Sputter Erosion Measurement Results

This document gives results of sputter erosion experiments performed by cavity ring-down spectroscopy (CRDS) and presents the method of obtaining numerical values of number density, electronic temperature, and an approximation to translational temperature using the theory and formulae discussed in the previous chapters. As mentioned earlier, Titanium and molybdenum results are only presented.

5.1 Acquisition of Absorbance Spectrum

The oscilloscope records the PMT signal and is as shown in figure 4.1. The signal on the scope is transferred to a computer using a GPIB card (National Instruments). The PMT trace is negative and is converted to a positive signal by multiplying by -1. The PMT trace is fit with an exponential to yield the ring-down (1/e) time. The exponential fit uses data between 90% and 10% of the maximum signal amplitude. The 90-10 fitting improves the fidelity, and is used to exclude early data, and the data in the tail, both of which are subject to interferences. The laser is wavelength scanned in order to collect the absorbance spectrum. Thus as a function of wavelength, ringdown times are obtained and stored in a text file. The above tasks are controlled by a custom written Labview code.

The text file contains two columns of data: wavelength and ring down time. Equation 3.x is used to infer absorbances from the ring-down times. To get the absolute absorbance, the empty cavity baseline should be subtracted. Typically, peakfit is used to fit and subtract the baseline, thus yielding absolute absorbance versus wavelength (absorbance spectrum). In order to determine particle number densities, the wavelength-integrated areas of the absorbance profiles are needed (Equation 3.x). Peakfit has numerical routines to fit various lineshapes (Gaussian, Lorentz, Voigt etc.) and thus is a useful tool to obtain the required absorbance areas.

5.2 Sputtering of Titanium by Argon Ions

In these experiments, an argon beam with 750eV energy and a current of 18mA is incident on a Ti target. The absorbance model is used to determine appropriate wavelength scanning regions for CRDS experiments. Based on the model output, the titanium absorbance spectrum is recorded by CRDS in the vicinity of 395 nm. Figure 5.3 shows the absorbance spectrum of titanium: symbols are the experimental data, the solid line is the spectrum fitted to peaks (using Peakfit), and the dotted line is the simulated spectrum from the absorbance model (using the measured T_elec=1570 K, and with line broadening matched to data). The absorption lines are the electronic titanium transitions and are labeled in the figure 5.1.

Figure 5.1 Titanium absorbance spectrum recorded by CRDS.

From the absorbance spectrum, the area under each peak is determined using Peakfit analysis and the number density of atoms present in each energy level is calculated from Equation 3.x as shown in Table 5.1. The distribution of energy levels for titanium is such that for the excitation temperatures of interest, virtually all of the population resides in the three measured states. Therefore, the overall titanium number density can be determined by adding the populations of the three measured states. Assuming a path length of 8cm, the spatially averaged number density of sputtered titanium atoms obtained is 6.5±0.6x10⁸ cm^-3. The error bar corresponds to one standard deviation and arises primarily form uncertainties in the fitted areas.

Titanium sample calculation table
lactual(nm)	Area(ppm-nm)	gk	gi	Ei(J)	Ek(J)	Aki(s^-1)	ln(Area/l^4*gk*Aki)	Ni(m^-3)
394.979	1.4225	3	5	0	5.02E-19	4.85E+07	-42.35880553	1.89E+14
395.745	1.25	5	7	3.38E-21	5.05E-19	3.00E+07	-42.52642072	2.24E+14
395.933	1.95	7	9	7.68E-21	5.09E-19	4.04E+07	-42.71838719	2.38E+14

Table 5.1 Titanium calculations. N_i is the spatially averaged number density in the three energy levels probed. The sum of these N_i yields the overall titanium number density.

Figure 5.2 shows a Boltzmann plot, the slope of which is from which electronic temperature, T_elec is determined. Note that the electronic temperature is the temperature describing the populations of electronic energy levels. The slope of the plot is –4.67x10¹⁹ and the error associated with the measurement is 3%, which yields electronic temperature of 1550+/-50 K. Number density can also be calculated by knowing the population of a single state in combination with the measured electronic excitation temperature. (Owing to the linearity of the Boltzmann plot both methods give consistent results.)

Figure 5.2. Boltzmann plot for determining electronic temperature. The slope yields T_elec=1550+/- 50 K.

