J . Phys. Chem. 1990, 94, 3269-3272 droplet. We want to know the temperature of the gas molecules colliding with the droplet surface. That can be estimated by evaluating T from (AI) at one mean free path in the gas above the surface. For the worst case in the experiments reported here, for 200-pm droplets at 268 K in 3. I6 Torr of H20in a flow tube at 31 I K , at x = IO pm, T = 272 K, i.e., the gas is 4 K warmer than the droplet surface.30 (30) In ref 2, an error was made in calculating the mean free path. As a result, the temperature gradient estimated from eq AI (A7 in ref 2) is 8 times larger than quoted there. However, as discussed here, the effective gas temperature at the surface is well-described by the droplet surface temperature, though the uncertainty in the effective temperature is somewhat larger than indicated there. Thus, within the uncertainties quoted in ref 2, there is no significant correction to the temperature dependence of H 2 0 2 uptake in ref 2 (reproduced here as the dashed line in Figure 2).
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This calculation should be regarded as an upper limit to the actual gas-surface temperature gradient. Equation A1 is rigorously valid only for distances much longer than the mean free path. At shorter distances there are not enough collisions to establish an equilibrium temperature. Since energy transfer for gas-surface collisions is much more efficient than gas-gas collisions, the average energy of gas molecules at one mean free path above the surface will be closer to that of the surface as compared to the gas above. In fact, the gas molecules will not have a true equilibrium temperature. However, even for the worst case above, the effective gas temperature will be within several degrees of the droplet surface temperature. The temperatures reported in Table 11 are derived from the ambient water vapor pressure and, based on this calculation, have an uncertainty that ranges from f l K at 290 K to f 2 K at 270 K.
Plasma Kinetic Measurements Using Time-Resolved Actinometry: Comparisons with Laser- Induced Fluorescence Graham Hancock,* John P. Sucksmith, and Matthew J. Toogood Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, 0x1 3QZ, U.K. (Received: October 31, 1989: In Final Form: February 21, 1990)
Optical diagnostics have been used to study the steady-state concentrations and kinetics of reactive species in CF4 and CF4/02 plasmas. The CF2 radical was studied by two techniques, laser-induced fluorescence (LIF) and optical emission, in order to test the validity of using the latter method as a way of determining relative changes in concentration of the ground-state radical. Both techniques were first used under steady-state conditions and then for measurements of time-resolved behavior following plasma extinction. For the optical emission studies a new method, time-resolved actinometry, was developed. The kinetics of F atoms, which cannot conveniently be measured by other methods such as LIF, were then studied by this technique, under a variety of conditions and in the presence and absence of Si surfaces.
Introduction The manufacture of microelectronic components is now dominated by plasma-based technology.’ A full understanding of these plasmas is, however, far from complete, and further knowledge of the processes taking place in the discharge, particularly of their rates, is still required. Some of these rates, such as those for gas-phase reactions,* can be measured outside the reactor vessel, but others have to be monitored in situ in order to maintain the correct conditions. In this paper, we report a method for obtaining the rate of removal of species from the plasma using only optical emission spectroscopy, a nonperturbative, in situ technique. Optical emission spectroscopy has been extensively used as a diagnostic technique for processing plasmas, partially due to its applicability to a large number of species present. However, the emission is produced from electronically excited states, and thus the intensity is related to the concentration of these excited species, whereas it is the ground-state species, with their much higher concentrations, which are of importance in etching and deposition. To allow for this, Coburn and Chen3 developed the technique of actinometry, which attempts to relate the emission intensity to the ground-state concentration by adding a small amount of inert gas. called the actinometer, to the processing gas mix. In the discharge, the emission from this actinometer is used as a measure of the electron excitation in the plasma, and thus normalization of the emission from the species of interest to the actinometer emission yields information on the relative ground-state concentration of the species of interest. ( I ) Flamm. D. L.; Donneiiy, V . M. Plasma Chem. Plasma Process. 1981, I . 317. ( 2 ) Ryan, K.; Plumb, I . Plasma Chem. Plasma Process. 1986, 6, 1 1 . ( 3 ) Coburn, J . W.; Chen. M . J . Appl. Phys. 1980, 5 / , 3134.
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For actinometry to work, the excited states of both the species of interest and the actinometer should be formed by electron impact of the ground state. Furthermore, if the electron energy distribution function changes with an experimental parameter, the electron impact excitation cross section of the inert gas needs to be similar to that of the species of interest or at least have a similar excitation threshold (e.g., Ar for F detection). Actinometry is used widely but has only been validated in a few cases by simultaneous observation of the ground state. Ibbotson et aL4 compared actinometered optical emission (AOE) to absorption in a Br2 plasma and demonstrated a good correlation, and a similar method was used on C1 atoms by Richards et a L S who showed that for a CF,CI plasma AOE gives an accurate representation of the variation in the ground-state concentration of atomic CI. However, in a C12 plasma large discrepancies were seen, and as previously proposed? following a study of the Doppler line widths of atomic emission lines, these were explained by the production of excited-state Cl by electron impact dissociation of C12. Production pathways to the emitting state, independent of the ground state, have also been used to explain differences between AOE and laser-induced fluorescence (LIF) measurements for both CCI and 0 atoms.’.* Downstream titration techniques have been used to measure ground-state F atom concentrations and have generally shown good agreement with AOE? but this (4) Ibbotson, D. E.; Flamm, D. L.; Donnelly, V. M . J . Appl. Phys. 1983,
54, 5974.
( 5 ) Richards, A. D.; Thompson, B. E.; Allen, K. D.; Sawin, H. H. J . Appl. Phys. 1987,62, 792. (6) Gottscho, R. A.; Donnelly, V. M. J . Appl. Phys. 1984, 56, 245. (7) Gottscho, R. A.; Davis, G. P.; Burton, R. H. Plasma Chem. Plasma Process. 1983, 3, 193. (8) Walkup, R. E.; Saenger, K.; Selwyn, G. S.J . Chem. Phys. 1986,84,
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3270 The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 method suffers from the disadvantage that it does not measure the ground-state concentration at the same position as the emission. Thus, despite its widespread use in plasma diagnostics, the technique of AOE needs to be applied with caution if it is to be used to infer mechanisms of the plasma processes. As well as steady-state information, optical emission has been used to study time-dependent behavior of the plasma species. Such studies range from the widespread application of optical emission to end-point detection,I0 with a time scale of tens of seconds, to following the variation in excitation as a function of phase of the rf cycle where the time scale is tens of nanoseconds. The latter has been carried out in nitrogen," oxygen,I2 and silane13 plasmas with 13.56-MHz applied rf power and in a chlorine-based plasma over a range of freq~encies.'~Similar time scales have been probed by using time-resolved LIF, and here again a comparison with ground-state concentration has been made. Gottscho et al.I5 studied the ion dynamics and kinetics of N2+and C12+in N2/CI2 plasmas during the cycle of a low-frequency (
