Experimental and theoretical study of the evolution of surface roughness in amorphous silicon films grown by low-temperature plasma-enhanced chemical vapor deposition

Using real-time spectroscopic ellipsometry the evolution of the surface roughness of amorphous silicon thin films grown by low-temperature $\left(200°\text{C}\right)$ plasma-enhanced chemical vapor deposition (PECVD) at high process gas pressure (3 mTorr) has been studied as a function of the hydrogen dilution gas-flow ratio $R_H=\left[{\text{H}}_2\right]/\left[{\text{SiH}}_4\right]$ with $15\le R_H\le 60$. To describe the roughness evolution, we have used a $3\mathrm{D}$ linearized continuum equation which includes a negative surface-tension term to take into account the destabilizing effects of short-range attraction and/or shadowing, as well as a smoothing term corresponding to surface diffusion. Using this model we have obtained very good agreement with experimental results for the evolution of the surface roughness in the case of large dilution ratio. However, our results indicate that for small dilution ratio the surface slopes are significantly larger and as a result additional nonlinear terms need to be included at large thicknesses. Our results also indicate that surface diffusion plays an important role during PECVD film growth while the diffusion rate increases with increasing hydrogen dilution ratio. We also find that the early stages of island nucleation play an important role in determining the subsequent roughness evolution. In particular, the assumption of a large wetting angle $\left({\theta }_W\simeq 90°\right)$ for the $3\mathrm{D}$ islands formed in the initial stages leads to significantly better agreement with experiments than a smaller wetting angle $\left({\theta }_W\simeq 45°\right)$. This is consistent with recent experiments on liquid Si droplets on ${\text{SiO}}_2$ [H. Kanai et al., J. Mater. Sci. 42, 9529 (2007)] substrates in which a wetting angle of $90°$ was observed.

Figure 1

Experimental roughness (solid lines) and theoretical fits (dashed lines) using Eq. (2) as function of average film thickness for ${\text{H}}_2$ dilution ratios $R_H=15,20,40,60$. Fits correspond to initial surface profile with wetting angle ${\theta }_W=90°$.

Figure 2

Experimental roughness (solid lines) and theoretical fits using Eq. (2) (dashed lines) as function of average film thickness for ${\text{H}}_2$ dilution ratios $R_H=15,20,40,60$. Fits correspond to initial profile with wetting angle ${\theta }_W=45°$.

Figure 3

Dependence of parameters ${\nu }_2$ and ${\nu }_4$ on hydrogen dilution ratio $R_H$ for ${\theta }_W=90°$ and ${\theta }_W=45°$

Figure 4

Gray-scale pictures $\left(1024\text{Å}\times 1024\text{Å}\right)$ of simulated a-Si:H film surface for $R_H=40$ for thicknesses (going from left to right) $\overline{h}=20\text{Å}$, $\overline{h}=500\text{Å}$, and $\overline{h}=2000\text{Å}$. (a)–(c) correspond to ${\theta }_W=90°$ while (d)–(f) correspond to ${\theta }_W=45°$. Value of $\Delta$ indicates total height variation in each picture.

Figure 5

Lateral length-scale parameter $\xi$ as a function of average film thickness for $R_H=15$,20,40, and 60 and ${\theta }_W=90°$. Saturation value of $\xi$ corresponds to most unstable mode $k_m=k_c/\sqrt{2}=\sqrt{{\nu }_2/2{\nu }_4}$.

Figure 6

Distribution $F\left(m\right)$ of surface slopes $m\left({\theta }_W=90°\right)$ for $R_H=60$ (solid lines) and $R_H=15$ (dashed lines).