Quasi-periodic nanostructures grown by oblique angle deposition

Transcription

1 JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER DECEMBER 2003 Quasi-periodic nanostructures grown by oblique angle deposition T. Karabacak, a) G.-C. Wang, and T.-M. Lu Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York Received 2 July 2003; accepted 5 September 2003 We report that tungsten nanocolumns grown by oblique angle sputter deposition develop a quasi-periodic morphology which is not observed for continuous films deposited at normal incidence. The maximum position in power spectral density of the quasi-periodic nanostructures decreases exponentially as a function of thickness. We explain the formation of the quasi-periodic nature by a shadowing length concept which plays a similar role to conventional surface diffusion length. Also, we show that the change of the spatial frequency of the periodicity is a result of the elimination of shorter columns due to the shadowing effect during growth American Institute of Physics. DOI: / I. INTRODUCTION Oblique angle deposition technique also know as glancing angle deposition has attracted the interest of many researchers 1 7 due to its ability to generate nanostructures relatively easily. Oblique angle growth, as illustrated in Fig. 1, basically combines a typical deposition system with a tilted and rotating substrate. Due to the shadowing effect, the incident flux of material that comes to the surface with an oblique angle is preferentially deposited on to the top of surface features with larger values in height. This preferential growth dynamic gives rise to the formation of isolated columnar structures. The nanostructures obtained by oblique angle deposition on flat surfaces can show quasi-periodic height correlations. Controlling the periodicity of these nanostructures stands as an important technological issue. However, there has been no detailed quantitative study on the formation of quasi-periodic nanostructures by oblique angle deposition. In this article, we will present the results and analysis obtained from both experiments and simulations. The experiments consist of the deposition, atomic force microscopy AFM measurements, and power spectral density PSD function analysis to extract the periodicity of the surface of tungsten nanocolumns at different thicknesses by oblique angle sputter deposition. Our simulations are based on a three-dimensional Monte Carlo method, which includes the shadowing and surface diffusion effects. We also perform a similar PSD analysis for the simulated columns and compare them with our experimental results. We then explain how shadowing effects play a role, similar to a conventional surface diffusion length, in the formation of correlated surface features. II. EXPERIMENT A dc magnetron sputtering system was used to deposit tungsten nanocolumns. The films were deposited on oxidized p-si 100 resistivity cm substrates ( 2 2 cm 2 size using a 99.95% pure W cathode target diameter 7.6 a Electronic mail: karabt@rpi.edu cm. The substrate was Radio Corporation of America cleaned 8 and mounted on the sample holder located at a distance of 15 cm from the cathode. The substrate was tilted so that the angle between the surface normal of the target and the surface normal of the substrate was 87. The substrate was rotating around the surface normal with a speed of 0.5 Hz 30 rpm. The base pressure of Torr was achieved by a turbomolecular pump backed by a mechanical pump. In all of the deposition experiments, the power was 200 W at an ultrapure Ar pressure of 1.5 mtorr. The deposition rate was measured to be 5.0 nm/min by a step profilometer and also verified by scanning electron microscopy SEM cross-sectional images. The thickness of the films ranged from 15 nm up to 450 nm. The maximum temperature of the substrate during the deposition was found to be 85 C. At the similar deposition conditions described above, we also deposited tungsten films at normal incidence ( 0 ) for comparison. Figure 2 shows SEM top and cross sectional views of a columnar tungsten film grown by the oblique angle sputter deposition technique. It is seen that some of the columns stop growing and the surviving columns grow larger in size which leads to reduced column density as deposition proceeds. The quantitative surface morphology was measured using contact-mode AFM Park Scientific Auto CP, Woodbury, NY. The radius of the silicon tip is about 10 nm, and the side angle is about 12. The scan sizes were nm 2 with pixels. Representative surface morphologies of columnar films are shown in Figs. 3 a 3 g for various film thicknesses. It is seen that the columnar structure starts to form from the very early times of the growth. The quasiperiodic nature can be qualitatively realized especially at a larger thickness. The morphology of a tungsten film deposited by normal incidence angle deposition is also shown in Fig. 3 h for comparison. The films of normal incidence deposition appear to be continuous and have relatively very small height fluctuations compared to oblique angle deposited columnar tungsten films at a similar thickness. We analyzed the quasi-periodic evolution of the nanocolumns by using the method of PSD analysis. PSD, which is a /2003/94(12)/7723/6/$ American Institute of Physics

