The 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 2-3 over the full range of conditions and samples. But a factor of 2-3 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.
For mathematical convenience we use here the term: 'inverse relative emission yield', Ri.
Building on the work of many people, but especially of Bengtson,(1) Payling was able to show that if we consider current ig, voltage Ug and pressure pg to be independent then(2)
where a, b, c and U0 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 Ri because of varying pressure is only about 10-20%.
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 Ri. In an otherwise excellent paper, Kim Marshall concludes: "... this weakness severely limits the applicability of the PP [constant power-pressure] 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 Ri 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)
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 ri is a fitted parameter determined by regression during calibration and p0 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 Ri will also be linear, ie
where Ki(n) are constants determined by regression.
As an example, in RF GD-OES it is common to keep power and pressure constant (PP mode). The free parameter pthen becomes the DC bias voltage, VDC. The following graphs show calibrations using RF GD-OES, for a variety of certified reference materials, including Al-Si alloys, Al-Zn alloys, brass, steel, stainless steel, etc., before correction (blue) and after VDCcorrection (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 Al-Si 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 self-absorption)
Without correction, variations in emission yield increase scatter and disguise the effect of self-absorption. With correction, the scatter is greatly reduced and the effect of self-absorption can be clearly seen in the non-linearity of the calibration curve.
Higher Order Calibration
When there is appreciable self-absorption, ie when it is necessary to use third or fourth or even fifth order then inclusion of a linear function for Ri becomes a little cumbersome. Fortunately for the types of corrections envisaged in GD-OES, the product ri.(p-p0) is less than 1. For example, for a pressure correction, ri.(p-p0) is about 0.1, for a VDC correction, ri.(p-p0) is about 0.4. The inclusion of powers of Ri is then given exactly by
(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); 568-586; DOI10.1007/S00216-006-0412-7
First published on the web: 1 June 2000.
Authors: Richard Payling and Thomas Nelis