Quantification Method Using the Inverse Velocity Dependence of Ion Intensities in Secondary Ion Mass Spectrometry: the High-Energy Method

Abstract

Secondary ion mass spectrometry (SIMS) is a highly effective analytical method for measuring in-depth and lateral concentration distributions of trace elements. However, the elemental sensitivity in SIMS is strongly influenced by not only the element species but also the surrounding matrix. That is, the elemental secondary ion yield varies by several orders of magnitude with the composition and/or chemical state of the matrix. This is called the matrix effect. The variation in the secondary ion yield cannot fully be explained by theories. For accurate quantification of an element in a sample, first a standard sample must be prepared that consists of the same matrix as the subject sample and that includes the same element at a concentration which is already known. Then the sensitivity factor of the element must be obtained by measuring the standard sample under the same experimental conditions as those for measuring the subject sample. However, a standard sample cannot always be prepared unless it is a sample whose matrix is usual and is a pure material such as Si or GaAs. Without a standard sample, the quantification method that employs sensitivity factors cannot be applied. Furthermore, an elemental sensitivity factor can fluctuate (sometimes by a factor of 2) due to experimental conditions such as the sample's position on the sample holder, unless the experimental setup is fixed when measuring both the standard and the analyzed samples.Besides this experimental method, various semi-theoretical quantification methods have been proposed although there is no theory that has succeeded in explaining secondary ion yields completely. Probably the most well known is the method whose model assumes the plasma to be in local thermodynamic equilibrium (LTE).1,2 In this method, the secondary ion yield is expressed using two parameters: the plasma temperature and the electron density. Their values must be obtained from the ion intensities of two elements included in the sample and whose concentrations are known (internal standards). That is, this method usually needs two internal standard elements. Moreover, the assumption of the presence of the LTE itself is difficult for most people to accept, because ion sputtering is not a phenomenon in equilibrium. Many other semi-theoretical methods are based on quantum-mechanical models.3 Of interest among them are the tunneling ionization model for ion emission from a metallic surface 4,5 and the bond-breaking model for ion emission from an ionic solid surface.6-8 They are acceptable phenomenologically and helpful for us in understanding negative ion emission by bombarding a cesium-covered surface with a Cs + beam, and positive ion emission by bombarding an oxidized surface with an O 2 + beam in actual SIMS measurements. The two models deal with different phenomena, but have a similarity in that the ionization probability is exponentially dependent on the time taken by a sputtered atom to pass through the characteristic distance for electron exchange and the time should be proportio...