Page 203 - Inorganic Mass Spectrometry - Fundamentals and Applications

Secondary Ion Mass Spectro~etry 189

where Ip is the total primary ion current, yq is the isotopic abundance of isotope j,
of
and qv is the acceptance, transmission, and detection efficiency the ins~ment
for this isotope. Iq may be for any selected positive or negative secondary ion and
Si is the corresponding positive or negative ion yield.
The object of any quantitative scheme is to convert the measured Iij to ele-
mental concen~ation. The unknowns are the ai ion yield fraction and qij instru-
ment ~ans~ssion parameters.
Many attempts have been made to quantify
SIMS data by using theoretical
models of the ionization process. One of the early ones was the local thermal equi-
librium model of Andersen and Hinthorne [36-381 mentioned in the Introduction.
The hypothesis for this model states that the majority sputtered ions, atoms, mol-
of
other
ecules, and electrons are in thermal equilibrium with each and that these equi-
librium concen~ations can be calculated by using the proper Saha equations. An-
to
dersen and Hinthorne developed a computer model, CARISMA, quantify SIMS
data, using these assumptions and the Saha-Eggert ionization equation E39-411.
They reported results within 10% error for most elements with the use of oxygen
bomb~~ent on mineralogical sarnples. Some elements such as zirco~um, nio-
bium, and molybdenum, however, were underestimated by factors 2 to 6. With
of
two internal standards, CARISMA calculated a plasma temperature and electron
density to be used in the ionization equation. For similar matrices, temperature and
pressure could be entered and the ion intensities quantified without standards. Sub-
sequent research has shown that the temperature and electron densities derived by
this method were not realistic and the establishment of a true thermal equilib~um
is unlikely under SMS ion ~omb~dment. With too many failures in other matri-
ces, the method has fallen into disuse.
Other early attempts at quantification from first principles included use of
the Dobretsov equation for surface ionization through nonequilibrium thermody-
namics [W], use of quantum mechanical models [88,89], and others, including sur-
face bond breaking and dissociative E901 or chemical ionization [S l]. None of these
led to successful quantification schemes. An evaluation of several of these meth-
ods was made by Rudat and Morrison [92].
A recent proposal for quantification of SIMS data from first principles is the
infinite velocity (IV) method of van der Heide et al. [93]. The basis for this method
is the quantum mechanical argument derived by Norskov and Lundquist [94]; the
SIMS matrix effect is removed if secondary ions are emitted from the sample sur-
face with “infinite velocity” (i.e., the secondary ion yield for all elements is the
same at infinite emission velocity). Under this condition, the relative concentra-
tion of an element, i, can be calculated from

(4.4)