Mechanics and Tribology of MEMS Materials - prod.sandia.gov ...

Dose/(Equilibrium Dose)
1.25
1.20
1.15
1.10
1.05
1.00
0.1 1 10 100
ODTS Layer Thickness (nm)
Fig. 7.3. Simulation results for thin ODTS (a) and PFTS (b) coatings at the GIF.
The spectrum emitted when a 15 keV electron impacts an aluminum target at normal
incidence was first calculated. About 80% of the photons emitted are Al Kα with the remainder
brehmsstrahlung. For the remainder of the analysis, the brehmsstrahlung radiation was
neglected. The Al Kα yield is 2.64×10 -3 photons per incident electron. The region within 13° of
a normal to the surface contains about 24% of the total emitted photons per steradian. The tube
runs at a maximum filament current of 30 mA, at which 4.95×10 14 Al Kα photons/s will be
emitted. Based upon the geometry and absorption in the Al window, the fluence of Al Kα
photons on the sample is 2.3×10 13 (s·cm 2 ) -1 .
Having estimated the fluence of Al Kα photons at the sample, an additional series of
simulations were performed to estimate the ionizing dose in the alkylsilane coating. The
simulation consisted of Al Kα photons impinging at normal incidence with a fluence of one
photon/cm 2 on a layer of ODTS/PFTS, of variable thickness, on a silicon substrate. As before,
the thickness of the alkylsilane coating was varied over the range 1 nm to 0.1 mm, both to check
that the solutions were well behaved at small thicknesses and to examine the variation of dose
with film thickness.
Results of the simulations are plotted in Figure 7.4, which shows both kerma, the total
energy transferred from the incident photons to electrons in the material, and dose, the energy
deposited by those electrons, as a function of alkylsilane coating thickness. Both are given in
units of MeV/g; note that 1 MeV/g = 1.602×10 -10 rad. The figure plots the average dose/kerma
in an alkylsilane coating of the specified thickness, and should not be interpreted as a dose-depth
profile. The main difference between the geometry of the XPS experiments and that of the
irradiations at GIF is that in the XPS there is no material in front of the sample to equilibrate it.
Thus, electrons are free to escape from near-surface areas, reducing the dose in thin layers.
Kerma, on the other hand, remains constant in thin layers, where it has values of 2.22 MeV/g and
1.05 MeV/g for PFTS and ODTS, respectively.
As the thickness of the alkylsilane layer increases, dose and kerma both drop
exponentially as the primary photons are absorbed with a characteristic absorption length of
roughly 4 mm in PFTS and 15 mm in ODTS. PFTS, which contains a fluorinated (Z=9) carbon
chain, absorbs more strongly than ODTS, which contains a hydrogenated (Z=1) carbon chain.
This is a sensible result, as the photoelectric cross section per atom varies as Z 4 .
66
Dose/(Equilibrium Dose)
1.25
1.20
1.15
1.10
1.05
1.00
0.1 1 10 100
PFTS Layer Thickness (nm)
(a) (b)