An analytical expression for describing Auger sputter depth profile shapes of interfaces

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Abstract
The composition versus depth distribution of a solid/solid interface as determined by Auger sputter depth profiling can be described by a logistic function of the form Y=[A+a(T−T0)]/(1+ex) +[B+b(T−T0)]/(1+e−x), where Y is a measure of the elemental surface concentration of one of the components that defines the interface. T is a measure of the sputtering depth and is usually expressed as sputtering time assuming a constant sputtering rate. A is a measure of the preinterface surface concentration for one of the elements of the interface and B is a measure of the postinterface surface concentration, where ‘‘pre’’ and ‘‘post’’ are taken in the sense of time. The empirical parameters a and b are introduced to account for additional time dependence of instrumental effects. T0 is the apparent midpoint of the interface region and x is a dimensionless, reduced time defined as (T−T0)/D. The scaling factor D is the characteristic time for sputtering through the interface region. All measures of the interface width will be proportional to D. Asymmetry in the depth profile can be accommodated by allowing D to vary with time. A least squares fitting program has been written which fits measured Auger spectral intensities to the above equation to within measurement error (approximately 1%). The statistics associated with the least squares fit allow confidence limits to be placed on the measured widths of interface regions and on the asymmetry associated with each such region.

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