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J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
Zhu et al.
0
Ͻ␣Ͻ1 is indicative of the texture of self-affine surface.9,12
In addition, as shown in Fig. 1 the slight separation of the
D peak and G peak is observed at 400 °C. With increasing
growth temperature, sp2 bonded atoms increases in the
films, leading to more roughening. This should be contrib-
uted to the difference of the roughness exponents shown in
Fig. 3.
One model determined by a nonlinear growth equation
describes an intermediate range diffusion with the scaling
exponents ␣ϭ2/3 and ϭ1/5.1
0,11
The ‘‘unstable growth’’
FIG. 3. The height–height correlation function based on the data from the
AFM images at 200 °C and 400 °C in Fig. 2. The roughness exponents are
determined to be about 0.8.
described by a linear equation yields scaling exponents of
ϭ1 and ϭ1/4, suggesting a local diffusion corresponding
␣
2,10
to mounded morphologies.
The physical nature for this
unstable growth is often ascribed to the ‘‘Ehrilich–
Schwoebel’’ barrier. In our case, the roughness exponent ␣ is
closer to 2/3, far from the value predicted by the linear
growth equation. This is not entirely surprising, because the
the deposited films. In such high temperature, thermal diffu-
sion is primary smoothing mechanism, while ion irradiation
induced viscous flow is weakened compared with the case at
relatively low temperature. Because of curvature-dependent
sputtering effect, ripple structures form during deposition. At
low temperature, however, the samples exhibit the evident
amorphous feature. Viscous flow relaxation induced by ion
irradiation enhances in the amorphous surface. The surface
morphology acquired during deposition at last relies on the
‘‘Ehrilich–Schwoebel’’ barrier is not known to be present in
amorphous system due to the lack of well- defined steps. We
think the process might be better described by nonlinear dif-
fusion. This deduction is supported by the work of Mayer
et al. recently.13 They determined the roughness exponent
␣
ϭ0.8 in the growth of vapor-deposited amorphous
Zr Al Cu films. This value is close to that of our ex-
6
5
7.5
27.5
microscopic dynamic of roughening and smoothening. The8
periments. In order to understand the growth process, they
have carried out a numerical simulation of a Monte Carlo
large values of viscous relaxation hinder ripple formation.
Thus, the growth mounds appear in the film as the tempera-
ture is below 550 °C. It can be concluded that the transition
from growth mounds to ripple formations with substrate tem-
peratures should be ascribed to the different dominant
smoothening mechanisms, where the relaxation level of ion
irradiation induced viscous-flow varies with the substrate
temperature due to graphitization.
Further, the scaling analysis of surface is carried out
based on height–height correlation function in order to ob-
tain better insight into the mounding roughening. The scaling
2
2
model and added a nonlinear term C/2ٌ (ٌh) to the con-
tinuum growth equation that includes surface diffusion and
the curvature dependent deposition process. The numerical
simulation is quantitative agreement of the experimental re-
sults.
In summary, we have shown that ion beam assisted
deposition exhibits a potential to adjust surface morphology
in nanometer scale for DLC film. By controlling deposition
parameters to drive the competition between smoothing and
roughness, we can tune mounding coarsening to ripple struc-
ture. The transition is due to the change of ion irradiation
induced viscous-flow relaxation caused by graphitization
during DLC deposition. The ripple formations are in qualita-
tively agreement with BH model as a consequence of
curvature-dependent sputtering yield. The vectors of ripples
are parallel to projection of incident ion beam. At relatively
low temperature 200 °C and 400 °C, the roughness exponent
␣ is determined to be around 0.8Ϯ0.04, suggesting self-
affine growths.
theory has been applied for nonequilibrium processes in film
growth or postsputtering,9
–11
a dynamic scaling hypothesis
where the growth surface is assumed to have both short-
range space scaling and long-range time scaling is expected.
According to this scaling theory, the rms roughness ,
i.e., the standard deviation of the surface height h(r,t) can
2
be expressed in the form, (r,t)ϭG(r,t)ϭ
͗
͓h(r,t)
2
2
2␣
Ϫh(0,t)͔
͘
, which reduces to (r,t)ϭG(r,t)ϰr
for
2
2
small r with tϭconstant, and to (r,t)ϰt as r→ϱ, where
G(r) is the height–height correlation function, r is the length
scale over which the roughness is measured, ␣ and  are the
roughness and dynamic scaling exponents, respectively, and
z is ␣/. The exponents ␣ and  depend on the special
growth models, their experimental determination and com-
parison with theory can be valuable in identifying the domi-
nating underlying kinetic process. The roughness exponent ␣
is determined from the fit to the linear part of the log–log
plot of G(r) vs r. AFM images in Fig. 2 is further analyzed,
log–log plots of G(r) as a function of lateral distance r for
the DLC films at substrate temperatures of 200 °C and
Zhu appreciates the support by the STA Exchange Sci-
entist Program in Japan.
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