Sputter rate equations

Transient Regime. Equation 7 is separable and may be integrated to obtain the time dependence of the oxide thickness. Assuming a finite sputtering rate, the result is... 

Since sputtered atoms originate primarily from the top atomic layer, it is reasonable to assume that the sputtering rate of a given constituent is proportional to its surface concentration. This leads to the following equation ... 

Self-absorption, which has a critical influence on AES sensitivity, could not be accurately quantified by using an equation relating the emission intensity of a resonance line affected by this phenomenon to the sputtering rate of the analyte concentration in the matrix [196]. Subsequent studies revealed that, for Cu and V, ionic lines are more sensitive than atomic lines — the latter proved independent of self-absorption but were strongly influenced by the type of plasma used (Ar or Ne) [197]. 

As no Cesium is present in the substrate before analysis, the enhancement or suppression effect continues to increase with increasing sputtering time until steady-slate sputtering is reached. Steady state refers to the condition where the primary ion implantation rate equates to the sputtering rate of implant primary ions. 

Theoretical methods in the form of sputter rate/sputter yield equations... 

Surface profilometry along with sputter rate/yield equations can be thought of as ex-situ methods as these are not routinely applied during depth profiling. The term not routinely is used as there have been attempts to implement surface profilometry, in the form of interferometry within SIMS instruments for providing real time data. Although this has met with some success, design constraints and limitations to specific matrices have not resulted in its wide spread use. Ex-situ methods are discussed further in Section 5.4.1.1. 

Sputter rate or sputter yield equations/simulations... 

Equation (94) describes the condensation rate of sputtered material from a long planar magnetron cathode at an arbitrary point Xp in the substrate plane. Since, however, such cathodes have two erosion zones of equal size both rate contributions are, under consideration of the parallel displacement of the coordinates, superimposed to the total rate. 

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