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Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation
G Model APSUSC-24443; No. of Pages 5
ARTICLE IN PRESS Applied Surface Science xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation Shuhan Chen a,b , Jingshu Liang a , Yunjie Mo a , Difan Luo a , Shaoji Jiang a,∗ a b
State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China School of Physics and Optical Information Sciences, Jia Ying University, Meizhou, 514015, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 30 August 2012 Received in revised form 11 October 2012 Accepted 11 October 2012 Available online xxx Keywords: Shadowing-dominnated growth Glancing angle deposition Kinetic Monte Carlo simulation
a b s t r a c t A three-dimensional (3D) kinetic Monte Carlo simulation was performed for the growth evolution of Ag films during glancing angle deposition (GLAD). Under the GLAD conditions, we demonstrate that without substrate rotation the nanorods are grown aslant due to shadowing anisotropy, while with the rapid substrate rotation the nanorods are grown vertically aligned due to shadowing isotropy. Good agreement of growth trends between simulations and experiments has been achieved. In the case of substrate rotation, the critical rotate rate of nanorods just vertical to the substrate has been found. The growth exponent evolutions of Ag films in normal and glancing angle depositions are found similar in the very early stages of growth. The diverging of growth exponents with film height increasing indicates that shadowing instabilities overpower the smoothing effects associated with surface diffusion. Furthermore, we demonstrate the transition from two-dimensional to 3D islanded growth under the condition of high glancing angle deposition. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Recently, materials scientists have adopted glancing angle deposition (GLAD) as an important tool for nanostructure fabrication [1]. During traditional film deposition, a stream of vapor-phase atoms strikes a substrate perpendicularly. In GLAD method, materials are deposited at a highly oblique angle from substrate normal, resulting in a flexible and straightforward method of producing nanostructure and porous thin-film materials in unusual configurations. The ability to control the column orientation and porosity of nanostructure leads to particularly interesting applications of GLAD, such as nanostructure thin films, catalyst support, micromechanical systems, optoelectronics, and sensing systems [2–8]. For example, recently, a negative index metamaterial with double negative or single negative property can be easily formed by GLAD in the visible spectrum [9]. The interest in nanostructure materials fabricated by GLAD has given a new impulse to the study of the phenomena at the atomic level, which contributes to the formation and growth of nanoclusters and nanorods. Many kinetic Monte Carlo (KMC) simulation works have been proposed recently to study this topic [10–15]. It is known that diffusion and shadowing effect are critical factors which influence surface morphology of thin film grown by GLAD. During thin film growth, an adatom may diffuse on a flat surface, along a step, or across a step. The diffusion barrier of an adatom
down a step is usually larger than that on a flat surface and the extra barrier is the Ehrlich–Shwoebel (ES) barrier [16–21]. Larger diffusion barriers may lead to more roughly surfaced thin films and smaller diameters of nanorods. To successfully synthesize the thin films produced by GLAD with both a well-defined value of surface roughness and well-defined surface morphologies, it is of great importance to gain a fundamental understanding of the interplay between the mechanisms involved in the growth process of thin films. Various attempts have been made to explain the tilt angle. Due to the sensitivity of the columnar structure on deposition conditions and material dependent parameters, all materials behave differently and accurate predictions are difficult [22]. Recently, shadowing instabilities can dramatically alter the very early stages of growth of amorphous thin films on nominally smooth surfaces by experiment [23]. In this work, we demonstrate the growth mechanism under conditions of rapid rotation and no rotation of substrates at high glancing angle conditions both through KMC simulations and experiments. Moreover, we discuss the growth exponent evolution and the onset of shadowing-dominated growth of Ag films grown at normal and high glancing angle deposition of the vapor flux theoretically. The competing process between surface diffusion and shadowing is also discussed.
2. Theoretical model of KMC ∗ Corresponding author. Tel.: +86 20 84113306; fax: +86 20 84113306. E-mail address: [email protected] (S. Jiang).
