Ballistic aggregation on two-dimensional arrays of seeds with oblique incident flux: Growth model for amorphous Si on Si

Amorphous silicon (Si) structures on two-dimensional arrays of seeds on a Si substrate were experimentally prepared at near room temperature using a physical vapor deposition system with an $85°$ oblique incident flux. In the stationary deposition case where the substrate is fixed at a position, the Si on the seeds form a ballistic inclined fanlike structure with an initial cone shape and the fan size $R$ grows with time in a power law form $t^p$, where $p\sim 1$. We show that with a swing rotation where the substrate is rotated back-and-forth azimuthally, the fan size grows slower $(p<1)$ relative to that of the stationary deposition case and then saturates at a size depending on the swing angle. We proposed a modified ballistic deposition model considering the ballistic sticking, shadowing, surface diffusion, and substrate rotation in a three-dimensional Monte Carlo simulator. The evolution of the fanlike structures at different deposition times was simulated for both stationary deposition and swing rotation. The growth of the fan size $R$ with time $t$ in simulations was quantitatively analyzed and the exponents $p\sim 1.0$ and $p\sim 0.46$ were extracted for the stationary deposition and the swing rotation, respectively. For stationary deposition, the exponent 1 does not change significantly with the strength of surface diffusion. However, the fan-out angle decreases with the increased strength of surface diffusion. For swing rotation, the reduced exponent 0.46 at the initial stages of growth is primarily due to the self-shadowing of the fan itself under rotation. At the later stages of growth, the saturation of the fan size produces uniform rods and is due to the global shadowing from the adjacent fan structures. The morphology and the exponent obtained from our simulations are consistent with our experimental observations.

Figure 1

Schematics of (a) the oblique angle deposition system with a flux incident angle $\theta$ and substrate rotation by a motor and (b) the “swing” substrate rotation method. $\varphi$ is the swing angle.

Figure 2

“Fan-out” growth on tungsten pillars arranged in a square lattice at an oblique angle incidence $(\theta =85°)$ and under stationary substrate. (a) The SEM top-view image of the seeds (tungsten pillars) before deposition. (b) and (c) are the SEM top views and cross-sectional views of the final structures deposited on the seeds. The $8°$ measurement shown in (c) indicates the global shadowing by adjacent structures along the direction of the incident flux. The normal thickness of the deposition was $2000\mathrm{nm}$.

Figure 3

(a) The SEM image of the “fan-out” growth at $\theta =85°$ and under stationary substrate before the structures merging in the $y$ direction. The normal thickness of the deposition was $1000\mathrm{nm}$. (b) The geometrical relationship between the projected “fan-out” angle $\chi$ and the real “fan-out” angle $\phi$.

Figure 4

Top view and cross-sectional view of fan-out growth at various simulation time $t^{\prime }$ under stationary substrate in the Monte Carlo simulations with nearest-neighbor sticking model. The particles were sent into the system from the left at an incident angle $\theta =85°$. The diffusion strength was set to $D∕F=100$.

Figure 5

(Color online) The simulated width $R$ of the fan-out structures under stationary substrate in the $y$ direction follows a power law in the form of $R\sim k{t}^p$. The simulation time $t$ was adjusted to meet the boundary condition of $R=0$ at $t=0$. Three diffusion strengths ($D∕F=50$, 100, and 150) were presented.

Figure 6

SEM images of slanted Si structures grown on seeds (tungsten pillars) arranged in the square lattice by swing rotation. SEM top views (left column) and cross-sectional views (right column) of the Si structures grown at $\theta =85°$ with (a) swing angle $\varphi =45°$ and (b) swing angle $\varphi =75°$. Fanlike structures were still observed. The white scale bar corresponds to a length of $1000\mathrm{nm}$. The normal thickness of the deposition was $1000\mathrm{nm}$.

Figure 7

(a) SEM top view and (b) cross-sectional view of uniform slanted Si structures on seeds (tungsten pillars) by swing rotation at $\theta =85°$ and swing angle $\varphi =90°$. The structures maintain a uniform width after the initial stage of growth.

Figure 8

Top view and cross-sectional view of the Monte Carlo simulations of swing rotation at $\varphi =90°$ and $\theta =85°$ for two different simulation time $t^{\prime }$. The structures have no significant fan-out in this simulation with the swing rotation.

Figure 9

(Color online) The growth behavior of the aggregates in the Monte Carlo simulations of swing rotation with various swing angles. The width $R$ grows with the simulation time in a power law with the exponent $p<0.6$. The width eventually is saturated at a maximum value $R_{\max }$ as indicated by the horizontal solid lines. The inset is the extracted growth exponent $p$ and the maximum width $R_{\max }$ for different swing angles from the simulations.