To understand the dependence of number density on beam current, we varied the beam current and collected the absorbance spectra. Figure 5.3 shows the absorbance profiles for a single absorption feature at various ion beam currents. The number densities are calculated from the area under the peak for each case and a plot of number density Vs beam current is obtained. Figure 4.6 shows the number density of sputtered titanium for beam currents of 10, 14, and 18 mA respectively. Neglecting beam-focusing effects, the dependence of the number density on beam current should be linear and through the origin. Figure 5.4 indeed shows a best fit line constrained to pass through the origin that well describes the data (R²=0.9821).

Figure 5.3 Titanium Absorption feature at 394.979 nm collected for different beam currents of 10,14, and 18 mA.

Figure 5.4 Titanium number density versus beam current.

5.2.1 Comparison of Titanium CRDS Data with Sputter Model

One can compare the number densities obtained by CRDS with estimates from a simplified sputtering model. The model assumes a cosine-distribution for the sputter yield and uses the experimental beam current and target/optical-axis geometry (Fig.3.2). As mentioned, the ion beam has an active area of 8 cm by 2.5 cm (with the 8 cm extent oriented parallel to the optical axis), and the optical axis is 7.8 cm from the target. A total sputter yield of 0.7+/-0.2 is adopted for titanium [reference11]. The sputter model requires the angular profile of (average) ejected velocity of the sputtered particles, which have been found using the TRIM sputtering simulation software [reference12]. Using these parameters and the sputtering model in Chapter 2, the number density profile along the beam is determined, which then is integrated to yield the path-integrated number density. (The chamber has a diameter of 20 cm, so the model profiles are truncated accordingly, “losing” about 15% of the integrated number density.).

For the 18 mA beam current, the sputter model yields a path-integrated titanium number density of 5.9+/-1.7x10⁹ cm^-2, while the corresponding value measured by CRDS is 5.1+/-0.5x10⁹ cm^-2. One could use the shapes of the modeled number density profiles and scale them according to the measured path-integrated number densities as a means to obtain spatially resolved profiles from the CRDS data. The CRDS and sputter model give consistent values for titanium. Note that in many cases (e.g. sputter yield not known, material not well characterized) it would not be possible to model the sputtering and an experimental approach such as CRDS is required.

5.2.2 Titanium Translational Temperature from CRDS

The determination of erosion rate or flux of sputtered particles requires the knowledge of two parameters namely number density and velocity of sputtered particles. This thesis does not cover the full details of obtaining the velocity of sputtered particles, but in future work, obtaining velocity measurements using CRDS is discussed. The lineshapes obtained in the CRD spectra are indicative of the velocities of the sputtered particles. The current experiments operate at low pressures and with relatively narrow linewidth lasers (~0.002 nm), and so the width of the measured lines is dominated by Doppler effects, owing to velocity components in the direction parallel to the probe laser beam. The symmetry is such that there is no bulk-velocity component along the optical axis, and therefore no net Doppler shift. From the Peakfit analysis, the Full-Width at Half-Maximum (FWHM) of the absorbance peaks for titanium is found to be 7.5+/-0.8 pm. And therefore, translational temperature can be approximated as 34000 ± 4000 K (~2.9 eV) (equation 3.x). The effective translational temperature corresponds to the velocity projection along the optical axis, weighted by the number density, and is reasonably consistent with values from the modeling.

5.2.3 Sensitivity of CRDS for Titanium Number density Measurement

The noise in the CRDS measurements enables the determination of the detection limits of the current system. The noise in the absorbance baseline is ~2 ppm for titanium. The baseline noise can be used to predict detection limits for the present conditions. For the absorption line at 379.979 nm, the peak absorbance measured is 140 ppm corresponding to a number density of 6.5+/-0.6x10⁸ cm^-3. Scaling these values, 2 ppm corresponds to a number density of ~9x10⁶ cm^-3. Thus the minimum detectable number density of the CRDS system for Ti is ~9x10⁶ cm^-3 for a collection time of about 30 seconds and over a path length of 8 cm.

5.3 Sputtering of Molybdenum by Argon Ions

In these experiments, an argon beam with 750eV energy and a current of 18mA is incident on molybdenum target. The absorbance model is used to determine appropriate wavelength scanning regions for CRDS experiments. Based on model output, the molybdenum absorbance spectrum is recorded by CRDS in the vicinity of 379.9 and 386.5 nm. Figure 5.5 shows the absorbance spectrum of molybdenum, symbols are the experimental data, solid line is the spectrum fitted to peaks (using peakfit), and dotted line is simulated spectrum from the absorbance model (using T_elec=1570 K, and with line broadening matched to data). The absorption lines are both electronic transitions from the ground state and are labeled in the figure. The next lowest energy level is at 10,768 cm^-1, so that Boltzmann calculation reveals that to a good approximation all population is in the ground state (and the exact temperature used in our simulations is inconsequential).