Our simulation is performed with a finite volume V = Lx × Ly × Lz arranged according to the ABC sequence of (1 1 1) fcc surfaces which
0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.10.062
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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are described by triangular lattices, where Lx = Ly = 512 but Lz can be changed according to the surface coverage. The lattice period is 0.3 nm. There are two main ways to handle the boundaries of the simulation during deposition, diffusion and ballistic transport: mirrored and periodic. In this study, however, periodic boundary conditions are applied to the four extremes of the samples to reduce discontinuity. A particle can move across one extreme and appear at the opposite one; particles placed at two opposite sites of the sample can be part of the opposite columns. To investigate the general characteristics of Ag films in the early stage of growth, our model does not involve the substrate patterning prior to GLAD. In our model, Ag atom deposits with an appointed deposition rate, incident angle. A uniform rand number generator which decides the evaporated atom’s arriving site has been carefully chosen. The arrival of incident Ag particle at the substrate is modeled as a Monte Carlo ballistic deposition models (BD) process [24] and the self-shadowing effect is considered. It is assumed that, as in the ballistic deposition model [25], particles stick initially onto the first position where they touch the surface [26–28]. The assumption of our model is that we have abandoned the solid-on-solid approximation and allowed the system to form voids and overhangs during film growth. The schematic of 3D Monte Carlo simulation of ballistic deposition at glancing incidence has been introduced in detail in our previous work [29]. For GLAD growth of Ag films in this work, the diffusion processes are identified according to their number of nearest neighbors in an initial and finial state of a jumping atom in our simulation model. The extended model in this work has been developed by introducing ES barrier, edge diffusion and kink rounding diffusion barriers. The barrier a particle encounters while diffusing on a flat surface is Et , and each diffusion event is a nearest neighboring jump. The barrier a particle encounters while diffusing down a monolayer step is Es . The corresponding atomic diffusion jump frequencies are Dt , Ds . Besides, the effects of edge diffusion Ee and kink rounding diffusion Ek are also considered in our model. The corresponding diffusion rates are De and Dk . In our model, the atomic diffusion jump frequency is described by the form Di = 0 exp [−Ei /kT], where 0 is the attempt frequency, Ei is the barrier for process i, k is Boltzmann’s constant, and T is the temperature of the substrate.
We use 0.097 eV, 0.13 eV for terrace diffusion barrier Et and ES barrier Es respectively [30]. Besides, we take edge diffusion barrier is Ee = 0.28 eV and kink rounding barrier is Ek = 0.08 eV [31]. Furthermore, we set 1 × 1011 s−1 as the attempt frequency 0 of atomic diffusion jump [32]. The film growth rate r is determined by L2 F [32,33], where F is the flux of incoming particles (deposition rate) in ML/s, and L2 is the computational dimension of substrate. The average time has an inverse relationship with r. The value of surface diffusion strength D/F depends on the energetic of the film material, the film temperature, the deposition rate, and the concentration of residual gases in the deposition chamber in a complicated manner [34,35]. Here, we may adjust D/F to change the growth conditions. 3. Results and discussions It is well known that there is strong shadowing effect in the GLAD growth. In Fig. 1, the schematic of the growth process is shown. The difference in the growth orientation can be attributed to the different distribution of shadowing effect. In the case of no rotation, the shadowing effect is unidirectional, which leads to the formation of columns inclined toward the source. While under the condition of rapid rotation, the shadowing effect can be assumed to revolve around the substrate normal. The rotate rate is so rapid that the shadowing distribution is isotropic around the substrate normal and lead to vertically aligned growth of nanorods. In order to study the dynamics of surface morphology and growth of nanostructures, we perform KMC simulation with the scheme described above. The deposition angles are both 86◦ . The substrate temperature is 300 K. The substrate rotation rate is 0.56 rev/ML. As can be seen from Fig. 2(a) and (b), the nanorods were grown aslant with no substrate rotation, while with rapid substrate rotation the nanorods were grown vertically aligned. We deposited Ag films on nonrotation and rapid rotation substrates respectively at high incident angle of 86◦ . The deposition was carried out at room temperature in a high vacuum chamber with a base pressure of 5 × 10−4 Pa. For both experiments, the deposition rate was kept constant at nominal 3 A˚ s−1 . At rapid rotation condition, the substrate was rotated continuously with a speed of 10 rpm. Film microstructures were investigated by using
Fig. 1. Schematic illustrations of the Ag nanorod growth by glancing angle deposition on substrate with rotation and without rotation.
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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Fig. 2. The simulated morphologies of Ag films deposited at 86◦ without rotation (a) and with rapid rotation (0.56 rev/ML) (b) respectively. Here, the temperature of substrate is 300 K, and the deposition rate is 32 ML/s.
Fig. 3. Scanning electron micrograph of Ag films deposited at 86◦ without substrate rotation (a) and with rapid substrate rotation (10 rpm) (b) respectively.
