The lumped model described above has been solved numerically and
compared to results from measurements in a PSII chamber. Because the
target and base for this comparison were made of the same material,
they could be considered to be a single material and the temperature
simulation thus involved solution of a single ordinary differential
equation. The experiment consisted of 4 Ti-6Al-4V samples (2.54
cm2.54 cm
0.16 cm each) placed on a round base (6.6 cm
diameter
0.2 cm thickness) of the same material. The samples
were implanted with nitrogen ions, with a nominal energy of 25 keV, to
a fluence of
n/cm
. The average current into the
chamber was 2.2 mA. The temperature of the base was measured using a
Luxtron, which is a phosphorescent probe. This situation was
simulated using the lumped model described above, with only radiative
cooling considered (conduction was ignored).
The emissivity of the target/base combination was chosen to provide a good comparison between the simulation and the cooling portion of the measured temperature history. That is, a curve fit of the cooling curve to the temperature data during the cooling phase of the implant was carried out, using the target emissivity as an adjustable parameter. This fitting process yielded an emissivity of 0.4, which is reasonable for polished Ti-6Al-4V alloys. The applied power density was varied to fit the heating portion of the measured data. That is, a second curve fit was carried out by adjusting the applied power to the target to achieve a good fit the the measured temperature during the implant portion of the process. The resulting temperature history, shown in Figure 8, shows good agreement between the simulation and the measured data. Unfortunately, the value of this result is diminished by the need to fit two parameters. On the other hand, the fact that the rates of change agree well does lend credence to the assumptions that the cooling is dominated by radiation.
The emissivity was taken from a data fit because it is difficult to determine the emissivity of a sample, especially since it may change during the implant. The need to obtain the heating rate from a curve fit was necessary for a more complicated reason related to the PSII process. It is trivial to measure the current applied to a PSII target, but this current includes both an ion inflow and an outflow of electrons known as secondary electrons. Secondary electrons are electrons which are emitted when the energetic ions strike the target surface. For steels, there are typically about 5 electrons emitted for each ion which strikes the surface, while for other materials (such as aluminum) there can be as many as 15-20 electrons emitted for each entering ion [7]. The existence of secondary electrons produces a discrepancy between the measured current to the target/base combination and the ion current. Therefore, there is large uncertainty in the applied target heating (due to the uncertainty in the secondary electron emission coefficient) and we must determine the applied heating from a curve fit. On the other hand, this liability can be turned into a benefit by determining the ion power from a curve fit of the heating curve to measured temperature data. By comparing the ion current corresponding to this ion power to the measured total current, one can estimate the secondary electron current and the corresponding secondary emission coefficient. This can then be compared to secondary emission coefficients which are measured using more direct techniques. This will provide independent confirmation of these direct methods.
