Nonlinear evolution of surface morphology under shadowing

Fluorocarbon thin-film deposition is studied, which shows an anomalous high dynamic growth exponent and therefore does not fit in any universal class of fractal surface growth models. A detailed analysis of the nonlinear behavior of the surface morphology evolution is carried out, quantifying several features of the shadowing instability. A synergy effect with the Kardar-Parisi-Zhang nonlinearity, which couple the large scales induced by shadowing with intermediate scales, may explain the anomalous high growth exponent.

Figure 1

AFM images ($15\mu \text{m}\times 15\mu \text{m}$) at different times and film thickness (a) $\langle h\rangle =0.050$, (b) 0.075, (c) 0.100, (d) 0.125, (e) 0.150, (f) 0.200, (g) 0.250, and (h) 0.300 $\mu$m, respectively.

Figure 2

Cross-coherence and- phase between surface height and exposure angle perturbations during fluorocarbon thin-film deposition.

Figure 3

Cross-bispectrum between surface height, exposure angle, and normal surface growth fluctuations during fluorocarbon thin-film deposition at different times and film thickness (a) $\langle h\rangle =0.050$, (b) 0.075, (c) 0.100, (d) 0.125, (e) 0.150, (f) 0.200, (g) 0.250, and (h) 0.300 $\mu$m, respectively. The cross-bispectrum is shown normalized to its maximum absolute value. Positive (negative) values are depicted in orange (blue). Information on the impact of its amplitude can be found in Fig. 4.

Figure 4

Integrated cross-bispectrum between surface height, exposure angle, and normal surface growth fluctuations during fluorocarbon thin-film deposition.

Figure 5

(a) Comparison of the measured roughening (black, solid) with the roughening due to quasilinear (QL, blue, dashed) and nonlinear shadowing (NL, red, dotted) and KPZ nonlinearity (KPZ, green, dash-dotted). (b) The ratio between nonlinear and quasilinear roughening.

Figure 6

Zoom on a grown surface under incident bombardment of highly sticking and low sputtering yield particles (in black). Implementation sites are discrete. The surface function $h\left(x\right)$ is locally defined by the position of the highest particle, as illustrated by the two red curves. The bottom one is the initial surface, and the top one is the surface a short time prior to the end of the run.

Figure 7

Cross-coherence and -phase between surface height and exposure angle perturbations from MC simulations.

Figure 8

Evolution of the cross-bispectrum between surface height, exposure angle, and normal surface growth fluctuations from MC simulations in the same representation as in Fig. 3.

Figure 9

Integrated cross-bispectrum between surface height, exposure angle, and normal surface growth fluctuations from MC simulations.

Figure 10

(a) Comparison of the measured roughening (black, solid) with the roughening due to quasilinear (QL, blue, dashed) and nonlinear shadowing (NL, red, dotted) for the MC simulation. (b) The ratio between NL and QL roughening.

Figure 11

Bispectrum (weighted by $-q_1{q}_2$) between surface height fluctuations during fluorocarbon thin-film deposition in the same representation as in Fig. 3.

Figure 12

Integrated bispectrum (weighted by $-q_1{q}_2$) between surface height fluctuations during fluorocarbon thin-film deposition.