"Enhanced Layer Coverage of Thin Films by Oblique Angle Deposition"

Mater. Res. Soc. Symp. Proc. Vol. 859E 2005 Materials Research Society JJ9.5.1 "Enhanced Layer Coverage of Thin Films by Oblique Angle Deposition" * karabt@rpi.edu Tansel Karabacak *, Gwo-Ching Wang, and Toh-Ming Lu Department of Physics, Applied Physics, and Astronomy Rensselaer Polytechnic Institute Troy, NY 12180-3590 ABSTRACT The characteristics of nucleation and island growth in oblique angle deposition with substrate rotation have recently attracted interest due to the formation of novel 3D nanostructures by a physical self-assembly process. In this study, we present the results of a solid-on-solid growth simulation by a kinetic Monte Carlo algorithm that explores the layer coverage evolution of thin films during oblique angle deposition. The simulations accounted for oblique incidence flux, shadowing effect, surface diffusion, and substrate rotation. The layer coverage, the ratio of average island volume to average island size, and root-mean-square (RMS) roughness values are reported for the initial stages of island growth from submonolayer thicknesses up to a few monolayers. RMS roughness was also investigated for later stages of the growth. Our results show that, for small deposition angles and with limited or no surface diffusion included, the average growth rate of islands is faster in lateral directions that results in enhanced layer coverages and smoother films. This is due to that the sides of the islands can be exposed to the incident flux more effectively at small deposition angles. On the other hand, normal incidence and high oblique angle depositions give poorer layer coverages and much rougher films due to the slower growth rates in lateral directions. INTRODUCTION Although detailed studies have been performed [1-9] on the evolution of islands at the initial stages of molecular-beam epitaxy, very little work has been reported for the early-stage of growth during oblique angle deposition. Previously, we investigated the fundamental nucleation and growth mechanism during oblique angle growth with substrate rotation [10]. Through the analysis of island density, island size distribution, and island-island correlation during the initial stages of oblique angle growth, it was shown that isolated islands with quasi-periodic distribution were formed as a natural consequence of the shadowing effect. When the deposition angle is large, these isolated islands could lead to the formation of novel 3D nanostructures (e.g. nanorods at a fast substrate rotation speed and nanosprings at a slow substrate rotation speed) at later stages of growth. These films are extremely rough and the layer coverages are very poor. On the other hand, in this study we will present our simulation results that indicate that for a range of small deposition angles, it is possible to obtain smoother films with superior layer coverages compared to the films deposited either by a normal incidence or a high oblique angle flux. The results may apply well to the experimental systems with little or insignificant surface diffusion, where the surface roughness and layer coverage are often challenging issues. MONTE CARLO SIMULATIONS In a typical oblique angle deposition, an atom approaches the rotating surface with an oblique angle θ, the polar angle measured from the surface normal. Some of the important parameters in

JJ9.5.2 this type of deposition are the oblique angle, the ratio of diffusion-to-deposition rate (D/F), and the rotation speed. Due to the lack of an appropriate analytical model, a solid-on-solid growth simulation code by a kinetic Monte Carlo algorithm that includes these parameters has been developed. The growth simulations start with the approach of a uniform flux of atoms towards a flat substrate surface at an angle θ. In each simulation step, an atom is sent towards a randomly chosen lattice point on a surface of size L L. For a substrate rotation, the substrate plane is kept stationary and each atom is sent with a change of φ in the azimuthal angle. A freshly deposited adatom may land on top of an existing island, or on top of another monomer, or simply on the bare substrate surface. Overhangs are not allowed in this part of study that the growth of 2D islands at early stages was investigated. If the surface diffusion is allowed, then a choice is made between another deposition step and a diffusion step of a randomly chosen monomer (an adatom with no nearest-neighbors except the underlying atom) on the surface. In the diffusion step, a randomly chosen monomer executes a single hop to a nearest-neighbor lattice site. In order to properly keep track of competing diffusion and deposition rates, the deposition step is carried out with a probability p F = 1/[1+N 1 (D/F)], where N 1 is the monomer density per site, D is the diffusion rate, and F is the deposition rate [1]. A list of monomers is continuously updated, and if a monomer encounters another particle (i.e. another monomer or a part of a cluster) as its nearest neighbor, then that monomer is added to the cluster and removed from the monomer list (irreversible growth where detachment of an edge atom is not included). Once this step is complete, another atom is sent and the deposition and diffusion steps are repeated. We note that, due to the lack of overhangs in the model used, the atom that land on the sidewalls of a steep island slides down to the bottom surface. Therefore, this may incorporate an intrinsic surface diffusion in addition to the given D/F. The simulations typically involved a system size of L L = 512 512, with periodic boundary conditions. For substrate rotation we set φ = 3.6 10-3 degrees. Averages of the analyzed results were taken over 10 runs, and simulations were conducted for different θ ranging from 0 o to 85 o, and different D/F ranging from 0 to 10 8. The simulations created average thicknesses up to a few monolayers. In our case, one monolayer thick film (d = 1) corresponds to 512 512 deposited particles. The following quantities were extracted from each simulation: layer coverage Θ n, average island volume to average island size ratio V/S, and root-mean-square (RMS) roughness w as a function of average film thickness d and deposition angle θ. The layer coverage Θ n is defined as the ratio of the occupied sites to non-occupied ones at the n th layer. The substrate is labeled as n = 0, the first layer just on top of the substrate is labeled as n = 1, and so on. The 2 RMS roughness w is calculated by w = [ h( r ) < h > ], where h(r) is the height of a surface at a position r, and <h> is the average height of a surface. RESULTS AND DISCUSSION In order to see the effects of oblique angle more clearly, we first set the surface diffusion rate to zero (D/F = 0). Figure 1(a) shows the evolution of layer coverage for the first initial layer (Θ n=1 ) as a function of average film thickness for various deposition angles θ. As expected, high oblique angles give poor layer coverages due to the shadowing effect and the formation of isolated