2 7724 J. Appl. Phys., Vol. 94, No. 12, 15 December 2003 Karabacak, Wang, and Lu 2 /. Also, z is the surface height at surface point r and A represents the surface area of integration. Therefore, the peak position observed in a PSD profile gives the spatial frequency of a periodic surface component. PSD from a discrete height profile can be estimated as: 9 PSD k x,k y 1 N x N x N y m 1 N y n 1 y 2 z m,n e imk x x ink y, 2 where N x and N y are the dimensions of a discrete surface along x and y directions, respectively. Furthermore, for an isotropic surface, PSD can be circularly averaged in order to obtain better statistics, FIG. 1. A schematic of a oblique angle sputter deposition with substrate rotation and b columnar growth due to the shadowing effects. Fourier transform of surface heights, is defined as: 9 PSD k 1 A 1 2 z r e ikr dr 2, where r r(x,y) is the lateral position vector and k k(k x,k y ) is the spatial frequency with wavelength k FIG. 2. SEM images of tungsten nanocolumns grown by oblique angle deposition: a cross section, and b top view images. The film is 450 nm thick. 1 PSD k 1 N k PSD k x,k y k k x 2 ky 2, where N k is the number of points at constant distance k k 2 x k 2 y, and the summation is the overall points having the same distance. Figure 4 plots the PSD curves obtained using Eq. 3 from the height data of columnar surfaces measured by AFM. It is seen that the surfaces contain a clear PSD peak of maximum value at a well-defined spatial frequency k max. The shape of the PSD intensity distribution, which is centered at k max, sharpens with the increase of thickness. This reflects the improvement of the quasi-periodic nature of the growth morphology. The shift of the PSD peak versus thickness is shown as the inset of Fig. 4. The fit to the data reveals that the change of the peak position has an exponential decay form (k max k o be ad, where d is the thickness and k o, a, and b are constants. This implies that the spatial wavelength increases with the thickness. On the other hand, the films deposited at normal incidence do not show any clear PSD peak. III. SIMULATIONS In order to understand this morphological growth behavior, we use a three-dimensional Monte Carlo method to simulate the oblique angle deposition. As illustrated in Fig. 5, a three-dimensional lattice, which allowed overhangs, is formed by cubic lattice points and each incident atom had the dimensions of one lattice point. The simulations include an obliquely incident flux, substrate rotation, and surface diffusion. We assume a uniform flux of atoms approaching the surface with an angle 85. At each simulation step, an atom is sent toward a randomly chosen lattice point on the surface of size L L. To take into account the substrate rotation, each atom is sent with a change degrees in the azimuthal angle from the previous one. After the incident atom is deposited onto the surface, an atom that is chosen randomly within a box around the impact point is allowed to diffuse to another nearest-neighbor random location. The diffusion step is repeated until D number of jumps is made. Then another atom is sent, and the deposition and diffusion steps are repeated in the similar way. This strategy mimics the surface diffusion at the first impact point during the growth by vapor deposition. It is similar to previous simulation work on surface diffusion during growth

3 J. Appl. Phys., Vol. 94, No. 12, 15 December 2003 Karabacak, Wang, and Lu 7725 FIG. 3. a g AFM images of the tungsten nanocolumns grown by oblique angle deposition at various thicknesses. Vertical scales are different for each image. Notice the formation of quasi-periodic morphology as thickness increases. h Morphology of a continuous tungsten film by normal incidence deposition at similar deposition conditions. Our simulations typically involved a system size of L L N , with periodic boundary conditions. The simulations were conducted for different values of D. Figure 6 shows representative simulated cross sections with increasing rates of D from Figs. 6 a to 6 c. Itis realized that when the diffusion rate approaches zero, columns are fractal-like and it is difficult to define column borders. As we increase the diffusion rate, we start to get columns with smoother borders and they look very much like the experimentally obtained nanocolumns. Diffusion is shown to improve the columnar structure by making columns denser and column edges smoother. After each simulation, PSD data are calculated as a function of thickness d. Figure 7 plots a sample PSD data for a diffusion rate of D 300. We see that there exists a peak shift with thickness qualitatively similar to our experimental results. The PSD maximum k max in spatial frequency as a function of thickness d is also plotted in the inset of Fig. 7. The peak position changes with an exponential decay function that is consistent with the experimental results of tungsten columns in Fig. 4. The results are similar for other values of diffusion. Interestingly, as shown in Fig. 8, even for the simulations without diffusion (D 0), we still get a similar quasi-periodic morphology and also a similar change of the PSD peak position with thickness. IV. DISCUSSIONS We learned that the nanocolumns in films deposited at an oblique incident angle show a clear quasi-periodic structure.

