Methods of counting single ions and compositional analysis

7 Methods of counting single ions and compositional analysis 

Consider a binary alloy. Because of the statistical nature of single atom counting, the statistical uncertainty in the compositional analysis is given by 

Assuming that/A is 0.01, and we would like to determine this value with the atom-probe to an accuracy of 5% of fA, then the number of ions collected should be at least 39 600. This is already near an impractically large number in the atom-probe analysis. It quickly becomes impractical to determine accurately the concentration of a minority species with the atom-probe at a low counting rate if its concentration is smaller than —0.5%. The following statistical analysis points to a method with which this difficulty can be overcome. 

It is a well recognized fact that in field ion microscopy field evaporation does not occur at a constant rate because of the atomic step structures of the tip surface. For the sole purpose of a compositional analysis of a sample, one should try to aim the probe hole at a high index plane where the step height is small and field evaporation occurs more uniformly. But even so, the number of atoms field evaporated per HV pulse or laser pulse within the area covered by the probe-hole will not be the same every time. It is reasonable to assume that the field evaporation events are nearly random even though there has been no systematic study of the nature of such field evaporation events. Let the average number of atoms field evaporated per pulse within the area covered by the probe-hole area be n. The probability that n atoms are field evaporated by a pulse is then given by the Poisson distribution 

The fractional abundances for A- and B-type atoms, atom-probe signals, are given by as registered in the 

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