scanning electron microscope (SEM). Fig. 3(a) and (b) shows that without substrate rotation the nanorods were grown aslant on the substrate, while with rapid substrate rotation the nanorods were grown vertically aligned. We can see that the growth trend of the simulation agrees with the experiment above well. The dynamic scaling hypothesis suggests that the growth exponent ˇ has the scaling form w ∼ tˇ , where w is called the rootmean-square (rms) roughness, w =
N −1
i
2
(hi − h) and t is the
film height [36,37]. Here, N is the total number of surface sites, hi is the height of ith site, and h is the average height of the surface. The ˇ can be used as reference to describe the growth mode, and a smaller value of ˇ leads to a smoother surface [38,39]. For small rotation rates of substrate, rotation forces the mounds to grow in a spiral fashion as the substrate is rotated. In the case of ballistic deposition, this “spiral growth” tends to fill in the gaps between mounds, thus, reducing the surface roughness. As the rotation rate increases, the amount of spiral growth is reduced, thus, leading to an increase in the surface roughness [40]. In order to explore the effects of substrate rotation on the surface morphology, we have investigated the roughness distributions with various rotation rates. As can be seen in Fig. 4, the surface roughness is found to increase sharply with rotation rate for small rotation rates ˝ < 0.3 rev/ML due to the fact that the amount of spiral growth is reduced. As the rotation rate continues to increase, the surface roughness increases asymptotically, which indicates there is an intrinsic transition of growth mode. In this case, the growth mode turns from “spiral growth” to “vertical growth”, which leads to a transition of surface roughness. Therefore, the critical rotate of the nanorods just vertical to the substrate can be deduced to be 0.3 rev/ML here. As the rotation rate continues to increase, due to the fact that the nanorods become more regular in “vertical growth”, the surface roughness increases asymptotically and then saturates for ˝ > 1 rev/ML. Fig. 5 shows the growth exponent ˇ obtained from a linear analysis of the log w via log t as a function of film height at D/F = 3.7 × 106 . We can see that growth at normal incidence starts with a small growth exponent, suggesting producing a low porosity film. The
growth exponent then increases quite sharply for the initial stage t < 14 ML and peaks at t ∼ 35 ML, after which ˇ turns to decrease. We observe a qualitatively similar behavior in the growth exponent evolution of the GLAD film for t < 14 ML. Besides, we can find that ˇ is always smaller than 0.5 at normal incidence. However, ˇ continues to rise monotonously and asymptotically in the case of the GLAD growth, which means it leads to a rougher surface. As is shown in Fig. 5, the growth exponent evolutions are diverging in normal and high glancing incidence at t ∼ 18 ML, which proves that shadowing instabilities overpower the smoothing effects associated with surface diffusion at t ∼ 14 ML. Therefore, the growth model transition from two dimensional to 3D islanded growth occurs. As the growth proceeds, ˇ continues to rise and larger than 0.5 with growth height increasing in the case of 86◦ incidence. In addition, we find that rapid substrate rotation tends to reduce the growth exponent moderately in the case of ballistic deposition. This is due to the fact that rotation tends to reduce
FIG. 4. The root-mean-square (rms) roughness distributions as a function of the rotation rate at the mean film thickness of 45 ML for = 86◦ (F = 32 ML/s and T = 300 K).
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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because surface diffusion still dominates the growth process. As the growth proceeds, the nanorod growth is observed obviously after t > 14 ML, which indicates that the shadowing effect dominates the formation of nanostructure. Furthermore, one can see that as D/F decreases, the thickness where the transition of growth modes occur decreases. For small D/F, the particle will be difficult to diffuse into the shadowed region and lead more readily to a porous structure. So we can adjust D/F to change the thickness where the transition of growth mode occurs. 4. Conclusions
Fig. 5. The growth exponent evolution as a function of film height under the conditions of normal incidence and glancing angle deposition (D/F = 3.7 × 106 ).
the amount of shadowing, thus, reducing the roughness [40] and growth exponent. According theoretical considerations, the high deposition angle will lead to the preferential growth of the tallest features on the surface and the shadowing effect. Mounds are pinched off and deep grooves are formed, causing vacancies and voids to get trapped, resulting in a porous film [41]. As the film growth proceeds, the shadowing effect becoming more and more significant and then the gaps between columns completely prevent the incorporation of new material in the gaps. Therefore, under the GLAD condition, the evolution of growth exponent indicates that with film coverage increasing, the surface of thin film becomes rougher. The growth process transition occurs due to an enhanced shadowing effect with increasing film height. Furthermore, we investigate the relative density distributions as a function of thin film thickness for different ratios of diffusion coefficient to deposition rate (D/F) as shown in Fig. 6. It is found that the relative density of Ag film drops dramatically in the early stage of growth and becomes stable at a thickness of about 14 ML (D/F = 3.7 × 106 ), which can also prove the transition from two dimensional to 3D islanded growth. The insets in Fig. 6 demonstrate the evolution of morphologies at the deposition angle of 86◦ with the film thicknesses of 7 ML, 41 ML. We can see that the nanorod growth is not apparent at t < 14 ML,
FIG. 6. The relative density distributions as a function of film thickness with various values of D/F at the deposition angle of 86◦ . The insets show the evolution of morphologies at the deposition angle of 86◦ when the film thicknesses are 7 ML, 41 ML respectively.
