Biomedical Engineering Reference
In-Depth Information
Considering carbon ions incident on an amorphous carbon surface [11], a low energy ion
will not have enough energy to penetrate the surface, so it will just stick on the surface and
remain in its lowest energy state, which is sp
2
. If the ion energy is greater than
E
p
, then it
will have a probability to penetrate the surface and enter a subsurface interstitial site. This
will cause an increase in local density, and so the local bonding will reform around that
atom according to the new density. Robertson assumed that, in the highly energetic condi-
tions of ion bombardment existing during film growth, atomic hybridizations will adjust
easily to changes in the local density and become more sp
2
if the density is low and more
sp
3
if the density is high.
When the ion energy increases, the ion range increases as well, hence the ion can pen-
etrate deeper into the substrate. A rather small fraction of this energy is used to penetrate
the surface, and another fraction of about 30% is dissipated in atom displacements [16].
The ion must dissipate the rest of this energy ultimately as phonons. This whole process
consists of three stages: (a) a collisional stage of 10
−13
s, (b) a thermalization stage of 10
−12
s,
and (c) a relaxation stage of 10
−10
s. Process (b) and/or (c) allow the excess density to relax
to zero and cause a loss of sp
3
bonding at higher ion energies.
Referring to Figure 2.3, consider an incident beam of flux
F
with a fraction
→
of energetic
ions of energy
E
i
. The nonenergetic fraction of the atoms or ions (1 −
f
→
) will just stick on
the outer surface, while some of the penetrating ions will relax back to the surface. This
flux is proportional to a driving force, the fraction of interstitials below the surface,
n
.
In the steady state, the fraction of the ions remaining at the interstitial sites to give den-
sification is
n
=
f
→
−
β
n
, where
β
is a constant. This gives:
f
φ
β
n
=
(2.2)
1
+
A fraction
n
of the beam becomes subplanted inside the film, and a fraction (1 −
n
) is left on
the surface as sp
2
sites. The subplanted fraction creates a density increment of:
∆
ρ
ρ
=
n
(2.3)
1
−
n
Incident beam
Ion fraction,
φ
Outward growing sp
2
layer
Original
surface
Relaxing fraction,
nβ
Range
φf
penetrating fraction
Densifying layer
Interstitials,
n
FIGURE 2.3
Schematic diagram of densification by subplantation. A fraction of incident ions penetrates the film and densi-
fies it, and the remainders end up on the surface to give thickness growth. (Reprinted with permission from
Robertson,
J., Mater. Sci. Eng. R
, 37, 129, 2002.)