4 7726 J. Appl. Phys., Vol. 94, No. 12, 15 December 2003 Karabacak, Wang, and Lu FIG. 4. PSD function curves calculated at different thicknesses of tungsten nanocolumns. The peak position corresponds to the spatial frequency of the quasi-periodic structure. The inset shows the change of the maximum peak in spatial frequency as a function of thickness. The continuous films of tungsten, deposited at normal incidence, are relatively smooth and do not show any periodic mound structures. This indicates that our experimental conditions normally do not favor the formation of quasi-periodic morphology. Therefore, the periodic structure of a nanocolumn should be due to the shadowing effects of oblique incident flux. Our Monte Carlo simulations also show that shadowing effects actually give rise to quasi-periodic morphological growth even in the absence of diffusion. The spatial wavelength of periodicity increases exponentially as a function of thickness, similar to our experimental results. Both the experiments and simulations reveal that the morphology of oblique angle deposition, even at low diffusion rates, evolves toward a quasi-periodic structure. The rate of change of the peak is shown to be exponential as a function of thickness. The behavior of growth is similar; almost independent of the diffusion. This shows that during oblique angle deposition, the shadowing effects control the evolution of the quasiperiodic surface morphology. Our results bring the question of how the shadowing effects would give rise to the quasi-periodic morphology. Figure 9 illustrates a cartoon showing the shadowing mechanism during oblique angle deposition. The higher surface FIG. 5. A schematic of the three-dimensional Monte Carlo simulations for oblique angle deposition. FIG. 6. Cross-sectional images of simulated columns by a threedimensional Monte Carlo code are shown for various surface diffusion rates: a D 20, b D 100, and c D 500. features shadow a nearby region of lower surface heights. All of the incident atoms that approach this region are captured by the taller surface object. In fact, this mimics the conventional surface diffusion length concept. In the conventional island growth mode, an adatom joins an existing island by hoping through a distance, which is called the diffusion length. 13 Often, the diffusion length is proportional to the ratio D c /F, where D c is the diffusion constant and F is the deposition rate. Each island has a chance to incorporate the randomly diffusing adatoms within the distance of a diffusion length. The typical island island separation can be determined by the diffusion length. Therefore, the lateral distance shadowed by a surface object, which we will call shadowing length, plays a similar role as the diffusion length. The capturing radius due to the shadowing increases

5 J. Appl. Phys., Vol. 94, No. 12, 15 December 2003 Karabacak, Wang, and Lu 7727 FIG. 9. A schematic that shows the definition of shadowing length L. FIG. 7. PSD function curves obtained from simulations are plotted as a function of normalized spatial frequency. The inset shows the maximum PSD peak in spatial frequency as a function of thickness. with the height of the surface feature and the oblique angle, and we estimated this shadowing length to be L h tan, 4 where h is the height of the surface feature. Due to the random effect during growth, some surface columns can become higher by h than the nearby ones and they get additional flux by the increase in shadowing length. As the thickness increases, this can give rise to a competition of columns that can lead to a reduction of the number of surviving columns. After a critical thickness, the columns get long enough so that the height increase h due to the random effect becomes insignificant compared to the height h of the column (h h). From Eq. 4, after this critical thickness, the shadowing length does not increase significantly and all the columns start to grow uniformly. Therefore, column density and spatial frequency of periodicity k max starts to converge to a limiting value, as observed in our results from experiments and simulations. In addition, the mechanism above can explain the almost constant size of columns after a critical thickness, which is also observed in nanocolumns of other materials. 14 During the initial times, the columns can grow in the lateral directions due to the side flux coming through the nearby gaps of nonsurviving columns. When the column density of surviving columns reaches the limiting values, the incident flux starts to be uniformly consumed by mainly the tops of the columns, and this can give rise to constant column size as the thickness increases. V. CONCLUSIONS In conclusion, we have shown that the nanocolumns deposited by oblique angle deposition develop a quasi-periodic morphology which is not observed for continuous films deposited at normal incidence under similar deposition conditions. The spatial frequency of periodic nanostructures decreases exponentially as a function of thickness. We explain the formation of quasi-periodic nature by the shadowing length which plays a similar role to the surface diffusion length in the conventional island formation morphology. Also, the change of the spatial frequency of periodicity is described by a competition mechanism of survival/ nonsurvival of columns. ACKNOWLEDGMENTS This work is supported in part by the NSF. One of the authors T.K. was supported by the Harry F. Meiners Fellowship. The authors thank Dexian Ye for taking SEM images. FIG. 8. The value of the maximum PSD peaks in spatial frequency is plotted as a function of thickness for various simulation cases: Oblique angle deposition with and without surface diffusion. 1 Y.-P. Zhao, D.-X. Ye, P.-I. Wang, G.-C. Wang, and T.-M. Lu, Int. J. Nanosci. 1, Y.-P. Zhao, D.-X. Ye, G.-C. Wang, and T.-M. Lu, Nano Lett. 2, R. N. Tait, T. Smy, and M. J. Brett, Thin Solid Films 226, K. Robbie, M. J. Brett, and A. Lakhtakia, Nature London 384, R. Messier, V. C. Venugopal, and P. D. Sunal, J. Vac. Sci. Technol. A 18, F. Liu, M. T. Umlor, L. Shen, J. Weston, W. Eads, J. A. Barnard, and G. J. Mankey, J. Appl. Phys. 85, M. Malac, R. F. Egerton, M. J. Brett, and B. Dick, J. Vac. Sci. Technol. B 17, S. A. Campbell, The Science and Engineering of Microelectronic Fabrication Oxford University Press, New York, 1996, p Y.-P. Zhao, G.-C. Wang, and T.-M. Lu, Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications Academic, San Diego, 2001, p J. G. Amar, F. Family, and P.-M. Lam, Phys. Rev. B 50,

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