The initial growth behavior of Ag film by GLAD is studied both through KMC simulations and experiments. We demonstrate that without substrate rotation the nanorods were grown aslant on the substrate due to shadowing anisotropy, while with rapid substrate rotation the nanorods were grown vertically aligned due to shadowing isotropy. Good agreement of growth trends between simulations and experiments have been achieved. We quantitatively explore the growth exponent evolution and discuss the kinetic mechanism behind the experiment theoretically. In the case of substrate rotation, effects of the substrate rotation rate on the surface roughness and growth mode are pursued, and the critical rotate of the nanorods just vertical to the substrate is revealed. Furthermore, the growth exponent evolutions of Ag films in normal and glancing angle depositions are found similar in the very early stage of growth. The value of ˇ continues to rise asymptotically in case of GLAD, while there is a peak and turns to decrease in normal incidence deposition. The competing effect between surface diffusion and ballistic shadowing is studied. The diverging of growth exponents with film height increasing indicates that shadowing instabilities overpower the smoothing effects associated with surface diffusion. Furthermore, our results also demonstrate the transition from two dimensional to 3D islanded growth under the condition of high glancing angle depositions. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant no. 60977042). References [1] M.J. Brett, M.M. Hawkeye, Science 319 (2008) 1192. [2] S.R. Kennedy, M.J. Brett, Nano Letters 2 (2002) 59. [3] K.D. Harris, J.R. McBride, K.E. Nietering, M.J. Brett, Sensors and Materials 13 (2001) 225. [4] Y.P. Zhao, D.X. Ye, P.I. Wang, G.-C. Wang, T.-M. Lu, International Journal of Nanoscience 1 (2002) 87. [5] M.W. Seto, B. Dick, M.J. Brett, Journal of Micromechanics and Microengineering 11 (2001) 582. [6] M. Malac, R.F. Egerton, Journal of Vacuum Science and Technology A 19 (2001) 158. [7] Y.-P. Zhao, D.-X. Ye, G.-C. Wang, T.-M. Lu, Nano Letters 2 (2002) 351. [8] A.T. Wu, M.J. Brett, D.J. Broer, Sensors and Materials 13 (2001) 399. [9] Y.J. Jen, A. Lakhtakia, C.W. Yu, C.T. Lin, Optics Express 17 (2009) 7784. [10] J. Krug, P. Meakin, Physical Review A 40 (1989) 2064. [11] T. Smy, D. Vick, M.J. Brett, S.K. Dew, A.T. Wu, J.C. Sit, K.D. Harris, Journal of Vacuum Science and Technology A 18 (2000) 2507. [12] T. Karabacak, G.-C. Wang, T.-M. Lu, Journal of Vacuum Science and Technology A 22 (2004) 1778. [13] Y. Shim, J.G. Amar, Physical Review Letters 98 (2007) 046103. [14] S. Dijken, L.C. Jorritsma, B. Poelsema, Physical Review Letters 82 (1999) 4038. [15] F.L.W. Rabbering, G. Stoian, R. van Gastel, H. Wormeester, B. Poelsema, Physical Review B 81 (2010) 115425. [16] G. Ehrlich, F.G. Hudda, Journal of Chemical Physics 44 (1966) 1039. [17] R.L. Schwoebel, E.J. Shipsey, Journal of Applied Physics 37 (1966) 3682. [18] S.K. Xiang, Hanchen Huang, Applied Physics Letters 92 (2008) 101923. [19] S.J. Liu, H.C. Huang, C.H. Woo, Applied Physics Letters 80 (2002) 3295. [20] J. Wang, H.C. Huang, T.S. Cale, Modelling and Simulation in Materials Science and Engineering 12 (2004) 1209. [21] L.G. Zhou, H.C. Huang, Physical Review Letters 101 (2008) 266102.
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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[22] M.M. Hawkeye, M.J. Brett, Journal of Vacuum Science and Technology A 25 (2007) 1317. [23] A. Amassian, K. Kaminska, M. Suzuki, L. Martinu, K. Robbie, Applied Physics Letters 91 (2007) 173114. [24] P. Meakin, P. Ramanlal, L.M. Sander, R.C. Ball, Physical Review A 34 (1986) 5091. [25] J. Yu, J.G. Amar, Physical Review E 65 (2002) 060601(R). [26] A. Yanguas-Gil, J. Cotrino, A. Barranco, A.R. G-Elipe, Physical Review Letters 96 (2006) 236101. [27] T. Karabacak, G.-C. Wang, T.-M. Lu, Journal of Applied Physics 94 (2003) 7723. [28] T. Karabacak, J.P. Singh, Y.-P. Zhao, G.-C. Wang, T.-M. Lu, Physical Review B 68 (2003) 125408. [29] J.S. Ji, Y.M. Yin, W.Y. Wei, T.J. Jia, Chinese Physics Letters 25 (2008) 4456. [30] M.Z. Li, P.-W. Chung, E. Cox, C.J. Jenks, P.A. Thiel, J.W. Evans, Physical Review B 77 (2008) 033402. [31] J.W. Evans, P.A. Thiel, M.C. Bartelt, Surface Science Reports 61 (2006) 61. [32] S.J. Jiang, Y.W. Wei, Z.Y. Chen, H.Z. Wang, Journal of Applied Physics 107 (2010) 034303.