JJ9.5.3 vertical islands. On the other hand, when the flux is incident at smaller oblique angles, a larger portion of the substrate seems to be covered compared to the depositions at the normal and high oblique angle incidences. In more detail, Fig. 1(b) plots the layer coverage Θ n=1 values extracted from a given film thickness as a function of the deposition angle. In other words, the figure compares the coverage of films that contain the same number of deposited particles but at different angles of flux. Interestingly, the layer coverage is improved as the angle is changed from normal incidence up to ~45 o, starts to fall gradually between 45 o - 70 o, and more rapidly for θ > 70 o. In fact, as can be seen in Fig. 1(c), the layer coverage for oblique angle growth is improved almost linearly with θ up to ~20% at ~45 o as compared to the normal incidence deposition. In addition, the enhancement percentage reaches the high values for a range of angles at thicknesses close to one monolayer. As the growth proceeds to thicker layers, at deposition angles > 70 o, the coverage values start to become similar or poorer compared to the normal incidence deposition due to the severe shadowing effect at these high angles. Layer coverage Θ n=1 D/F = 0 (a) θ = 0 o θ = 30 o θ = 80 o 0.0 0.0 0.5 1.5 2.0 2.5 3.0 Layer coverage Θ n=1 0.9 0.7 0.5 0.3 (b) d = 1.50 d = 0 d = 0.35 d = 5 Relative layer coverage Θ n=1 enhancement compared to θ = 0 o 20% 15% 10% 5% 0% -5% -10% (c) Improvement in coverage d = 5 d = 0.35 Poorer coverage d = 0 d = 1.25 Figure 1: (a) Evolution of layer coverage (Θ n=1 ) vs. film thickness for various deposition angles, (b) Evolution of layer coverage (Θ n=1 ) vs. deposition angles θ for various film thicknesses, (c) Enhancement in the layer coverage (compared to normal incidence films) vs. deposition angles θ for various film thicknesses. All are oblique angle deposition with substrate rotation. Surface diffusion is set to zero (D/F = 0).

JJ9.5.4 The V/S (ratio of average island volume to average island size) provides information about the relationship between the vertical growth rate and the lateral growth rate of islands along the surface plane. Figure 2 shows the plots of V/S as a function of θ calculated for different film thicknesses. V/S decreases as θ increases up to θ 45 o that indicates that lateral growth is enhanced at low deposition angles, while vertical growth is promoted at high angles (θ > 70 o ). This is consistent with the enhanced relative layer coverage shown in Fig. 1(c). Average island volume/size ratio V/S 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 d = 1.50 d = 0 d = 5 Figure 2: The ratio of average island volume to average island size (V/S) is plotted as function of deposition angle for various film thicknesses. The enhancement in lateral growth during oblique angle growth is believed to be due to that the sides of islands can be exposed to the incident flux more effectively, especially at smaller deposition angles. However, in order to achieve this, the substrate has to be rotated. Otherwise, under no rotation, one side of the island becomes shadowed and it can cancel the enhancement effect on the exposed side facing the incident flux. RMS roughness w 1.4 1.3 1.2 1.1 0.9 0.7 0.5 (a) d = 1.50 d = 0 d = 0.35 d = 5 RMS roughness w 10 3 10 2 10 1 10 0 10-1 (b) θ = 0 o θ = 30 o θ = 45 o 10-1 10 0 10 1 10 2 10 3 Figure 3: Evolution of RMS roughness (w) during oblique angle deposition. (a) w vs. deposition angle for various film thicknesses and (b) w vs. film thickness for various deposition angles. Due to the improved tendency towards a layer-by-layer growth at small deposition angles, these films are expected to be smoother, too. Figure 3(a) compares the RMS roughness w of the films having the same thickness but deposited at different angles. It is realized that w follows a trend

