar growth, then a broadened columnar growth and last a multiple nanorod growth, reaching a good agreement with mimic results and the analysis above.
4. Conclusion The morphology evolution of Ag columnar films through initial and later growth through GLAD on various substrates is studied both by atomic KMC simulations and experiments. We first demonstrate that a periodic spherical seed layer rather than a bare substrate can enforce controlled uniform columns within certain film thickness. Then the morphology evolution of the Ag films indicates that as Ag films continue to deposit, the uniform columnar growth translates to the stage of column broadening and extinction, and finally multiple Ag rods are separated by the effect of shadowing and tend to a random growth, which is similar to the competing growth on the smooth substrate. The variation of the growth exponent with film height increasing also suggests the same three stages
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in the columnar growth. We can find the critical values of film height at different stages from the exponent-height curve, and larger spherical period contributes to longer durations of each stage, which may facilitate the design of periodic seed layers. Additionally, the experimental morphologies reach an agreement with the simulations and the analysis. These results provide insight into the growth mechanism in the integrated depositing process behind the experiments and offer a constructive understanding to designing nanostructures with well-defined surface morphologies on the close-packed seed layers experimentally. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant Nos. 61275159, 60977042 and 11074 311). References [1] M.J. Brett, M.M. Hawkeye, Science 319 (2008) 1192–1193. [2] Y.P. Zhao, D.X. Ye, P.I. Wang, G.-C. Wang, T.-M. Lu, Int. J. Nanosci. 1 (2002) 87– 97. [3] S.R. Kennedy, M.J. Brett, Nano Lett. 2 (2002) 59–62. [4] K.D. Harris, J.R. McBride, K.E. Nietering, M.J. Brett, Sens. Mater. 13 (2001) 225– 234. [5] A.T. Wu, M.J. Brett, D.J. Broer, Sens. Mater. 13 (2001) 399–431. [6] K. Robbie, D.J. Broer, M.J. Brett, Nature (London) 399 (1999) 764–766. [7] Y. He, J. Fu, Y. Zhang, Y. Zhao, L. Zhang, A. Xia, J. Cai, Small 3 (2007) 153–160. [8] M. Moskovits, Rev. Mod. Phys. 57 (1985) 783–826. [9] S.B. Chaney, S. Shanmukh, R.A. Dluhy, Y.P. Zhao, Appl. Phys. Lett. 87 (2005) 031908. [10] H.Y. Chu, Y.J. Liu, Y.W. Huang, Y.P. Zhao, Opt. Express 15 (2007) 12230–12239. [11] T. Karabacak, G.-C. Wang, T.-M. Lu, J. Vac. Sci. Technol. A 22 (2004) 1778–1784. [12] N. Fazouan, E. Atmani, M. Djafari-Rouhani, A. Estève, Comput. Mater. Sci. 33 (2005) 382–387. [13] Andrzej Sikorski, Comput. Mater. Sci. 43 (2008) 132–136. [14] Y. Shim, J.G. Amar, Phys. Rev. Lett. 98 (2007) 046103.
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