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[33] Z.Y. Chen, Y. Zhu, S.H. Chen, Z.R. Qiu, S.J. Jiang, Applied Surface Science 257 (2011) 6102. [34] D.-X. Ye, C.L. Ellison, B.-K. Lim, T.-M. Lu, Journal of Applied Physics 103 (2008) 103531. [35] D. Vick, L.J. Friedrich, S.K. Dew, M.J. Brett, K. Robbie, M. Seto, T. Smy, Thin Solid Films 339 (1999) 88. [36] X. Tan, Y.C. Zhou, X.J. Zheng, Surface Science 588 (2005) 175. [37] X. Tan, G. Ouyang, G.W. Yang, Physical Review B 73 (2006) 195322. [38] A.-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995. [39] J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang, Physical Review B 62 (2000) 2118. [40] Y. Shim, M.E. Mills, V. Borovikov, J.G. Amar, Physical Review E 79 (2009) 051604. [41] L.A. Zepeda-Ruiz, E. Chason, G.H. Gilmer, Y. Wang, H. Xu, A. Nikroo, A.V. Hamza, Applied Physics Letters 95 (2009) 151910.
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
ARTICLE IN PRESS Applied Surface Science xxx (2012) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation Shuhan Chen a,b , Jingshu Liang a , Yunjie Mo a , Difan Luo a , Shaoji Jiang a,∗ a b
State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China School of Physics and Optical Information Sciences, Jia Ying University, Meizhou, 514015, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 30 August 2012 Received in revised form 11 October 2012 Accepted 11 October 2012 Available online xxx Keywords: Shadowing-dominnated growth Glancing angle deposition Kinetic Monte Carlo simulation
a b s t r a c t A three-dimensional (3D) kinetic Monte Carlo simulation was performed for the growth evolution of Ag films during glancing angle deposition (GLAD). Under the GLAD conditions, we demonstrate that without substrate rotation the nanorods are grown aslant due to shadowing anisotropy, while with the rapid substrate rotation the nanorods are grown vertically aligned due to shadowing isotropy. Good agreement of growth trends between simulations and experiments has been achieved. In the case of substrate rotation, the critical rotate rate of nanorods just vertical to the substrate has been found. The growth exponent evolutions of Ag films in normal and glancing angle depositions are found similar in the very early stages of growth. The diverging of growth exponents with film height increasing indicates that shadowing instabilities overpower the smoothing effects associated with surface diffusion. Furthermore, we demonstrate the transition from two-dimensional to 3D islanded growth under the condition of high glancing angle deposition. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Recently, materials scientists have adopted glancing angle deposition (GLAD) as an important tool for nanostructure fabrication [1]. During traditional film deposition, a stream of vapor-phase atoms strikes a substrate perpendicularly. In GLAD method, materials are deposited at a highly oblique angle from substrate normal, resulting in a flexible and straightforward method of producing nanostructure and porous thin-film materials in unusual configurations. The ability to control the column orientation and porosity of nanostructure leads to particularly interesting applications of GLAD, such as nanostructure thin films, catalyst support, micromechanical systems, optoelectronics, and sensing systems [2–8]. For example, recently, a negative index metamaterial with double negative or single negative property can be easily formed by GLAD in the visible spectrum [9]. The interest in nanostructure materials fabricated by GLAD has given a new impulse to the study of the phenomena at the atomic level, which contributes to the formation and growth of nanoclusters and nanorods. Many kinetic Monte Carlo (KMC) simulation works have been proposed recently to study this topic [10–15]. It is known that diffusion and shadowing effect are critical factors which influence surface morphology of thin film grown by GLAD. During thin film growth, an adatom may diffuse on a flat surface, along a step, or across a step. The diffusion barrier of an adatom
down a step is usually larger than that on a flat surface and the extra barrier is the Ehrlich–Shwoebel (ES) barrier [16–21]. Larger diffusion barriers may lead to more roughly surfaced thin films and smaller diameters of nanorods. To successfully synthesize the thin films produced by GLAD with both a well-defined value of surface roughness and well-defined surface morphologies, it is of great importance to gain a fundamental understanding of the interplay between the mechanisms involved in the growth process of thin films. Various attempts have been made to explain the tilt angle. Due to the sensitivity of the columnar structure on deposition conditions and material dependent parameters, all materials behave differently and accurate predictions are difficult [22]. Recently, shadowing instabilities can dramatically alter the very early stages of growth of amorphous thin films on nominally smooth surfaces by experiment [23]. In this work, we demonstrate the growth mechanism under conditions of rapid rotation and no rotation of substrates at high glancing angle conditions both through KMC simulations and experiments. Moreover, we discuss the growth exponent evolution and the onset of shadowing-dominated growth of Ag films grown at normal and high glancing angle deposition of the vapor flux theoretically. The competing process between surface diffusion and shadowing is also discussed.