Figure 5.5 Molybdenum absorbance spectrum recorded by CRDS

From the absorbance spectrum, the area under each peak of the absorbance spectrum is determined using Peakfit analysis. Therefore, one can use the area (from Peakfit) of either measured line to determine the ground state population, and set this equal to the total molybdenum population. To find (spatially averaged) number densities, a path length of 8cm (corresponding to the ion beam extent) is assumed, yielding 5.1±0.5x10⁸ cm^-3 for the given conditions. The error bar on the measurement is obtained from the peakfit area fit and corresponds to one standard deviation.

Again the beam current is varied to study the number density dependence. Figure 5.6 shows the absorbance profiles for a single absorption feature at various ion beam currents. The number densities are calculated from the area under the peak for each case and a plot of number density Vs beam current is obtained. Figure 5.7 shows the number density of sputtered molybdenum for beam currents of 10, 14, and 18 mA respectively. Neglecting beam-focusing effects, the dependence of the number density on beam current should be linear and through the origin. Again, Figure 5.7 shows a fitted straight line constrained to pass through the origin (R²=0.9874) indicating the expected dependence.

Figure 5.6 Single Absorption feature at 386.5nm for different beam currents

Figure 5.7 Molybdenum number density versus beam current

4.3.1 Comparison of Molybdenum CRDS Data with Sputter Model

One can compare the number densities obtained by CRDS with estimates based on a simplified sputtering model. Assume a cosine-distribution for the sputter yield and use the experimental beam current and target/optical-axis geometry (Fig.3.2). As mentioned, the ion beam has an active area of 8 cm by 2.5 cm (with the 8 cm extent oriented parallel to the optical axis), and the optical axis is 7.8 cm from the target. Sputter yields of 0.9+/-0.9 are adopted for molybdenum [reference11]. The sputter model requires the angular profile of (average) ejected velocity of the sputtered particles, which have been found using the TRIM sputtering simulation software [reference12]. Using these parameters and the sputter model in chapter 2, the number density profile along the beam is determined, which then is integrated to yield the path-integrated number density.

For the 18 mA beam current, the sputter model yields a path-integrated molybdenum number density of 9.9+/-3.3x10⁹ cm^-2, while the corresponding value measured by CRDS is 4.1+/-0.4x10⁹ cm^-2. While the CRDS and sputter model give consistent values for titanium, there is a discrepancy of roughly a factor of 2 for molybdenum. Given the simplicity and potential shortcomings of the sputter model, one can view this as reasonable agreement. Note that the modeling approach may suffer from the following: incorrect total sputter yields from the literature, incorrect ejected velocities from TRIM, non-cosine behavior of the sputter yield, divergence or focusing effects of the ion beam, and target material preparation or contamination effects.

4.3.2 Molybdenum Translational Temperature from CRDS

From the peak fit analysis, the Full-Width at Half -Maximum (FWHM) of the absorbance peaks for molybdenum is 6.4+/-0.4 pm. This FWHM corresponds to a translational temperature of approximately 51000 ± 3000 K (~4.4 eV) (equation 3.xx).

4.2.3 Sensitivity of CRDS for Molybdenum Number density Measurement

The baseline noise in the CRDS measurements enables the determination of the detection limits of the current system. For the molybdenum measurements, the noise in the absorbance baseline is also ~2 ppm (for the 386.5 nm feature). This yields a minimum detectable number density of ~7x10⁵ cm^-3 for a collection time of about 30 seconds and over a path length of 8 cm. (The baseline noise for the 379.9 nm feature is larger owing to lower mirror reflectivity at this wavelength.).

The CRDS detection limits are more than adequate to detect the number densities commonly of interest in EP applications, and compare favorably to those found in laser induced fluorescence (LIF) experiments. For example, Orsitto et al. used a calibration lamp to quantify an LIF measurement scheme and estimated a detection limit of ~2.5x10⁸ cm^-3 for molybdenum number density measurements near the toroidal limiter of a Tokomak (for a scattering volume of ~2x10^-7 m^-3). Gaeta et al used LIF to make measurements of sputtered particles for EP investigations but did not quantify the number densities [reference 13].