Emission yieldsThe ProblemThe emission yield is the term which relates the number of photons coming from the source to the number of atoms entering the plasma. If it is constant then counting the photons is equivalent to counting the number of atoms in the plasma. It is therefore only changes in emission yield which upset this counting process. Fortunately in a glow discharge, for a particular line from a particular element, the emission yield doesn't change by much, perhaps by a factor of 23 over the full range of conditions and samples. But a factor of 23 is still too much for quantitative analysis, so we have to reduce the change in emission yield or correct for any changes. Unfortunately, the emission yield depends on just about everything that is happening in the plasma: collisions, sputtering, etc., and from outside the plasma we cannot measure all these events. So we are forced to use what we can measure, namely the gas pressure and the electrical parameters, such as current, voltage and power.
The Solution?For mathematical convenience we use here the term: 'inverse relative emission yield', R_{i}. Building on the work of many people, but especially of Bengtson,^{(1)} Payling was able to show that if we consider current i_{g}, voltage U_{g} and pressure p_{g} to be independent then^{(2)} where a, b, c and U_{0} are constants for a particular emission line. Typically a ~ 1, b ~ 0.5, and c is positive, provided the pressure is not too low. Hence the inverse relative emission yield generally decreases with increasing current, and increases with increasing voltage and pressure. This work was with a DC source but there is no reason to suppose that an RF source would be essentially different. Given the normal ranges of these variables, the most important effect is from varying current, next is varying voltage and thirdly varying pressure. If we keep current and voltage constant then the variation in R_{i} because of varying pressure is only about 1020%. This work has been interpreted to mean that we should operate a glow discharge with constant current and voltage and variable pressure, to minimise the variation in R_{i}. In an otherwise excellent paper, Kim Marshall concludes: "... this weakness severely limits the applicability of the PP [constant powerpressure] mode ..."^{(3)} But there are many advantages to keeping the pressure constant, and in fact the work showed we can use any source control and then correct for the variations in R_{i} and obtain the same result. A detailed discussion of thie topic can be found in a recent (2006) review article by Arne Bengtson and Thomas Nelis (4) The Solution!For each possible way of operating the GD source, there will always be at least one free parameter. In constant current/constant voltage (IV) mode, it is pressure; in constant power/constant pressure (PP) mode, it is the ratio of voltage to current (impedance). This ratio can be expressed either as a function of voltage or of current since, at constant power, when one increases the other decreases. Hence we can assume any change in inverse relative emission yield will be a function of this free parameter, f(p). Further, if we use the same conditions in calibration and analysis, any variation in the free parameter will be restricted to a limited range. Hence the function will be nearly linear where r_{i} is a fitted parameter determined by regression during calibration and p_{0} is a reference value chosen somewhere near the middle of the range, eg 700 V for DC bias voltage. If the calibration function is linear, then inclusion of a linear function for R_{i} will also be linear, ie where K_{i}^{(n)} are constants determined by regression. As an example, in RF GDOES it is common to keep power and pressure constant (PP mode). The free parameter pthen becomes the DC bias voltage, V_{DC}. The following graphs show calibrations using RF GDOES, for a variety of certified reference materials, including AlSi alloys, AlZn alloys, brass, steel, stainless steel, etc., before correction (blue) and after V_{DC}correction (pink): for Si 288 nm Without correction, the calibration appears as two distinct families, corresponding to differences in emission yield, due mainly to Si in steel at the low values and Si in AlSi at the high values. With correction, the separation of families disappears and one calibration curve results for all samples.
for Al 396 nm (known to show selfabsorption) Without correction, variations in emission yield increase scatter and disguise the effect of selfabsorption. With correction, the scatter is greatly reduced and the effect of selfabsorption can be clearly seen in the nonlinearity of the calibration curve.
Higher Order CalibrationWhen there is appreciable selfabsorption, ie when it is necessary to use third or fourth or even fifth order then inclusion of a linear function for R_{i} becomes a little cumbersome. Fortunately for the types of corrections envisaged in GDOES, the product r_{i}.(pp_{0}) is less than 1. For example, for a pressure correction, r_{i}.(pp_{0}) is about 0.1, for a V_{DC} correction, r_{i}.(pp_{0}) is about 0.4. The inclusion of powers of R_{i} is then given exactly by where
References: (1) A Bengtson and M Lundholm, J. Anal. Atom. Spectrom. 3, 879 (1988). (2) R Payling, Surf. Interface Anal. 23, 12 (1995). (3) K A Marshall, J. Anal. Atom. Spectrom. 14, 923 (1999). (4) A.Bengtson, Th.Nelis; "The concept of constant emission yield in GDOES"; Anal. Bioanal. Chem.; 385; (2006); 568586; DOI10.1007/S0021600604127 First published on the web: 1 June 2000. Authors: Richard Payling and Thomas Nelis