2. Theoretical model of KMC ∗ Corresponding author. Tel.: +86 20 84113306; fax: +86 20 84113306. E-mail address: [email protected] (S. Jiang).
Our simulation is performed with a finite volume V = Lx × Ly × Lz arranged according to the ABC sequence of (1 1 1) fcc surfaces which
0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2012.10.062
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
G Model APSUSC-24443; No. of Pages 5 2
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are described by triangular lattices, where Lx = Ly = 512 but Lz can be changed according to the surface coverage. The lattice period is 0.3 nm. There are two main ways to handle the boundaries of the simulation during deposition, diffusion and ballistic transport: mirrored and periodic. In this study, however, periodic boundary conditions are applied to the four extremes of the samples to reduce discontinuity. A particle can move across one extreme and appear at the opposite one; particles placed at two opposite sites of the sample can be part of the opposite columns. To investigate the general characteristics of Ag films in the early stage of growth, our model does not involve the substrate patterning prior to GLAD. In our model, Ag atom deposits with an appointed deposition rate, incident angle. A uniform rand number generator which decides the evaporated atom’s arriving site has been carefully chosen. The arrival of incident Ag particle at the substrate is modeled as a Monte Carlo ballistic deposition models (BD) process [24] and the self-shadowing effect is considered. It is assumed that, as in the ballistic deposition model [25], particles stick initially onto the first position where they touch the surface [26–28]. The assumption of our model is that we have abandoned the solid-on-solid approximation and allowed the system to form voids and overhangs during film growth. The schematic of 3D Monte Carlo simulation of ballistic deposition at glancing incidence has been introduced in detail in our previous work [29]. For GLAD growth of Ag films in this work, the diffusion processes are identified according to their number of nearest neighbors in an initial and finial state of a jumping atom in our simulation model. The extended model in this work has been developed by introducing ES barrier, edge diffusion and kink rounding diffusion barriers. The barrier a particle encounters while diffusing on a flat surface is Et , and each diffusion event is a nearest neighboring jump. The barrier a particle encounters while diffusing down a monolayer step is Es . The corresponding atomic diffusion jump frequencies are Dt , Ds . Besides, the effects of edge diffusion Ee and kink rounding diffusion Ek are also considered in our model. The corresponding diffusion rates are De and Dk . In our model, the atomic diffusion jump frequency is described by the form Di = 0 exp [−Ei /kT], where 0 is the attempt frequency, Ei is the barrier for process i, k is Boltzmann’s constant, and T is the temperature of the substrate.
We use 0.097 eV, 0.13 eV for terrace diffusion barrier Et and ES barrier Es respectively [30]. Besides, we take edge diffusion barrier is Ee = 0.28 eV and kink rounding barrier is Ek = 0.08 eV [31]. Furthermore, we set 1 × 1011 s−1 as the attempt frequency 0 of atomic diffusion jump [32]. The film growth rate r is determined by L2 F [32,33], where F is the flux of incoming particles (deposition rate) in ML/s, and L2 is the computational dimension of substrate. The average time has an inverse relationship with r. The value of surface diffusion strength D/F depends on the energetic of the film material, the film temperature, the deposition rate, and the concentration of residual gases in the deposition chamber in a complicated manner [34,35]. Here, we may adjust D/F to change the growth conditions. 3. Results and discussions It is well known that there is strong shadowing effect in the GLAD growth. In Fig. 1, the schematic of the growth process is shown. The difference in the growth orientation can be attributed to the different distribution of shadowing effect. In the case of no rotation, the shadowing effect is unidirectional, which leads to the formation of columns inclined toward the source. While under the condition of rapid rotation, the shadowing effect can be assumed to revolve around the substrate normal. The rotate rate is so rapid that the shadowing distribution is isotropic around the substrate normal and lead to vertically aligned growth of nanorods. In order to study the dynamics of surface morphology and growth of nanostructures, we perform KMC simulation with the scheme described above. The deposition angles are both 86◦ . The substrate temperature is 300 K. The substrate rotation rate is 0.56 rev/ML. As can be seen from Fig. 2(a) and (b), the nanorods were grown aslant with no substrate rotation, while with rapid substrate rotation the nanorods were grown vertically aligned. We deposited Ag films on nonrotation and rapid rotation substrates respectively at high incident angle of 86◦ . The deposition was carried out at room temperature in a high vacuum chamber with a base pressure of 5 × 10−4 Pa. For both experiments, the deposition rate was kept constant at nominal 3 A˚ s−1 . At rapid rotation condition, the substrate was rotated continuously with a speed of 10 rpm. Film microstructures were investigated by using
Fig. 1. Schematic illustrations of the Ag nanorod growth by glancing angle deposition on substrate with rotation and without rotation.
