Sputtering linear cascade

The sputtering yield is proportional to the number of displaced atoms. In the linear cascade regime that is appUcable for medium mass ions (such as argon), the number of displaced atoms, E (E, is proportional to the energy deposited per unit depth as a result of nuclear energy loss. The sputtering yield Y for particles incident normal to the surface can be expressed as foUows (31). 

Figure 1. Three types of ion/solid interactions that can lead to sputtering. A) Knock-off, B) Linear Cascade, C) Spike.

The angular and energy distribution of the sputtered atoms have also been extensively studied (10). The linear cascade theory predicts an isotropic angular distri-... 

As electronic excitation is not considered within kinetic sputtering, the collisions can be likened to an atomic-scale billiard ball game that is initiated on primary ion impact. The valence electron shells of the atoms/ions involved would thus represent the billiard ball s surfaces. The linear cascade model, which describes the most prevalent form of ion-induced sputtering, at least that from atomic ions and ions comprising small molecules (common examples used in SIMS include 0 , 02 , Cs, Ar" ", Xe" ", and Ga ), assumes a specific form of kinetic sputtering in which a full isotropic collision cascade is produced close to the surface. This is one form of knock-on sputtering. 

When a full isotropic collision cascade is not formed, the sputtering process becomes more anisotropic. This is noted in recoil sputtering, which is another form of knock-on sputtering. As fewer colhsions occur in this form of sputtering, deviations from the trends implied by the linear cascade model are noted. The linear cascade model is covered in Section 3.2.1.1. 

Models describing all forms of sputtering other than that described by the linear cascade model are covered in Section 3.2.I.2. 

Linear Cascade Model Sputtering resulting from elastic collisions knock-on sputtering) is the most well understood of all the other forms of... 

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 ... 

In summary, the linear cascade model applies most effectively when using medium to heavy mass primary atomic or small molecular ions (i.e. 0 , O2, Ar, Xe, Ga , Cs, etc.) in the low-to-medium keV energy range (within 0.1-50 keV). These energies are used as sputter yields for such ions peak at between 10 and... 

The inability of knock-on mechanisms, inclusive of the linear cascade model, to effectively predict sputter yields in the cases described earlier arises from the fact that such mechanisms describe sputter yields as arising from many individual momentum transfer processes occurring in a linear sequence. However, as outlined in Section 3.2, ejection of atoms/ions or molecules from a solid surface can also occur through ... 

As introduced in Section 3.2.1, potential sputtering, whether kinetically assisted or not, results from inelastic energy transfer processes, with electron-phonon interactions playing a part. Cooperative motion describes a kinetic process in which a single primary ion impact induces the movement of a collective body of atoms within the solid. All of the above result in sputter yields (these are covered in Section 3.2.2) that are greater than that expected based on the linear cascade model (see Section 3.2.1.1). 

Kinetically assisted potential sputtering can take several forms depending on the primary ions, the conditions used, and the matrix examined. For dense atomic and the small molecular ion impact (In ", Bi ", Au , SFj" ", etc.), these generally tend to assume the presence of overlapping collision events within the lattice that occur as a result of the same initial collision event (the linear cascade model assumes individual events). This overlap ensues when momentum transfer is constrained within a more localized volume and/or when multiple atoms from the same impacting ion strike the same region. 

The primary reason why various simulations of sputtering resulting from momentum transfer, as described within the linear cascade model, are successful lies in the fact that the collision events can be treated using classical arguments, that is, Newtonian mechanics as opposed to quantum mechanics. Owing to the insignificant wavelength of ions ( 10" A), quantum mechanics is not needed. In addition, calculations are simplified for isotropic linear cascades as these represent a linear sequence of independent collision events that occur over time scales much shorter than lattice vibrations. 

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. 

Lastly, calculation methods can be usefnl in providing apriori insight into sputter rate trends, particnlarly if an isotropic linear cascade prevails (see Section 3.2.1.1). On the assumption that this form of kinetic spnttering prevails, the sputtered depth has been approximated as (O Connor et al. 2003) ... 

Linear cascade model A model for describing sputtering... 

These trends, which are fully supported by empirical data, confer with the supposition that the sputtered population arises from a sequence of many collisions (the collision cascade) with each collision acting independently of all other collisions (linear collision cascade) (Eckstein 1989, Rabalais 1994, Gnaser 1999). 

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.

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