Sigmund-Thompson relation

The energy and angular distributions resulting from a full isotropic collision cascade as described by the linear cascade model have been modeled nsing the Sigmund-Thompson relation (Thompson 1968 Sigmund 1969). This predicts the sputtered neutral energy distribution to scale as ... 

Because the Sigmund-Thompson relation is derived from a linearized Boltzmann transport equation (a statistical approach), it can only approximate macroscopic properties arising from an isotropic collision cascade in nonstructured solids,... 

Figure 3.9 Normalized energy distributions of sputtered Aluminum atoms resulting from 17.5 KeV Ar and Cs impact on an Aluminum surface at an impact angle of 20 as defined by MARLOWE (symbols) overlaid that predicted by the Sigmund-Thompson relation as defined by Relation 3.4 (lines). Reprinted with permission from van der Heide and Karpusov (1998) Copyright 1998 John WUey and Sons.

The majority of the velocity distribution studies have used the Sigmund-Thompson relation as this is the easier of the two methodologies, and the relative values derived tend to agree with the studies in which the secondary neutral population is measured (see Figure 3.9). 

Figure 3.32 Example of the derivation of velocity distributions from the collected energy distribution (1(E)) after correcting for the transmission function of the instrument (T(E)) and the sputter yield (S(E)) assuming a linear collision cascade took place (Sigmund-Thompson relation is assumed). In the inset is shown the velocity distribution plotted as a function of inverse velocity (1/vj ). The line applied in the velocity distribution shown in the inset assumes an exponential yield dependence on 1/vj hence the reason for plotting such distributions in this manner. Reproduced with permission from van der Heide and Karpusov (2000) Copyright 2000 Elsevier.

The outcome is referred to as the corrected intensity If actual yields are known, this corrected intensity can then be scaled to provide absolute ion yields as a function of emission velocity. Note However, similar to the sputtered neutral distribution, absolute secondary ion yields are difficult to derive. An example of the procedure described earlier is illustrated in Figure 3.32 for Cu secondary ions resulting from 7.5 keV 0 impact. This combination is shown as the relatively low energy and mass of 0 should result in a full isotropic linear cascade as assumed by the Sigmund-Thompson relation. The derived velocity distribution is shown in the inset of Figure 3.32. 

Figure 2.6) or the introduction of an additional sputtering pathway not described by the Sigmund-Thompson relation (a nonhnear sputtering process leading to the generation of heat spikes as described in Section 3.2.1.2). 

Note The inclusion of processes not described by the Sigmund-Thompson relation will introduce inaccuracies into the corrected intensity values derived in such velocity distributions at higher 1 /vj (lower emission energies) when using... 

Figure 3.34 Collected energy distributions for (a) Ti , (b) V , and (c) Cu secondary ions resulting from 14.5-keV Cs impact on the respective elemental matrices. The lines represent the extrapolation of the velocity dependence exhibited by the higher energy secondary ions where the characteristic velocity was derived from the slope of the respective velocity distributions (see lines in Figure 3.33). The reverse calculation was then applied (reverse to that shown in Figiure 3.32) on the bases that a linear cascade prevails (that approximated by the Sigmund-Thompson relation). The deviations between these lines and the collected energy distribntions reflect the deviations from the velocity dependence implied by Relation 3.10(b) and the collected data at lower anission enagies. Anther s rmpnblished work.

Figure 3.33 Overlay of the apparent velocity distributions derived on the assumption that the sputtered neutral population follows the Sigmund-Thompson distributions (Relation 3.4) for Cu" and Cn secondary ions emanating from a polycrystalline surface under 17.5 KeV Ar" " impact, 14.0 KeV Cs" " impact, 17.5 KeV02 impact, and7.5 KeV0 impact. The same calculations were applied to all data sets and with all plots arbitrarily normalized to unity at zero 1 jv. The lines represent the trends relayed by Relation 3.10(a) or (b) fitted to the lower 1 (higher emission energy) populations. Reproduced with permission from van der Heide and Karpusov (2000) Cop)night 2000 Elsevier.

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