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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Fig. 2. The simulated morphologies of Ag films deposited at 86◦ without rotation (a) and with rapid rotation (0.56 rev/ML) (b) respectively. Here, the temperature of substrate is 300 K, and the deposition rate is 32 ML/s.
Fig. 3. Scanning electron micrograph of Ag films deposited at 86◦ without substrate rotation (a) and with rapid substrate rotation (10 rpm) (b) respectively.
scanning electron microscope (SEM). Fig. 3(a) and (b) shows that without substrate rotation the nanorods were grown aslant on the substrate, while with rapid substrate rotation the nanorods were grown vertically aligned. We can see that the growth trend of the simulation agrees with the experiment above well. The dynamic scaling hypothesis suggests that the growth exponent ˇ has the scaling form w ∼ tˇ , where w is called the rootmean-square (rms) roughness, w =
N −1
i
2
(hi − h) and t is the
film height [36,37]. Here, N is the total number of surface sites, hi is the height of ith site, and h is the average height of the surface. The ˇ can be used as reference to describe the growth mode, and a smaller value of ˇ leads to a smoother surface [38,39]. For small rotation rates of substrate, rotation forces the mounds to grow in a spiral fashion as the substrate is rotated. In the case of ballistic deposition, this “spiral growth” tends to fill in the gaps between mounds, thus, reducing the surface roughness. As the rotation rate increases, the amount of spiral growth is reduced, thus, leading to an increase in the surface roughness [40]. In order to explore the effects of substrate rotation on the surface morphology, we have investigated the roughness distributions with various rotation rates. As can be seen in Fig. 4, the surface roughness is found to increase sharply with rotation rate for small rotation rates ˝ < 0.3 rev/ML due to the fact that the amount of spiral growth is reduced. As the rotation rate continues to increase, the surface roughness increases asymptotically, which indicates there is an intrinsic transition of growth mode. In this case, the growth mode turns from “spiral growth” to “vertical growth”, which leads to a transition of surface roughness. Therefore, the critical rotate of the nanorods just vertical to the substrate can be deduced to be 0.3 rev/ML here. As the rotation rate continues to increase, due to the fact that the nanorods become more regular in “vertical growth”, the surface roughness increases asymptotically and then saturates for ˝ > 1 rev/ML. Fig. 5 shows the growth exponent ˇ obtained from a linear analysis of the log w via log t as a function of film height at D/F = 3.7 × 106 . We can see that growth at normal incidence starts with a small growth exponent, suggesting producing a low porosity film. The
growth exponent then increases quite sharply for the initial stage t < 14 ML and peaks at t ∼ 35 ML, after which ˇ turns to decrease. We observe a qualitatively similar behavior in the growth exponent evolution of the GLAD film for t < 14 ML. Besides, we can find that ˇ is always smaller than 0.5 at normal incidence. However, ˇ continues to rise monotonously and asymptotically in the case of the GLAD growth, which means it leads to a rougher surface. As is shown in Fig. 5, the growth exponent evolutions are diverging in normal and high glancing incidence at t ∼ 18 ML, which proves that shadowing instabilities overpower the smoothing effects associated with surface diffusion at t ∼ 14 ML. Therefore, the growth model transition from two dimensional to 3D islanded growth occurs. As the growth proceeds, ˇ continues to rise and larger than 0.5 with growth height increasing in the case of 86◦ incidence. In addition, we find that rapid substrate rotation tends to reduce the growth exponent moderately in the case of ballistic deposition. This is due to the fact that rotation tends to reduce
FIG. 4. The root-mean-square (rms) roughness distributions as a function of the rotation rate at the mean film thickness of 45 ML for = 86◦ (F = 32 ML/s and T = 300 K).
Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062
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because surface diffusion still dominates the growth process. As the growth proceeds, the nanorod growth is observed obviously after t > 14 ML, which indicates that the shadowing effect dominates the formation of nanostructure. Furthermore, one can see that as D/F decreases, the thickness where the transition of growth modes occur decreases. For small D/F, the particle will be difficult to diffuse into the shadowed region and lead more readily to a porous structure. So we can adjust D/F to change the thickness where the transition of growth mode occurs. 4. Conclusions
Fig. 5. The growth exponent evolution as a function of film height under the conditions of normal incidence and glancing angle deposition (D/F = 3.7 × 106 ).
