Optimisation of the RSM Experiment

An un-optimised, multi-level full factorial experiment design requires that all possible combinations of the experimental parameters are considered. Increasing

the number of parameters and also the number of levels (the variance of each parameter) will increase the number of analyses required as:

(no. levels factor 1)× (no. levels factor 2)×…(no. levels factor n) (5.1)

The software package used in this RSM study was StatGraphics 5.1, which is a highly specified multivariate statistical analysis package. StatGraphics 5.1 provides the capability to optimise a designed experiment. Optimisation of an experimental design reduces the number of experimental runs required to model the response of a system, whilst retaining a comparable level of model accuracy. Algorithmic logic is used to estimate the minimum number of candidate runs required for the optimised design to adequately describe the system under investigation. The data obtained from the candidate runs is analysed in the same manner as in a full experimental design. The fewer candidate runs one conducts, the less accurately the optimised design models the response of the full design. D-optimality is a criterion calculated by the package and gives a measure of the variability of all the estimated parameters.

5.4 Experimental Set-up

The apparatus shown in Figure 5-2 was designed to be flexible and allow the LIBS analysis of solids, liquids and gases through a range of pressure regimes, from atmosphere down to <10-6 mbar. The set-up includes a Nd:YAG laser (Continuum, Surelite), frequency doubled to produce an output at 532 nm, with a 4-6 ns pulse length and a peak energy of 200 mJ. The laser may be operated at repetition rates of up to 10 Hz, but for this investigation was limited to 1 Hz in

order to reduce the gas load on the vacuum pump set. Laser radiation was focused onto the sample using a 300 mm plano-convex glass lens mounted in a micrometer stage allowing positional adjustment along the axis of the laser beam of 30 mm either side of the focal position.

The sample was mounted in the vacuum chamber on an x-y stage such that each LIBS analysis was performed away from previous ablation sites. The laser was focused onto the material under test inside the vacuum chamber through a quartz window mounted in a CF carrier. A Leybold TurboVac 50 turbomolecular pump backed by a Leybold TriVac rotary pump was used to evacuate the chamber to pressures <10-6mbar. A molecular sieve foreline trap was employed in order to reduce pump oil contamination back-streaming into the chamber. A schematic of this vacuum system is presented in Figure 5-3.

The main chamber is a stainless steel bell jar of approximate volume 21 litres, with an “L”-shaped elastomer gasket seal at the base. A Leybold TriVAC rotary pump is connected to the chamber via a length of convoluted tubing in order to pump down the chamber to a rough vacuum (~10-3mbar). This roughing pump may be isolated from the chamber by the roughing valve to prevent back- streaming when the turbo-molecular pump is in operation. Once a suitable rough vacuum has been obtained, the turbo pump may be turned on, reducing the system to a base pressure of ~10-6 mbar. The turbopump may be isolated from the chamber by a gate valve mounted above its inlet, allowing the pump to remain at full speed whilst the chamber is brought back to atmospheric pressure for sample changes.

Originally it was intended that the TriVAC roughing pump would also be used to back the turbo; however this dictated that the turbo would be momentarily un- backed whilst the chamber open to atmospheric pressure. This ordinarily would not pose a problem for a short period of time, but due to the large chamber volume, and subsequent lengthy pump-down time to reach a pressure suitable for the turbo to operate safely, this was decided against.

It was deemed necessary to introduce a second TriVAC rotary pump to the rig specifically to back the turbo. Using this pumping configuration the chamber may remain at atmospheric pressure indefinitely whilst the turbo remains at full speed operation, thus reducing pump-down time and the time taken for the turbo to spin-up to normal operation with each sample change.

Optical emission from the plasma plume was collected through a two metre long fibre-optic cable, manufactured by Roper Scientific, with a wavelength transmission range of 190 to 1100 nm. The fibre-optic cable was inserted into the vacuum chamber using a specially designed, elastomer sealed feed-through, as described in Section 5.4.1., and was coupled to the same imaging spectrometer, ICCD camera and programmable timing generator described in Section 4.2.

Figure 5-3 Schematic diagram of the ablation chamber vacuum apparatus

As before, the plasma imaging set-up allowed for temporal resolution of the plasma plumes, with the capacity to vary both the gate delay and integration times independently. Roper Scientific’s WinSpec/32 spectrum capture and manipulation software enabled both capture of the dispersed plasma emission and identification of any prominent emission lines present.

Table 5-1 Spectroscopic constants of six selected neutral Si (I) emission lines used in the RSM study (CRC Press 1988) Wavelength (nm) A (× 108s-1) gk Ek(cm-1) 250.690 0.4666 5 39955 251.611 1.21 5 39955 251.920 0.456 3 39760 252.411 1.81 1 39683 252.851 0.77 3 39760 253.238 0.26 3 54871

In this RSM study, standard semiconductor grade [111] silicon wafers were analysed. A single sample was used throughout this work and the optimisation process concerned only the silicon emission spectrum. Six Si (I) lines in the 250 - 253 nm wavelength range were monitored using the 2400 lines mm-1 grating; the spectroscopic constants for the emission lines analysed in this study are given in Table 5-1. Each data set was the accumulation of ten individual spectra.