JJ9.5.5 similar to the enhanced layer coverage and V/S as the deposition angle increases, and the films reach the lowest roughness values at angles 45 o - 70 o. However, as shown in Fig. 3(b), at later stages of growth the shadowing effect can lead to an evolution of very rough surfaces even for small oblique angles. In this regime, the w increases linearly with thickness d obeying the power law w ~ d β with β = 1 consistent with the shadowing growth [11]. Therefore, during the oblique angle growth, there is a stage where the enhancements in the layer coverage and film smoothening start to diminish. In fact, this transitional regime can be estimated as the time of the deposition where the average aspect ratio (AR) of surface features becomes AR > tanθ. At this stage, surface slopes become steeper and sidewalls of the islands get shadowed. For a typical morphology, the average aspect ratio can be approximated as AR w/(ξ/2) = 2w/ξ. Here, ξ is the lateral correlation length and can be measured from the heightheight correlation function analysis [12,13]. Our calculations of AR on the surfaces of simulated films at different θ agree well with this prediction. This stage is reached much quickly for high deposition angles that lead to larger w, and 2w/ξ > tanθ. On the contrary, at small angles it takes longer simulation times to reach 2w/ξ > tanθ due to the relatively slower and faster evolutions of w and ξ, respectively. We have neglected surface diffusion in all discussion up to this point. When the diffusion is switched on (D/F > 0), we observe that the surface diffusion starts to take over the growth process and dominates the island growth mechanism. For example, Fig. 4 plots the evolution of layer coverages for layers n = 1 and n = 2 at intermediate (D/F = 10 3 ) and high surface diffusion (D/F = 10 8 ) rates. At lower D/F (Fig. 4(a)), the effect of oblique incidence is still apparent but it becomes insignificant when surface diffusion reaches high values (Fig. 4(b)). At very high surface diffusion rates, a surface grows layer-by-layer. However, we note that especially at low surface diffusion rates, the surface can become rougher and the effect of oblique angles is expected to be pronounced again. Layer coverage Θ n (a) n = 1 n = 2 θ = 0 o θ = 30 o D/F = 10 3 0.0 0.0 0.5 1.5 2.0 2.5 3.0 Layer coverage Θ n (b) n = 1 n = 2 θ = 0 o θ = 30 o D/F = 10 8 0.0 0.0 0.5 1.5 2.0 2.5 3.0 Figure 4: Evolution of layer coverages Θ n=1 and Θ n=2 vs. film thickness for various deposition angles with surface diffusion included (D/F > 0). (a) D/F = 10 3 and (b) D/F = 10 8.

JJ9.5.6 CONCLUDING REMARKS In conclusion, a summary of our observations above is illustrated in Fig. 5. When the flux is incident at normal incidence (Fig. 5(a)), the nucleation of islands is random and the layer coverage is poor. For small oblique angle depositions with substrate rotation (Fig. 5(b)), the incident flux can reach more efficiently to the sides of islands. Therefore, these islands can grow faster in lateral directions that lead to smoother films and enhanced layer coverages. On the other hand, at high deposition angles (Fig. 5(c)), the growth rate of islands in the vertical direction is higher due to the shadowing effect that makes layer coverages poor, and films get very rough. The effect of oblique angle is significant especially at small or insignificant surface diffusion rates. (a) Normal incidence flux (b) Oblique incidence flux at small angles (c) Oblique incidence flux at high angles Rotating substrate Rotating substrate Figure 5: Layer coverages for (a) normal incidence (b) small oblique angle, and (c) high oblique angle growth. The layer coverage is enhanced for small angle deposition due to the efficient exposure of the island sides to the incident flux. Acknowledgements: The work was supported by NSF. REFERENCES [1] J. G. Amar, F. Family, and P.-M. Lam, Phys. Rev. B 50, 8781 (1994). [2] M. C. Bartelt and J. W. Evans, Phys. Rev. B 46, 12675 (1992). [3] J. W. Evans and N. C. Bartelt, J. Vac. Sci. Technol. A 12, 1800 (1994). [4] G. S. Bales and D. C. Chrzan, Phys. Rev. Lett. 74, 4879 (1995). [5] B.-G. Liu, J. Wu, E.G. Wang, and Z. Zhang, Phys. Rev. Lett. 83, 1195 (1999). [6] J. Wu, B.-G. Liu, Z. Zhang, and E. G. Wang, Phys. Rev. B 61, 13 212 (2000). [7] C. Ratsch and J. A. Venables, J. Vac. Sci. Technol. A 21, S96 (2003). [8] R. Altsinger, H. Busch, M. Horn, and M. Henzler, Surf. Sci. 200, 235 (1988). [9] M. Horn Von Hoegen, J. Falta, and M. Henzler, Thin Solid Films 183, 213 (1989). [10] T. Karabacak, G.-C. Wang, and T.-M. Lu, J. Vac. Sci. Technol. A 22, 1778 (2004). [11] T.-M. Lu, Y.-P. Zhao, J.T. Drotar, T. Karabacak, and G.-C. Wang, Mat. Res. Soc. Symp. Proc. 749, 3 (2003). [12] A.-L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995). [13] Y.-P. Zhao, G.-C. Wang, and T.-M. Lu, Characterization of Amorphous and Crystalline Rough Surfaces: Principles and Applications (Academic Press, 2001).