the amount of shadowing, thus, reducing the roughness [40] and growth exponent. According theoretical considerations, the high deposition angle will lead to the preferential growth of the tallest features on the surface and the shadowing effect. Mounds are pinched off and deep grooves are formed, causing vacancies and voids to get trapped, resulting in a porous film [41]. As the film growth proceeds, the shadowing effect becoming more and more significant and then the gaps between columns completely prevent the incorporation of new material in the gaps. Therefore, under the GLAD condition, the evolution of growth exponent indicates that with film coverage increasing, the surface of thin film becomes rougher. The growth process transition occurs due to an enhanced shadowing effect with increasing film height. Furthermore, we investigate the relative density distributions as a function of thin film thickness for different ratios of diffusion coefficient to deposition rate (D/F) as shown in Fig. 6. It is found that the relative density of Ag film drops dramatically in the early stage of growth and becomes stable at a thickness of about 14 ML (D/F = 3.7 × 106 ), which can also prove the transition from two dimensional to 3D islanded growth. The insets in Fig. 6 demonstrate the evolution of morphologies at the deposition angle of 86◦ with the film thicknesses of 7 ML, 41 ML. We can see that the nanorod growth is not apparent at t < 14 ML,
FIG. 6. The relative density distributions as a function of film thickness with various values of D/F at the deposition angle of 86◦ . The insets show the evolution of morphologies at the deposition angle of 86◦ when the film thicknesses are 7 ML, 41 ML respectively.
The initial growth behavior of Ag film by GLAD is studied both through KMC simulations and experiments. We demonstrate that without substrate rotation the nanorods were grown aslant on the substrate due to shadowing anisotropy, while with rapid substrate rotation the nanorods were grown vertically aligned due to shadowing isotropy. Good agreement of growth trends between simulations and experiments have been achieved. We quantitatively explore the growth exponent evolution and discuss the kinetic mechanism behind the experiment theoretically. In the case of substrate rotation, effects of the substrate rotation rate on the surface roughness and growth mode are pursued, and the critical rotate of the nanorods just vertical to the substrate is revealed. Furthermore, the growth exponent evolutions of Ag films in normal and glancing angle depositions are found similar in the very early stage of growth. The value of ˇ continues to rise asymptotically in case of GLAD, while there is a peak and turns to decrease in normal incidence deposition. The competing effect between surface diffusion and ballistic shadowing is studied. The diverging of growth exponents with film height increasing indicates that shadowing instabilities overpower the smoothing effects associated with surface diffusion. Furthermore, our results also demonstrate the transition from two dimensional to 3D islanded growth under the condition of high glancing angle depositions. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant no. 60977042). References [1] M.J. Brett, M.M. Hawkeye, Science 319 (2008) 1192. [2] S.R. Kennedy, M.J. Brett, Nano Letters 2 (2002) 59. [3] K.D. Harris, J.R. McBride, K.E. Nietering, M.J. Brett, Sensors and Materials 13 (2001) 225. [4] Y.P. Zhao, D.X. Ye, P.I. Wang, G.-C. Wang, T.-M. Lu, International Journal of Nanoscience 1 (2002) 87. [5] M.W. Seto, B. Dick, M.J. Brett, Journal of Micromechanics and Microengineering 11 (2001) 582. [6] M. Malac, R.F. Egerton, Journal of Vacuum Science and Technology A 19 (2001) 158. [7] Y.-P. Zhao, D.-X. Ye, G.-C. Wang, T.-M. Lu, Nano Letters 2 (2002) 351. [8] A.T. Wu, M.J. Brett, D.J. Broer, Sensors and Materials 13 (2001) 399. [9] Y.J. Jen, A. Lakhtakia, C.W. Yu, C.T. Lin, Optics Express 17 (2009) 7784. [10] J. Krug, P. Meakin, Physical Review A 40 (1989) 2064. [11] T. Smy, D. Vick, M.J. Brett, S.K. Dew, A.T. Wu, J.C. Sit, K.D. Harris, Journal of Vacuum Science and Technology A 18 (2000) 2507. [12] T. Karabacak, G.-C. Wang, T.-M. Lu, Journal of Vacuum Science and Technology A 22 (2004) 1778. [13] Y. Shim, J.G. Amar, Physical Review Letters 98 (2007) 046103. [14] S. Dijken, L.C. Jorritsma, B. Poelsema, Physical Review Letters 82 (1999) 4038. [15] F.L.W. Rabbering, G. Stoian, R. van Gastel, H. Wormeester, B. Poelsema, Physical Review B 81 (2010) 115425. [16] G. Ehrlich, F.G. Hudda, Journal of Chemical Physics 44 (1966) 1039. [17] R.L. Schwoebel, E.J. Shipsey, Journal of Applied Physics 37 (1966) 3682. [18] S.K. Xiang, Hanchen Huang, Applied Physics Letters 92 (2008) 101923. [19] S.J. Liu, H.C. Huang, C.H. Woo, Applied Physics Letters 80 (2002) 3295. [20] J. Wang, H.C. Huang, T.S. Cale, Modelling and Simulation in Materials Science and Engineering 12 (2004) 1209. [21] L.G. Zhou, H.C. Huang, Physical Review Letters 101 (2008) 266102.
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Please cite this article in press as: S. Chen, et al., Onset of shadowing-dominated growth of Ag films in glancing angle deposition: Kinetic Monte Carlo simulation, Appl. Surf. Sci. (2012), http://dx.doi.org/10.1016/j.apsusc.2012.10.062