Biomedical Engineering Reference
In-Depth Information
the sp
2
and sp
3
atoms would be displaced at certain rates into interstitial sites and then
fall back at similar rates into sp
2
and sp
3
sites. The fraction of sp
3
sites increases if there
is a preferential displacement of sp
2
atoms. However, this model arose from some early
estimates of the displacement threshold in graphite and diamond of 25 and 80 eV, respec-
tively. The more recent direct measurements find similar values for graphite (35 eV) and
diamond (37-47 eV) [7, 8], so preferential displacement is unlikely.
McKenzie et al. [9] noted that sp
2
bonded graphite occupies 50% more volume than sp
3
bonded diamond. This leads to the phase diagram of diamond and graphite shown in
Figure 2.2, with diamond stable at a higher pressure above the Berman-Simon curve, and
therefore it stabilizes the high-pressure diamond-like phase.
Robertson [10,11] proposed that subplantation would create a metastable increase in den-
sity, causing the local bonding to change into sp
3
. Preferential displacement is not required,
as only the subsurface growth in a restricted volume is needed to get sp
3
bonding.
A number of numerical and analytical simulations substantiate the basic idea of the subplan-
tation model [12-14]. The unsolved problem is in the details of the relaxation process, which
suppresses sp
3
bonding at higher ion energies and higher deposition temperatures.
In the following, the atomic scale processes will be discussed using Robertson's data
[10,11,15]. In the energy range of 10-1000 eV, the carbon ions have a range of a few nm,
and their energies are lost mainly by elastic collisions with the substrate atoms (nuclear
stopping). The cross section of the collisions decreases as the energy is raised due to the
repulsive part of the interatomic potential. Therefore, an ion of low energy incident on a
surface sees an impenetrable wall of touching spheres. At a higher energy, the atomic radii
decrease, so the interstices of the substrate are relatively wider. At some energy, the ion can
pass through an interstice and so penetrate the surface layer. This ion energy is termed the
penetration threshold,
E
p
.
The displacement threshold,
E
d
, is the minimum energy of an incident ion needed to
displace an atom from a bonded site and create a permanent vacancy-interstitial pair. The
ions when entering the surface must also overcome the substrate's surface binding energy,
E
B
. Thus, the net penetration threshold for free ions is:
E
p
≈
E
d
+
E
B
(2.1)
10
8
6
Diamond
4
Graphite
2
0.03 eV
0
0
1000
2000
3000
T (K)
FIGURE 2.2
Berman-Simon P-T phase diagram for carbon. (Reprinted with permission from Robertson,
J., Mater. Sci. Eng.
R
, 37, 129, 2002.)
