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RBS Theory: Density Effects
As noted in the discussion of Stopping Power, a probing He atom loses finite amounts of energy during encounters with atoms in a sample. As a result, the spacing (density) of atoms will have a direct effect on the amount of energy lost by a probe atom versus the distance (depth) it traverses.
For example, RBS analysis of a Ti film might produce a two-dimensional Ti concentration of 5.66 E 27 atoms/cm2. In order to calculate a thickness for this film, the density of the titanium must be assumed. If we use a value of 5.66 E 22 atoms/cm2 (density of bulk Ti), a thickness of 100 nm is obtained. Depending upon the method used to deposit this Ti film the actual film density may be significantly less than bulk density. In this case, the thickness obtained by measuring the film with a profilometer or using an SEM will be significantly higher than the value calculated from the RBS results.
It is easier to present RBS results in the form of concentration versus depth, so density assumptions are frequently used to convert the RBS results into this format. It should be pointed out whenever such an assumption has been made. If RBS thicknesses are presented without an appropriate warning about the assumptions made, however, questions should be raised about the accuracy of the technique. Whenever the actual density of a film is significantly different than the density assumed in an RBS calculation, the thickness obtained by RBS will diverge significantly from the thickness obtained by another technique. It is useful to note that
where TRBS is the thickness obtained by RBS, and DRBS is the density assumed when calculating the RBS thickness, TReal and DReal are the actual film thickness and density, and atoms/cm2 is the two-dimensional concentration of atoms in the film (the concentration which can be accurately calculated from the RBS results without making any assumptions). Another useful feature of RBS is that since RBS will provide an accurate concentration of the total atoms/cm which are present in a film, if the actual thickness of the film can be measured by another method, then the density of the film can be calculated.
